AgilentFundamentals of RF and MicrowavePower Measurements (Part 1)

Application Note 1449-1

Introduction to Power, History, Definitions,International Standards & Traceability

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For user convenience, Agilent’sFundamentals of RF andMicrowave Power Measurements,application note 64-1, literaturenumber 5965-6330E, has beenupdated and segmented into fourtechnical subject groupings. The following abstracts explain how thetotal field of power measurementfundamentals is now presented.

Fundamentals of RF and Microwave Power Measurements (Part 1) Introduction to Power, History, Definitions, InternationalStandards, and TraceabilityAN 1449-1, literature number 5988-9213ENPart 1 introduces the historical basis for power measurements, and providesdefinitions for average, peak, and complex modulations. This applicationnote overviews various sensor technologies needed for the diversity of testsignals. It describes the hierarchy of international power traceability, yielding comparison to national standards at worldwide national measure-ment institutes (NMIs) like the U.S. National Institute of Standards andTechnology. Finally, the theory and practice of power sensor comparisonprocedures are examined with regard to transferring calibration factors anduncertainties. A glossary is included which serves all four parts.

Fundamentals of RF and Microwave Power Measurements (Part 2) Power Sensors and InstrumentationAN 1449-1, literature number 5988-9214ENPart 2 presents all the viable sensor technologies required to exploit the widerange of unknown modulations and signals under test. It starts with explana-tions of the sensor technologies, and how they came to be to meet certainmeasurement needs. Sensor choices range from the venerable thermistor tothe innovative thermocouple to more recent improvements in diode sensors.In particular, clever variations of diode combinations are presented, whichachieve ultra-wide dynamic range and square-law detection for complex modulations. New instrumentation technologies, which are underpinned withpowerful computational processors, achieve new data performance.

Fundamentals of RF and Microwave Power Measurements (Part 3) Power Measurement Uncertainty per International GuidesAN 1449-1, literature number 5988-9215ENPart 3 discusses the all-important theory and practice of expressing meas-urement uncertainty, mismatch considerations, signal flowgraphs, ISO17025, and examples of typical calculations. Considerable detail is shown onthe ISO 17025, Guide for the Expression of Measurement Uncertainties, hasbecome the international standard for determining operating specifications.Agilent has transitioned from ANSI/NCSL Z540-1-1994 to ISO 17025.

Fundamentals of RF and Microwave Power Measurements (Part 4)An Overview of Agilent Instrumentation for RF/MicrowavePower MeasurementsAN 1449-1, literature number 5988-9216ENPart 4 overviews various instrumentation for measuring RF and microwavepower, including spectrum analyzers, microwave receivers, network/spec-trum analyzers, and the most accurate method, power sensors/meters. Itbegins with the unknown signal, of arbitrary modulation format, and drawsapplication-oriented comparisons for selection of the best instrumentationtechnology and products.

Most of the chapter is devoted to the most accurate method, power metersand sensors. It includes comprehensive selection guides,frequency coverages,contrasting accuracy and dynamic performance to pulsed and complex digital modulations. These are especially crucial now with the advances inwireless communications formats and their statistical measurement needs.

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Table of Contents I. Introduction ......................................................................................... 4

The importance of power .......................................................................... 5

A brief history of power measurements ................................................. 6

A history of peak power measurements ................................................. 7

II. Power Measurement Fundamentals................................ 9

Understanding the characteristics of the signal under test ................ 9

Units and definitions.................................................................................. 11

IEEE video pulse standards adapted for microwave pulses ............... 15

Peak power waveform definitions............................................................ 16

A typical wireless modulation format ..................................................... 17

Three technologies for sensing power .................................................... 17

An overview of power sensors and meters for pulsed and complex

modulations ............................................................................................ 18

Key power sensor parameters .................................................................. 18

Data computation for statistical parameters of power analysis ......... 20

III. The Chain of Power Traceability ......................................... 21

The hierarchy of power measurement, national standards and

traceability .............................................................................................. 21

The theory and practice of sensor calibration....................................... 23

Some measurement considerations for power sensor comparisons .. 24

Typical sensor comparison system.......................................................... 24

Thermistors as power transfer standards .............................................. 26

Other DC substitution meters................................................................... 26

Peak power sensor calibration traceability ............................................ 27

Network analyzer source system.............................................................. 28

NIST Six-port calibration system............................................................. 28

IV. Glossary and List of Symbols ................................................ 30

The purpose of the new series of Fundamentals of RF and Microwave PowerMeasurements application notes, which were leveraged from former note 64-1,is to

1) Retain tutorial information about historical and fundamental considerations of RF/microwave power measurements and technology which tend to remain timeless.

2) Provide current information on new meter and sensor technology.

3) Present the latest modern power measurement techniques and test equipment that represents the current state-of-the-art.

Part 1, Chapter 1 reviews the commercial and technical importance of makingpower measurements, equity in trade, the cost of measurement uncertainties,and the need for two power measurements of the same unit under test will bethe same at two locations in the world. It then presents a brief history of powertechniques, and additionally a history of peak power techniques.

Chapter 2 shows why it is crucial to begin a power measurement task with aclear understanding of the characteristics of the signal under test. With theadvent of new complex combinations of modulations in the 1990s and forward,it also presents signal format considerations that users must evaluate whenpondering which sensor technologies to use.

The application note then defines the variety of terminology of units and definitions of various power measuring terms. It shows how IEEE video pulsestandards were adapted by Agilent for use in microwave pulsed powerenvelopes. Brief descriptions of modern wireless formats show how key sensorperformance is required to faithfully capture the system power. Various sensortechnologies and instrumentation are previewed from the complete descrip-tions in Fundamentals Part 2.

Considerations necessary for capturing and digitizing microwave signals whichare used in modern wireless systems are presented. These often consist ofpulsed carriers plus digital phase modulations, which look like noise, combinedon the same signal. When measured with digital sampling type instrumenta-tion, the powerful micro-processors can run statistical routines to reveal computed data, oriented to particular customer requirements.

Chapter 3 presents the matter of basic measurement traceability to nationaland world standards. It describes the hierarchy of international traceability,including comparison processes to national standards at worldwide NMIs suchas the U.S. National Institute of Standards and Technology, Boulder, CO.

The application note reviews the theory and practice of sensor calibrationprocesses and the need for transportable sensor artifacts which can transferhigher-echelon uncertainties of the NMIs to company primary lab standards. It reviews special procedures needed for extended calibration processes onpulse-power sensors.

Note: In this application note numerous technical references will be made tothe other published parts of the Fundamentals of RF and Microwave PowerMeasurements series. For brevity, we will use the format Fundamentals Part X.This should insure that you can quickly locate the concept in the other publication. Brief abstracts for the four-part series are provided on the insidethe front cover.

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I. Introduction

The importance of powerThe output power level of a system or component is frequently the critical fac-tor in the design, and ultimately the purchase and performance of almost allradio frequency and microwave equipment. The first key factor is the conceptof equity in trade. When a customer purchases a product with specified powerperformance for a negotiated price, the final production-line test results needto agree with the customer’s incoming inspection data. These shipping, receiv-ing, installation or commissioning phases often occur at different locations,and sometimes across national borders. The various measurements must beconsistent within acceptable uncertainties.

Secondly, measurement uncertainties cause ambiguities in the realizable per-formance of a transmitter. For example, a 10-W transmitter costs more than a5-W transmitter. Twice the power output means twice the geographical area iscovered or 40% more radial range for a communication system. Yet, if the over-all measurement uncertainty of the final product test is on the order of ±0.5dB, the unit actually shipped could have output power as much as 10% lowerthan the customer expects, with resulting lower operating margins.

Because signal power level is so important to the overall system performance,it is also critical when specifying the components that build up the system.Each component of a signal chain must receive the proper signal level from theprevious component and pass the proper level to the succeeding component.Power is so important that it is frequently measured twice at each level, onceby the vendor and again at the incoming inspection stations before beginningthe next assembly level. It is at the higher operating power levels where eachdecibel increase in power level becomes more costly in terms of complexity ofdesign, expense of active devices, skill in manufacture, difficulty of testing, anddegree of reliability.

The increased cost per dB of power level is especially true at microwave fre-quencies, where the high-power solid state devices are inherently more costlyand the guard-bands designed into the circuits to avoid maximum device stressare also quite costly. Many systems are continuously monitored for outputpower during ordinary operation. This large number of power measurementsand their importance dictates that the measurement equipment and techniquesbe accurate, repeatable, traceable, and convenient.

The goal of this application note, and others, is to guide the reader in makingthose measurement qualities routine. Because many of the examples citedabove used the term “signal level,” the natural tendency might be to suggestmeasuring voltage instead of power. At low frequencies, below about 100 kHz,power is usually calculated from voltage measurements across an assumedimpedance. As the frequency increases, the impedance has large variations, sopower measurements become more popular, and voltage or current are the calculated parameters. At frequencies from about 30 MHz on up through theoptical spectrum, the direct measurement of power is more accurate and easier. Another example of decreased usefulness is in waveguide transmissionconfigurations where voltage and current conditions are more difficult todefine.

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A brief history of power measurementsFrom the earliest design and application of RF and microwave systems, it wasnecessary to determine the level of power output. Some of the techniques werequite primitive by today’s standards. For example, when Sigurd and RussellVarian, the inventors of the klystron microwave power tube in the late 1930s,were in the early experimental stages of their klystron cavity, the detectiondiodes of the day were not adequate for those microwave frequencies. Thestory is told that Russell cleverly drilled a small hole at the appropriate posi-tion in the klystron cavity wall, and positioned a fluorescent screen alongside.This technique was adequate to reveal whether the cavity was in oscillationand to give a gross indication of power level changes as various drive condi-tions were adjusted.

Some early measurements of high power system signals were accomplished byarranging to absorb the bulk of the system power into some sort of terminationand measuring the heat buildup versus time. A simple example used for highpower radar systems was the water-flow calorimeter. These were made by fabricating a glass or low-dielectric-loss tube through the sidewall of the wave-guide at a shallow angle. Since the water was an excellent absorber of themicrowave energy, the power measurement required only a measurement of theheat rise of the water from input to output and a measure of the volumetricflow versus time. The useful part of that technique was that the water flow alsocarried off the considerable heat from the source under test at the same time itwas measuring the desired parameter. This was especially important for meas-urements on kilowatt and megawatt microwave sources.

Going into World War II, as detection crystal technology grew from the earlygalena cat-whiskers, detectors became more rugged and performed at higherRF and microwave frequencies. They were better matched to transmissionlines, and by using comparison techniques with sensitive detectors, unknownmicrowave power could be measured against known values of power generatedby calibrated signal generators.

Power substitution methods emerged with the advent of sensing elementswhich were designed to couple transmission line power into the tiny sensingelement.[1] Barretters were positive-temperature-coefficient elements, typicallymetallic fuses, but they were frustratingly fragile and easy to burn out.Thermistor sensors exhibited a negative temperature coefficient and weremuch more rugged. By including such sensing elements as one arm of a 4-armbalanced bridge, DC or low-frequency AC power could be withdrawn as RF/MWpower was applied, maintaining the bridge balance and yielding a substitutionvalue of power.[2]

Through the 1950s and 60s, coaxial and waveguide thermistor sensors were theworkhorse technology. Agilent was a leading innovator in sensors and powermeters with recognizable model numbers such as 430, 431 and 432. As the thermocouple sensor technology entered in the early 1970s, it was accompa-nied by digital instrumentation. This led to a family of power meters that wereexceptionally long-lived, with model numbers such as 435, 436, 437, and 438.

Commercial calorimeters also had a place in early measurements. Drycalorimeters absorbed system power and by measurement of heat rise versustime, were able to determine system power. Agilent’s 434A power meter (circa,1960) was an oil-flow calorimeter, with a 10-W top range, which also used aheat comparison between the RF load and another identical load driven by DCpower.[3] Water-flow calorimeters were offered by several vendors for mediumto high power levels.

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A history of peak power measurementsHistorically, the development of radar and navigation systems in the late 1930sled to the application of pulsed RF and microwave power. Magnetrons and kly-strons were invented to provide the pulsed power, and, therefore, peak powermeasurement methods developed concurrently. Since the basic performance ofthose systems depended primarily on the peak power radiated, it was impor-tant to have reliable measurements.[4]

Early approaches to pulse power measurement have included the followingtechniques: 1) calculation from average power and duty cycle data; 2) notchwattmeter; 3) DC-pulse power comparison; 4) barretter integration. Moststraightforward is the method of measuring power with a typical averaging sen-sor, and dividing the result by the duty cycle measured with a video detectorand an oscilloscope.

The notch wattmeter method arranged to combine the unknown pulsed signalwith another comparison signal usually from a calibrated signal generator, intoa single detector. By appropriate video synchronization, the generator signalwas “notched out” to zero power at the precise time the unknown RF pulseoccurred. A microwave detector responded to the combined power, whichallowed the user to set the two power levels to be equal on an oscilloscopetrace. The unknown microwave pulse was equal to the known signal generatorlevel, corrected for the signal attenuation in the two paths.

The DC-power comparison method involved calibrating a stable microwavedetector with known power levels across its dynamic range, up into its lineardetection region. Then, unknown pulsed power could be related to the calibra-tion chart. Agilent’s early 8900A peak power meter (acquired as part of theBoonton Radio acquisition in the early 1960s) was an example of that method.It used a biased detector technique to improve stability, and measured in the50 to 2000 MHz range, which made it ideal for the emerging navigation pulsedapplications of the 1960s.

Finally, barretter integration instrumentation was an innovative solution whichdepended on measuring the fast temperature rise in a tiny metal wire sensor(barretter) which absorbed the unknown peak power.[5] By determining theslope of the temperature rise in the sensor, the peak power could be measured,the higher the peak, the faster the heat rise and greater the heat slope. Themeasurement was quite valid and independent of pulse width, but unfortunate-ly, barretters were fragile and lacked great dynamic range. Other peak powermeters were offered to industry in the intervening years.

In 1990, Agilent introduced a major advance in peak power instrumentation,the 8990A peak power analyzer. This instrument and its associated dual peakpower sensors provided complete analysis of the envelope of pulsed RF andmicrowave power to 40 GHz. The analyzer was able to measure or compute 13different parameters of a pulse waveform: 8 time values such as pulse widthand duty cycle, and 5 amplitude parameters such as peak power and pulse topamplitude.

Figure 1-1. Typical envelope of pulsed system with overshoot and pulse ringing, shown with 13 pulseparameters which the Agilent 8990A characterized for time and amplitude.

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Peak powerPulse-top amplitude Overshoot

PRF

Fall timeRise time

Pulse width

Duty cycle PRI

Pulse-base amplitude

Off time

Pulsedelay

Averagepower

Because it was really the first peak power analyzer which measured so manypulse parameters, Agilent chose that point to define for the industry certainpulse features in statistical terms, extending older IEEE definitions of videopulse characteristics. One reason was that the digital signal processes insidethe instrument were themselves based on statistical methods. These pulsedpower definitions are fully elaborated in Chapter II on definitions.

However, as the new wireless communications revolution of the 1990s tookover, the need for instruments to characterize complex digital modulation for-mats led to the introduction of the Agilent E4416/17A peak and average powermeters, and to the retirement of the 8990 meter. Complete descriptions of thenew peak and average sensors, and meters and envelope characterizationprocesses known as “time-gated” measurements are given in FundamentalsPart 2.

This application note allocates most of its space to the more modern, conven-ient, and wider dynamic range sensor technologies that have developed sincethose early days of RF and microwave. Yet, it is hoped that the reader willreserve some appreciation for those early developers in this field for havingendured the inconvenience and primitive equipment of those times.

[1] B.P. Hand, "Direct Reading UHF Power Measurement,” Hewlett-Packard Journal, Vol. 1, No. 59 (May, 1950).[2] E.L. Ginzton, "Microwave Measurements,” McGraw-Hill, Inc., 1957.[3] B.P. Hand, "An Automatic DC to X-Band Power Meter for the Medium Power Range,” Hewlett-Packard Journal,

Vol. 9, No. 12 (Aug., 1958).[4] M. Skolnik, "Introduction to Radar Systems,” McGraw-Hill, Inc., (1962).[5] R.E. Henning, "Peak Power Measurement Technique,” Sperry Engineering Review, (May-June 1955).

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Understanding the characteristics of the signal under testThe associated application note, Fundamentals Part 2, will be presenting thevariety of power sensor technologies. There are basically four different sensorchoices for detecting and characterizing power. It should be no surprise that allare needed, since users need to match the best sensor performance to the spe-cific modulation formats of their signals under test. Users often need to havedata pre-computed into formats common to their industry specifications. Anexample would be to measure, compute and display peak-to average powerratio.

System technology trends in modern communications, radar and navigationsignals have resulted in dramatically new modulation formats, some of whichhave become highly complex. Some radar and EW (countermeasures) transmit-ters use spread spectrum or frequency-chirped and complex phase-coded pulseconfigurations. These are used to reveal more precise data on the unknown target returns.

New wireless systems depend on digital modulations at very high data rates,and other spread-spectrum formats. Some combine these digital data withpulsed time-share, and have precise requirements on rise times and off-timenoise levels, see Figure 2-1. In other production and field measurements, a cel-lular base station transmitter might combine many channels of modulated car-riers, through the same broadband power amplifier and up to the antennas.This can result in some statistical processes working to create extremely highpeak power spikes, based on a concept called “crest factor.” Such spikes needto be captured by the power metering, to assure that amplifier saturation willnot occur. If it does, it creates intermodulation that smears one sub-carrier intoanother.

Figure 2-1. This time-gated wireless signal format requires accurate determination of peak power,average power and peak-to-average ratio.

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II. Power Measurement Fundamentals

Multiple signals, whether intentional or unintentional always stress a powersensor’s ability to integrate power, or to capture the modulation envelope.Average power sensors such as thermistors and thermocouples inherently cap-ture all power. No matter what the format, they respond to the heat generatedby the signal under test. Diode sensors, feature much more sensitivity anddynamic range, but their conversion characteristic ranges from square lawdetection (input power proportional to output voltage) through a quasi-square-law region, to a linear region (input voltage proportional to output voltage).

Thus diode sensors can often be substituted for thermal sensors within theirsquare-law range, but if peak power or crest factors caused spikes ofRF/microwave to exceed the square-law range, data errors will result. Diodesensors are the only choice for characterizing pulsed waveform modulationenvelopes or time-dependent formats like spread-spectrum used in wirelesssystems.

Modern peak and average diode sensors are pre-calibrated for operation acrossa wide dynamic range from square-law through the transition region to lineardetection. They do it by capturing calibration data and storing it internal to thesensor component in an EEPROM. This correction data is then accessed for thefinal digital readout of the associated instrument. Diode calibration data alsoincludes corrections for the all-important sensitivity to temperature environ-ments. Complete information on peak and average diode sensors is given inFundamentals Part 2.

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Units and definitions

WattThe International System of Units (SI) has established the watt (W) as the unitof power; one watt is one joule per second. Interestingly, electrical quantitiesdo not even enter into this definition of power. In fact, other electrical units arederived from the watt. A volt is one watt per ampere. By the use of appropriatestandard prefixes the watt becomes the kilowatt (1 kW = 103W), milliwatt (1 mW = 10-3W), microwatt (1 µW = 10-6W), nanowatt (1 nW = 10-9W), etc.

dBIn many cases, such as when measuring gain or attenuation, the ratio of twopowers, or relative power, is frequently the desired quantity rather thanabsolute power. Relative power is the ratio of one power level, P, to some otherlevel or reference level, Pref. The ratio is dimensionless because the units ofboth the numerator and denominator are watts. Relative power is usuallyexpressed in decibels (dB).

The dB is defined by

The use of dB has two advantages. First, the range of numbers commonly usedis more compact; for example +63 dB to –153 dB is more concise than 2 x 106

to 0.5 x 10-15. The second advantage is apparent when it is necessary to findthe gain of several cascaded devices. Multiplication of numeric gain is thenreplaced by the addition of the power gain in dB for each device.

dBmPopular usage has added another convenient unit, dBm. The formula for dBmis similar to the dB formula except that the denominator, Pref, is always one milliwatt:

In this expression, P is expressed in milliwatts and is the only variable, so dBmis used as a measure of absolute power. An oscillator, for example, may be saidto have a power output of 13 dBm. By solving for P using the dBm equation, thepower output can also be expressed as 20 mW. So dBm means “dB above onemilliwatt” (no sign is assumed positive) but a negative dBm is to be interpretedas “dB below one milliwatt.” The advantages of the term dBm parallel those for dB; it uses compact numbers and allows the use of addition instead of multiplication when cascading gains or losses in a transmission system.

PowerThe term “average power” is very popular and is used in specifying almost allRF and microwave systems. The terms “pulse power” and “peak envelopepower” are more pertinent to radar and navigation systems, and recently,TDMA signals in wireless communication systems.

In elementary theory, power is said to be the product of voltage (V) and current (I). But for an AC voltage cycle, this product V x I varies during thecycle as shown by curve P in Figure 2-2, according to a 2f relationship. Fromthat example, a sinusoidal generator produces a sinusoidal current as expected,but the product of voltage and current has a DC term as well as a component attwice the generator frequency. The word “power” as most commonly used,refers to that DC component of the power product.

All the methods of measuring power to be discussed (except for one chapter onpeak power measurement) use power sensors which, by averaging, respond tothe DC component. Peak power instruments and sensors have time constants inthe sub-microsecond region, allowing measurement of pulsed power modula-tion envelopes.

dB = 10 log10 ( )PPref

(Equation 2-1)

dBm = 10 log10 ( )P1 mW

(Equation 2-2)

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The fundamental definition of power is energy per unit time. This correspondswith the definition of a watt as energy transfer at the rate of one joule per sec-ond. The important question to resolve is over what time is the energy transferrate to be averaged when measuring or computing power? From Figure 2-2 it isclear that if a narrow time interval is shifted around within one cycle, varyinganswers for energy transfer rate are found. But at radio and microwave frequencies, such microscopic views of the voltage-current product are notcommon. For this application note, power is defined as the energy transfer perunit time averaged over many periods of the lowest frequency (RF ormicrowave) involved.

A more mathematical approach to power for a continuous wave (CW) is to findthe average height under the curve of P in Figure 2-2. Averaging is done byfinding the area under the curve, that is by integrating, and then dividing bythe length of time over which that area is taken. The length of time should bean exact number of AC periods. The power of a CW signal at frequency (l/T0 )is:

where T0 is the AC period, ep and ip represent peak values of e and i, φ is thephase angle between e and i, and n is the number of AC periods. This yields(for n = 1, 2, 3 . . .):

If the integration time is many AC periods long, then, whether or not n is a precise integer makes a vanishingly small difference. This result for large n isthe basis of power measurement.

For sinusoidal signals, circuit theory shows the relationship between peak andrms values as:

Using these in (2-4) yields the familiar expression for power:

DC component

e

P

Am

plit

ude

R

e

i

t

i

Figure 2-2. The product of voltage and current, P, varies during the sinusoidal cycle.

P = 1nT0

(Equation 2-3)

nT0

∫0

ep sin ( ) • ip sin ( )2πT0

t 2πT0

+ φ

P = cos φepip2

(Equation 2-4)

ep = √ 2 Erms and ip = √ 2 Irms (Equation 2-5)

P = Erms • Irms cos φ (Equation 2-6)

Average powerAverage power, like the other power terms to be defined, places further restric-tions on the averaging time than just “many periods of the highest frequency.”Average power means that the energy transfer rate is to be averaged over manyperiods of the lowest frequency involved. For a CW signal, the lowest frequencyand highest frequency are the same, so average power and power are the same.For an amplitude modulated wave, the power must be averaged over many peri-ods of the modulation component of the signal as well.

In a more mathematical sense, average power can be written as:

where T is the period of the lowest frequency component of e(t) and i(t).The averaging time for average power sensors and meters is typically from several hundredths of a second to several seconds and therefore this processobtains the average of most common forms of amplitude modulation.

Pulse powerFor pulse power, the energy transfer rate is averaged over the pulse width, τ.Pulse width τ is considered to be the time between the 50% risetime/fall-time amplitude points.

Mathematically, pulse power is given by:

By its very definition, pulse power averages out any aberrations in the pulseenvelope such as overshoot or ringing. For this reason it is called pulse powerand not peak power or peak pulse power as is done in many radar references.The terms peak power and peak pulse power are not used here for that reason.Building on IEEE video pulse definitions, pulse-top amplitude also describesthe pulse-top power averaged over its pulse width. Peak power refers to thehighest power point of the pulse top, usually the risetime overshoot. See IEEEdefinitions below.

The definition of pulse power has been extended since the early days ofmicrowave to be:

where duty cycle is the pulse width times the repetition frequency. See Figure 2-3. This extended definition, which can be derived from Equations 2-7and 2-8 for rectangular pulses, allows calculation of pulse power from an average power measurement and the duty cycle.

For microwave systems which are designed for a fixed duty cycle, peak poweris often calculated by use of the duty cycle calculation along with an averagepower sensor. See Figure 2-3. One reason is that the instrumentation is lessexpensive, and in a technical sense, the averaging technique integrates all thepulse imperfections into the average.

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Pavg = 1nT

(Equation 2-7)nT

∫ e(t) • i(t)dt

0

Pp = 1τ

(Equation 2-8)

τ

∫0

e(t) • i(t)dt

Pp = Pavg

Duty Cycle(Equation 2-9)

The evolution of highly sophisticated radar, electronic warfare and navigationsystems, which is often based on complex pulsed and spread spectrum technol-ogy, has led to more sophisticated instrumentation for characterizing pulsed RF power. Fundamentals Part 2 presents the theory and practice of peak andaverage sensors and instrumentation.

Peak envelope powerFor certain more sophisticated, microwave applications and because of theneed for greater accuracy, the concept of pulse power is not totally satisfactory.Difficulties arise when the pulse is intentionally non-rectangular or when aberrations do not allow an accurate determination of pulse width τ. Figure 2-4shows an example of a Gaussian pulse shape used in certain navigation systems, where pulse power, by either Equation 2-8 or 2-9, does not give a true picture of power in the pulse. Peak envelope power is a term for describing the maximum power. Envelope power will first be discussed.

Envelope power is measured by making the averaging time greater than 1/fmwhere fm is the maximum frequency component of the modulation waveform.The averaging time is therefore limited on both ends: (1) it must be large com-pared to the period of the highest modulation frequency, and (2) it must besmall compared to the carrier.

By continuously displaying the envelope power on an oscilloscope (using adetector operating in its square-law range), the oscilloscope trace will show thepower profile of the pulse shape. (Square law means the detected output volt-age is proportional to the input RF power, that is the square of the input volt-age.) Peak envelope power, then, is the maximum value of the envelope power.

Average power, pulse power, and peak envelope power all yield the sameanswer for a CW signal. Of all power measurements, average power is the mostfrequently measured because of convenient measurement equipment with highly accurate and traceable specifications.

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Figure 2-3. Pulse power Pp is averaged over the pulse width.

Figure 2-4. A Gaussian pulse and the different kinds of power.

t

P

Pp

Pavg

Tr = Duty cycle

1fr

= fr τ

τ

t

P

Pp

Pavg

Tr = Duty cycle

1fr

= fr τ

τ

Peak envelopepowerP

Pp using (2-9)

Pp using (2-8)

Instantaneouspower at t=t1

t1 t

IEEE video pulse standards adapted for microwave pulsesAs mentioned in Chapter I, the 1990 introduction of the Agilent 8990 peakpower analyzer (now discontinued) resulted in the promulgation of some newterminology for pulsed power, intended to define pulsed RF/microwave wave-forms more precisely. For industry consistency, Agilent chose to extend olderIEEE definitions of video pulse characteristics into the RF/microwave domain.

One reason that pulsed power is more difficult to measure is that user-wave-form envelopes under test may need many different parameters to characterizethe power flow as shown in Figure 2-5.

Two IEEE video standards were used to implement the RF/microwave definitions:

1) IEEE STD 194-1977, “IEEE Standard Pulse Terms and Definitions,”July 26, 1977.[1]

2) ANSI/IEEE STD 181-1977, “IEEE Standard on Pulse Measurement and Analysis by Objective Techniques,” July 22, 1977. (Revised from 181-1955, Methods of Measurement of Pulse Qualities.[2]

IEEE STD 194-1977 was the primary source for definitions. ANSI/IEEE STD181 is included here for reference only, since the 8990 used statistical tech-niques to determine pulse top characteristics as recommended by IEEE STD181 histogram process.

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Peak powerPulse-top amplitude Overshoot

PRF

Fall timeRise time

Pulse width

Duty cycle PRI

Pulse-base amplitude

Off time

Pulsedelay

Averagepower

Figure 2-5. Typical envelope of pulsed system with overshoot and pulse ringing, shown with 13 pulseparameters which characterize time and amplitude.

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It was recognized that while terms and graphics from both those standardswere written for video pulse characteristics, most of the measurement theoryand intent of the definitions can be applied to the waveform envelopes ofpulse-modulated RF and microwave carriers. Several obvious exceptions wouldbe parameters such as pre-shoot, which is the negative-going undershoot thatprecedes a pulse risetime. Negative power would be meaningless. The same reasoning would apply to the undershoot following the fall time of a pulse.

For measurements of pulse parameters such as risetime or overshoot to bemeaningful, the points on the waveform that are used in the measurement mustbe defined unambiguously. Since all the time parameters are measuredbetween specific amplitude points on the pulse, and since all the amplitudepoints are referenced to the two levels named “top” and “base,” Figure 2-6shows how they are defined.

Peak power waveform definitionsThe following are definitions for 13 RF pulse parameters as adapted from IEEEvideo definitions:

Rise time The time difference between the proximal and distal first transition points, usually 10 and 90% of pulse-top amplitude (vertical display is linear power).

Fall time Same as risetime measured on the last transition.

Pulse width The pulse duration measured at the mesial level; normally taken as the 50% power level.

Off time Measured on the mesial (50%) power line; pulse separation, the interval between the pulse stop time of a first pulse waveform and the pulse start time of the immediately following pulse waveform in a pulse train.

Duty cycle The previously measured pulse duration divided by the pulserepetition interval.

PRI (pulse repetition interval) The interval between the pulse starttime of a first pulse waveform and the pulse start time of theimmediately following pulse waveform in a periodic pulse train.

Figure 2-6. IEEE pulse definitions and standards for video parameters applied to microwave pulseenvelopes. ANSI/IEEE Std 194-1977, Copyright © 1977, IEEE all rights reserved.

PRF (pulse repetition frequency) The reciprocal of PRI.

Pulse delay The occurance in time of one pulse waveform before (after)another pulse waveform; usually the reference time would be a video system timing or clock pulse.

Pulse-top Pulse amplitude, defined as the algebraic amplitude difference between the top magnitude and the base magnitude; calls for aspecific procedure or algorithm, such as the histogram method.1

Pulse-base The pulse waveform baseline specified to be obtained by the histogram algorithm.

Peak power The highest point of power in the waveform, usually at the firstovershoot; it might also occur elsewhere across the pulse top ifparasitic oscillations or large amplitude ringing occurs; peak power is not the pulse-top amplitude which is the primary measurement of pulse amplitude.

Overshoot A distortion that follows a major transition; the difference between the peak power point and the pulse-top amplitude computed as a percentage of the pulse-top amplitude.

Average power Computed by using the statistical data from pulse-top amplitudepower and time measurements.

A typical wireless modulation formatModern wireless system designs use TDMA (time division multiple access) andCDMA (code division multiple access) for combining many channels into broad-band complex signal formats. For the typical signal of Figure 2-1, the EDGE system (enhanced data rate for GSM evolution) requires a characterization ofpeak, average and peak-to-average ratios during the pulse-burst interval.

The power sensor used must faithfully capture the fast rise/fall times of thesystem pulse, plus respond to the digital phase modulation in the time gate,without being influenced by the statistical crest factor spikes of the modula-tion. To render the power metering instrumentation insensitive to off-timenoise, the instrument requires a time-gating function which can capture dataduring specified time intervals.

Modern digital computation routines provide for peak-to-average determina-tions. Design engineers can obtain more complicated statistical data such asthe CCDF, a distribution function which states the percentage of the time awireless signal is larger than a specified value. This is of great value in testingand troubleshooting non-linearity of power amplifiers. [3]

Three technologies for sensing powerThere are three popular devices for sensing and measuring average power atRF and microwave frequencies. Each of the methods uses a different kind ofdevice to convert the RF power to a measurable DC or low frequency signal.The devices are the thermistor, the thermocouple, and the diode detector. Eachof the next three chapters discusses in detail one of those devices and its asso-ciated instrumentation. Fundamentals Part 2 discusses diode detectors usedto measure pulsed and complex modulation envelopes.

Each method has some advantages and disadvantages over the others. Afterthe individual measurement sensors are studied, the overall measurementerrors are discussed in Fundamentals Part 2.

The general measurement technique for average power is to attach a properlycalibrated sensor to the transmission line port at which the unknown power isto be measured. The output from the sensor is connected to an appropriatepower meter. The RF power to the sensor is turned off and the power meterzeroed. This operation is often referred to as “zero setting” or “zeroing.” Poweris then turned on. The sensor, reacting to the new input level, sends a signal tothe power meter and the new meter reading is observed.

1. In such a method, the probability histogram of power samples is computed. This is split in two around the mesialline and yields a peak in each segment. Either the mode or the mean of these histograms gives the pulse top and pulse bottom power. 17

18

An overview of power sensors and meters for pulsed and complex modulationsAs the new wireless communications revolution of the 1990s took over, theneed for instruments to characterize the power envelope of complex digitalmodulation formats led to the introduction of the Agilent E4416/17A peak andaverage power meters, and to the retirement of the 8990 meter. Completedescriptions of the new peak and average sensors and meters along with enve-lope characterization processes known as “time-gated” measurements are givenin Fundamentals Part 2. “Time-gated” is a term that emerged from spectrumanalyzer applications. It means adding a time selective control to the powermeasurement.

The E4416/17A peak and average meters also led to some new definitions ofpulsed parameters, suitable for the communications industry. For example,burst average power is that pulsed power averaged across a TDMA pulse width.Burst average power is functionally equivalent to the earlier pulse-top ampli-tude of Figure 2-5. One term serves the radar applications arena and the other,the wireless arena.

Key power sensor parametersIn the ideal measurement case above, the power sensor absorbs all the powerincident upon the sensor. There are two categories of non-ideal behavior thatare discussed in detail in Fundamentals Part 3, but will be introduced here.

First, there is likely an impedance mismatch between the characteristic imped-ance of the RF source or transmission line and the RF input impedance of thesensor. Thus, some of the power that is incident on the sensor is reflected backtoward the generator rather than dissipated in the sensor. The relationshipbetween incident power Pi , reflected power Pr , and dissipated power Pd , is:

The relationship between Pi and Pr for a particular sensor is given by the sensor reflection coefficient magnitude ρ.

Reflection coefficient magnitude is a very important specification for a powersensor because it contributes to the most prevalent source of error, mismatchuncertainty, which is discussed in Fundamentals Part 3. An ideal power sensor has a reflection coefficient of zero, no mismatch. While a ρ of 0.05 or 5% (equivalent to an SWR of approximately 1.11) is preferred for most situations, a 50% reflection coefficient would not be suitable for most situationsdue to the large measurement uncertainty it causes. Some early waveguide sensors were specified at a reflection coefficient of 0.35.

Pi = Pr + Pd (Equation 2-10)

Pr = ρ2 Pi

(Equation 2-11)

Figure 2-7. This chart shows a typical distribution of uncertainty values for its three largest causes;mismatch, sensor and meter specifications. It reveals why a low SWR specification for the powersensor is critical.

Fundamentals Part 3 will describe in great depth, the 13 individual contribu-tors to the total measurement uncertainty of a power measurement. But oneshould always understand that the main culprit is the mismatch uncertaintycaused by the SWR of the test signal port, which is usually uncontrollable. But,bad as the SWR of the port under test is, the mismatch uncertainty is alwaysminimized in effect by choosing a sensor with the lowest practical SWR. [4]

Previously, tuner stubs were used for narrow band measurements to maximizetransmitted power. But in modern broadband systems, tuners are useless, andthe better solution is to choose power sensors with the lowest possible SWR.

Another cause of non-ideal behavior occurs inside the sensor when RF power isdissipated in places other than in the power sensing element. Only the actualpower dissipated in the sensor element gets metered. This effect is defined asthe sensor’s effective efficiency ηe. An effective efficiency of 1 (100%) means that all the power entering the sensor unit is absorbed by the sensing elementand metered — no power is dissipated in conductors, sidewalls, or other components of the sensor.

The most frequently used specification of a power sensor is called the calibra-tion factor, Kb. Kb is a combination of reflection coefficient and effective efficiency according to

If a sensor has a Kb of 0.90 (90%) the power meter would normally indicate apower level that is 10% lower than the incident power Pi. Modern power sensors are calibrated at the factory and carry a calibration chart or have thecorrection data stored in EEPROM. Power meters then correct the lower-indi-cated reading by setting a calibration factor dial (or keyboard or GPIB on digital meters) on the power meter to correspond with the calibration factor ofthe sensor at the frequency of measurement. Calibration factor correction isnot capable of correcting for the total effect of reflection coefficient, due to the unknown phase relation of source and sensor. There is still a mismatchuncertainty that is discussed in Fundamentals Part 3.

19

• Sensor and Source Mismatch Errors

• Power Sensor Errors

• Power Meter Errors

MismatchSensor

Meter

Kb = ηe (1 – ρ2) (Equation 2-12)

Data computation for statistical parameters of power analysisWith the advent of Agilent digital sampling power meters such as theE4416A/17A models, massive amounts of digital data can be harnessed todeliver power parameters far more complex than average or peak power. Sincemany system modulations are characterized by noisy or digitally complexenvelopes, digital data points are ideal for providing computed results in for-mats useful to the customer.

A typical noisy waveform might be the combined channel output from a wire-less base station power amplifier. For operating efficiency, many wireless chan-nels are multiplexed onto a single output power stage. This technique worksvery well as long as the power amplifier is not overdriven with crest factor sig-nal spikes that move up out of the linear amplifier portion of the transmitter.This then presents the station installation and maintenance personnel withthe responsibility of assuring the power data indicates the amplifier linearityhas not been exceeded.

Modern power meters like the E4417A with appropriate computational soft-ware can process the digital data to display such power parameters as theCCDF (complementary cumulative distribution function). This parameter iscritically important to design engineers who need to know what percentage ofthe time their peak-to-average ratio is above a specified signal level. [5]

[1] IEEE STD 194-1977, “IEEE Standard Pulse Terms and Definitions,” (July 26, 1977), IEEE, New York, NY.[2] ANSI/IEEE STD181-1977, “IEEE Standard on Pulse Measurement and Analysis by Objective Techniques,”

July 22, 1977. Revised from 181-1955, Methods of Measurement of Pulse Qualities, IEEE, New York, NY.[3] Anderson, Alan, “Measuring Power Levels in Modern Communications Systems,” Microwaves/RF, October 2000.[4] Lymer, Anthony, “Improving Measurement Accuracy by Controlling Mismatch Uncertainty” TechOnLine,

September 2002. Website: www.techonline.com[5] Breakenridge, Eric, “Use a Sampling Power Meter to Determine the Characteristics of RF and Microwave Devices,”

Microwaves/RF, September 2001

20

The hierarchy of power measurements, national standards and traceabilitySince power measurement has important commercial ramifications, it is impor-tant that power measurements can be duplicated at different times and at different places. This requires well-behaved equipment, good measurementtechnique, and common agreement as to what is the standard watt. The agree-ment in the United States is established by the National Institute of Standardsand Technology (NIST) at Boulder, Colorado, which maintains a NationalReference Standard in the form of various microwave microcalorimeters for dif-ferent frequency bands.[1, 2] When a power sensor can be referenced back tothat National Reference Standard, the measurement is said to be traceable toNIST.

The usual path of traceability for an ordinary power sensor is shown in Figure 3-1. At each echelon, at least one power standard is maintained for thefrequency band of interest. That power sensor is periodically sent to the nexthigher echelon for recalibration, then returned to its original level.Recalibration intervals are established by observing the stability of a devicebetween successive recalibrations. The process might start with recalibrationevery few months. Then, when the calibration is seen not to change, the inter-val can be extended to a year or so.

Each echelon along the traceability path adds some measurement uncertainty.Rigorous measurement assurance procedures are used at NIST because anyerror at that level must be included in the total uncertainty at every lowerlevel. As a result, the cost of calibration tends to be greatest at NIST andreduces at each lower level. The measurement comparison technique for cali-brating a power sensor against one at a higher echelon is discussed in otherdocuments, especially those dealing with round robin procedures.[3, 4]

21

NIST

NIST

Commercial standards laboratory

Manufacturingfacility

User

Working standards

Measurementreference standard

Transfer standard

Microcalorimeternational reference

standard

General testequipment

Figure 3-1. The traceability path of power references from the United States NationalReference Standard.

III. The Chain of Power Traceability

22

The National Power Reference Standard for the U.S. is a microcalorimetermaintained at the NIST in Boulder, CO, for the various coaxial and waveguidefrequency bands offered in their measurement services program. These meas-urement services are described in NIST SP-250, available from NIST onrequest.[5] They cover coaxial mounts from 10 MHz to 50 GHz and waveguidefrom 18 GHz to the high millimeter ranges of 96 GHz.

A microcalorimeter measures the effective efficiency of a DC substitution sen-sor which is then used as the transfer standard. Microcalorimeters operate onthe principle that after applying an equivalence correction, both DC andabsorbed microwave power generate the same heat. Comprehensive andexhaustive analysis is required to determine the equivalence correction andaccount for all possible thermal and RF errors, such as losses in the transmis-sion lines and the effect of different thermal paths within the microcalorimeterand the transfer standard. The DC-substitution technique is used because thefundamental power measurement can then be based on DC voltage (or current)and resistance standards. The traceability path leads through the micro-calorimeter (for effective efficiency, a unit-less correction factor) and finallyback to the national DC standards.

In addition to national measurement services, other industrial organizationsoften participate in comparison processes known as round robins (RR). A RRprovides measurement reference data to a participating lab at very low costcompared to primary calibration processes. For example, the NationalConference of Standards Laboratories International (NCSLI), a non-profit association of over 1400 world-wide organizations, maintains RR projects formany measurement parameters, from dimensional to optical. The NCSLIMeasurement Comparison Committee oversees those programs.[3]

For RF power, a calibrated thermistor mount starts out at a “pivot lab,” usuallyone with overall RR responsibility, then travels to many other reference labs tobe measured, returning to the pivot lab for closure of measured data. Suchmobile comparisons are also carried out between National Laboratories of vari-ous countries as a routine procedure to assure international measurements atthe highest level.

Microwave power measurement calibration services are available from manyNational Laboratories around the world, such as the NPL in the UnitedKingdom and PTB in Germany. Calibration service organizations are numeroustoo, with names like NAMAS in the United Kingdom.

Figure 3-2. Schematic cross-section of theNIST coaxial microcalorimeter at Boulder, CO.The entire sensor configuration is maintainedunder a water bath with a highly-stable temperature so that RF to DC substitutionsmay be made precisely.

23

The theory and practice of sensor calibrationEvery power sensor, even the DC-substitution types such as thermistor types,require data correction for frequency response, temperature effects, substitu-tion errors from RF to DC, or conversion and heating effects. The ultimatepower standard is usually a microcalorimeter at a NMI, for example, in theUnited States, the NIST, as described previously. By carefully transferring themicrocalorimeter power measurement data to secondary standard sensors, theNMIs can supply comparison services to customer sensors. These are trans-portable between the NMI and their organization’s primary standards labs, andin turn, down to the production line or field measurement.

The comparison process varies according to the frequency range required.Usually the comparison equipment is based on the power splitter technique, to be described below in Figure 3-3. The popularity of the power splitter technique is that they operate all the way from DC, thus including desired calibration frequencies such as 100 kHz. They offer ultra low impedance matchat their output, such that devices-under-test (sensors) see a relatively low SWRlooking back into the source.

The basic idea is to run a frequency response on a standard sensor applied tothe test port of the splitter and capture that power data in a computer database. Then the sensor to be calibrated is applied to the same port, and anotherfrequency run made with a new data capture. The standard sensor has powerdata which is traceable to the company’s primary lab, and, in turn, further upto the national standard. Thus this data with known uncertainties may betransferred to the sensor under test.

Modern techniques take the accuracy another step up by measuring the com-plex impedance of the system’s test port (splitter), as well as the impedance ofthe sensor under test. A network analyzer usually measures both, and the com-plex reflection coefficient data stored in the computer data base. This imped-ance then is used to correct the power transfer equation for each calibrationfrequency.

The impedance correction routines are of course applied to the test run of thestandard sensor as well as the sensor under test. Some sensor calibrators uti-lize a system which combines a network analyzer with a configuration that fur-nishes the test power for the sensor. While this alleviates some connecting/disconnecting, it does not optimize the throughput of the systems because thenetwork analyzer has to idle while the power splitter frequency run is made. Soseparating the two measurement functions is normally prudent. Each metrolo-gy laboratory tasked with sensor calibration workloads needs to do their ownanalysis.

Figure 3-3. A two-resistor power splitter serves as a very broadband method for calibrating powersensors.

Note: Technical descriptions of sensor calibration and traceability here includesome mathematical concepts on scattering parameters and signal flowgraphs,which are explained in detail in Fundamentals Part 3.

Stablemicrowavesource

1

2

3

Two-resistorpower splitter

Ref

Test

Referencepower sensor

Referencepower meter PR

STD/DUTpower sensor

Testpower meter PT

Some measurement considerations for power sensor comparisonsFor metrology users involved in the acquisition, routine calibration, or round-robin comparison processes for power sensors, an overview might be useful.Since thermistor sensors are most often used as the transfer reference, theprocesses will be discussed in this section.

Typical sensor comparison system The most common setup for measuring the effective efficiency or calibrationfactor of a sensor under test (DUT) is known as the power ratio method, asshown in Figure 3-3.[4] The setup consists of a three-port power splitter that is usually a two-resistor design. A reference detector is connected to port 3 of thepower splitter, and the DUT and standard (STD) sensors are alternately connected to port 2 of the power splitter. Other types of three-ports can also beused such as directional couplers and power dividers.

The signal source that is connected to port 1 must be stable with time. Theeffects of signal source power variations can be reduced by simultaneouslymeasuring the power at the reference and the DUT or the reference and theSTD. This equipment setup is a variation of that used by the Agilent 11760Spower sensor calibration system, (circa 1990), now retired.

For coaxial sensors, the two-resistor power splitters are typically very broad-band and can be used down to DC. Because the internal signal-split commonpoint is effectively maintained at zero impedance by the action of the powersplit ratio computation, Γg for a well balanced two-resistor power splitter isapproximately zero. Unfortunately, at the higher frequencies, two-resistorpower splitters are typically not as well balanced and Γg can be 0.1 or larger.The classic article describing coaxial splitter theory and practice is,“Understanding Microwave Power Splitters.”[6] For waveguide sensors, similarsignal splitters are built up, usually with waveguide directional couplers.

In the calibration process, both the DUT and STD sensors are first measuredfor their complex input reflection coefficients with a network analyzer. The ref-erence sensor is usually a sensor similar to the type of sensor under calibra-tion, although any sensor/meter will suffice if it covers the desired frequencyrange.

The equivalent source mismatch of the coaxial splitter (port 2) is determinedby measuring the splitter’s scattering parameters with a network analyzer andusing that data in Equation 3-1. That impedance data now represents the Γg.Measurement of scattering parameters is described in Fundamentals Part 3.

S21 S32Γg = S22 – (Equation 3-1)

S31

24

There is also a direct-calibration method for determining Γg, that is used atNIST.[7] Although this method requires some external software to set it up, itis easy to use once it is up and running.

Next, the power meter data for the standard sensor and reference sensor aremeasured across the frequency range, followed by the DUT and reference sensor. It should be noted that there might be two different power meters usedfor the “test” meter, since an Agilent 432 meter would be used if the STD sensor was a thermistor, while an Agilent EPM meter would be used to readthe power data for a thermocouple DUT sensor. Then these test power meterdata are combined with the appropriate reflection coefficients according to theequation:

PTdut PRstd |1 - Γg Γd|2

Kb = Ks (Equation 3-2)PTstd PRdut |1 - Γg Γs|2

Where:Kb = cal factor of DUT sensorKs = cal factor of STD sensorPTdut = reading of test power meter with DUT sensorPTstd = reading of test power meter with STD sensorPRstd = reading of reference power meter when STD measuredPRdut = reading of reference power meter when DUT measuredΓg = equivalent generator reflection coefficient ρg = |Γg|Γd = reflection coefficient of DUT sensor ρd = |Γd|Γs = reflection coefficient of STD sensor ρs = |Γs|

A 75 Ω splitter might be substituted for the more common 50 Ω splitter if theDUT sensor is a 75 Ω unit.

Finally, it should also be remembered that the effective efficiency and calibra-tion factor of thermocouple and diode sensors do not have any absolute powerreference, compared to a thermistor sensor. Instead, they depend on their 50 MHz reference source to set the calibration level. This is reflected by theEquation 3-2, which is simply a ratio.

25

26

Thermistors as power transfer standardsFor special use as transfer standards, the U.S. NIST, accepts thermistormounts, both coaxial and waveguide, to transfer power parameters such as calibration factor, effective efficiency and reflection coefficient in their meas-urement services program. To provide those services below 100 MHz, NISTinstructions require sensors specially designed for that performance.

One example of a special power calibration transfer is the one required toprecisely calibrate the internal 50 MHz, 1 mW power standard in the Agilentpower meters, which use a family of thermocouples or diode sensors. That internal power reference is needed since those sensors do not use the powersubstitution technique. For standardizing the 50 MHz power reference, a specially-modified Agilent 478A thermistor sensor with a larger RF coupling capacitor is available for operation from 1 MHz to 1 GHz. It is designated the478A Special Option H55 and features an SWR of 1.35 over its range. For aneven lower transfer uncertainty at 50 MHz, the 478A Special Option H55 can be selected for 1.05 SWR at 50 MHz. This selected model is designated the 478A Special Option H75.

478A Special Option H76 thermistor sensor is the H75 sensor that has beenspecially calibrated in the Agilent Microwave Standards Lab with a 50 MHzpower reference traceable to NIST. Other coaxial and waveguide thermistorsensors are available for metrology use.

NIST sensor calibration services while mainly focused on DC-substitution tech-nology using thermistor sensors ran out of frequency range at the upper limitof coaxial thermistors. NIST now offers calibration service for thermocouplesensors that reach 50 GHz. [5]

Other DC-substitution metersOther self-balancing power meters can also be used to drive thermistor sensorsfor measurement of power. In particular, the NIST Type 4 power meter,designed by the NIST for high-accuracy measurement of microwave power iswell suited for the purpose. The Type 4 meter uses automatic balancing, alongwith a four-terminal connection to the thermistor sensor and external high precision DC voltage instrumentation. This permits lower uncertainty thancommercial power meters are designed to accomplish.

Peak power sensor calibration traceabilityFor years, ultimate power sensor traceability to national standards was limitedto average power parameters. One can understand this because themicrocalorimeter-based standard inherently depends on a long-term powerabsorption at very stable signal conditions. With the very long time-constantsof microcalorimeters, the process calls for characterizing the power transfer fora long averaging period.

The average power of real-world signal formats is seldom the only parameter ofinterest. New wireless communications signals combine multiplexed channelsthat look like noise power with pulsed formats for time-share. The EDGE signalof Figure 2-1 is a good example. Naturally, manufacturers and users of peakpower sensors would be requesting traceability for such special formats.

As of this writing, the National Physical Laboratory (NPL) in the UK has sponsored a research program into the complexities of characterizing peakpower sensors. These are not trivial considerations because bandwidth of theinstrumentation and the linearity of the sensor both contribute to computederrors. In particular, the linearity of peak-detecting sensors at low power levelswas generally poorer than CW sensors. Peak sensors also reveal more non-linearities in the higher power areas where corrections are applied to thedetection characteristic. Range-switching transitions can lead to minor datadiscontinuities. These all can lead to uncertainties in computed data such aspeak-to-average power and power statistics which are required for CDMA systems like cdmaOne and W-CDMA.

The NPL calibration system work was validated against the sampling oscillo-scope measurements that validated the waveform characteristics of the pulsedRF signal. This is important because of the generally limited bandwidth of thepeak power instrumentation associated with pulsed or complex-modulationpower signals. Of course, the ultimate power standard was still a CW sensor,which served as the traceable link to the NPL power standard.

NPL’s peak power project has involved various popular frequency bands andpower levels. It is suggested that potential users of peak power sensor calibra-tion services make direct contact with the NPL website [10].

In a summary presentation for peak power uncertainty budget for a DECT signal (1900 MHz region), the total was computed at a 3.2% uncertainty for 95%confidence. The overall expanded uncertainty included sensor efficiency, powerratio, standard sensor mismatch, DUT sensor mismatch and repeatability, plusthe CW—pulse transfer.

27

28

Network analyzer source method For production situations, it is possible to modify an automatic RF/microwavenetwork analyzer to serve as the test signal source, in addition to its primaryduty measuring impedance. The modification is not a trivial process, however,due to the fact that the signal paths inside the analyzer test set sometimes donot provide adequate power output to the test sensor because of directionalcoupler roll off.

NIST six-port calibration system For its calibration services of coaxial, waveguide, and power detectors, theNIST uses a number of different methods to calibrate power detectors. The primary standards are calibrated in either coaxial or waveguide calorime-ters .[9, 11] However, these measurements are slow and require specially builtdetectors that have the proper thermal characteristics for calorimetric meas-urements. For that reason the NIST calorimeters have historically been used tocalibrate standards only for internal NIST use.

The calibration of detectors for NIST’s customers is usually done on either thedual six-port network analyzer or with a two-resistor power splitter setup suchas the one described above.[11] While different in appearance, both of thesemethods basically use the same principles and therefore provide similar resultsand similar uncertainties.

The advantage of the dual six-ports is that they can measure Γg, Γs, and Γd,and the power ratios in Equation 3-2 at the same time. The two-resistor powersplitter setup requires two independent measurement steps since Γg, Γs, andΓd are measured on a vector network analyzer prior to the measurement of thepower ratios. The disadvantage of the dual six-ports is that the NIST systemstypically use four different systems to cover the 10 MHz to 50 GHz frequencyband. The advantage of the two-resistor power splitter is its wide bandwidthand DC-50 GHz power splitters are currently commercially available.

29

[1] J. Wade Allen, Fred R. Clague, Neil T. Larsen, and M. P. Weidman, “NIST Microwave Power Standards in Waveguide,” NIST Technical Note 1511, February 1999.

[2] F.R. Clague, “A Calibration Service for Coaxial Reference Standards for Microwave Power,”NIST Technical Note 1374, May, 1995.

[3] National Conference of Standards Laboratories, Measurement Comparison Committee, Suite 305B, 1800 30th St. Boulder, CO 80301.

[4] M.P. Weidman, “Direct Comparison Transfer of Microwave Power Sensor Calibration,” NIST Technical Note 1379, January, 1996.

[5] NIST Special Publication 250; NIST Calibration Services. The latest up-to-date information on NIST calibration services is also maintained on the following website:www.ts.nist.gov/ts/htdocs/230/233/calibrations/index.htm

[6] Russell A. Johnson, “Understanding Microwave Power Splitters,” Microwave Journal, Dec 1975.[7] R.F. Juroshek, John R., “A direct calibration method for measuring equivalent source mismatch,”,Microwave

Journal, October 1997, pp 106-118.[8] Clague, F. R. , and P. G. Voris, “Coaxial reference standard for microwave power,” NIST Technical Note 1357,

U. S. Department of Commerce, April 1993.[9] Allen, J.W., F.R. Clague, N.T. Larsen, and W. P Weidman, “NIST microwave power standards in waveguide,”

NIST Technical Note 1511, U. S. Department of Commerce, February 1999.[10] Website for National Physics Laboratory, UK, pulsed power information (note caps):

www.npl.co.uk/measurement_services/ms_EG.html#EG04[11] Engen, G.F., “Application of an arbitrary 6-port junction to power-measurement problems,” IEEE Transactions on

Instrumentation and Measurement, Vol IM-21, November 1972, pp 470-474.

General referencesR.W. Beatty, “Intrinsic Attenuation,” IEEE Trans. on Microwave Theory and Techniques, Vol. I I, No. 3

(May, 1963) 179-182.R.W. Beatty, “Insertion Loss Concepts,” Proc. of the IEEE. Vol. 52, No. 6 (June, 1966) 663-671.S.F. Adam, “Microwave Theory & Applications,” Prentice-Hall, 1969.C.G. Montgomery, “Technique of Microwave Measurements,” Massachusetts Institute of Technology, Radiation

Laboratory Series, Vol. 11. McGraw-Hill, Inc., 1948.Mason and Zimmerman. “Electronic Circuits, Signals and Systems,” John Wiley and Sons, Inc., 1960.Fantom, A, “Radio Frequency & Microwave Power Measurements,” Peter Peregrinus Ltd, 1990“IEEE Standard Application Guide for Bolometric Power Meters,” IEEE Std. 470-1972.“IEEE Standard for Electrothermic Power Meters,” IEEE Std. 544-1976.20

30

ADC analog-digital converterag incident wave upon a generatorANSI American National Standards InstituteAM amplitude modulationa incident wave upon a loadbg emerging wave from a generatorb reflected wave from a loadBPSK binary phase-shift keyedbs generated wave of a sourceCb bypass capacitanceCc coupling capacitanceCDMA Code-Division-Multiple-AccessCo diode junction capacitanceCW continuous waveC, C1, C2 capacitorsdB decibeldBm decibels referenced to 1 mWD power meter driftDECT Digital Enhanced Cordless TelecommunicationsDSP digital signal processore instantaneous voltageEDGE Enhanced Data rates for GSM Evolution (wireless standard)emf electromotive forceep peak voltageErms root mean-square of a voltage waveformes source voltageFDM frequency-division-multiplexFET field effect transistorfm maximum modulation frequency componentfr repetition frequencyFM frequency modulationGaAs Gallium arsenideGPIB general purpose interface busGSM Groupe Spêciale Mobile, a wireless standard sometimes

read as Global System for Mobile communicationi instantaneous currenti instrumentation uncertaintyi load currentip peak currentIrms root mean-square of a current waveformIs diode saturation currentIS-95A wireless communication standardISO International Standards OrganizationK Boltzmann’s constantKb calibration factorKc sensor cal factor at cal frequencyL inductanceLw wire lead inductancem power meter magnification (gain)mi instrument magnification uncertaintyMMIC microwave monolithic integrated circuitMu gain due to mismatch between unknown generator and sensorMuc gain due to mismatch between sensor and cal sourcen a diode correction constantN power meter noiseNADC North American Digital CellularNAMAS National Measurement Accreditation Scheme (UK)NBS National Bureau of Standards (now NIST)NCSLI National Conference of Standards Laboratories InternationalNIST U.S. National Institute of Standards & Technology (formerly NBS)NMI National Measurement Institute (such as NIST or NPL or PTB, etc)NPL National Physics Laboratory (UK)P product of voltage and currentP powerPav available generator powerPavg average powerPcal power delivered to Zo load by meter cal sourcePd dissipated powerPfs power at full scalePg net power transferred to load from generator

IV. Glossary and List of Symbols

This glossary is applicable to all fourparts of the Fundamentals of RF and Microwave Power Measurementsapplication note series.

Pgzo power delivered to Zo load from generatorPi incident powerPm meter indication of powerPmc power level indicated during calibrationPp pulse powerPr reflected powerPref reference powerPrf radio frequency powerPsub substituted power, dc or low frequency equivalent of an RF powerPDB planar-doped-barrier (diode)PTB Physikalisch-Technische Bundesanstalt (Germany)Pl power sensor linearityq charge of electronQAM quadrature-amplitude-modulationQPSK quadrature-phase-shift-keyed (digital modulation)R resistanceRF radio frequencyRSS root-sum-of-the-squaresRb bulk resistance of siliconRc resistance of compensating thermistorRd resistance of detecting thermistorRo diode origin resistanceR, R1, R2, RL resistorRR round robinRs source resistanceRt thermistor resistanceSWR1 voltage standing wave ratioSI International System of Unitst time as a variablet power meter translation (offset) errorT temperature in KelvinsT time lapseTDMA Time-Division-Multiple-AccessTo period of a waveformT period of the lowest frequencyTr period of the repetition frequencyTime-gated time window for power measurement u standard uncertaintyU expanded uncertainty (for example catalog spec)v instantaneous voltagev voltage across a loadvo output voltageV0, V1, V2, VT voltagesVc voltage driving the compensating bridgeVh Peltier emf at a hot junctionVrf voltage driving the rf thermistor bridgeVrfo voltage driving the rf thermistor bridge when no rf power is appliedW wattZ load impedanceZc power meter zero carryover valueZg generator impedanceZo reference impedanceZr reference impedanceZs power meter zero set valueπ/8 8PSK π/8 shifted, 8-phase-shift-keyed (digital modulation)α q/nKTΓg complex reflection coefficient looking back into a generatorΓ complex reflection coefficient of a loadηe effective efficiencyρ reflection coefficient magnitude of a loadρg reflection coefficient magnitude of a generatorτ pulse widthφ phase angle between a sinusoidal waveform and a

reference waveformφg reflection coefficient angle of a generatorφ reflection coefficient angle of a loadΩ ohms3G third-generation wireless systems8-PSK 8 phase-shift keyed (digital modulation)64-QAM 64 quadrature-amplitude-modulation

1. Due to infrequent use of the term power standing wave ratio, common usage in the U.S.A. has shortened VSWR to SWR. Some parts of the world continue to use VSWR to refer to voltage standing wave ratio.

31

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AgilentFundamentals of RF and MicrowavePower Measurements (Part 2)

Application Note 1449-2

Power Sensors and Instrumentation

Fundamentals of RF and Microwave PowerMeasurements (Part 1)Introduction to Power, History, Definitions, InternationalStandards, and TraceabilityAN 1449-1, literature number 5988-9213ENPart 1 introduces the historical basis for power measurements, and providesdefinitions for average, peak, and complex modulations. This applicationnote overviews various sensor technologies needed for the diversity of testsignals. It describes the hierarchy of international power traceability, yield-ing comparison to national standards at worldwide National MeasurementInstitutes (NMIs) like the U.S. National Institute of Standards andTechnology. Finally, the theory and practice of power sensor comparisonprocedures are examined with regard to transferring calibration factors anduncertainties. A glossary is included which serves all four parts.

Fundamentals of RF and Microwave PowerMeasurements (Part 2)Power Sensors and InstrumentationAN 1449-2, literature number 5988-9214ENPart 2 presents all the viable sensor technologies required to exploit theusers’ wide range of unknown modulations and signals under test. Itexplains the sensor technologies, and how they came to be to meet certainmeasurement needs. Sensor choices range from the venerable thermistor tothe innovative thermocouple to more recent improvements in diode sensors.In particular, clever variations of diode combinations are presented, whichachieve ultra-wide dynamic range and square-law detection for complexmodulations. New instrumentation technologies, which are underpinnedwith powerful computational processors, achieve new data performance.

Fundamentals of RF and Microwave PowerMeasurements (Part 3)Power Measurement Uncertainty per International GuidesAN 1449-3, literature number 5988-9215ENPart 3 discusses the all-important theory and practice of expressing meas-urement uncertainty, mismatch considerations, signal flowgraphs, ISO17025, and examples of typical calculations. Considerable detail is shown onthe ISO 17025, Guide for the Expression of Measurement Uncertainties,has become the international standard for determining operating specifica-tions. Agilent has transitioned from ANSI/NCSL Z540-1-1994 to ISO 17025.

Fundamentals of RF and Microwave PowerMeasurements (Part 4)An Overview of Agilent Instrumentation for RF/MicrowavePower MeasurementsAN 1449-4, literature number 5988-9216ENPart 4 overviews various instrumentation for measuring RF and microwavepower, including spectrum analyzers, microwave receivers, network/spectrum analyzers, and the most accurate method, power sensors/meters.It begins with the unknown signal, of arbitrary modulation format, anddraws application-oriented comparisons for selection of the best instrumen-tation technology and products.

Most of the chapter is devoted to the most accurate method, power metersand sensors. It includes comprehensive selection guides, frequency cover-ages, contrasting accuracy and dynamic performance to pulsed and complexdigital modulations. These are especially crucial now with the advances inwireless communications formats and their statistical measurement needs.

2

For user convenience, Agilent’sFundamentals of RF andMicrowave Power Measurements,application note 64-1, literaturenumber 5965-6330E, has beenupdated and segmented into fourtechnical subject groupings. The following abstracts explain how thetotal field of power measurementfundamentals is now presented.

I. Introduction ......................................................................................... 4

II. Thermistor Sensors and Instrumentation .................... 5

Thermistor sensors..................................................................................... 5

Coaxial thermistor sensors ....................................................................... 6

Bridges, from Wheatstone to dual-compensated DC types.................. 6

Thermistors as power transfer standards .............................................. 8

III. Thermocouple Sensors and Instrumentation ............ 9

Principles of thermocouple ...................................................................... 9

The thermocouple sensor .......................................................................... 10

Linearity characteristics for thermocouple and thermistor sensors... 14

Power meters for thermocouple sensors ................................................ 15

Traceable power reference oscillator ..................................................... 16

EPM Series power meters.......................................................................... 18

IV. Diode Sensors and Instrumentation................................. 19

Principles of diode detectors .................................................................... 19

Using diodes for sensing power .............................................................. 21

Wide-dynamic-range CW-only power sensors ........................................ 23

Wide-dynamic-range average power sensors.......................................... 24

Traceable power reference oscillator ..................................................... 28

Signal waveform effects on measurement uncertainty of diode sensors ........................................................................................... 29

V. Peak and Average Diode Sensors and Instrumentation ..................................................................... 32

Traditional pulsed modulation formats .................................................. 32

Complex modulation of wireless formats ............................................... 33

Other modern signal formats.................................................................... 35

Peak and average power sensing.............................................................. 36

EPM-P Series power meters ...................................................................... 38

Computation power-gated data concept ................................................. 43

Video bandwidth considerations.............................................................. 44

Versatile user interface.............................................................................. 46

Measurement considerations for traditional peak pulses.................... 47

Analysis software package for complex modulation manipulations.. 48

P-Series power meter ................................................................................. 49

Internal zero and calibration.................................................................... 49

Bandwidth considerations ........................................................................ 50

Versatile user interface.............................................................................. 50

Applications................................................................................................. 51

Flexible configurations .............................................................................. 52

Predefined measurement setups.............................................................. 52

Measurement speed.................................................................................... 52

Theory of operation.................................................................................... 53

CCDF measurement.................................................................................... 55

Special peak sensor calibration for temperature and range ............... 56

Recent research on linearity and pulse-shape characterization of peak and average sensors ..................................................................... 57

3

Table of Contents

The purposes of the new series of Fundamentals of RF and Microwave PowerMeasurements application notes, which were leveraged from former note AN 64-1, is to

1) Retain tutorial information about historical and fundamental considerations of RF/microwave power measurements and technology which tend to remain timeless.

2) Provide current information on new meter and sensor technology.

3) Present the latest modern power measurement techniques and test equipment that represents the current state-of-the-art.

Part 2 of this series, Power Sensors and Instrumentation, is a comprehensiveoverview of the broad array of power sensors and instrumentation availabletoday.

Chapter 2 starts with a brief look at the classic thermistor sensor and dc-sub-stitution meter technology. Since thermistors remain the predominant methodto trace standard power from National Measurement Institutes such as theNational Institute of Standards and Technology (NIST), Agilent maintains a significant line of such products.

Chapter 3 introduces the thermocouple sensors and instruments that came onthe scene in the early 1970s. They featured a truly dramatic increase in rangeand lowered uncertainty of measurements because the sensors featured fullsquare-law conversion and wider dynamic range. They had significantly lowerSWR, which reduced measurement uncertainty greatly. And they were far morerugged than thermistors. Soon, Agilent enhanced them by combining with integral, calibrated attenuators for accepting input powers up to 25 watts.

Chapter 4 describes the theory and practice of diode-based power sensors.Although diodes were used for power detection as far back as World War II, ittook Agilent’s introduction of the 8484A diode power sensor in 1975 to providebroadband matching to the coaxial structure and temperature isolation fromexternal elements to make the technology succeed. Since diodes were 30 dBmore sensitive, and also exhibited true square conversion for about the lowest50 dB of range, they quickly achieved an important place in user requirements.

Chapter 5 presents the latest technology for applying diode sensors to charac-terization of RF/microwave signals with complex modulation typical of wirelesssystems, or pulsed formats typical of radar and navigation systems. Such com-plex modulations required wider-bandwidth instrumentation to accommodatethe fast pulses and wideband digital modulations of the wireless technologies.But, in addition, new microprocessor-based technology plus the digital sampling data capture of the new instrumentation permitted dramatic expansion of computed characterization of power, such as peak-to-averageratios. New research data is provided for peak and average sensor linearity andpulse shape characterization.

Note: In this application note, numerous technical references will be made tothe other published parts of the Fundamentals of RF And Microwave PowerMeasurements series. For brevity, we will use the format Fundamentals Part X.This should insure that you can quickly locate the concept in the other publica-tion. Brief abstracts for the four-part series are provided on the inside frontcover.

4

Introduction

Bolometer sensors, especially thermistors, have held an important historicalposition in RF/microwave power measurements. However, in recent years thermo-couple and diode technologies have captured the bulk of those applicationsbecause of their increased sensitivities, wider dynamic ranges, and higherpower capabilities. Yet, thermistors are still the sensor of choice for powertransfer standards because of their DC power substitution capability. The following material reviews the basic theory and operation of thermistor sensorsand their associated dual-balanced bridge power meter instruments.

Bolometers are power sensors that operate by changing resistance due to achange in temperature. The change in temperature results from converting RFor microwave energy into heat within the bolometric element. There are twoprinciple types of bolometers, barretters and thermistors. A barretter is a thinwire that has a positive temperature coefficient of resistance. Thermistors aresemiconductors with a negative temperature coefficient. Barretters are nolonger used.

The thermistor sensor used for RF power measurement is a small bead ofmetallic oxides, typically 0.4 mm diameter with 0.03 mm diameter wire leads.Thus the balanced-bridge technique always maintains the thermistor elementat a constant resistance, R, by means of DC or low frequency AC bias. As RFpower is dissipated in the thermistor, tending to lower R, the bias power iswithdrawn by an equal amount to balance the bridge and keep R the samevalue. That decrease in bias power is then displayed on a meter to indicate RFpower.

Thermistor sensorsThermistor elements are mounted in coaxial structures so they are compatiblewith common transmission line systems used at microwave and RF frequencies.Modern thermistor sensors have a second set of compensating thermistors tocorrect for ambient temperature variations.

5

II. Thermistor Sensors and Instrumentation

Coaxial thermistor sensorsThe Agilent 478A and 8478B thermistor mounts (thermistor mount was theearlier name for sensor) contain four matched thermistors and measure powerfrom 10 MHz to 10 and 18 GHz. The two RF-detecting thermistors, bridge-bal-anced to 100 Ω each, are connected in series (200 Ω) as far as the DC bridgecircuits are concerned. For the RF circuit, the two thermistors appear to beconnected in parallel, presenting a 50 Ω impedance to the test signal. The prin-ciple advantage of this connection scheme is that both RF thermistor leads tothe bridge are at RF ground. See Figure 2-1.

Compensating thermistors, which monitor changes in ambient temperature butnot changes in RF power, are also connected in series. These thermistors arealso biased to a total of 200 Ω by a second bridge in the power meter, called thecompensating bridge. The compensating thermistors are completely enclosed ina cavity for electrical isolation from the RF signal but they are mounted on thesame thermal conducting block as the detecting thermistors. The thermal massof the block is large enough to prevent sudden temperature gradients betweenthe thermistors. This improves the isolation of the system from thermal inputssuch as human hand effects.

There is a particular error, called dual element error, that is limited to coaxialthermistor mounts where the two thermistors are in parallel for the RF energy,but in series for DC. If the two thermistors are not quite identical in resistance,then more RF current will flow in the one of least resistance, but more DCpower will be dissipated in the one of greater resistance. The lack of equiva-lence in the dissipated DC and RF power is a minor source of error that is proportional to power level. For thermistor sensors, this error is less than 0.1%at the high power end of their measurement range and is therefore consideredas insignificant in the uncertainty analysis of Fundamentals Part 3.

Bridges, from Wheatstone to dual-compensated DC typesOver the decades, power bridges for monitoring and regulating power sensingthermistors have gone through a major evolution. Early bridges such as thesimple Wheatstone type were manually balanced. Automatically-balancedbridges, such as the 430C of 1952, provided great improvements in conveniencebut still had limited dynamic range due to thermal drift on their 30 µW (fullscale) range. In 1966, with the introduction of the first temperature-compensat-ed meter, the 431A, drift was reduced so much that meaningful measurementscould be made down to 1 µW.[1]

The Agilent 432A power meter uses DC to maintain balance in both bridges.The 432A has the further convenience of an automatic zero set, eliminating theneed for the operator to precisely reset zero for each measurement.

6

Figure 2-1. 478A coaxial sensor simplified diagram

RF bridgebias

Compensationbridge bias

Thermal conducting block

RF power

Rc

Rd

Cb

Rd

Cc

Rc

Cb

The 432A features an instrumentation accuracy of 1%. It also provides the ability to externally measure the internal bridge voltages with external higheraccuracy DC voltmeters, thus permitting a higher accuracy level for powertransfer techniques to be used. In the 432A, thermo-electric voltages are sosmall, compared to the metered voltages, as to be insignificant.

The principal parts of the 432A (Figure 2-2) are two self-balancing bridges, themeter-logic section, and the auto-zero circuit. The RF bridge, which containsthe detecting thermistor, is kept in balance by automatically varying the DCvoltage Vrf, which drives that bridge. The compensating bridge, which containsthe compensating thermistor, is kept in balance by automatically varying theDC voltage Vc, which drives that bridge.

The power meter is initially zero-set (by pushing the zero-set button) with noapplied RF power by making Vc equal to Vrfo (Vrfo means Vrf with zero RFpower). After zero-setting, if ambient temperature variations change thermistorresistance, both bridge circuits respond by applying the same new voltage tomaintain balance.

Figure 2-2. Simplified diagram of the 432A power meter.

If RF power is applied to the detecting thermistor, Vrf decreases so that

where Prf is the RF power applied and R is the value of the thermistor resistance at balance, but from zero-setting, Vrfo = Vc so that

which can be written

7

Prf = Vrfo 2

4R(Equation 2-1)– Vrf

2

4R

Prf = 14R (Equation 2-2)(Vc

2 – Vrf2)

Prf = 14R (Equation 2-3)(Vc – Vrf) (Vc + Vrf)

The meter logic circuitry is designed to meter the voltage product shown inEquation 2-3. Ambient temperature changes cause Vc and Vrf to change sothere is zero change to Vc

2 – Vrf2 and therefore no change to the indicated Prf.

As seen in Figure 2-2, some clever analog circuitry is used to accomplish themultiplication of voltages proportional to (Vc – Vrf ) and (Vc + Vrf) by use of avoltage-to-time converter. In these days, such simple arithmetic would beperformed by the ubiquitous microprocessor, but the 432A predated thattechnology and performs well without it.

The principal sources of instrumentation uncertainty of the 432A lie in themetering logic circuits. But Vrf and Vc are both available at the rear panel ofthe 432A. With precision digital voltmeters and proper procedure, those out-puts allow the instrumentation uncertainty to be reduced to ±0.2% for manymeasurements. The procedure is described in the operating manual for the432A.

Thermistors as power transfer standardsAlmost 100% of the popularity of the Agilent 432A is driven by its unique useas an adjunct to transferring power standards from NMIs to secondary stan-dards labs and production facilities. The DC substitution technique has beenaccepted by standards labs the world over, for tracing power uncertainties andcalibration factors from complex microcalorimeters in pristine primary labs tofield measurements. This alleviates the necessity for every organization in theworld to build, maintain and feed those complex microcalorimeters.

The use of thermistor sensors permits highly accurate and repeatable measurements of calibration factor, since the DC can be measured to very lowuncertainty with external instruments such as digital voltmeters. The sensorsare highly portable, the cal factors are stable over time, and the technologiesare accepted by common usage all over the world.

Regular use is also made of “round robins” between various user groups ofcompanies, whereby an artifact sensor is moved from one secondary standardslab to another, all coordinated by a “pivot lab.” When finished, all measureddata are combined and analyzed from start to finish, yielding specific perform-ance data on the individual participating labs, both for equipment and for theirmeasuring procedures.

Detailed descriptions of the use of thermistor sensors in the power transferprocess are found in Fundamentals Part 1, under Chapter III on the hierarchyand traceability of power. It is not included here because the theory and practice of sensor calibration and tracing of power standards are part of thesame system considerations.

8

[1] Pramann, R.F. “A Microwave Power Meter with a Hundredfold Reduction in Thermal Drift,” Hewlett-Packard Journal, Vol. 12, No. 10 (June, 1961).

Thermocouple sensors have been the detection technology of choice for sensingRF and microwave power since their introduction in 1974. The two main reasons for this evolution are: 1) they exhibit higher sensitivity than previousthermistor technology, and 2) they feature an inherent square-law detectioncharacteristic (input RF power is proportional to DC voltage out).

Since thermocouples are heat-based sensors, they are true “averaging detectors.”This recommends them for all types of signal formats from continuous wave(CW) to complex digital phase modulations. In addition, they are more ruggedthan thermistors, make useable power measurements down to 0.3 µW (–30 dBm,full scale), and have lower measurement uncertainty because of better voltagestanding wave radio (SWR).

The evolution to thermocouple technology is the result of combining thin-filmand semiconductor technologies to give a thoroughly understood, accurate,rugged, and reproducible power sensor. This chapter briefly describes the prin-ciples of thermocouples, the construction and design of modern thermocouplesensors, and the instrumentation used to measure their rather tiny sensor DC-output levels.

Principles of thermocouplesThermocouples are based on the fact that dissimilar metals generate a voltagedue to temperature differences at a hot and a cold junction of the two metals.As a simple example of the physics involved, imagine a long metal rod that isheated at the left end as in Figure 3-1. Because of the increased thermal agita-tion at the left end, many additional electrons become free from their parentatoms. The increased density of free electrons at the left causes diffusiontoward the right. There is also a force attempting to diffuse the positive ions tothe right but the ions are locked into the metallic structure and cannot migrate.So far, this explanation has not depended on Coulomb forces. The migration ofelectrons toward the right is by diffusion, the same physical phenomenon thattends to equalize the partial pressure of a gas throughout a space.

Each electron that migrates to the right leaves behind a positive ion. That iontends to attract the electron back to the left with a force given by Coulomb’slaw. The rod reaches equilibrium when the rightward force of heat-induced dif-fusion is exactly balanced by the leftward force of Coulomb’s law. The leftwardforce can be represented by an electric field pointing toward the right. The elec-tric field, summed up along the length of the rod, gives rise to a voltage sourcecalled the Thomson electromotive force (emf). This explanation is greatly simplified but indicates the principle.

9

III. Thermocouple Sensors and Instrumentation

Figure 3-1. Heat at one end of a metal rod gives rise to an electric field.

The same principles apply at a junction of dissimilar metals where differentfree electron densities in the two different metals give rise to diffusion and anemf. The name of this phenomenon is the Peltier effect.

A thermocouple is usually a loop or circuit of two different materials as shownin Figure 3-2. One junction of the metals is exposed to heat, the other is not. Ifthe loop remains closed, current will flow in the loop as long as the two junc-tions remain at different temperatures. If the loop is broken to insert a sensi-tive volt-meter, it will measure the net emf. The thermocouple loop uses boththe Thomson emf and the Peltier emf to produce the net thermoelectric voltage.The total effect is also known as the Seebeck emf.

Figure 3-2. Total thermocouple output is the resultant of several thermoelectrical voltages generatedalong the two-metal circuit.

Sometimes many pairs of junctions or thermocouples are connected in seriesand fabricated in such a way that the first junction of each pair is exposed toheat and the second is not. In this way the net emf produced by one thermo-couple adds to that of the next, and the next, etc., yielding a larger thermoelec-tric output. Such a series connection of thermocouples is called a thermopile.Early thermocouples for sensing RF power were frequently constructed of themetals bismuth and antimony. To heat one junction in the presence of RFenergy, the energy was dissipated in a resistor constructed of the metals mak-ing up the junction. The metallic resistor needed to be small in length and crosssection to form a resistance high enough to be a suitable termination for atransmission line. Yet, the junction needed to produce a measurable change intemperature for the minimum power to be detected and measured. Thin-filmtechniques were normally used to build metallic thermocouples. These smallmetallic thermocouples tended to have parasitic reactances and low burnoutlevels. Further, larger thermopiles, which did have better sensitivity, tended tobe plagued by reactive effects at microwave frequencies because the devicedimensions became too large for good impedance match at higher microwavefrequencies.

The thermocouple sensorThe modern thermocouple sensor was introduced in 1974[1] and is exemplifiedby the Agilent 8481A power sensor. It was designed to take advantage of bothsemiconductor and microwave thin-film technologies. The device, shown inFigure 3-3, consists of two thermocouples on a single integrated-circuit chip.The main mass of material is silicon.

The principal structural element is the frame made of p-type silicon, whichsupports a thin web of n-type silicon. The smoothly sloped sides of the frameresult from an anisotropic etch acting on the silicon crystal planes. The thinweb is produced by epitaxially growing it on the p-type substrate and then suitably controlling the etch, which also reveals the surface of the diffusedregions in the web.

10

Thermocouples

The principles behind the thermocouple

Vh

Hot junction

Metal 1

Metal 2

- +V1

- +V2

Coldjunction

-

+

1 2hV = V + V - V0

E-field

Bound Ions Diffused Electrons

Figure 3-3. Photo-micrograph of the structureof the 8481A thermocouple chip on a thin silicon web.

Figure 3-4. Cross section of one thermocouple. Power dissipated in the tantalum-nitride resistorheats the hot junction.

Figure 3-4 is a cross section through one of the thermocouples. One gold beamlead terminal penetrates the insulating silicon oxide surface layer to contactthe web over the edge of the frame. This portion of the web has been moreheavily doped by diffusing impurities into it. The connection between the goldlead and the diffused region is the cold junction of the thermocouple and thediffused silicon region is one leg of the thermocouple.

At the end of the diffused region near the center of the web, a second metalpenetration to the web is made by a tantalum nitride film. This contact is thehot junction of the thermocouple. The tantalum nitride, which is deposited onthe silicon oxide surface, continues to the edge of the frame where it contactsthe opposite beam lead terminal. This tantalum nitride forms the other leg ofthe thermocouple.

The other edge of the resistor and the far edge of the silicon chip have goldbeam-lead contacts. The beam leads not only make electrical contact to theexternal circuits, but also provide mounting surfaces for attaching the chip toa substrate, and serve as good thermal paths for conducting heat away fromthe chip. This tantalum-nitride resistor is not at all fragile in contrast to similarterminations constructed of highly conductive metals like bismuth/antimony.

As the resistor converts the RF energy into heat, the center of the chip, whichis very thin, gets hotter than the outside edge for two reasons. First, the shapeof the resistor causes the current density and the heat generated to be largestat the chip center. Second, the outside edges of the chip are thick and wellcooled by conduction through the beam leads. Thus, there is a thermal gradientacross the chip which gives rise to the thermoelectric emf. The hot junction isthe resistor-silicon connection at the center of the chip. The cold junction isformed by the outside edges of the silicon chip between the gold and diffusedsilicon region.

The thin web is very important, because the thermocouple output is propor-tional to the temperature difference between the hot and cold junctions. In thiscase the web is fabricated to be 0.005 mm thick. Silicon is quite a good thermalconductor, so the web must be very thin if reasonable temperature differencesare to be obtained from low power inputs.

11

SiliconOxideSiO2

TantalumNitrideTa2N

Hot junction

WebDiffused

regionColdjunction

SiO2

Frame

SiO2

GoldAu

GoldAu

Figure 3-5. Schematic diagram of the 8481A thermocouple power sensor.

The 8481A power sensor contains two identical thermocouples on one chip,electrically connected as in Figure 3-5. The thermocouples are connected inseries as far as the DC voltmeter is concerned. For the RF input frequencies,the two thermocouples are in parallel, being driven through coupling capacitorCc. Half the RF current flows through each thermocouple. Each thin-film resis-tor and the silicon in series with it has a total resistance of 100 Ω. The twothermocouples in parallel form a 50 Ω termination to the RF transmission line.

The lower node of the left thermocouple is directly connected to ground andthe lower node of the right thermocouple is at RF ground through bypasscapacitor Cb. The DC voltages generated by the separate thermocouples add inseries to form a higher DC output voltage. The principal advantage, however, ofthe two-thermocouple scheme is that both leads to the voltmeter are at RFground; there is no need for an RF choke in the upper lead. If a choke wereneeded it would limit the frequency range of the sensor.

The thermocouple chip is attached to a transmission line deposited on a sap-phire substrate as shown in Figure 3-6. A coplanar transmission line structureallows the typical 50 Ω line dimensions to taper down to the chip size, whilestill maintaining the same characteristic impedance in every cross-sectionalplane. This structure contributes to the very low reflection coefficient of theAgilent 8480 Series sensors, its biggest contribution, over the entire 100 kHz to50 GHz frequency range.

The principal characteristic of a thermocouple sensor for high frequency powermeasurement is its sensitivity in microvolts output per milliwatt of RF powerinput. The sensitivity is equal to the product of two other parameters of thethermocouple, the thermoelectric power and the thermal resistance.

The thermoelectric power (not really a power but physics texts use that term)is the thermocouple output in microvolts per degree Celsius of temperaturedifference between the hot and cold junction. In the 8481A thermocouple sen-sor, the thermoelectric power is designed to be 250µV/°C. This is managed bycontrolling the density of n-type impurities in the silicon chip.

The thickness of the 8481A silicon chip was selected so the thermocouple has athermal resistance 0.4 °C/mW. Thus, the overall sensitivity of each thermocou-ple is 100 µV/mW. Two thermocouples in series, however, yield a sensitivity ofonly 160 µV/mW because of thermal coupling between the thermocouples; thecold junction of one thermocouple is heated somewhat by the resistor of theother thermocouple giving a somewhat smaller temperature gradient.

12

RF input

Thin-filmresistor

n - Typesilicon

Hot

Coldjunction

To dc voltmeter

C c

C b

Gold leads Gold leads

RF power

Thermocouples

ColdThin-filmresistor

n - Typesilicon

Hot junction

Figure 3-6. Sketch of the thermocouple assembly for the 8481A.

Bypasscapacitor

Thermocouplechip

Input blockingcapacitor

Sapphiresubstrate

Housing

13

The thermoelectric voltage is almost constant with external temperature. Itdepends mainly on the temperature gradients and only slightly on the ambienttemperature. Still, ambient temperature variations must be prevented fromestablishing gradients. The chip itself is only 0.8 mm long and is thermallyshort-circuited by the relatively massive sapphire substrate. The entire assem-bly is enclosed in a copper housing. Figure 3-7 depicts the superior thermalbehavior of a thermocouple compared to a thermistor power sensor.

The thermoelectric output varies somewhat with temperature. At high powers,where the average thermocouple temperature is raised, the output voltage islarger than predicted by extrapolating data from low power levels. At a powerlevel of 30 mW the output increases 3%, at 100 mW, it is about 10% higher. Thecircuitry in the power meters used with thermocouples compensates for thiseffect. Circuitry in the sensor itself compensates for changes in its ambienttemperature.

The thermal path resistance limits the maximum power that can be dissipated.If the hot junction rises to 500 °C, differential thermal expansion causes thechip to fracture. Thus, the 8481A is limited to 300 mW maximum averagepower.

The thermal resistance combines with the thermal capacity to form the thermaltime constant of 120 µs. This means that the thermocouple voltage falls to within 37% of its final value 120 µs after the RF power is removed. Responsetime for measurements, however, is usually much longer because it is limited bynoise and filtering considerations in the voltmeter circuitry.

The only significant aging mechanism is thermal aging of the tantalum nitrideresistors. A group of devices were stress tested, producing the results of Figure 3-8. These curves predict that if a device is stressed at 300 mW for 1 year, the resistance should increase by about 3.5%. Nine days at a half wattwould cause an increase in resistance of 2%. On the other hand, aging effects of the tantalum-nitride termination are compensated by use of the power calibration procedure, whereby a precision 1 mW, 50 MHz source is used to seta known level on the meter.

Figure 3-8. Results of a step stress aging test show percent change in thermocouple resistance whenleft at various power levels continuously for various periods of time.

It is relatively easy to adapt this sensor design for other requirements. Forexample, changing each tantalum-nitride resistor to a value of 150 Ω yields a75 Ω system. To enhance low frequency RF performance, larger blocking andbypass capacitors extend input frequencies down to 100 kHz. This usually compromises high frequency performance due to increased loss and parasiticreactance of the capacitors. The Agilent 8482A power sensor is designed for100 kHz to 4.2 GHz operation,while the standard 8481A operates from 10 MHzto 18 GHz.

Figure 3-7. Zero drift of thermocouple andthermistor power sensors due to beinggrasped by a hand.

Time

10

8

4

6

0

2Pow

er (m

icro

wat

ts)

Hand grasp

Typical thermocouple sensor (8481A)

1 Minute

2 Microwatts

Typical thermistor mount (8478B)

1.00

1.50

0.75

0.50

0.25

00.01

1.25

0.1 1 10 100 1000

1 Year

Time (days)

Pow

er (w

atts

)

% Change

510

21

Linearity characteristics for thermocouple and thermistor sensorsIn the application of power sensors, there are two cases where the user wouldselect sensors which exhibit the best detection linearity.

1. A measurement might involve using the linearity of the sensor itself to measure the linearity characteristic of some other component, such as an amplifier. This might be done by setting increasing power into the device under test, and monitoring the increase with a power sensor. In such a setup,the linearity of the sensor transfers directly to the measurement results.

2. Thermocouple sensors, as just described in this chapter, are “indirectly” calibrated by use of the 50 MHz, 1 mW reference source on the front panel of most Agilent power meters. This transfers that reference power to the sensor,but for all other powers, both higher and lower, the power readout depends on the linearity of the sensor. For thermocouple sensors, which depend on heating up the thermo-electric junctions, they are quite linear, and that characteristic is included in the basic power uncertainty specifications.

Recent research at the National Physical Laboratory in Teddington, UK, focusedon characterizing the detection linearity of two types of sensors, thermistorsand thermocouples.[6] Measurements were made on multiple sensors in eachclass, and are shown in Figure 3-9 and 3-10.

Data courtesy of NPL, Teddington, UK.

Figure 3-9. Mean linearity of seven units of model 8478A coaxial thermistor sensors from 0.1 to 10 mW. (8478A is an older model, the current model is 8478B.)

Data courtesy of NPL, Teddington, UK.

Figure 3-10. Mean linearity of four units of model 8481A coaxial thermocouple sensors from0.1 to 10 mW.

The results seem reasonable, considering the technology involved. In the caseof thermistor sensors, the DC-substitution process keeps the tiny bead of ther-mistor, at a constant temperature, backing off bias power as RF power isadded. In the case of thermocouple sensors, as power is added, the detectionmicrocircuit substrate with its terminating resistor runs at higher temperaturesas the RF power increases. This naturally induces minor deviations in thedetection characteristic. Linearity uncertainty for sensors is also treated inFundamentals Part 3, and generally specified on product data sheets.

14

Offs

et (

%)

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.1 1 10

Power level (mW)

Coaxial thermistors

-0.6

-0.5

-0.4

-0.3

-0.1

-0.2

0

0.1

0.2

0.3

0.1 1 10

Power level (mW)

Thermocouple sensors

Offs

et (

%)

Power meters for thermocouple sensorsIntroduction of thermocouple sensor technology required design of a newpower meter architecture that could take advantage of increased power sensi-tivity, yet be able to deal with the very low output voltages of the sensors. Thisled to a family of power meter instrumentation starting with the 435A analogpower meter, to the 436A digital power meter.[2, 3, 4, 5] Some years later thedual-channel 438A was introduced, which provided for computation of powerratios of channels A and B as well as power differences of channels A and B.The most recent Agilent 437B power meter offered digital data manipulationswith the ability to store and recall sensor calibration factor data for up to tendifferent power sensors. All of those models have been replaced.

To understand the principles of the instrument architecture, a very briefdescription will be given for the first-introduced thermocouple meter, the 435Aanalog power meter. This will be followed by an introduction of Agilent’sE4418B (single channel) and E4419B (dual channel) power meters. They will be completely described in Chapter IV, after a new wide-dynamic-range diode sensor is introduced. Two peak and average power meters are introduced inChapter V, the Agilent E4416/17A meters. The newest peak and average powermeters, Agilent N1911/12A, will also be described in Chapter V.

Thermocouple sensor DC output is very low-level (approximately 160 nV for 1microwatt applied power), so it is difficult to transmit in an ordinary flexibleconnection cable. This problem is multiplied if the user wants a long cable(25 feet and more) between the sensor and power meter. For this reason it wasdecided to include some low-level AC amplification circuitry inside the powersensor, so only relatively high-level signals appear on the cable.

One practical way to handle such tiny DC voltages is to “chop” them to form asquare wave, then amplify them with an AC-coupled system. After appropriateamplification (some gain in the sensor, some in the meter), the signal is syn-chronously detected at the high-level AC. This produces a high-level DC signalthat is then further processed to provide the measurement result. Figure 3-11shows a simplified block diagram of the sensor/meter architecture.

Cabling considerations led to the decision to include the chopper and part ofthe first AC amplifier inside the power sensor. The chopper itself (Figure 3-12)uses field-effect transistor switches that are in intimate thermal contact. It isessential to keep the two FET’s at exactly the same temperature to minimizedrift. To eliminate undesired thermocouple effects (in circuitry external to theRF sensor thermocouples), only one metal, gold, is used throughout the entireDC path. All these contributions were necessary to help achieve the low driftalready shown in Figure 3-7.

15

16

Figure 3-11. Basic power meter and thermocouple sensor block diagram.

The chopping frequency of 220 Hz was chosen as a result of several factors.Factors that dictate a high chopping frequency include lower 1/f noise and alarger possible bandwidth, and thereby faster step response. Limiting the chop-ping to a low frequency is the fact that small transition spikes from choppinginevitably get included with the main signal. These spikes are at just the properrate to be integrated by the synchronous detector and masquerade as valid sig-nals. The fewer spikes per second, the smaller this masquerading signal.However, since the spikes are also present during the zero-setting operation,and remain the same value during the measurement of a signal, the spikes areessentially removed from the meter indication by zerosetting and cause noerror. The spikes do, however, use up dynamic range of the amplifiers.

Figure 3-12. Simplified schematic of chopper amplifier.

One way to minimize noise while amplifying small signals is to limit the chan-nel bandwidth. Since the noise generating mechanisms are broadband, limitingthe amplifier bandwidth reduces the total noise power. The narrowest band-width is chosen for the weakest signals and the most sensitive range. As thepower meter is switched to higher ranges, the bandwidth increases so thatmeasurements can be made more rapidly. On the most sensitive range, the timeconstant is roughly 2 seconds, while on the higher ranges, the time constant is0.1 seconds. A 2-second time constant corresponds to a 0 to 99% rise time ofabout 10 seconds.

Power meterPower sensor

One halfof inputamplifier

Low levelAC

One halfof inputamplifier

ChopperDC

Thermocouple

220 Hzmultivibrator

Autozero

Zero

Cal factor

Amplifiersand

attenuators

50 MHzreferenceoscillator

Synchronousdetector

DCamplifier

Range

RFinput

V

Cable

Meter

To DC amplifier

Thermocoupleoutput

DC path (all gold)

Multivibratorinput

200 Ω

17

Traceable power reference oscillatorAn inherent characteristic of thermocouple power measurements is that suchmeasurements are open-loop, and thus thermistor power measurements areinherently more accurate because of their DC-substitution, closed-loop process.The bridge feedback of substituted DC power compensates for differencesbetween thermistor mounts and for drift in the thermistor resistance-powercharacteristic without recalibration.

With thermocouples, where there is no direct power substitution, sensitivitydifferences between sensors or drift in the sensitivity due to aging or tempera-ture can result in a different DC output voltage for the same RF power. Becausethere is no feedback to correct for different sensitivities, measurements withthermocouple sensors are said to be open-loop.

Agilent thermocouple power meters solve this need for sensitivity calibrationby incorporating a 50 MHz power-reference oscillator whose output power iscontrolled with great precision (±0.4%). To verify the accuracy of the system, oradjust for a sensor of different sensitivity, the user connects the thermocouplesensor to the power reference output and, using a calibration adjustment, setsthe meter to read 1.00 mW. By applying the 1 mW reference oscillator to thesensor’s input port just like the RF to be measured, the same capacitors, con-ductors and amplifier chain are used in the same way for measurement as forthe reference calibration. This feature provides confidence in a traceabilityback to company and NMI standards.

Note: The calculation of the uncertainty budget, including the 50 MHz powerreference, is covered in greater detail in Fundamentals Part 3. It should alsobe noted that Agilent has recently made improvements in the specifications ofthe 50 MHz reference oscillator.

The previous specification has been improved in the following areas. It is now“factory set to ±0.4% and traceable to the National Physical Laboratory of theUK.” Expansion of the operating specification includes the following agingcharacteristics, which are now valid for 2 years:

EPM & EMP-P** P-SeriesAccuracy for 2 years Accuracy for 2 years±0.5% (23 ±3 °C)** ±0.4% (23 ±10 °C)±0.6% (23 ±10 °C)** ±1.2% (0 - 55 °C)±0.9% (0 - 55 °C)

Since the reference oscillator represents a reasonably large portion of the ulti-mate power measurement uncertainty budget, the smaller accuracy numbers inthe specification leads to a lower overall measurement uncertainty. Anotherpositive note is that the meters require less downtime in the calibration lab,now having a 2-year calibration cycle.

18

EPM Series power metersThe two-decade industry acceptance of thermocouple (and diode) sensortechnology for RF power measurements has resulted in tens of thousands ofunits in the installed base around the world. Yet new technologies now allowfor design of diode sensors with far larger dynamic range and new powermeters with dramatically-expanded user features.

The E4418B (single channel) and E4419B (dual channel) power meters offersome significant user features:

• Menu-driven user interface, with softkeys for flexibility.• Dedicated hardkeys for frequently used functions, such as Zero and Cal.• Large LCD display for ease of reading.• Built for wide-dynamic-range E-Series CW and average power sensors.• Backward compatible with all 8480 Series sensors

(except the discontinued 8484A).• Fast measurement speed, up to 200 readings per second via the GPIB.• Form, fit, function replacement with 437B and 438A power meters

(preserves automation software code). See Chapter IV.

Since the meters provide more powerful measurement capability when teamedwith the E-Series CW and average wide-dynamic range diode sensors, thedetailed description of the meters will be presented in Chapter IV. This willfirst allow for a presentation of the technology for the new diode sensors withthe range from –70 to +20 dBm, and then the meters that take advantage of thisincreased capability.

ConclusionBecause of their inherent ability to sense power with true square-law charac-teristics, thermocouple sensors are best suited for handling signals with com-plex modulations or multiple tones. They always respond to the true average power of a signal, modulation, and multiple signals. They are rugged,stable, and reliable.

The large installed worldwide base of Agilent thermocouple and diode sensorsand their compatible power meters argues that any new power meters bedesigned to be backward compatible with older sensors. All current 8480 Seriessensors will work with the EPM, EPM-P, and P-Series power meters. The newer E-Series sensors are not backwards-compatible with Agilent’s older meters dueto a modified interface design, which allows for download of EEPROM-storedconstants.

Thermocouple sensors are based on a stable technology that will be used tomeasure RF power in many applications for a long time in the future.

[1] W.H. Jackson, “A Thin-Film Semiconductor Thermocouple for Microwave Power Measurements,”Hewlett-Packard Journal, Vol. 26, No. 1 (Sept., 1974).

[2] A.P. Edwards, “Digital Power Meter Offers Improved Accuracy, Hands-Off Operation, Systems Capability,”Hewlett-Packard Journal, Vol. 27 No. 2 (Oct. 1975).

[3] J.C. Lamy, “Microelectronics Enhance Thermocouple Power Measurements,”Hewlett-Packard Journal, Vol. 26, No. 1 (Sept., 1974).

[4] “Power Meter-New Designs Add Accuracy and Convenience.” Microwaves, Vol. 13, No. 11 (Nov., 1974).[5] R.E. Pratt, “Very-Low-Level Microwave Power Measurements,”

Hewlett-Packard Journal, Vol. 27, No. 2 (Oct., 1975).[6] Holland, K., and Howes, J., “Improvements to the Microwave Mixer and Power Sensor Linearity Measurement

Capability at the National Physical Laboratory,” (Teddington, UK) IEE Proc.-Sci Meas. Technology, Nov. 2002.

Figure 3-13. E4418B features many user-conveniences and a 90 dB dynamic measure-ment range. The 50 MHz, 1 mW reference output connector is at the top-right.

19

Rectifying diodes have long been used as detectors and for relative powermeasurements at microwave frequencies. The earliest diodes were used mostlyfor envelope detection and as nonlinear mixer components in super-heterodynereceivers. For absolute power measurement, however, diode technology hadbeen limited mainly to RF and low microwave frequencies.

High-frequency diodes began with point-contact technology which evolved fromthe galena crystal and cat-whisker types of early radio and found application asearly as 1904.[1] Point-contact diodes were extremely fragile, not very repeat-able, and subject to change with time. It was the low-barrier Schottky (LBS)diode technology that made it possible to construct diodes with metal-semicon-ductor junctions for microwave frequencies that were very rugged and consis-tent from diode to diode. These diodes, introduced as power sensors in 1974,were able to detect and measure power as low as –70 dBm (100 pW) at frequen-cies up to 18 GHz.[2]

This chapter will review the semiconductor principles as they apply tomicrowave detection, briefly review LBS technology and then describe the lat-est planar-doped-barrier (PDB) diode technology. It will describe how suchdevices are designed into power sensor configurations and introduce a newCW-diode sensor with an impressive 90 dB dynamic power range using digital-detection-curve correction techniques. Then, a novel two-path diode sensorwith wide dynamic range is discussed. Signal and waveform effects for non-CWsignals operating above the square-law range will also be examined.

The EPM Series power meters will be described, which exploit the advantagesof the new 90-dB-range sensors and offer major user-conveniences as well.

Principles of diode detectors Diodes convert AC signals to DC by way of their rectification proper-ties, whicharise from their nonlinear current-voltage (i-v) characteristic. It might seemthat an ordinary silicon p-n junction diode would, when suitably packaged, be asensitive RF detector. However, stored charge effects limit the bandwidth of thep-n junction. The Schottky1 barrier diode does not store charge in its junctionbut most of them have extremely high impedance at low signal levels. A RF sig-nal in the rage of –20 dBm is required to overcome the 0.3-volt junction voltageof a conventional Schottky diode. One alternative is to bias the diode to 0.3 Vand is a usable approach if the detected output can be AC coupled with elimi-nates the drift introduced by the bias. With AC coupling, the minimum powerthat can be metered by a biased diode may be improved by about 10 dB due tothe drift and noise introduced by bias current. A typical application for thistechnique would be the diode detectors used for scalar network analyzers.

Metal-semiconductor junctions, exemplified by point-contact technology, exhib-it a low potential barrier across their junction, with a forward voltage of about0.3 V. They have superior RF and microwave performance, and were popular inearlier decades. LBS diodes, which are metal-semiconductor junctions, succeeded point-contacts and vastly improved the repeatability and reliability.Figure 4-1 shows a typical diode i-v characteristic of an LBS junction, expandedaround the zero-axis to show the square-law (see below) region.

IV. Diode Sensors and Instrumentation

millivolts

v

10

-5

-10

-15

-30 20-20 -10 10 30

15

i µamps

5

Figure 4-1. The junction rectifying characteris-tic of a low-barrier Schottky diode, showingthe small-signal, square-law characteristicaround the origin.

1. The diode metal-semiconductor junction rectifying effect was named for physicist Walter Schottky (1886-1976) who advanced the theory for the process.

Mathematically, a detecting diode obeys the diode equation

where α = q/nKT, and i is the diode current, v is the net voltage across thediode, Is is the saturation current and is constant at a given temperature. K isBoltzmann’s constant, T is absolute temperature, q is the charge of an electronand n is a correction constant to fit experimental data (n equals approximately1.1 for the devices used here for sensing power). The value of α is typically alittle under 40 (v)-1, in this case approximately 36 v -1.

Equation 4-1 is often written as a power series to better analyze the rectifyingaction,

It is the second and other even-order terms of this series which provide therectification. For small signals, only the second-order term is significant so thediode is said to be operating in the square-law region. In that region, output i(and output v) is proportional to RF input voltage squared. When v is so highthat the fourth and higher order terms become significant the diode response isno longer in the square law region. It then rectifies according to a quasi-square-law i-v region which is sometimes called the transition region. Above that rangeit moves into the linear detection region (output v proportional to input v).

For a typical packaged diode, the square-law detection region exists from thenoise level up to approximately –20 dBm. The transition region ranges fromapproximately –20 to 0 dBm input power, while the linear detection regionextends above approximately 0 dBm. Zero dBm RF input voltage is equivalentto approximately 220 mV (rms) in a 50 Ω system. For wide-dynamic-rangepower sensors, it is crucial to have a well-characterized expression of the tran-sition and linear detection range.

Figure 4-2 shows a typical detection curve, starting near the noise level of–70 dBm and extending up to +20 dBm. It is divided up into the square law,transition and linear regions. (Noise is assumed to be zero to show the square-law curve extends theoretically to infinitely small power.) Detection diodes cannow be fabricated which exhibit transfer characteristics that are highly stablewith time and temperature. Building on those stable features, data correctionand compensation techniques can take advantage of the entire 90 dB of powerdetection range.

20

Figure 4-2. The diode detection characteristicranges from square law through a transitionregion to linear detection.

-70 -60 -50 -40 -30 -20 -10 0 +10 +20100nv

10µv

1mv

100mv

10v

Det

ecte

d ou

tput

-v

1µv

100µv

10mv

1v

Input power -dBm

-60 -50 -40 -30 -20 -10 0 +10 +20-14

-10

-6

-2

+2

Dev

iatio

n fr

om s

quar

e la

w -d

B

-12

-8

-4

0

Input power -dBm

i = Is (eαv–1) (Equation 4-1)

i = Is (αv + + + . . . ) (Equation 4-2)(αv) 2

2 !

(αv) 3

3 !

21

Figure 4-3. Circuit diagram of a source and a diode detector with matching resistor.

The simplified circuit of Figure 4-3 represents an unbiased diode device fordetecting low level RF signals. Detection occurs because the diode has a nonlin-ear i-v characteristic; the RF voltage across the diode is rectified and a DC out-put voltage results.

If the diode resistance for RF signals were matched to the generator sourceresistance, maximum RF power would be delivered to the diode. However, aslong as the RF voltage is impressed across the diode, it will detect RF voltageefficiently. For reasons explained below, diode resistance for small RF signalsis typically much larger than 50 Ω and a separate matching resistor is used toset the power sensor’s input termination impedance. Maximum power is trans-ferred to the diode when the diode resistance for small RF voltages is matchedto the source resistance. The diode resistance at the origin, found by differenti-ating Equation 4-1, is:

Resistance Ro is a strong function of temperature which means the diodesensitivity and the reflection coefficient are also strong functions of tempera-ture. To achieve less temperature dependence, Ro is much larger than thesource resistance and a 50 Ω matching resistor serves as the primary termina-tion of the generator. If Ro of the diode of Figure 4-3 were made too large, how-ever, there would be poor power conversion from RF to DC; thus, a larger Rodecreases sensitivity. An origin resistance of 1–2 kΩ will be obtained withdiodes having a reverse saturation current (Is) of between 27.5 to 13.8 µA. Acompromise between good sensitivity to small signals and good temperatureperformance results from making Is about 10 microamps and Ro approximately2.75 kΩ.

The desired value of saturation current, Is, can be achieved by constructing thediode of suitable materials that have a low potential barrier across the junc-tion. Schottky metal-semiconductor junctions can be designed for such a low-barrier potential.

The origin resistance Ro is a very useful concept in understanding how a detec-tor diode will operate under a wide variety of conditions. It forms the real partof the source impedance of the detected output, so the effect of finite loadresistance can be estimated. If the value of the RF bypass capacitor, Cb, isknown, the overall risetime may be accurately estimated. If the variation in Isversus temperature (Silicon LBSD’s double every 10 ˚C rise) is considered, thetemperature coefficient of the loaded detector can also be estimated.

Of course, Ro is also sensitive to the input power into the device, and can onlybe considered to be constant for junction voltages which are lower than the“thermal voltage” Vt=nKT/q, or about 28 mV peak. This limit correlates wellwith the power level where the output departs from square law response in a50 Ω system.

Using diodes for sensing powerPrecision semiconductor fabrication processes for silicon allowed the Schottkydiodes to achieve excellent repeatability and, because the junction area waslarger, they were more rugged. Agilent’s first use of such a low-barrier Schottkydiode (LBSD) for power sensing was introduced in 1975 as the 8484A powersensor.[2] It achieved an exceptional power range from –70 (100 pW) to –20 dBm (10 µW) from 10 MHz to 18 GHz.

R matching Cb Vo

Rses

Ro = 1αIs

(Equation 4-3)

22

As Gallium-Arsenide (GaAs) semiconductor material technology advanced inthe 1980s, such devices exhibited superior performance over silicon in themicrowave frequencies. A sophisticated diode fabrication process known asplanar-doped-barrier (PDB) technology offered real advantages for powerdetection.[3] It relied on a materials preparation process called molecularbeam epitaxy for growing very thin epitaxial layers. Figure 4-4 shows thedevice cross sections of the two types of diode junctions, low-barrier Schottky(Figure 4-4(a)) and planar-doped barrier (Figure 4-4(b)) diodes. The dopingprofile of the PDB device is n+ —I—p+—I—n+, with intrinsic layers spacedbetween the n+ and p+ regions. The i/v characteristic has a high degree of sym-metry which is related to the symmetry of the dopants.

The p+ region is fabricated between the two intrinsic layers of unequal thick-ness. This asymmetry is necessary to give the PDB device the characteristics ofa rectifying diode. An important feature of the PDB diode is that the device canbe designed to give a junction capacitance, Co, that is both extremely small(20 fF or less) (femto Farad) and nearly independent of the bias voltage. Co is also independent of the size of the metal contact pad.

As a result of the very stable Co versus bias voltage, the square-law characteris-tics of this device versus frequency are significantly more constant than thoseof metal-to-semiconductor devices. Low capacitance coupled with low junctionresistance allows excellent microwave signal performance since the low junc-tion resistance lowers the radio correction (RC) time constant of the junctionand raises the diode cutoff frequency.

A PDB diode is far less frequency-sensitive than a normal p-n junction diodebecause of the intrinsic layer at the junction.[4] In a p-n junction diode theequivalent capacitance of the junction changes with power level, but in the pla-nar-doped-barrier diode, junction capacitance is determined by the intrinsiclayer, which remains almost constant as a function of power.

Agilent uses a specialized integrated circuit process that allows custom tailor-ing of the doping to control the height of the Schottky barrier. This controlleddoping makes it practical to operate the detector diode in the current mode,while keeping the video resistance low enough to maintain high sensitivity.

The first power sensor application for PDB diodes was the Agilent 8481/85/87DSeries power sensors, introduced in 1987.[4] The 8481D functionally replacedthe low-barrier-Schottky 8484A sensor. The new PDB sensor employed twodiodes, fabricated on the same chip using microwave monolithic integrated circuit (MMIC) chip technology. The two diodes were deposited symmetricallyabout the center of a coplanar transmission line and driven in a push-pull manner for improved signal detection and cancellation of common-mode noiseand thermal effects. This configuration features several advantages:

• Thermoelectric voltages resulting from the joining of dissimilar metals,a serious problem below –60 dBm, are cancelled.

• Measurement errors caused by even-order harmonics in the input signalare suppressed due to the balanced configuration.

• A signal-to-noise improvement of 1 to 2 dB is realized by having two diodes.The detected output signal is doubled in voltage (quadrupled in power) whilethe noise output is doubled in power since the dominant noise sources areuncorrelated.

• PDB devices also have higher resistance to electrostatic discharge and are more rugged than Schottky’s.

• Common-mode noise or interference riding on the ground plane is cancelled at the detector output. This is not RF noise but metallic connection noises on the meter side.

PDB diode technology provides some 3000 times (35 dB) more efficient RF-to-DC conversion compared to the thermocouple sensors of Chapter III.

Metal contactn+

p+I

n+Substrate

Metal contact

Metal for low barrierPassivation layer

Epitaxial layer

Bulk silicon substrate

I

Figure 4-4. Idealized cross sections of twodiode configurations. (a) low-barrier Schottky. (b) planar-doped-barrier.

(a)

(b)

23

Figure 4-5 shows two regions of the i-v characteristic of a typical PDB diode.Figure 4-5(a) shows the small signal region, while Figure 4-5(b) shows the larg-er signal characteristics to include the linear region as well as the breakdown region on the left.

They also provide accurate square-law performance from –70 to –20 dBm.Diode sensor technology excels in sensitivity, although realistically, thermocou-ple sensors maintain their one primary advantage as pure square-law detectorsfor the higher power ranges of –30 to +20 dBm. Hence neither technologyreplaces the other and the user’s measuring application determines the choiceof sensors.

In detecting power levels of 100 pW (70 dBm) the diode detector outputis about 50 nanovolts. This low signal level requires sophisticated amplifier andchopper circuit design to prevent leakage signals and thermocouple effectsfrom dominating the desired signal. Earlier diode power sensors required addi-tional size and weight to achieve controlled thermal isolation of the diode. Thedual-diode configuration balances many of the temperature effects of thosehighly-sensitive circuits and achieves superior drift characteristics in a smaller,lower-cost structure.

Wide-dynamic-range, CW-only power sensorsDigital signal processing and microwave semiconductor technology have nowadvanced to the point where dramatically improved performance and capabili-ties are available for diode power sensing and metering. New diode power sensors are now capable of measuring over a dynamic power range of –70 to+20 dBm, an impressive range of 90 dB. This permits the new sensors to beused for CW applications which previously required two separate sensors.

The E4412A power sensor features a frequency range from 10 MHz to 18 GHz.The E4413A power sensor operates to 26.5 GHz (Option H33 extends the rangeto 33 GHz). Both provide the same –70 to +20 dBm power range. A simplifiedschematic of the new sensors is shown in Figure 4-6. The front end construc-tion is based on MMIC technology and combines the matching input pad, balanced PDB diodes, FET choppers, integrated RF filter capacitors, and theline-driving pre-amplifier. All of those components operate at such low signallevels that it was necessary to integrate them into a single thermal space on asurface-mount-technology PC board.

Figure 4-6. Simplified schematic for the E4412/13A power sensors. The 90 dB power range isachieved using data stored in the individual sensor EEPROM which contains linearization, temperature compensation and calibration factor corrections.

12.010.08.06.0

4.02.0

-2.00

-4.0-6.0-8.0

-10.0-4.0 -3.5 -3.0 -2.5 -2.0 -0.5-1.5 -1.0 0 0.5 1.0

i (m

a)

v (volts)

Large signal

i (µa

)100

50

0

-50

-100-50 -25 0 25 50

v (mv)

Small signal(a)

(b)

Figure 4-5. The i-v characteristics of a PDBdiode are shown for two different drive voltage regions. The assymetry of the p+ layercan be used to modify the shape of the i-vcurve, while not affecting some of the otherdiode parameters such as Co and Ro.

Balanced chopper

Feedback

RF inputAC signal

Chop signal

Chop signal

Serial EEPROM

Serial latch

Serial data

Temp comp

Range switch

+5V Rectifer & regulator

Serial clock

Bias

Temperature sensor

50Ω

3dB

µcircuitGaAs IC

24

To achieve the expanded dynamic range of 90 dB, the sensor/meter architec-ture depends on a data compensation algorithm that is calibrated and stored inan individual EEPROM in each sensor. The data algorithm stores informationof three parameters, input power level vs frequency vs temperature for therange 10 MHz to 18 or 26.5 GHz and –70 to +20 dBm and 0 to 55 °C.

At the time of sensor power-up, the power meter interrogates the attached sensor using an industry-standard serial bus format, and in turn the meterreceives the upload of sensor calibration data. An internal temperature sensorsupplies the diode’s temperature data for the temperature-compensation algo-rithm in the power meter.

Since the calibration factor correction data will seldom be used manually, it isno longer listed on the sensor label of the E-Series sensors. The data is alwaysuploaded into the power meter on power-up or when a new sensor is connected.The new sensors store cal factor tables for two different input power levels toimprove accuracy of the correction routines. If the cal factor changes uponrepair or recalibration, the new values are re-loaded into the sensor EEPROM.For system users who need the cal factor for program writing, the data is furnished on a calibration certificate.

Wide-dynamic-range average power sensorsToday’s average power measurement needs, as highlighted by complex digitalmodulation formats such as code division multiple access (CDMA), are foraccurate measurements in the presence of high crest factors (peak-to-averageratio), and often require a dynamic range greater than 50 dB. As the Agilent E4412A and E4413A sensors are designed to measure the averagepower of CW signals, they cannot satisfy this requirement.

Agilent’s approach to creating a wide-dynamic-range, average powersensor to meet this need is based on a dual sensor, diode pair/attenuator/diodepair topology as proposed by Szente et. al. in 1990.[5] This topology has theadvantage of always maintaining the sensing diodes within their square lawregion and therefore will respond properly to complex modulation formats aslong as the sensor’s correct range is selected.

This approach was further refined by incorporating diode stacks in place ofsingle diodes to extend square law operation to higher power levels at theexpense of sensitivity. A series connection of m diodes results in a sensitivitydegradation of 10 log(m) dB and an extension upwards in power limits of thesquare law region maximum power of 20 log(m) dB, yielding a net improvementin square law dynamic range of 10 log(m) dB compared to a single diode detector.

The Agilent E-Series E9300 power sensors are implemented as a modified barrier integrated diode (MBID)[6] with a two diode stack pair for the lowpower path (–60 to –10 dBm), a resistive divider attenuator and a five diodestack pair for the high power path (–10 to +20 dBm), as shown in Figures 4-7(a) and 4-7(b). Additionally, series FET switches are used off-chip toallow the low path diodes to self-bias off when not in use.

Lsense -

Lsense +

Hsense +

Hsense -

RF in

Figure 4-7 (a) Photograph of MBID.(b) Schematic of MBID.

Resistive power splitter

(a)

(b)

Typical deviation from square law for the low power path (–60 to –10 dBm)and high power path (–10 to +20 dBm) for the E-Series E9300 power sensors isshown in Figure 4-8.

Figure 4-8. E9300 power sensor linearity. The linearity at the –10 dBm switching point is specified asbeing typically ≤ ±0.5% (≤ ±0.02 dB). The E9300 power sensors switch quickly and automaticallybetween ranges, providing a transparent 80 dB dynamic range.

The decision for switching between the low and high power paths is made onthe basis of the average power detected by the meter. For example, a –12 dBmaverage power signal with a high crest factor (peak-to-average ratio) would bemeasured by the low power path. For most CDMA signals, such as IS-95A,E9300 sensors will give better than ±0.05 dB accuracy up to –10 dBm averagepower using the low power path. However, for some 3G CDMA signals, withaligned symbols that have almost 20 dB maximum peak-to-average ratio, theaccuracy of the measurement during the high power crests would be compro-mised. This is due to the sensor being in the low power path and the diodesbeing operated well outside the square law region of the low power path duringthe crests. A Range Hold function for the high power path deals with this situa-tion as it allows both the peak and average powers to be measured in thesquare law region of the high power path.

To avoid unnecessary switching when the power level is near –10 dBm, switching point hysteresis has been added. This hysteresis causes the low powerpath to remain selected as the power level is increased up to approximately –9.5 dBm, above this power the high power path is selected. The high powerpath remains selected until approximately –10.5 dBm is reached as the signallevel decreases. Below this level the low power path is selected.

To provide user-meaningful sensor information relevant to the numerous powermeasurement scenarios, from a temperature controlled manufacturing or R&Denvironment to field installation and maintenance applications, warrantedspecifications for E9300 sensors are provided over the temperature ranges 25 ±10 °C as well as 0 to 55 °C. Also, supplemental information is provided at25 °C to illustrate the typical performance achievable, as shown in Figure 4-9.

25

90%

95%

100%

105%

110%

–40 –30 –20 –10 0 10 20

Power (dBm)

Line

arity

(%)

26

Power range –30 to –20 dBm –20 to –10 dBm –10 to 0 dBm 0 to +10 dBm +10 to +20 dBm

Measurement ± 0.9% ± 0.8% ± 0.65% ± 0.55% ± 0.45%uncertainty

Power Linearity Linearityrange (25 ±10 °C) (0 to 55 °C)

–60 to –10 dBm ± 3.0% ± 3.5%

–10 to 0 dBm ± 2.5% ± 3.0%

0 to +20 dBm ± 2.0% ± 2.5%

Figure 4-9. Typical power linearity performance at 25 °C, after a zero and calibration, (top chart)along with the measurement uncertainty for different power ranges is shown (lower plot). By provid-ing this type of specification data, users can better understand how the power sensor will performfor their particular application and environment and so allow informed sensor selection.

A versatile power meter to exploit the E-Series power sensors

Figure 4-10. E4419B dual-channel power meter measures insertion loss of a 11.245 GHz waveguidebandpass filter, using the meter’s power ratio mode, plus a sweeper and power splitter. Agilent’s 90 dB dynamic-range sensors are ideal for such high-attenuation measurements.

Two power meters, E4418B (single channel) and E4419B (dual channel)take advantage of the sensor’s 90 dB power measuring range. More importantly,advances in digital signal processing (DSP) technology now provide significantincreases in measurement speeds. Digital processing permits functionalconveniences resulting in a dramatically more versatile power meter.

Linearity verify data

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

-30 -25 -20 -15 -10 -5 0 5 10 15 20

Power (dBm)

% E

rror

27

The basic meter architecture is based on DSP technology that improvesperformance by removing meter range switching and their delays (except for asingle range-switching transition point). It also provides faster signal detection.The DSP module performs several other functions, synchronous detection(de-chopping), matches up the two analog-to-digital converter (ADC) channels,and does the programmable filtering. It provides a 32-bit digital number that isproportional to the detected diode voltage over a 50 dB power range.

The power meter uses the uploaded calibration data from each connectedsensor to compensate for the three critical sensor parameters, power from –70 to +20 dBm, frequency for its specified band, and operating temperature.

The calibration routine requiring connection to the 50 MHz power referencefurnishes the power traceability path for the sensor connected. The operatorthen keys in the frequency of the RF signal under test so that the meter cor-rects for the sensor calibration factor. Mismatch uncertainty must still be exter-nally calculated because the reflection coefficient of the unknown power sourceis usually not available.

Figure 4-11 shows a simplified schematic of the E4418B meter (see Figure 4-6for reference to the associated E-Series sensors). The pre-amplified sensor out-put signal receives some early amplification, followed by some signal condition-ing and filtering. The signal then splits, with one path receiving amplification.Both low and high-level chopped signals are applied to a dual ADC. A serialoutput from the ADC takes the sampled signals to the digital signal processorthat is controlled by the main microprocessor. A differential drive signal, syn-chronized to the ADC sampling clock, is output to the sensor for its choppingfunction.

Figure 4-11. Simplified schematic of E4418B shows the transition to digital signal processing (DSP)architecture.

The dual-sigma-delta ADC provides a 20-bit data stream to the digital signalprocessor, which is under control of the main microprocessor. There is norange switching as in traditional power meters which maintain an analog signalpath. Even the synchronous detection is performed by the ADC and DSP ratherthan use of a traditional synchronous detector.

Computation power permits the user to manipulate the basic measurementdata to get desired units or format. Power reads out in watts or dBm, andinputs may be keyed in to compensate for attenuators or directional couplerlosses to the unknown signal in front of the power sensor. Cabling losses can becompensated by entering the loss as a digital offset value.

KeyboardSerial bus

Logic

µP clock

µProcessorOdBm Refcalibrator

GPIB

ADC

Display

Equalizer

BPF

Chopperdriver

X100Dual sigmadelta ADC

DSP

AC input

Feedback

Temp comp

Serial data

Chop

Chop

For the E4419B two-channel power meter, either input power or both may bedisplayed, or for certain applications power ratios A/B or B/A might be useful.For example, if the two power sensors are sampling forward and reverse powerin a transmission line using a dual directional coupler, these ratios would yieldpower reflection coefficient. The power difference, A–B or B–A, can be used forother applications. For example, using a dual directional coupler to sample for-ward and reverse power in a line, the power difference is a measure of net for-ward power being absorbed by a device under test. This is quite important intesting devices with very high reflections, such as mixer diodes, which areoften deliberately mis-matched for better noise figure.

Power changes are displayed with the relative power function. And althoughthe main display is all digital, a simple “peaking” display simulates an analogmeter pointer and allows a user to adjust a unit under test for maximizingpower output.

In system applications, the new single-channel power meter, when used withthe wide-dynamic-range sensors can achieve 200 measurements per second.The programming code is also designed to be backward compatible with theprevious 437B (for programming applications, the E4419B is code compatiblewith the 438A). Of course, the new meter offers far more versatile program-ming functions too, to handle modern complex test procedures. However, oldsoftware can be re-used to make programming projects more efficient.

When old sensors are utilized with the new meter, the calibration factor vs.frequency table printed on the label of the sensor must be keyed into the newpower meters to take the fullest advantage of the measurement accuracy. Atable of frequencies vs. cal factor is displayed and the routine prompted by thesoftkey display to ease editing.

Potential users of the new power meters will find that specification listings forthis DSP-architecture meter without range switching will not follow traditionalpower meter range specifications, yet the meter meets the same range performance as the 43X-Series meters.

Traceable power referenceAll thermocouple and diode power sensors require a power reference toabsolute power, traceable to the manufacturer or national standards. Powermeters accomplish this power traceability by use of a highly stable, internal 50 MHz power reference oscillator. When used together, the 50 MHz referenceand the sensor calibration factor data supplied with each sensor yields the low-est measurement uncertainty. All Agilent sensors are supplied with calibrationfactor versus frequency data. This includes both the value and uncertainty ofeach point.

The 1 mW reference power output is near the center of the dynamic rangeof thermocouple power sensors, but above the range of the sensitive diode sensor series. Therefore, a special 30 dB calibration attenuator, designed forexcellent precision at 50 MHz, is supplied with each diode power sensor. Whenthat attenuator is attached to the power reference output on the power meter,the emerging power is 1 µW (–30 dBm). The attenuator design is such that amaximum error of 1% is added to the calibration step. See Chapter III, for specification detail on the reference oscillator.

28

Signal waveform effects on the measurement uncertainty of diode sensorsAlong with the great increase in measurement flexibility of the E4412/3A andE9300-Series power sensors, comes several new applications guidelines. Thesemust be understood and followed to obtain valid measurement results whendealing with complex and non-CW signals. The Agilent EPM-P peak and averagepower meter and associated sensors are described next in Chapter V.

These guidelines distinguish between earlier diode sensors of the 8481D vintage and the E-Series CW-only diode sensors or the E9300-Series dual-pathsensors.

The power range from approximately –20 to +20 dBm is above the square-lawregion, and one in which the Agilent EPM (or EPM-P, Chapter V) Series powermeters use digital-diode-curve correction to provide accurate power measure-ment for pure CW signals all the way from –70 to +20 dBm. The EPM metersand companion E-Series sensors provide fully specified performance over thatentire dynamic range of –70 to +20 dBm.

Since the unique design of the two-path E9300-Series sensors always keeps thediodes in their square-law range, they can accept non-CW signals across theirspecified power range, if the peak value remains below the maximum specifiedpower.

The following explanation reviews the effects of complex signals on existing8481D-type diode sensors for non-CW or complex modulation signals.

Some examples of complex (non-CW) signals are as follows: 1) Pulsed RF suchas radar or navigation formats, 2) Two-tone or multiple-tone signals such asthose that might be present in a telecommunications channel with multiplesub-channels, 3) AM signals that have modulation frequencies higher than thebandwidth of the power meter detection filtering (in the kHz range for theE4418B), 4) Digital-phase-shift-keyed (PSK) modulations, 5) quadrature ampli-tude modulation (QAM) modulated signals, and 6) Pulse-burst formats.

Here is a summary of the measurement guidelines for diode sensors:

1) Using the 8481D type diode power sensors, any complex signal will yieldhighly-accurate measurement results as long as the peak power levels of theunknown signal are maintained below –20 dBm. In addition, the lowest-fre-quency-component of any modulation frequency must be above approximately500 Hz. Since the power range of the 8481D-type diode sensors are automati-cally restricted by Agilent power meters to a top level of –20 dBm, the userneed only assure that no peak power levels go above –20 dBm.

When peak power levels exceed approximately –20 dBm, accurate measure-ments can be accomplished by the simple expedient of attenuating theunknown signal through an external precise fixed or step attenuator, such thatthe complex signal peak power does not exceed –20 dBm. If pulse modulationfrequencies are near the power meter chopping rate of 220 Hz or multiplesthereof, some meter “beats” may be observed.

2) Using the E4412/3A power sensors, pure-CW signals will yield accurateresults across their entire –70 to +20 dBm dynamic range. One reason E-Seriessensors may not be used for pulse power within their square-law range is thattheir output circuit filters are optimized for fast response to aid high data-rateautomation.

3) Using the E9300-Series sensors, pulsed and complex-modulated signals willyield accurate results if peak powers remain below the maximum specifiedinput power.

4) For non-CW signals with average powers between –20 and +20 dBm, use thethermocouple sensors for true average power sensing.

5) Peak and average sensor/meter technology, which is specifically designed forpeak and complex modulations, is introduced in the next chapter.

29

Thermal sensors such as the thermocouple are pure square law because theyconvert the unknown RF power to heat and detect that heat transfer.Conversely, it is less easy to understand how diode sensors can perform thesquare-law function without the heat transfer step in the middle. Diode detec-tors do deliver pure square-law performance in their lower power ranges below–20 dBm due to their mathematical detection transfer function as described bythe power series Equation 4-2.

A two-tone example might clarify the measurement example. Consider two CWsignals, f1 and f2 , of power level 0 dBm (1 mW) each, and separated by 1 MHz.In a 50 Ω system, each carrier would have voltage magnitudes of v1 = v2 =0.223 V (rms). If the two-tone signal were measured by an 8481A thermocouplesensor, each carrier would convert the 1 mW into heat for a total of 2 mW.

Using a voltage vector analysis, these two-tone signals would be represented bya voltage minimum of zero and a voltage maximum of 0.446 V occurring at afrequency of 1 MHz. The problem then becomes evident when one realizes thattwo times voltage represents four times power. A shaped diode detector theninterprets the 2 V maximum as four times power, and averages it out to thewrong power reading.

Another example shows how subtle signal imperfections can cause errors.Consider a CW signal with a harmonic signal –20 dBc (20 dB below the carrieramplitude or with a voltage equal to 10% of the carrier). Figure 4-12 shows amathematical model of the increasing maximum error caused by a –20 dBc har-monic signal, as the carrier power level ranges from –30 to +20 dBm. Whileactual deviation from true power is a function of the phase difference betweenthe carrier and its harmonic, the error limits are shown to be as high as 0.9 dB.If the harmonic was measured in the true square-law region, a –20 dBc har-monic represents only 1/100th of the power of the carrier or 1% added power tothe carrier.

It might also be observed that the design architecture of the PDB sensors utilizes a balanced, push-pull-diode configuration. This structure inherentlyrejects even-number harmonics of the RF input signal, therefore will provide 15 to 20 dB rejection of even-number harmonics above the square-law region.

Figure 4-12. Estimated error limits for diode detectors operated above square-law range, for CW signal with –20 dBc harmonic.

30

31

ConclusionUsed with the EPM Series of power meters, the E9300 wide-dynamic-rangeaverage power sensors provide accurate power measurements for digitally mod-ulated signals, multitone, and CW signals over a wider range of power levels(80 dB) than is currently achieved with traditional thermocouple or diodebased power sensors. This is because their two path architecture keeps thedetection diodes below their square-law limits.

The EPM Series of power meters, and E4412A and E4413A sensors, feature detector-shaping compensation to deliver dynamic range above square law(90 dB maximum), and should only be used for CW signals.

Average power measurements on pulsed and complex modulation signals canbe measured using Agilent thermocouple sensors and EPM Series powermeters. The 8480D-type diode sensors can be used below –20 dBm.

Peak and average sensor and meter technology described next in Chapter Vprovide accurate measurement of pulsed and complex modulation signals.

[1] S.M. Sze, Physics of Semiconductor Devices, Second Edition, Wiley, (1981).[2] P.A. Szente, S. Adam, and R.B. Riley, “Low-Barrier Schottky-Diode Detectors,”

Microwave Journal, Vol. 19 No. 2 (Feb., 1976).[3] R.J. Malik, T.R. Aucoin and R.L. Ross, “Planar-Doped Barriers in GaAs Molecular Beam Epitaxy,”

Electronics Letters, Vol 1G #22, (Oct., 1980).[4] A. A. Fraser, “A Planar-Doped-Barrier Detector for General Purpose Applications,”

Microwave Journal, (May, 1987).[5] US Patent #4943764, assigned to Hewlett-Packard Company[6] Zurakowski, M, et al, “Diode Integrated Circuits for MM Applications,” Hewlett-Packard Journal, Nov. 1986.

32

Measuring and characterizing parameters of signals with pulsed and/or complex-modulation is simple in theory but difficult in practice. The simple part is thatyou detect the modulation envelope in a diode sensor and feed that widebandvideo to the power instrument for amplification. In the power meter instrumentyou again detect the modulation envelope with a 100-megasample/second (Msa/s)continuous sampling detector, making it a double-detection system.

The hard part actually gets taken care of by Agilent, by providing innovativehardware for the signal processing in the Agilent EPM-P or P-Series powermeters. The firmware and software accompanying those meters feature a wholeseries of complex corrections for various anomalies. For example, the firstdetection diode(s) have to handle signal levels from the square-law detectionregion, through the quasi-square law range into the linear ranges. These arecompensated by a three-dimensional data matrix (for EPM-P) and four-dimen-sional data matrix (for P-Series) for frequency response and the transitionaldetection law versus power level. The data are measured and stored in eachindividual sensor EPROM. The data matrix also provides for temperature cor-rections since that parameter is pivotal in its sensor action.

Diode sensor technology is the ideal solution for characterizing high performancepulsed-modulation envelopes or complex digital formats. Since diode elementsrespond to fast video modulation, they easily provide detected video signals foramplification and measurement of the demodulated envelope parameters.

Agilent’s peak and average power sensors and meters are specifically designedfor video bandwidths as wide as 30 MHz. Besides pulsed and digital formats,this recommends them for additional applications such as two-tone tests (iftone separation is less than the sensor bandwidth) or full-channel signal for-mats that can exhibit statistical spikes in signals which average-sensing diodedetectors may not integrate correctly. This chapter will describe the theory andpractice of power measurements on these types of signals.

Traditional pulsed modulation formatsMost early pulsed system applications from the late 1930s were simple, rectangular formats for radiolocation (radar and navigation). In the military/aerospace technology race of the 1960s, pulsed formats became much moresophisticated. Radar and EW (countermeasures) transmitters moved from traditional pulsed formats to exploit complex and pseudo-random pulse-rateconfigurations for immunity to jamming and to reveal more precise data onunknown target returns. Simple computations with an average power measure-ment and duty cycle didn’t work anymore.

Navigation systems such as air-traffic control (ATC) or distance measuringequipment (DME) have non-traditional pulse configurations too, such as pulsepairs, triplets or Gaussian-shaped envelopes to conserve frequency spectrum andavoid spectrum overlap in multiple aircraft environments. (A Gaussian-shapedenvelope exhibits the interesting property that its spectrum has no side lobes,compared to the much-wider sin x

x side-lobe spectrum of a rectangular pulse.)

The now-discontinued Agilent 8990A peak power analyzer served for a time inthe 1990s as the leading instrument for characterizing these and many othercomplex modulation formats. However, as the new wireless communicationtechnologies of the mid-1990s accelerated rapidly, users needed power meas-urement equipment for wideband data transmission formats. This led to thepresent power measuring instruments and sensors which handle averagepower, as well as time-gated and peak power or peak-to-average ratios, with allthose measurements delivered at very high measurement-data rates.

The new 30 MHz video bandwidth P-Series peak and average power meters andsensors are well suited for modern radar or EW pulse formats, which featurerise time and fall time in the nanosecond range. The peak power meters andsensors allow accurate and repeatable wide bandwidth power, time, and statis-tical measurements up to 40 GHz (frequency range). They have warranted risetime and fall time specifications of 13 ns, a minimum pulse width of 50 ns, andare able to measure maximum pulse repetitive rates of up to 10 MHz.

V. Peak and Average Diode Sensors and Instrumentation

33

Complex modulation of wireless formatsDigital vector modulation became the modulation of choice as the digital revo-lution swept over RF and microwave communication systems some 20 yearsago. The need to pack the maximum amount of digital data into the limitedspectrum made it an obvious choice. For example, some early migrations ofmicrowave terrestrial links from traditional analog frequency-division-multi-plex (FDM), used 64 QAM (quadrature-amplitude-modulation) formats.

The advent of wireless communications technology in the 1990s accelerated themigration from analog to digital modulation formats. Then came an alphabetsoup of digital modulation formats including, BPSK, QPSK, 8-PSK, 16 QAM, etc.Then came important variations such as π/4DQPSK and π/8-8PSK and others.But the breakthrough to successful cellular technology came with the sophisti-cated carrier switching of transmit signals. This permitted time-shared information to and from thousands of mobile subscribers, who were arrayedaround in geographic regions (cells), communicating sequentially with one basestation after another as the user’s transceiver moved from cell to cell.

Some of those systems used data streams that featured time division multipleaccess (TDMA) technology, such as global system for mobile communication(GSM). Other system developers introduced a highly competitive code-division-multiple access (CDMA) format which includes IS-95 standards.

TDMA is the technology for time-sharing the same base station transmitterchannel. Encoded voice data and new high data rate wireless links are modu-lated onto the transmitted carrier in the phase plane. These modulation for-mats create “constellations” of bit symbol locations such as shown in the π/8shifted-8PSK configuration of Figure 5-1. This particular modulation format isused in the emerging Enhanced Data Rates for GSM Evolution (EDGE) systemswhich will offer high-speed data transfer over mobile wireless channels. Bypacking 3 bits per symbol, it increases data information rates, but therebyincreases amplitude peak swings up to 16+ dB, making amplifier saturationmore likely.

Figure 5-1. This π/8 8PSK digital modulation format is emerging for wideband data transmission onwireless channels, such as the EDGE technology.

In GSM, each TDMA wireless subscriber’s share of time allows a useful databurst of say 524.6 µS, during which it is crucial for the power amplifier toremain below its saturation region. Driving the output stage into non-linearamplification causes the outermost phase states to compress, thereby increasingdemodulation bit errors and lowering system reliability.

Figure 5-2. A time-domain oscilloscope shot of a wireless signal format, in this case, an EDGE signalin a GSM system. It is an ideal candidate for peak, average, and peak-to-average ratio measure-ments for time-gated wireless formats.

To make time-gated power measurements on TDMA type pulses, the measure-ment system must have sufficient rise and fall times. If overshoot is to be char-acterized, the power sensor rise/fall specifications must be fast enough tofollow the rising and falling edges of the signal ON period. It is generally recom-mended that the power sensor should have a rise time of no more than 1/8 ofthe expected signal’s rise time. Agilent’s E9320 peak and average sensors havea 200 ns rise/fall time specification (E9323A and E9327A sensors with 5 MHzvideo bandwidth), which make them ideal for wireless TDMA formats.

34

The TDMA system feeds multiple carriers through a common output amplifier,which results in a transmitted power spectrum with almost white-noise-likecharacteristics. In contrast, CDMA encodes multiple data streams onto a singlewider-band carrier using a pseudo-random code, with a similar transmittedpower spectrum and similar power spikes.

Just like white noise, the average power of the transmitted signal is only one ofthe important parameters. Because of the statistical way that multiple carriersignal voltages can add randomly, instantaneous peak voltages can approachratios of 10 to 30 times the carrier’s rms voltage, depending on formats and fil-tering. This ratio, calculated with voltage parameters, is commonly called crestfactor, and is functionally similar to the peak-to-average power ratio which ismeasured by Agilent peak and average power meters, described below.1

High peak-to-average power ratios imply dangers in saturation of the outputpower amplifiers. When saturation occurs, the outer bit-symbol locations com-press, increasing bit errors and system unreliability. System designers handlethis effect by “backing-off” the power amplifiers from their maximum peak rat-ings to assure that signal peak power operation is always within their linearrange.

Wireless handsets also contain frequency-agile local oscillators that “hand-off”the mobile signal as it moves from ground cell to cell and links up to each newbase-station frequency. Sometimes the transmitter power perturbations thatoccur during the frequency-switching transition also need to be characterized.

The new peak and average power meters and sensors (N1911A/12A andN1921A/22A) have a 13 ns warranted rise time/fall time specification, with avideo bandwidth of 30 MHz, that allows accurate measurement of fast risingpulse, overshoot, and other power spikes or parasitic oscillations. They are alsoideal for wide bandwidth wireless format testing, such as WLAN, WIMAX, andMCPA.

Other modern signal formatsOther application test signals cause problems for averaging diode sensors(above their square-law range) because of their complex spectrum content. Forexample, two-tone (or three-tone) test signals are often used for characterizingamplifiers for linearity of their amplification. If the amplification is non-linear,two pure input signals of f1and f2 result in intermodulation signals at the out-put, of the form 2f1 – f2, 2f2 – f1, and many more. The test is a very sensitiveindicator of amplifier linearity.

Measuring power of such tones needs user analysis because the phase of thetwo carriers adds or cancels at the rate of the offset frequency. In a two-toneexample, of V1 and V2, each with equal power, P, the constructive addition oftones results in a peak carrier of 2V, which is a peak power of 4P. An average-responding sensor would indicate 2P, but a peak-responding sensor would indicate 4P. It is the 2V effect that can saturate power amplifiers. When measuring peak power of such tone formats, the tone separation must be lessthan the sensor video bandwidth.

Other test signals, which contain high harmonic content, can also modify thecarrier vector randomly and thus yield random power results. See the wave-form analysis in Chapter IV.

Still other formats are generated by frequency-agile synthesizers, which cansimulate entire, full-channel communications traffic formats. Since their com-ponent signals also add statistically, their power envelope is random. If the frequency spectrum of those power spikes fall within the sensor video band-width, they can be measured.

35

1. Accepted definition of crest factor (pulsed carrier): The ratio of the pulse peak (voltage) amplitude to the root-mean-square (voltage) amplitude.

Peak and average power sensing (Agilent E9320 family)The Agilent E9320 family of peak and average sensors demonstrates the cur-rent art of power sensing. See Fundamentals Part 4 for product capabilitytables. They presently cover the 50 MHz to 6/18 GHz frequency ranges and –65to +20 dBm power range. Ideal for comprehensive measurements on pulsedenvelopes and signals with complex modulation, they also deliver data-correctedand reliable average power measurements. When teamed with the new AgilentEPM-P Series power meters (E4416A/17A), the combination can handle testsignal envelopes with up to 5 MHz video bandwidth.

The basic block diagram for Agilent peak and average sensor is shown in Figure 5-3. It features parallel amplification paths, one for CW (average-only)and one for video (normal). Both modes use the same micro-circuit diode-sensor (bulkhead) element at the RF input. Signal processing in the two amplification paths is optimized to their differing needs for selecting the videobandwidths, filtering, chopping and other data requirements. Amplification isdistributed, with an optimum gain in the sensor unit and more in the meter.

Figure 5-3. Simplified block diagram of the E9320 Series peak and average sensor, showing the parallel amplification paths, along with control lines and a temperature-sensing thermistor function,which corrects the diode’s data.

In the average-only mode, amplification and chopping parameters are much thesame as in previous Agilent averaging sensors, with typical dynamic powerrange of –65 to +20 dBm. In the normal (pulsed) mode, a separate-path dc coupled amplifier provides three sensor dependent maximum bandwidths of300 kHz, 1.5 MHz, or 5 MHz, allowing the user to match the test signal’s modu-lation bandwidth to the sophisticated instrument data processing. These con-siderations will be discussed later in this chapter.

Several functions are included in these peak and average sensors that are notavailable in most other diode sensors. First, all E-Series sensors have temperature corrections to improve stability and accuracy, with the correctiondata stored in an on-board EEPROM. The temperature-sensing thermistor element is mounted inside the bulkhead unit on the same microcircuit as theRF diode sensing elements.

36

Variable gaindifferential amplifier*(300 kHz, 1.5 MHz, 5 MHz)

RF IN 50 ohm

Sensor cableto power meter

Normalpath

Serial interface

Average only path

Average only path

Switchedgainpre-amp

Differential amp

ChopperLoad filter*(300 kHz, 1.5 MHz, 5 MHz low pass)

Normal path

To serial interface

Thermistor

Sensor diode bulkhead

* Bandwidth is sensor dependent

3 dB

Secondly, the peak and average sensors communicate with the E4416/7Ameters using the serial bus shown. It is bi-directional to allow calibration datato upload to the meter whenever a new sensor is connected. Sensor cal datacan even flow through the meter out the GPIB port for external computer pur-poses. In the other direction, the serial bus delivers control commands to thesensor, for example, to select which amplification path is to be activated.

Diode sensors used for peak pulse detection necessarily operate up into theirlinear detection regions and have various deviations from ideal. Power linearityis frequency dependent in the E9320 family, and the diodes also have sometemperature dependence. Figure 5-4 shows how the EEPROM, resident in eachsensor, stores the three-dimensional correction data that is derived from a special sensor calibration system at Agilent’s factory and service facilities. Thecalibration process includes a data run in a temperature oven, during whichtime the input power is ramped over the critical power and frequency range ateach calibration temperature.

Consider one axis of the temperature response in Figure 5-4 to be the frequen-cy response, and the other axis to be the response to the power dynamic range.The “warped” surface profile therefore represents a single temperature, somany such surfaces of data exist in the EEPROM.

Figure 5-4. Temperature, power and frequency correction data, stored in each E9320-family peak and average sensor, uploads into the meter each time a new sensor is connected to the meter, dramatically improving measurement accuracy and confidence.

37

Thermistor-t°

Sensor diode bulkhead

Temperature sensing thermistor located beside diode detectors

Calibration factors stored in EEPROM

Ref CF 100.0%

GHz CF%

.0100 98.9

.300 99.1

.500 98.8

1.0 98.7

2.0 98.6

.. ..

.. ..

18.0 98.5

Temperature response

EPM-P Series power metersFigure 5-5 shows an overview block diagram for the E4416A (single channel)power meter. Under microprocessor control, all the various functional compo-nents from panel keyboard to the logic and digital signal processor (DSP) functions are coordinated. For the average-only mode, signal processing is similar to previous meters. In fact, the EPM-P Series meters will accommodateall older Agilent thermocouple and diode sensors (but naturally won’t readpeak power). A 16-bit analog-to-digital converter (ADC) processes the averagepower signal.

Figure 5-5. Simplified block diagram for E4416A shows extensive use of digital signal processing andcontrol. Measurement confidence results from the comprehensive data correction routines.

A highly-sophisticated video amplifier design is implemented for the normalpath to preserve modulation envelope fidelity and accuracy. Innovative filtering and range-switching, as well as differential offset controls and zeroingfunctions are handled. A 12-bit ADC processes the amplified envelope into adata stream for the DSP.

38

I2C data

Temp compensation

CHOP

Serial bus. cal data, sensor control

Logic

12-bitADC

DSP

Acquisitionmemory

µProcessor

µPClock

Serial bus

GPIB0 dBm Ref.calibratorDisplayKeyboard

Normal pathamplifier, filters, range-switching, offsets,attenuators

From sensoraverage-onlyamplifier

From sensornormalamplifier

Signalsto/fromsensor

Average-only pathamplifier, filters, range-switching, equalizers,feedback

16-bitADC

Chopperdriver

ADC

39

The “second detection” process, which is the crucial envelope detection phase,is implemented in the EPM-P meters with a sophisticated 20 Msa/s ADC running with 12-bit precision, as shown in the diagram of Figure 5-5.

There is a tradeoff in sampling strategy between continuous and random sampling processes. The EPM-P power meters feature continuous sampling at20 Msa/s to ensure that all the peaks are captured, even on a single shot signal,therefore giving a true peak power reading. In simple terms, continuous sam-pling is quicker at building up the trace display compared to random samplingbecause you don’t have to build-up the trace over several iterations of the peri-odic signal, thus the single-shot capability.

Continuous sampling also allows for a digital filtering architecture and band-width correction within the power meter. Digital filtering in the EPM-P, thehigh, medium and low bandwidth settings, enhances the dynamic range of themeter/sensor combination. Its bandwidth correction provides optimum accura-cy for peak and statistical power measurements.

Other meters that employ random sampling have somewhat more ability onlarger bandwidth signals. For example, a random sampling rate of 2.5 to 5 Msa/s might yield a 10 MHz bandwidth; contrasted to the Agilent EPM-Ppower meter continuous method of 20 Msa/s delivers a 5 MHz video bandwidth.Random sampling is also claimed to minimize aliasing effects, but Agilent con-cluded that was an infrequent issue.

On balance, Agilent chose continuous sampling because it won’t miss data, cancharacterize single shot power pulses, and provides substantially higher meas-urement data rates for important production test applications. To illustrate themeasurement data transfer rates, which are achievable with the continuoussampling design, Table 5-1 shows the readings/second when using the GPIB.

Table 5-1. Impressive GPIB measurement data rates are available with the EPM-P meter.

Sensor type Measurement speed (readings/second)

Normal x 2 Fast

E-Series E9320 Average Only mode 20 40 400peak and average sensors Normal mode 20 40 1000

E-Series CW and E9300 20 40 400average power sensors

8480 Series sensors 20 40 N.A.

EPM-P Series power meters are compatible with all 8480 and E-Series powersensors. If you need average power only and fast measurement speed, the EPM-P power meters provide a speed advantage compared to the EPM meters(E4418B and E4419B). The E-Series CW (E4412A/13A) and E9300 averagepower sensors have a maximum speed, in FAST mode, of 400 readings per second with the EPM-P meters. That’s a doubling in measurement speed compared to the EPM meters.

To achieve 1,000 readings/second, over the GPIB, the EPM-P power meter mustbe used with an E9320 power sensor. The E9320 power sensor is configured tooperate in Normal mode in free run acquisition and the EPM-P power metershould be configured to operate in FAST mode. When operating in FAST mode,the limiting factors tends to be the speed of the controller being used toretrieve the results from the power meter, and to a certain extent, the volumeof GPIB traffic. Returning the results in binary format (SCPI command FORMatREAL) will reduce the volume of GPIB traffic. The speed of the associated controller is a combination of the hardware platform and the programmingenvironment being used.

Note: When operating in FAST mode, averaging, limits and ratio/differencemath functions are all disabled.

To ensure the maximum speed performance when using the EPM-P powermeter, the following factors should be considered:

Units: The power meter can output results in either linear (W) or log units(dB). The internal units are linear and therefore optimal performance will beachieved when the results output are also in linear units (since the overhead ofperforming a log function is removed).

Command: The FETCh command must be used to return a result, as low-levelcommands will ensure the best speed performance.

Trigger Mode: Free Run, as it continuously takes measurements on this channel.

Trigger Count: To get the fastest measurement speed the trigger count must beset to return multiple measurements for each FETCh command. To attain 1000readings/second a count of 50 is required (max GPIB width).

Output Format: The Real format is required for FAST mode as a means toreduced bus traffic, by returning the output in binary format.

The new P-Series peak and average power meters and sensors provide thefastest measurement speed among all Agilent power meters and sensors. Themeasurement speed via remote interface is greater than 1500 readings/sec. Formore information on the measurement speed of the P-Series instruments,please refer to the next section on P-Series power meters and sensors.

The central function for peak and average power meters is to provide reliable,accurate, and fast characterization of pulsed and complex modulationenvelopes. The EPM-P meters excel in versatility featuring a technique calledtime-gated measurements. For a descriptive example, Figure 5-6 shows fourtypical time-gated power measurements on a GSM signal.

40

Figure 5-6. For this typical GSM pulse, time-gated measurement techniques permit the EPM-P meteruser to configure four different measurement gate periods, each with its own delay time, measuredfrom a “trigger-point” pulse.

In Figure 5-6, Gate 2 provides the burst average power over the “useful” GSMtime period, which is in essence the averaged power during the gate period, atthe top of the pulse. It is therefore very similar to the Fundamentals Part 1definition of pulse-top amplitude, although pulse-top is defined between thehalf-power points. Remember that each gate may be programmed to measurepeak or average or ratio.

In this example, Gate 1 captures the peak power during its complete Gate 1period. In the E4416A, this definition of peak power is equivalent to theFundamentals Part 1 definition of peak power, which is the highest instanta-neous power spike to occur during the open measurement gate period.Functionally, the peak power data allows the user to measure the saturationeffect that power spike overloads create in test amplifier performance.

The E4416/7A meters measure three different selectable parameters duringeach gate, peak power, average power and peak-to-average ratio. Thus, anindustry-important peak-to-average ratio may be made during the same gatetime, or conversely, the ratio of peak power in one gate time may be computedagainst the average power in another gate time.

A pulse droop measurement can be obtained by subtracting the two powers,Gate 3 – Gate 4. All three of these measurements can be simultaneously displayed on the four-line numeric liquid-crystal display (LCD) screen, alongwith the peak power from Gate 1.

The trigger point may be selected from three sources, 1) an external pulse, 2) derived internally, digitally, from the measured pulse envelope, or 3) fromthe external GPIB source. The acquisition modes may be single, continuous orfree-run. Other trigger manipulations are also featured, such as holdoff ordelay. Once the trigger point is set, it may be output to other system instrumen-tation via a rear BNC connector.

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Gate 3

Ext triggerStart 4

Start 2Start 3

Start 1

Gate 4

Gate 25% to 95%, "useful" period

Gate 1

Current models of the EPM-P power meters feature pre-defined software/firmware measurement routines for eight popular wireless signal formats,including GSM-900, EDGE, iDEN, NADC, cdmaOne, cdma2000, W-CDMA, andBluetooth™. The following example is that for the GSM pre-defined measure-ment setup.

Figure 5-7. The pre-defined GSM routine takes 10,400 data samples in the time-gated period.

The pre-defined setups are one-button controls, which makes the instrumentsetup more convenient and enables users to actually making measurementsquicker. For example, the pre-defined GSM setup has a gate length of 520 µsec.With a sampling rate of 20 Msa/s, that’s 10,400 samples within the time-gatedperiod. To find out the number of samples taken in any gate length, simplydivide the length (in seconds) by 50-9.

On the screen, 234 pixels are used to generate the trace display, as shown inFigure 5-7. The height per window (two windows maximum for the whole display) in pixels is 85 of which 57 are used for the trace display.

42

Computation power–gated data conceptThe signal processing in the E4416/7A meters has been designed to provideexceptional data computation and display versatility. Figure 5-8 shows the datapaths for the four independent gate periods, each with its own delay time. Eachgate can be set to measure average, peak, and peak-to-average power data.

Each gate can then manipulate those three parameters into two computedparameters (F-feeds) such as F1 minus F2 or F1/F2, to be displayed in one ofthe four window partitions. The block shown as the “measurement highway”takes care of moving data to the user-configured display line on the LCD. Thehighway also permits computation of shared data between the four gates.

This computational power is particularly valuable in TDMA wireless test scenarios such as GSM, GPRS, EDGE, and NADC, where various simultaneouscombinations of computed parameters are required.

Figure 5-8. User-configured data manipulations are a major feature of the EPM-P series powermeters.

The large LCD display partitions up to four-line formats to help interpret andcompare measurement results, using the measurement highway. The user canalso select large character readouts to permit viewing from a distance. Forexample, Figure 5-9(b) shows how the four lines could be configured to displayaverage power in dBm and W, peak power and peak-to-average ratio. The user can also choose to show the analog power envelopes for two selectedtraces in the partitioned display. Figure 5-9(a) shows the user set-up displayfor four gate periods and delays.

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Gates 1 to 4 Measurement feeds(single or combined)

Display

12 m

easu

rem

ent h

ighw

ay

Gate 1 Upper windowUpper measurement

Upper windowLower measurement

Lower windowUpper measurement

Lower windowLower measurement

Gate 2

Gate 3

Gate 4

Feed 1

Feed 2

Single

Feed 1 – Feed 2

Feed 1 / Feed 2

Combined

Feed 1

Feed 2

Single

Feed 1 – Feed 2

Feed 1 / Feed 2

Combined

Feed 1

Feed 2

Single

Feed 1 – Feed 2

Feed 1 / Feed 2

Combined

Feed 1

Feed 2

Single

Feed 1 – Feed 2

Feed 1 / Feed 2

Combined

PeakAveragePk-to-avg

PeakAveragePk-to-avg

PeakAveragePk-to-avg

PeakAveragePk-to-avg

44

It should be noted that all the above configurations for feeding actual data pluscomputed data, such as power ratios, through the measurement highway is fora single sensor. When using the E4417A dual-power meter, the second sensorprovides a doubling of retrieved power data, all of which may be user-selectedto create combined ratios or power differences between sensor A and sensor Bchannels.

(a) (b)

Figure 5-9. The back-lighted LCD display delivers powerful readout versatility: (a) shows how theuser sets the delay and measurement times for each of four gates, (b) shows a simultaneous displayof four Gate A parameters; average power in dBm and µW, peak power, and peak to average ratio.The user could also choose a digitally-derived pulse envelope representation as well.

This may be a good juncture to consider power data averaging. The EPM-P doesnot have averaging for making peak power measurements. Peak power is by def-inition a single occurance defined as the maximum instantaneous power of thesignal-under-test, therefore averaging is not appropriate.

In terms of average power measurements, there are different ways to do theaveraging. In Normal operation the instrument shows a computed moving aver-age. For example, for an average of eight, when a new value is measured it isaveraged with the previous seven readings. If you want a “block” average,where you take eight measurements and average them, then take another eightmeasurements and average them, you can use the TRIG:DEL:AUTO ON com-mand. In that command the meter inserts a settling time before taking themeasurement. The average is adjustable and can be set by the user or it can beauto averaged, which depends on the sensor and the power level, being meas-ured. Auto averaging will increase the averaging as you get lower down inpower, to minimize display jumping.

When measuring a pulsed signal, video averaging can be used. For example,averaging on a GSM signal, the number of averages is actually the number ofpulses of the given setup - if you are making a measurement in timeslot 1 witheight averages it will average the next eight measurements of timeslot 1.

Video bandwidth considerationsPity the Agilent amplifier designer of the EPM-P peak power amplifier chain.Inside the diode sensor, values of R and C in the Figure 4-3 equivalent circuithave conflicting demands placed on them. For maximum detection sensitivityand dynamic range, R should be large. And for maximum RF input frequencyrange, C should also be large. However, for maximum detection flatness andstability of the video bandwidth, R and C should both be small. In addition,there are optimum values of R and C for linearity, temperature stability andmismatch. Other tradeoffs arise when considering low-input frequency (downto RF) range limits versus wide video bandwidth.

45

So optimizing for one set of sensor criteria would have the effect of severelyimpacting other key sensor specifications for users. Agilent has taken theapproach to introduce a family of E9320 sensors specifically optimized for maximum dynamic range and also to minimize errors for specific wireless standards, as follows:

• E9321A/25A: 300 kHz video bandwidth for GSM and EDGE• E9322A/26A: 1.5 MHz video bandwidth for CDMA (IS-95), and • E9323A/27A: 5 MHz video bandwidth for W-CMDA applications.

One instance where the conflicting demands on load circuit componentsbecomes apparent is when we consider the trade-off between the low frequencyRF range and wide video bandwidth. To remain sensitive at low input frequen-cies (< 100 MHz), high load resistance and capacitance are optimal. However,wide video bandwidth requires low values for these components. This leads toa compromise between variations in video bandwidth and the frequencydependence of sensor linearity.

Table 5-2 displays the complete user parameter tradeoffs for the available peakand average sensors, including video bandwidth and peak power dynamicrange. In cases when users need to measure the power of multiple signal typeswith a single sensor model, they can consider the dynamic range of the band-width settings. With this information, they can determine if they require onlyone sensor or need to obtain multiple sensors for their application.

The filter video bandwidths stated in the table are not the traditional 3 dBbandwidths, since these video bandwidths are optimized and corrected foroptimal flatness. Detailed response curves are shown in the product specifica-tions (see product reference literature on the Agilent Website). Video filtercharacteristics are measured using a technique of applying a two-tone signal,programming the power meter for a peak to average measurement, thenincreasing the separation of the two-tones until a frequency response curve isgenerated. With such a procedure, the curve shape is not a traditional roll-offcharacteristic.

Table 5-2. E9320 sensor bandwidth versus peak power dynamic range (normal mode).

Sensor model Modulation bandwidth / Max. peak power dynamic range6 GHz/18 GHz High Medium Low Off

E9321A/E9325A 300 kHz/–42 to 100 kHz/–43 to 30 kHz/–45 to –40 dBm to +20 dBm +20 dBm +20 dBm +20 dBm

E9322A/E9326A 1.5 MHz/–37 to 300 kHz/–38 to 100 kHz/–39 to –36 dBm to+20 dBm +20 dBm +20 dBm +20 dBm

E9323A/E9327A 5 MHz/–32 to 1.5 MHz/–34 to 300 kHz/–36 to –32 dBm to+20 dBm +20 dBm +20 dBm +20 dBm

If the video bandwidth is not sufficiently flat, errors will be introduced in peakpower measurements. The wider the video bandwidth, the greater the variationin linearity. In traditional wide-dynamic range sensors with minimal videobandwidth, only a 50-MHz linearity calibration is required. Figure 5-10 showshow only one frequency linearity correction at 50 MHz (50 MHz is the flat lineat 0 dB) will lead to linearity errors for sensors with a wide video bandwidth.

Figure 5-10. The frequency-dependent linearity of a wide video-bandwidth sensor is shown for vari-ous input frequencies from 50 to 900 MHz.

To achieve a wide, flat video bandwidth without compromising linearity, a frequency-dependent linearity correction (FDLC) has been implemented in theE9320 sensors. These sensors are factory calibrated at 50 MHz and at key fre-quency points up to 900 MHz in order to provide the correction data for theFDLC. This addresses the trade-off in linearity and video bandwidth, but it stillleaves the bandwidth susceptible to power and temperature variations in thedetection diode's resistance. The dc-coupled amplifier in the sensor’s Normalmode path has a different gain for each video bandwidth, the highest gain isemployed in the 300 kHz sensors.

The result of all this care is that conflicting tradeoffs have been corrected in allpossible cases by use of the internal stored data matrix.

All the above shows that when instrumenting for peak power measurements, itis crucial to analyze the effect of the instrumentation video bandwidths on theaccuracy of the resulting data. Agilent E4416/17A meters have been optimizedto avoid degrading key specifications like linearity, mismatch, dynamic rangeand temperature stability. For further information on this matter, see the fol-lowing article; “Power Measurements for the Communications Market.”[1]

Versatile user interfaceThe E4416A/17A meters feature a user-friendly interface and powerful displaycontrols. Hardkeys control the most-frequently used functions such as sensorcalibration and triggering, while softkey menus simplify configuring the meterfor detailed measurement sequences. A save/recall menu stores up to teninstrument configurations for easy switching of test processes.

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Input power (dBm)

Dev

iati

on fr

om 5

0 M

Hz

linea

rity

( %

)

–20 –10 0 10 20

50 MHz150 MHz300 MHz600 MHz900 MHz

4.5

4

3.5

3

2.5

2

1.5

1

0.5

0

–0.5

Measurement considerations for traditional peak pulsesModern radars and navigation systems have moved to narrower pulses, whichpermitted better separation of multiple targets or improved target resolution.Then came even newer technologies for pulsing with longer—but phase coded—formats that allowed for determining things like shape or size of targets.Multiple pulses and random pulse repetition rates are design strategies forresistance to countermeasures jamming.

All of these different directions of pulse power technologies means that specify-ing a measurement power meter requires a clear knowledge of the key parame-ters that need to be characterized. For some test sequences, measurement ofthe numerous pulse power and time parameters performed by full peak poweranalyzers may be needed. On others, only pulse-top and average power meas-urements are required, for which Agilent average or peak and average sensorswill suffice.

Design and production test for pulsed systems often require measurements ofboth peak pulse power (pulse top) as well as average power for the transmitterand other internal system components. Thermal sensors inherently respond tototal average power, as long as the peak power excursions do not exceed thepeak ratings of the sensor. By knowing the precise measurement specification,a test engineer might use a simpler and less expensive power meter to deter-mine that a subsystem is operating to its proper performance envelope.

The Agilent E9320 sensor family (using the EPM-P meter) can provide highlyaccurate and useful data for parameters such as pulse top or average power onpulses as narrow as 300 ns. While not specifically intended for narrow pulsecharacterization, its 5 MHz bandwidth amplifiers can deliver the measurementsof Table 5-3. [2] Please refer to the next section on P-Series power meters fornarrow and fast-rising pulse measurement.

Table 5-3. E9323A/27A power sensors can measure pulse parameters.

Key pulse parameter EPM-P/E9320specifications

Rise time 200 ns

Fall time 200 ns

Minimum pulse width 300 ns

Pulse repetition rate 2 MHz

Pulse repetition interval 500 ns

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48

Analysis software package for complex modulation manipulationsAn important development for product development and verification engineersis a powerful VEE analyzer software package that places the EPM-P metertotally in control of the PC or laptop. This EPM-P VEE software package isavailable free of charge.[3] It operates via the GPIB, and provides the statisti-cal, power, frequency, and time measurements that are required for CDMA andTDMA signal formats. The CD-ROM package includes a VEE installation program.

The statistical package includes the ability to capture

• cumulative distribution function (CDF)• complementary CDF (CCDF or 1-CDF)• probability density function (PDF)

These are crucial diagnostic parameters for system signals like CDMA formats.Figure 5-11 shows a typical distribution function display. Analyzing such powerdistribution computations can reveal how a power amplifier may be distortinga broadband signal that it is transmitting. Or a baseband DSP signal designercan completely specify the power distribution characteristics to the associatedRF subsystem designers. For example, for Figure 5-11, the data shows that for0.3% of the time, the signal power is at or above 8 dB peak-to-average ratio.

Figure 5-11. On this CCDF analysis screen, the Y-axis shows the percentage of time the wireless signal power is at or above the power specified by the X-axis.

For traditional pulse work, the analysis package also includes a powerful pulsecharacterization routine. It computes and displays the following power parame-ters: pulse top, pulse base, distal, mesial, proximal, peak, average, peak/averageratio, burst average, and duty cycle. It does the same for these time and frequency parameters: rise time, fall time, pulse repetition frequency (PRF),pulse repetition interval (PRI), pulse width and off time. All of these pulsedpower parameters were originally defined with the 1990 introduction of theAgilent 8990A peak power analyzer, and are described in Chapter II ofFundamentals Part 1.

P-Series power metersThe P-Series power meters have a 30 MHz video bandwidth and 100 M samplesper second continuous sampling rate for fast, accurate and repeatable widebandwidth power, time and statistical measurements. When these meters areused with the P-Series wideband power sensors, they provide up to 40 GHz fre-quency coverage, wide dynamic range and extensive measurement capabilitythat has been optimized for aerospace and defense, wireless communication,and wireless networking (IEEE 802.11a/b/g) applications.

With 100 M samples per second sampling rate, the P-Series power meters cancapture single-shot as well as repetitive events over a wide bandwidth. Forapplications such as radar and pulse component testing that require accuratepulse measurements, the power meter and sensor combination has ≤ 13 ns war-ranted rise and fall time specifications.

With up to 30 MHz of video bandwidth, the P-Series also enables a single-instru-ment solution for testing wide bandwidth products such as the multi-carrier poweramplifiers used in the 3G base stations. The 30 MHz bandwidth is also being cor-rected to 0.1 dB flatness for high accuracy peak power measurements.

P-Series power meters and sensors offer comprehensive measurements that sat-isfy the requirements of many power measurement applications in R&D andmanufacturing:

• Peak power, average power, and peak-to-average ratio power measurements• Time gated and free-run measurement modes• Automatic rise time, fall time, pulse width, pulse period, pulse repetitive

frequency, time to positive and time to negative occurrence measurements• Complementary cumulative distribution function (CCDF) statistical measurements

Internal zero and calibrationThe P-Series power sensors (N1921A and N1922A) are the first to provide“internal zero and calibration” which eliminates the need for sensor calibrationusing an external reference source. The P-Series sensors utilize Agilent’spatented technologies (see Figure 5-12) that integrate DC reference source andswitching circuits into each of the sensors. So, a user can zero and calibrate thesensor while it is still connected to a device under test. This feature removesthe need for connection and disconnection from the calibration source, therebyreducing test times, measurement uncertainty, and wear and tear on connec-tors. It is especially useful in manufacturing and automated test environmentswhere every second and every connection counts. Sensors can be embeddedwithin the test fixtures without the need to switch reference signals.

Figure 5-12. Internal zero and cal block diagram

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50

Bandwidth considerationsThe video bandwidths in the meter can be set to High, Medium, Low, or Off.The video bandwidth stated in Table 5-4 is not the 3 dB bandwidth, as thevideo bandwidth has been corrected for optimal flatness (except for the Offposition). The Off video bandwidth setting provides the fastest rise time, falltime specifications, and is the recommended setting for minimizing overshooton pulse signals. The High, Medium, and Low settings are aimed at measuringwide bandwidth, modulated signals and are designed to provide a flat responseacross the bandwidth. There are also trade-offs between bandwidth anddynamic range.

Table 5-4. Dynamic response – rise time, fall time, and overshoot, versus video bandwidth settings

Video bandwidth settingLow Medium High Off

Parameter 5 MHz 15 MHz 30 MHz < 500 MHz > 500 MHzRise time/fall time10 < 56 ns < 25 ns ≤ 13 ns < 36 ns ≤ 13 ns

Overshoot11 < 5% < 5%

For Option 107 (10 m cable), add 5 ns to the rise time and fall time specifications.

Refer to Figure 5-13 for the information on the flatness response. The peak flat-ness is the flatness of a peak-to-average ratio measurement for various tone-separations for an equal magnitude two-tone RF input. Figure 5-13 shows therelative error in peak-to-average ratio measurements as the tone separation isvaried.

Figure 5-13. N192XA error in peak-to-average measurements for a two-tone input (High, Medium,Low, or Off video bandwidth)

Versatile user interfaceThe P-Series power meters have improved user interface and display control.The meter has a new high-resolution color display with a display size of 320 x170 pixels in the largest mode.

A numerical keypad has also been added with new arrow styles and a centralSELECT key. These features simplify the configuration of the meter for detailedmeasurement procedures. Up to 10 instrument configurations can be stored foreasy switching of test processes.

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Figure 5-14a – b. Large display with automatic power and time measurements

The time-gated measurements are similar to the EPM-P, in that up to 4 inde-pendent gates can be setup with unique periods and delays, using three differ-ent parameters such as average, peak, or peak-to-average ratio power. Eachgate can then be manipulated to display two computed parameters, such as F1 – F2 or F1/F2. This computational power is important in wireless communi-cations, where various combinations of computed parameters are required.

Figure 5-15. Measurement flexibility with 4 independent time gates

ApplicationsThe P-Series power meters and sensors are optimized for radar testing byenabling accurate and repeatable measurements of output power and timingparameters of radar pulses. With warranted performance up to 40 GHz, 30 MHzvideo bandwidth and ≤ 13 ns rise and fall time, the P-Series covers most oftoday’s high frequency radar test applications.

With 30 MHz video bandwidth and optimized peak flatness, the P-Series is theideal tool for use in design or manufacturing of a multi-carrier power amplifier(MCPA). With 30 MHz of video bandwidth, the P-Series can measure peak andaverage power for up to six 3G carriers (5 MHz) over a wide dynamic range of–35 to +20 dBm. The complementary cumulative distribution function (CCDF)measurement capability enables designers to verify the power amplifier is notclipping.

(a) (b)

P-Series is also optimized for wireless LAN (IEEE 802.11a/b/g) component andsubsystem design and manufacturing. The P-Series can be used to verify thepower profile and output power of WLAN components. The 30 MHz video band-width is sufficient to measure all WLAN signals accurately and repeatedly. Incomponent manufacturing, time is money. The fast measurement speed of 1500reading/s enables high volume production of wireless network devices to maxi-mize throughput. Time can also be saved with internal zeroing and calibrationand with fast measurement speed achieved through a choice of I/O interfaces(LAN, USB or GPIB) for data transfer.

Flexible configurationsThe P-Series products come with flexible configurations:

P-Series power metersN1911A Single channel power meter 9 kHz to 110 GHz (sensor dependent)

N1912A Dual channel power meter 9kHz to 110GHz (sensor dependent)

P-Series power sensorsN1921A Wideband peak and average power sensor 50MHz to 18GHz

N1922A Wideband peak and average power sensor 50MHz to 40GHz

The P-Series power meters also work with the Agilent 8480, E4410, and E9300Series average power sensors. This gives a selection of more than 30 sensors forpeak and average power measurements over a wide dynamic range from –70 to+44 dBm, with frequency coverage of 9 kHz to 110 GHz.

Pre-defined measurement setupsThe P-Series power meters are loaded with time saving features. Predefinedtest setups for common measurements (see Figure 5-16) used in radar andwireless communication applications allow users to setup the meter easily tostart testing. The power meters also have LAN, USB, and GPIB connectivity asstandard features to accommodate the majority of modern interfaces.

Figure 5-16. Pre-defined test setups

Measurement speedThe P-Series power meters, when used with the P-Series sensors, provide thefastest measurement speed among all Agilent power meters. The measurementspeed via remote interface is greater than 1500 readings per second. To ensuremaximum speed performance, refer to the factors highlighted in the previoussection on EPM-P Series power meters.

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Table 5-2. GPIB measurement speeds with P-Series power meters and sensors

Measurement speed (readings/second)Sensor type Normal x2 FastN192xA power sensors 1500 1500 1500

E9320 power sensors* – average only mode 20 40 400

E9320 power sensors* – normal mode 20 40 1000

E441xA and E9300 power sensors 20 40 400

8480 Series power sensors 20 40 N/A* Compatibility with the E9320 will be available in 2007.

Theory of operation There are two measurement paths in the P-Series power meters; the normalpath and the average-only path.

The normal path in the P-Series power meter now uses differential inputs toimprove the dynamic range, thus the P-Series power meters have new dualcoaxial input connectors on the power meter. The differential inputs are con-nected to a signal conditioning block that amplifies, applies offsets to the videobandwidth signal from the peak sensor. The output from this block is split intotwo paths – the high gain and low gain paths. The high gain and low gain pathsare identical, except for an extra 30x gain in the high gain path.

Selection of data between the two samplers on different paths is performed inthe logic block. The selection is very fast and transparent to the user. Selection(note that this is not switching) is achieved in a 1-clock cycle, that is 10 ns.The criteria for path selection is to normally select the high gain path until theADC is near its maximum limit when the low gain path is selected.

In previous designs, a semiconductor switch was used to switch between twogain paths that eventually ended up at an ADC. The different gain pathsallowed for measurement of a wide dynamic range. However, data obtainedduring and immediately after the switch were corrupted due to the semicon-ductor switch.

In this new technique employed in the P-Series meter, the “switching” is donedigitally. This preserves the data integrity while simultaneously providing awide dynamic range.

The 14-bit output of the ADC is sampled by a 100 MHz sampler and fed into thetrigger and acquisition circuit in the logic block. The output of the trigger andacquisition circuit is effectively a 19-bit signal.

There are 5 dB of overlapping range between the two ADCs and a 6 dB/bit rela-tionship (voltage).

19 x 6 = 114 dB (voltage)

57 dB in power provides a wide dynamic range.

The acquisition memory is 2 MSamples. With a 100 MSa/s ADC, the maximumcapture without decimation is 20 ms. Random decimation is required to allowcapture times of up to 1 second.

53

Figure 5-17. P-Series power meter simplified block diagram

Figure 5-17 shows the overall P-Series power meter simplified block diagram.The logic sub-system provides functionality to capture the detected power sig-nal into memory, allowing it to be processed within the DSP.

The acquisition system works in one of two modes: real-time and free-run. Theyfacilitate different styles of analysis.

Real-time acquisitionIn this mode, data is stored in the acquisition memory controlled by the triggercontroller. The key emphasis of this mode is the relationship between samplesand trigger.

Free-run acquisitionFree-run acquisition continually stores data sampled in a random fashion intothe acquisition memory. This mode permits the statistical analysis of the inputsignal.

P-series power meter trigger

Figure 5-18. P-Series power meter trigger diagram

54

Triggering of the P-Series power meter is possible from three sources:• External trigger: TTL low to high or high to low transitions will trigger the

acquisition. The BNC connector for accepting the external trigger signal is located on the rear panel.

• Internal trigger: This is a selectable RF power level from either sensor input channels.

• External command: A remote control command is used to trigger the acquisition.

There are two internal trigger modes: • “Normal”, where the user sets up the trigger level, and • “Auto level” where the internal trigger level is automatically set up based on

a stable level for the input signal.

A trigger level threshold filter (hysteresis) also exists to reject triggers that donot pass through both the upper and lower thresholds.

The trigger delay range is ±1.0 seconds maximum, while the delay resolution isspecified as 1% of delay setting or 10 ns minimum. All the above settings willensure accurate and repeatable triggering under various scenarios.

CCDF measurementA frequently used measurement in digitally modulated radio systems is theCCDF curve. This consists of a curve indicating the percentage of time a radiosignal spends at a particular power level. It is usually shown as a graph of theratio of the instantaneous power to the average power against percentage oftime that the signal power is at, or above, the power specified by the X axis.Both axes of the graph are logarithmic.

During a CCDF measurement, a user may require the power level at which acertain percentage of the measurements lie in excess. Typically, percentagesare situated in the range of 0.01% to 0.0001%. For example, if a sample of100,000 measurements has taken place and 50% of these samples are posi-tioned at or above the average, then there are 50,000 samples lying at or abovethe average. If the user requires the power ratio at which 0.01% of samples liein excess then there will be 5 samples lying above the 0.01% percentage point(0.01% = 1/10,000).

The CCDF measurement appears in several kinds of instruments, from powermeters to spectrum analyzers and others. All these instruments have to gener-ate histograms of the power values received and then convert them to CCDFgraphs.

This task is carried out by sampling the incoming signal using an analog-to-digitalconverter (ADC), storing the resulting captures in memory, and then calculating ahistogram of the received values by scanning the captured values, converting eachreceived value from voltage to power if necessary, and then summing each valueor small set of values into many accumulators before using the resultant table ofoccurrences to draw a graph and/or work out the percentages. A typical systemcan take around 5 seconds to measure and process 100,000 samples. Samples tendto be captured at high speeds for short periods. Then the signal is processed andanother batch of samples is taken. Current ADC technologies are capable of run-ning at speeds in the range of 10 MSa/s up to several Gigasamples per second.What this means is that a typical system will take very short snapshots of a wave-form probably missing the elusive high peak levels that have the greatest effecton the resulting measurement numbers. Plus, 100,000 samples provide onlyaround 5 samples “above the line” for a 0.01% measurement. 0.001% or 0.0001%would require orders of magnitude more time to get the same accuracy. It couldbe argued that 5 samples is not exactly a large number on which to base ameasurement.

55

In the P-Series meters, one second worth of samples provides 100 million sam-ples. These samples are sorted and binned by the logic subsystem in real timebased on the sample’s level. An innovative and patented method was used toachieve the real time histogramming of the samples. Consequently, the CCDFmeasurement in the P-Series provides 1000 times more samples, as comparedto older meters. Previously, 5 samples were used for the 0.01% measurement;now there are 5000 samples. This greatly increases the accuracy of the meas-urements at smaller percentages.

At the end of the one second interval, the microprocessor will retrieve the bins,and cummulatively sum them to produce the CCDF data. The CCDF data at thispoint is still raw ADC data. The processor will have to go through another con-version process to translate the ADC data into power measurements.

The P-Series meter offers CCDF measurements in tabular or graphical formatson the front panel display. Alternatively, 501 points of the CCDF trace can bedownloaded via SCPI commands. The SCPI commands also allow the user toevaluate the peak-to-average ratio of the capture for a known probability orvice-versa.

Figure 5-19. CCDF measurement table shown on front panel display

Special peak sensor calibration for temperature and rangeAs mentioned in several previous chapters, Agilent E9320-Series peak andaverage sensors require a three-dimensional matrix of correction data to deliv-er their highest possible measurement accuracy. The production test systemsrun the input power throughout the frequency range and the power range ofthe specified limits of the sensor. Since the sensor detection characteristics aresensitive to operating temperature, the sensor is also subjected to a tempera-ture run which stores those correction data as well.

When factory tested, the internal ROM stores the correction data, which is useful for a long period of time, since the internal components do not exhibitmuch aging. For user metrology labs which are required to re-verify sensorsperiodically, it is recommended that they treat the various families of sensorsdifferently.

Thermistor and thermocouple—heat sensing technology—and older diode sen-sors such as the 8481D family can have their calibration factors verified usingthe standards procedures, usually the power splitter method covered in earlychapters. Changes to the calibration factors can be altered on the sensor’sprinted cal factor label and calibration certificate.

56

E-Series sensors, such as the E4412A/13A and the E930x-Series can have theircal factors verified, and can have their correction data "re-burned," althoughthese tests are usually run only at room temperature, since the temperaturecorrections are assumed not to change with time. These verification runsshould be made with the corrections function turned on. Naturally if a sensorhas been subject to observable abuse, deeper testing might be needed.

E9320 and N192XA peak and average sensors can be verified but should notattempt re-burn of correction data. The correction algorithm of the peak andaverage sensors is logically more complicated, and cal factor runs without tem-perature characterization will compromise the measurement uncertainty.

For external calibration laboratories with significant test loads of power sensors, it is recommended that you contact Agilent's support organization,which can furnish you with considerable detail on test recommendations foreach sensor family type.

Recent research on linearity and pulse-shape characterization ofpeak and average sensorsFor some decades now, the power measurement industry has offered peakpower analyzer instrumentation without direct traceability of the peak powerparameters to NMIs. This was a result of low priorities of NMI research fundingrelated to measurement uncertainty needs in the peak sensing products.Industry improvised with measurement configurations that carefully comparedpeak power sensors under calibration with average sensor/meter combinationswith known standardized and traceable power certifications.

However, with the rapid rise of complex and pulsed formats in the wirelesscommunications industry, the need for highest-level standards for peak powerbecame evident. Accordingly, for the past several years, the NPL in the UK hasundertaken projects to provide characterization of peak and average sensors,plus a provision of measurement services for traceability of peak parameters ofpower sensors.

As of this writing, the National Physical Laboratory (NPL) in the UK has spon-sored a research program into the complexities of characterizing peak powersensors. These are not trivial considerations because bandwidth of the instru-mentation and the linearity of the sensor both contribute to computed errors.In particular, sensor linearity at low power levels was generally poorer thanCW sensors. This can lead to uncertainties in computed data such as peak-to-average power and power statistics that are required for CDMA systems likecdmaOne and W-CDMA. [4]

57

Graphic courtesy of NPL, Teddington, UK (3rd RF Wireless Measurements Forum: 25 July 2000)

Figure 5-12. NPL (UK) peak power measurement system

The NPL calibration system of Figure 5-12 was validated against sampling oscil-loscope measurements, which provided an alternate method to characterize thewaveform characteristics of the pulsed RF signal. This is important because ofthe generally limited bandwidth of the peak power instrumentation associatedwith pulsed or complex-modulation power signals. Of course, the ultimatepower standard was still a CW sensor, which served as the traceable link to theNPL power standard.

For users who require additional information on peak power traceability, visitthe NPL website. [5]

58

Controllingcomputer

RF source

10 dBAttenuator

CW power reference meter

Peak power reference meter

IEEE-488 interface

Instrument under test

Voltage or IEEE-488 outputfrom instrument under test

Reference plane

RF source can generate avariety of signals in

telecommunications formats

DVM

Peak powersensor

Peak poweranalyzer

Filter Coupler

ReferencethermistorRF sensor

Powermeter

Peak powermeter

Peak powersensor

[1] Anderson, Alan, “Power Measurements for the Communications Market,” MW/RF Magazine, October, 2000.

[2] AN1438, “EPM-P Series Power Meters Used in Radar and Pulse Applications,” Agilent Technologies, literature number 5988-8522EN.

[3] CD-ROM: EPM and EPM-P Series Power Meters, part number E4416-90032.This CD-ROM contains the power meters and sensors Learnware (User’s Guides, Programming Guides, Operating Guides and Service Manuals). The CD-ROM also contains technical specifications, data sheets, product overviews, configuration guide, application and product notes, power meter tutorials, analyzer software for the EPM-P power meters, IVI-COM drivers, IntuiLink toolbar for the EPM power meters and VXI Plug & Play drivers for the EPM power meters.

This versatile CD-ROM package is shipped free with every EPM and EPM-P Series power meter. Most of the information is also available at: www.agilent.com/find/powermeters.

[4] Holland, K., and Howes, J., “Improvements to the Microwave Mixer and Power Sensor Linearity Measurement Capability at the National Physical Laboratory,” (In the UK) IEE Proc.-Sci Meas. Technology, Nov. 2002.

[5] Website for National Physics Laboratory, Teddington, UK, pulsed power information (note caps): www.npl.co.uk/measurement_services/ms_EG.html#EG04

59

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AgilentFundamentals of RF and MicrowavePower Measurements (Part 3)

Application Note 1449-3

Power Measurement Uncertainty per International Guides

Fundamentals of RF and Microwave PowerMeasurements (Part 1)Introduction to Power, History, Definitions, InternationalStandards, and TraceabilityAN 1449-1, literature number 5988-9213ENPart 1 introduces the historical basis for power measurements, and providesdefinitions for average, peak, and complex modulations. This applicationnote overviews various sensor technologies needed for the diversity of testsignals. It describes the hierarchy of international power traceability, yield-ing comparison to national standards at worldwide National MeasurementInstitutes (NMIs) like the U.S. National Institute of Standards andTechnology. Finally, the theory and practice of power sensor comparisonprocedures are examined with regard to transferring calibration factors anduncertainties. A glossary is included which serves all four parts.

Fundamentals of RF and Microwave PowerMeasurements (Part 2)Power Sensors and InstrumentationAN 1449-2, literature number 5988-9214ENPart 2 presents all the viable sensor technologies required to exploit theusers’ wide range of unknown modulations and signals under test. Itexplains the sensor technologies, and how they came to be to meet certainmeasurement needs. Sensor choices range from the venerable thermistor tothe innovative thermocouple to more recent improvements in diode sensors.In particular, clever variations of diode combinations are presented, whichachieve ultra-wide dynamic range and square-law detection for complexmodulations. New instrumentation technologies, which are underpinnedwith powerful computational processors, achieve new data performance.

Fundamentals of RF and Microwave PowerMeasurements (Part 3)Power Measurement Uncertainty per International GuidesAN 1449-3, literature number 5988-9215ENPart 3 discusses the all-important theory and practice of expressing meas-urement uncertainty, mismatch considerations, signal flowgraphs, ISO17025, and examples of typical calculations. Considerable detail is shown onthe ISO 17025, Guide for the Expression of Measurement Uncertainties,has become the international standard for determining operating specifica-tions. Agilent has transitioned from ANSI/NCSL Z540-1-1994 to ISO 17025.

Fundamentals of RF and Microwave PowerMeasurements (Part 4)An Overview of Agilent Instrumentation for RF/MicrowavePower MeasurementsAN 1449-4, literature number 5988-9216ENPart 4 overviews various instrumentation for measuring RF and microwavepower, including spectrum analyzers, microwave receivers, network analyzers,and the most accurate method, power sensors/meters. It begins with theunknown signal, of arbitrary modulation format, and draws application-oriented comparisons for selection of the best instrumentation technologyand products.

Most of the note is devoted to the most accurate method, power meters and sensors. It includes comprehensive selection guides, frequency cover-ages, contrasting accuracy and dynamic performance to pulsed and complexdigital modulations. These are especially crucial now with the advances inwireless communications formats and their statistical measurement needs.

2

For user convenience, Agilent’sFundamentals of RF andMicrowave Power Measurements,application note 64-1, literaturenumber 5965-6330E, has beenupdated and segmented into fourtechnical subject groupings. The following abstracts explain how thetotal field of power measurementfundamentals is now presented.

I. Introduction ......................................................................................... 4

II. Power Transfer, Signal Flowgraphs ................................. 5

Power transfer, generators and loads...................................................... 5RF circuit descriptions .............................................................................. 5Reflection coefficient ................................................................................. 7Signal flowgraph visualization ................................................................. 8

III. Measurement Uncertainties .................................................. 12

Mismatch loss uncertainty ........................................................................ 12

Mismatch loss and mismatch gain ........................................................... 13

Simple techniques to reduce mismatch loss uncertainty .................... 13

Advanced techniques to improve mismatch uncertainty..................... 17

Eliminating mismatch uncertainty by measuring source and load complex reflection coefficients and computer correcting ....... 18

Other sensor uncertainties ....................................................................... 18

Calibration factor ....................................................................................... 19

Power meter instrumentation uncertainties.......................................... 20

IV. Alternative Methods of Combining PowerMeasurement Uncertainties .................................................. 23

Calculating total uncertainty.................................................................... 23

Power measurement equation .................................................................. 23

Worst-case uncertainty method................................................................ 25

RSS uncertainty method............................................................................ 26

A new international guide to the expression of uncertainty in

measurement (ISO GUM) ....................................................................... 27

Power measurement model for ISO process........................................... 29

Standard uncertainty of mismatch model.............................................. 31

Example of calculation of uncertainty using ISO model...................... 32

3

Table of Contents

The purpose of the new series of Fundamentals of RF and Microwave PowerMeasurements application notes, which were leveraged from former note 64-1,is to

1) Retain tutorial information about historical and fundamental considerationsof RF/microwave power measurements and technology which tend to remain timeless.

2) Provide current information on new meter and sensor technology.

3) Present the latest modern power measurement techniques and test equipment that represents the current state-of-the-art.

Part 3 of this series, Power Measurement Uncertainty per InternationalGuides, is a comprehensive overview of all the contributing factors (there are12 described in the International Standards Organization (ISO) example) topower measurement uncertainty of sensors and instruments. It presents signalflowgraph principles and a characterization of the many contributors to thetotal measurement uncertainty.

Chapter 2 examines the concept of signal flow, the power transfer between gen-erators and loads. It defines the complex impedance, its effect on signal reflec-tion and standing waves, and in turn its effect on uncertainty of the power inthe sensor. It introduces signal flowgraphs for better visualizations of signalflow and reflection.

Chapter 3 breaks down all the various factors that influence measurementuncertainty. It examines the importance of each and how to minimize each ofthe various factors. Most importantly, considerable space is devoted to thelargest component of uncertainty, mismatch uncertainty. It presents manypractical tips for minimizing mismatch effects in typical instrumentationsetups.

Chapter 4 begins by presenting two traditional methods of combining the effectof the multiple uncertainties. These are the “worst-case” method and the “RSS”method. It then examines in detail the increasingly popular method of combin-ing uncertainties, based on the ISO Guide to the Expression of Uncertainty inMeasurement, often referred to as the GUM.[1] ISO is the InternationalStandards Organization, an operating unit of the International ElectrotechnicalCommission (IEC). The reason the GUM is becoming more crucial is that theinternational standardizing bodies have worked to develop a global consensusamong National Measurement Institutes (such as NIST) and major instrumenta-tion suppliers as well as the user community to use the same uncertainty stan-dards worldwide.

Note: In this application note, numerous technical references will be made tothe other published parts of the series. For brevity, we will use the formatFundamentals Part X. This should insure that you can quickly locate the con-cept in the other publication. Brief abstracts for the four-part series are provid-ed on the inside front cover.

[1] “ISO Guide to the Expression of Uncertainty in Measurement," International Organization for Standardization, Geneva, Switzerland, ISBN 92-67-10188-9, 1995.

4

I. Introduction

Power transfer, generators and loadsThe goal of an absolute power measurement is to characterize the unknownpower output from some source (for example a generator, transmitter, or oscil-lator). Sometimes the generator is an actual signal generator or oscillatorwhere the power sensor can be attached directly to that generator. On otheroccasions, however, the generator is actually an equivalent generator. For example, if the power source is separated from the measurement point by suchcomponents as transmission lines, directional couplers, amplifiers, mixers, etc.,then all those components may be considered as parts of the generator. Theport that the power sensor connects to, would be considered the output port ofthe equivalent generator.

To analyze the effects of impedance mismatch, this chapter explains mathemat-ical models that describe loads, including power sensors and generators, whichapply to the RF and microwave frequency ranges. The microwave descriptionsbegin by relating back to the equivalent low-frequency concepts for those famil-iar with those frequencies. Signal flowgraph concepts aid in analyzing powerflow between an arbitrary generator and load. From that analysis, the termsmismatch loss and mismatch loss uncertainty are defined.

RF circuit descriptionsAt low frequencies, methods for describing a generator include the Theveninand Norton equivalent circuits. The Thevenin equivalent circuit of a generator,for example, has a voltage generator, es, in series with an impedance, Zg, asshown in Figure 2-1. For a generator, even if composed of many components, esis defined as the voltage across the output port when the load is an open cir-cuit. Zg is defined as the impedance seen looking back into the generator whenall the sources inside the generator are reduced to zero.

Figure 2-1. A Thevenin equivalent generator connected to an arbitrary load.

5

II. Power Transfer, Signal Flowgraphs

The power delivered by a generator to a load is a function of the load imped-ance. If the load is a perfect open or short circuit, the power delivered is zero.Analysis of Figure 2-1 would show that the power delivered to the load is amaximum when load impedance, Z, is the complex conjugate of the generatorimpedance, Zg. This power level is called the “power available from a genera-tor,” or “maximum available power,” or “available power.” When Z= (R + jX)and Zg = (Rg + jXg) are complex conjugates of each other, their resistive partsare equal and their imaginary parts are identical in magnitude but of oppositesign; thus R = Rg and X = –Xg. Complex conjugate is written with an * so thatZ = Zg* is the required relationship for maximum power transfer.

The Thevenin equivalent circuit is not very useful at microwave frequencies fora number of reasons. First, the open circuit voltage is difficult to measurebecause of fringing capacitance and the loading effect of a voltmeter probe.Further, the concept of voltage loses usefulness at microwave frequencieswhere it is desired to define the voltage between two points along a transmis-sion path, separated by a significant fraction of a wavelength. If there is a“standing wave” along a transmission line, the voltage varies along the line.Also, there are problems with discussing voltage in rectangular waveguide. As aresult, the concept of power is much more frequently used than voltage forcharacterizing generators at RF and microwave frequencies.

The open circuit that defines the Thevenin equivalent voltage generator isuseless for measuring power because the power dissipated in an open termina-tion is always zero. The reference impedance used for characterizing RF gener-ators is almost always 50 Ω. The reason for this is that 50 Ω is easy to realizeover the entire frequency range of interest with a transmission line of 50 Ωcharacteristic impedance and with a reflection-less termination.

The standard symbol for characteristic impedance, Zo, is also the standardsymbol for reference impedance. In some cases, for example, where 75 Ω trans-mission lines are used in systems with a 50 Ω reference impedance, anothersymbol, such as Zr, should be used for reference impedance. Zo will be used inthis application note to mean reference impedance. A generator is character-ized, therefore, by the power it delivers to a reference load Zo = 50 Ω. In gener-al, that power is not equal to the maximum available power from the generator;they are equal only if Zg = Zo.

As frequencies exceed 300 MHz, the concept of impedance loses usefulness andis replaced by the concept of reflection coefficient. The impedance seen lookingdown a transmission line toward a mismatched load, varies continuously withthe position along the line. The magnitude and the phase of impedance arefunctions of line position. Reflection coefficient is well-behaved; it has a magni-tude that is constant and a phase angle that varies linearly with distance fromthe load.

6

7

Reflection coefficientAt microwave frequencies where power typically is delivered to a load by atransmission line that is many wavelengths long, it is very convenient toreplace the impedance description of the load, involving voltage and currentand their ratio (Ohm’s law), with a reflection coefficient description involvingincident and reflected traveling waves, and their ratio. To characterize a passive load, Ohm’s law is replaced by:

where a is proportional to the voltage of the incident wave, b is proportionalto the voltage of the reflected wave, and Γ is defined to be the reflection coefficient of the load. All three quantities are, in general, complex numbersand change with frequency. The quantities a and b are normalized1 in such away that the following equations hold:

where Pi is power incident on the load and Pr is power reflected by it. The netpower dissipated by the load, Pd , is given by:

This power is the total power obtained from the source; it includes not onlypower converted to heat, but also power radiated to space and power that leaksthrough accessory cables to other pieces of equipment.

Transmission line theory relates the reflection coefficient, Γ of a load to itsimpedance, Z, as follows:

where Zo is the characteristic impedance of the system. Further, the load volt-age, v, and load current, i, are given by:

since current in a traveling wave is obtained from the voltage by dividing by Zo.Solving for a and b results in:

1. If the transmission line characteristic impedance is Zo the normalization factor is √Zo; that is, a is obtained from the voltage of the incident wave by dividing by √Zo. Similarly, b is obtained from the voltage of the reflected wave by dividing by √Zo.

= Γba

(Equation 2-1)

|a|2 = Pi(Equation 2-2)

(Equation 2-3)|b|2 = Pr

Pd = Pi – Pr = |a|2 – |b|2 (Equation 2-4)

Γ = Z – ZoZ + Zo

(Equation 2-5)

i = Incident current – reflected current

= (a – b)

V = Incident voltage + reflected voltage

= √ Zo (a+ b)(Equation 2-6)

1

√Zo

(Equation 2-7)

1

2√Zo

a = (v + Zoi)1

2√Zo

(Equation 2-8)

b = (v − Zoi) (Equation 2-9)

These equations are used in much of the literature to define a and b (see thereference by Kurakawa.)[1] The aim here, however, is to introduce a and bmore intuitively. Although equations 2-8 and 2-9 appear complicated, the relationships to power (equations 2-2, 2-3, and 2-4) are very simple. TheSuperposition Theorem, used extensively for network analysis, applies to aand b; the Superposition Theorem does not apply to power.

Reflection coefficient, Γ, is frequently expressed in terms of its magnitude, ρ,and phase, φ. Thus ρ gives the magnitude of b with respect to a and φ givesthe phase of b with respect to a.

The most common methods of measuring reflection coefficient involve observ-ing a and b separately and then taking the ratio. Sometimes it is difficult toobserve a and b separately, but it is possible to observe the interference pat-tern of the counter-travelling waves formed by a and b on a transmission line.This pattern is called the standing wave pattern. The interference pattern hasregions of maximum and of minimum signal strength. The maximums areformed by constructive interference between a and b and have amplitude |a| + |b|. The minimums are formed by destructive interference and haveamplitude |a| –|b|. The ratio of the maximum to the minimum is called thestanding-wave ratio (SWR, sometimes referred to as voltage-standing-wave-ratio, VSWR).1 It can be measured with a slotted line and moveable probe, ormore commonly with network analyzers. SWR is related to the magnitude ofreflection coefficient ρ by:

Signal flowgraph visualizationA popular method of visualizing the flow of power through a component oramong various components is by means of a flow diagram called a signal flowgraph.[1,2] This method of signal flow analysis was popularized in the mid-1960’s, at the time that network analyzers were introduced, as a means ofdescribing wave travel in networks.

The signal flowgraph for a load (Figure 2-2) has two nodes, one to representthe incident wave, a, and the other to represent the reflected wave, b. Theyare connected by branch Γ, which shows how a gets changed to become b.

Just as the Thevenin equivalent had two quantities for characterizing a genera-tor, generator impedance, and open circuit voltage, the microwave equivalenthas two quantities for characterizing a microwave or RF generator, Γg and bs.

8

Figure 2-2. Signal flowgraph for a load.

SWR = |a| + |b|

|a| – |b| (Equation 2-10)= 1 + |b/a|

1 – |b /a|= 1 + ρ

1 – ρ

1. Traditionally VSWR and PSWR referred to voltage and power standing wave ratio. Since PSWR has fallen to dis-use, VSWR is shortened to SWR.

9

The equation for a generator is (see Figure 2-3):

where:

bg is the wave emerging from the generatorag is the wave incident upon the generator from other componentsΓg is the reflection coefficient looking back into the generatorbs is the internally generated wave

Γg is related to Zg by:

which is very similar to Equation 2-5. The bs is related to the power to a refer-ence load from the generator, Pgzo, by:

bs is related to the Thevenin voltage, es, by:

The signal flowgraph of a generator has two nodes representing the incident,wave ag and reflected wave bg. The generator also has an internal node, bs, thatrepresents the ability of the generator to produce power. It contributes to out-put wave, bg, by means of a branch of value one. The other component of bg isthat portion of the incident wave, ag, that is reflected off the generator.

Now that equivalent circuits for a load and generator have been covered, the flow of power from the generator to the load may be analyzed. When the load isconnected to the generator, the emerging wave from the generator becomes theincident wave to the load and the reflected wave from the load becomes theincident wave to the generator. The complete signal flowgraph (Figure 2-4)shows the identity of those waves by connecting node bg to a and node b toag with branches of value one.

Figure 2-4 shows the effect of mismatch or reflection. First, power from the generator is reflected by the load. That reflected power is re-reflected from thegenerator and combines with the power then being created by the generator, generating a new incident wave. The new incident wave reflects and theprocess continues on and on. It does converge, however, to the same result thatwill now be found by algebra.

The equation of the load (2-1) is rewritten with the identity of ag to b addedas:

The equation of the generator (2-11) is also rewritten with the identity of a tobg added as:

bg = bs + Γgag (Equation 2-11)

Γg = Zg – Zo

Zg + Zo

(Equation 2-12)

Pgzo = |bs|2 (Equation 2-13)

bs = es √Zo

Zo + Zg (Equation 2-14)

b = Γ a = ag(Equation 2-15)

Figure 2-3. Signal flowgraph of amicrowave generator.

Figure 2-4. The complete signal flowgraph of a generator connected to a load.

bg = bg + Γgag = a (Equation 2-16)

10

Equations 2-15 and 2-16 may be solved for a and b in terms of bs, Γ and Γg:

From these solutions the load’s incident and reflected power can be calculated:

Equation 2-19 yields the somewhat surprising fact that power flowing towardthe load depends on the load characteristics.

The power dissipated, Pd, is equal to the net power delivered by the generatorto the load, Pg:

Two particular cases of Equation 2-21 are of interest. First, if Γ were zero,that is if the load impedance were Zo, Equation 2-21 would give the powerdelivered by the generator to a Zo load:

This case is used to define bs as the generated wave of the source.

The second case of interest occurs when:

where * indicates the complex conjugate. Interpreting Equation 2-23 meansthat the reflection coefficient looking toward the load from the generator is thecomplex conjugate of the reflection coefficient looking back toward the genera-tor. It is also true that the impedances looking in the two directions are com-plex conjugates of each other. The generator is said to be “conjugatelymatched.” If Γ is somehow adjusted so that Equation 2-23 holds, the generatorputs out its “maximum available power,” Pav, which can be expressed as:

Comparing Equations 2-22 and 2-24 shows that Pav ≥ PgZo.

Unfortunately, the term “match” is popularly used to describe both conditions,Z = Zo and Z = Zg*. The use of the single word “match” should be dropped infavor of “Zo match” to describe a load of zero reflection coefficient, and infavor of “ conjugate match” to describe the load that provides maximum powertransfer.

a = bs

1 – ΓgΓ(Equation 2-17)

b = bsΓ1 – ΓgΓ

(Equation 2-18)

Pi = |a|2 = |bs|2 (Equation 2-19)1

|1 – ΓgΓ|2

Pr = |b|2 = |bs|2 (Equation 2-20)Γ

2

|1 – ΓgΓ|2

Pd = Pg = Pi – Pr = |bs|2 (Equation 2-21)1 – |Γ|2

|1 – ΓgΓ|2

Pg|Z = Zo= PgZo = |bs|2 (Equation 2-22)

Γg = Γ* (Equation 2-23)

Pav = (Equation 2-24)|bs|2

1 – |Γg|2

Now the differences can be plainly seen. When a power sensor is attached to agenerator, the measured power that results is Pgzo of Equation 2-21, but theproper power for characterizing the generator is Pgzo of Equation 2-22. Theratio of equations 2-22 to 2-21 is:

or, in dB:

This ratio (in dB) is called the “Zo mismatch loss.” It is quite possible that Equation 2-25 could yield a number less than one. Then Equation 2-26 wouldyield a negative number of dB.

In that case more power would be transferred to the particular load being usedthan to a Zo load, where the Zo mismatch loss is actually a gain. An example ofsuch a case occurs when the load and generator are conjugately matched.

A similar difference exists for the case of conjugate match; the measurement ofPg from Equation 2-21 differs from Pav of Equation 2-24. The ratio of thoseequations is:

or, in dB:

This ratio in dB is called the “conjugate mismatch loss.”

If Γ and Γg were completely known, or easily measured versus frequency, thepower corrections would be simplified. The power meter reading of Pg wouldbe combined with the proper values of Γ and Γg in Equations 2-25 or 2-27 tocalculate Pgzo or Pav. The mismatch would be corrected and there would be nouncertainty. Yet in the real world, most power measurements are made withoutthe Γ and Γg corrections in the interest of time. For certain special proce-dures, such as power sensor calibrations, where utmost accuracy is required,the time is taken to characterize the generator and load (sensor) complexreflection coefficients versus frequency, and corrections made for those effects.

11

(Equation 2-25)|1 – ΓgΓ|2

1 – |Γ|2

PgzoPg

=

dB = 10 log (Equation 2-26)Pgzo

Pg

dB = 10 log |1 – ΓgΓ|2 – 10 log (1 – |Γ|2)

(Equation 2-27)|1 – ΓgΓ|2

(1 – |Γg|2)(1 – |Γ|2)

PavPg

=

dB = 10 log

(Equation 2-28)

PavPg

dB = 10 log |1 – ΓΓg|2 – 10 log (1 – |Γg|2) – 10 log (1 – |Γ|2)

[1] K. Kurakawa, “Power Waves and the Scattering Matrix,” IEEE Trans. on Microwave Theory and Techniques,Vol. 13, No. 2, Mar 1965.

[2] N.J. Kuhn, “Simplified Signal Flow Graph Analysis,” Microwave Journal, Vol 6, No 10, Nov. 1963.

12

This chapter examines most of the power measurement uncertainty factors indetail. One example enumerates 12 different factors, some dominant and somealmost trivial. Because the mismatch term almost always predominates, it willreceive extra attention, especially in simple procedures for reducing and minimizing its effect.

Figure 3-1. This chart shows a typical distribution of uncertainty values for its three largest causes:mismatch, sensor and meter specifications. It reveals why low SWR specifications for the powersensor and source is so crucial.

Mismatch loss uncertaintyΓ and Γg are seldom completely known for both magnitude and phase. Onlythe magnitudes ρ and ρg are usually measured or specified. In these cases, thefirst term of the right side of Equations 2-26 and 2-27 cannot be exactly calcu-lated because of the lack of phase information, but the maximum and minimumvalues can be found. The maximum and minimum values of 10 log|1 – Γg Γ|2

are called “mismatch loss uncertainty limits” and are given the symbol Mu. Themaximum occurs when Γg Γ combines with “one” in phase to yield:

This maximum limit will always be a positive number but it cannot be largerthan 6 dB (this occurs when ρ = ρg = 1). The minimum value of the mismatchloss uncertainty occurs when Γg Γ combines with “one” exactly out of phase toyield:

The minimum limit will always be a negative number. It is also true that themagnitude of the minimum limit will be greater than the magnitude of the maximum limit, but usually by a very small amount.

Sometimes the mismatch loss uncertainty limits are given in percent deviationfrom “one” rather than in dB. In this case:

Mismatch loss uncertainty limits can be calculated by substituting the values ofρ and ρg into Equations 3-1, 3-2, and 3-3. For mismatches less than 2 percent,this approximation can be used; Mu ±200–g –l %.

Modern engineering electronic calculators have a series of programs availableespecially suited for electrical engineering problems. One of the programs isintended for calculating mismatch loss uncertainty limits, either in terms ofSWR or of ρ. Computer-aided engineering models often contain routines forsuch transmission line calculations.

III. Measurement Uncertainties

• Sensor and Source Mismatch Errors

• Power Sensor Errors

• Power Meter Errors

MismatchSensor

Meter

Mu max = 10 log (1 + ρgρ)2(Equation 3-1)

Mu min = 10 log (1 – ρgρ)2 (Equation 3-2)

%Mu = 100 [(1 ± ρgρ)2 – 1] (Equation 3-3)

13

Mismatch loss and mismatch gainTraditionally, the transmission power loss due to signal reflection was termedmismatch loss. This was done in spite of the fact that occasionally the tworeflection coefficient terms would align in a phase that produced a small“gain.” More recent usage finds the term mismatch gain more popular becauseit is a more inclusive term and can mean either gain (positive number) or loss(negative number). Similarly, it is more difficult to think of a negative mis-match loss as a gain. In this note, we use the terms interchangeably, with dueconsideration to the algebraic sign.

The second term on the right side of Equation 2-26, –10 log (1 –| Γ|2), iscalled mismatch loss. It accounts for the power reflected from the load. Inpower measurements, mismatch loss is usually taken into account when cor-recting for the calibration factor of the sensor, to be covered below.

The conjugate mismatch loss of Equation 2-28 can be calculated, if needed. Theuncertainty term is the same as the Zo mismatch loss uncertainty term and theremaining terms are mismatch loss terms, one at the generator and one at theload. The term conjugate mismatch loss is not used much anymore. It was usedwhen reflections were tuned out by adjusting for maximum power (correspon-ding to conjugate match). Now the various mismatch errors have been reducedto the point where the tedious tuning at each frequency is not worth the effort.In fact, modern techniques without tuning might possibly be more accuratebecause the tuners used to introduce their own errors that could not always beaccounted for accurately.

Mismatch in power measurements generally causes the indicated power to bedifferent from that absorbed by a reflection-less power sensor. The reflectionfrom the power sensor is partially accounted for by the calibration factor of thesensor which is considered in the next chapter. The interaction of the sensorwith the generator (the re-reflected waves) could be corrected only by knowl-edge of phase and amplitude of both reflection coefficients, Γ and Γg. If onlythe standing wave ratios or reflection coefficient magnitudes ρ and ρg areknown, then only the mismatch uncertainty limits can be calculated. The mismatch uncertainty is combined with all the other uncertainty terms laterwhere an example for a typical measurement system is analyzed.

Simple techniques to reduce mismatch loss uncertainty [1]Before embarking on some practical tips for controlling mismatch uncertain-ties, Figure 3-2 shows a graphical perspective for the mismatch uncertaintythat occurs when a signal passes between two different reflection coefficients.The power equations can easily compute the exact uncertainties based on themagnitude of Γ (ρ). One of the unknown reflection coefficients is plotted on thehorizontal and the other on the vertical axis. For example, if the source andload both had a ρ of 0.1, the approximate mismatch uncertainty would beapproximately 0.09 dB.

Figure 3-2. A profile of mismatch uncertainty (dB) values resulting from two reflection coefficients.

One important conclusion to draw from this chart is that if one of the reflec-tion coefficients (ρ1) is less than, for example 0.05 (SWR is about 1.1), you canlook along the horizontal line and see that even if the ρ2 reflection coefficientgoes up to 0.5 (SWR = 3.0), the mismatch uncertainty only increases to about0.2 dB. This gives us a strong hint that choosing a power sensor with the lowestSWR specification is recommended.

Controlling mismatch uncertainty is as simple as reducing the reflection coefficient on any transmission lines or components that are part of the testarrangement. Assuming that equipment with the lowest practical SWR has beenselected, many other simple measures can be taken to ensure that the perform-ance of the test system does not become degraded.

At lower frequencies, for example less than 300 MHz, minimize the length ofthe transmission lines to reduce the changes of phase with frequency. This isnot a viable method for higher frequencies, because even short lengths of cableform significant fractions of a wavelength, as shown in Example 1 below.

The use of good quality cables intended for many instrumentation and meas-urement applications is highly recommended. This means that connectorsshould be designed for hundreds of connection/disconnection cycles. The popular and inexpensive SMA coaxial connector would not be used because itis not designed to endure dozens or hundreds of connections.

This is particularly important for the connection to the unit-under-test (UUT),as this connection may be repeatedly made and broken. Some manufacturersproduce cables with specified SWR and loss values at frequencies up to 18 GHz.This is a good indication of the intended purpose of these cables. They shouldbe far more reliable than general-purpose test cables intended for use at lowerfrequencies.

Semi-rigid cables are preferred if the equipment is fixed in place. However, it isimportant not to use semi-rigid cables for connections to the UUT where it mayoften be flexed and will soon become damaged. In this regard, do not go belowthe minimum bend radius, specified by the cable manufacturer, or it may bepermanently damaged.

14

Example 1.A 75-Ω cable used between a 50-Ω impedance signal generator and 50-Ω power meter

You pull out an unmarked cable with BNC connectors from a drawer, or borrowone from a colleague. Unknowingly, you connect a 75-Ω cable into your 50-Ωtest-system. In that system, Figure 3-3, four components that do not individual-ly vary with frequency, can cause the power dissipated in the load to vary withfrequency. Figure 3-4 shows the simulated power dissipated in the load resistorfor a 75-Ω transmission line with a 1 ns delay. In practice, this cable would beonly 200 mm (8-in) long.

Figure 3-3. 50-Ω signal generator and 50-Ω power sensor connected by a 75-Ω cable.

At low frequencies, for example below 10 MHz, the system behaves as if thesource and load were connected directly together. The load sees half the sourcevoltage. However, as the frequency increases, the power dissipated in the loadreduces at first and then increases again in cyclic fashion. When the two-waytransit time of the cable is equal to one cycle of the generator frequency, thepower cycle begins again. This is at 500 MHz with a 1-ns cable delay. The peak-to-peak variation is about 0.7 dB, and can be calculated from the mismatchuncertainty limits.

Figure 3-4. Even a short (8-in) length of 75-Ω transmission line connecting two 50-Ω systems causes regular variations of power with frequency, with a peak excursion of 0.7 dB. All this is below1000 MHz.

15

R1

T150

2Vac0Vdc

O O

V150

Example 2. A power meter connected to a signal generator

Consider measuring the output power of a signal generator, using a powermeter at 2.4 GHz. This is the RF frequency for Bluetooth™ and IEEE 802.11bwireless LAN radio systems. Consider further that the Agilent E4433A signalgenerator, E4418B power meter and 8481A power sensor are chosen for themeasurements. The output SWR of the E4433B at 2.4 GHz is 1.9, with an electronically switched attenuator, or 1.35, with a mechanically switched attenuator.

The specified SWR of an 8481A sensor at 2.4 GHz is 1.18, with a reflection coefficient of 0.0826. The 1.9 SWR of the signal generator is equivalent to ρg = 0.310, so the mismatch uncertainty is +0.219, -0.225 dB.

If the mechanical attenuator version of the signal generator is acceptable as areplacement for the electronically switched standard attenuator, the SWRcomes down to 1.35, and the reflection coefficient equals 0.149. The mismatchuncertainty now is reduced by half, to +0.106 dB, -0.107 dB. Note that the manufacturer's accuracy specification cannot include mismatch uncertaintybecause the load SWR is unknown and variable. The electronically switchedattenuator is likely to be more reliable in an automatic test system; however,the mechanically switched version shows less mismatch uncertainty and allowsa higher maximum output-power level. The measurement application indicatesthe best choice, but knowledge of the effects of mismatch helps with the analysis.

Connector choice is also important. The connection on the UUT will probablynot be under your control, but for the other cables, choose precision threadedconnector types like type-N or APC-3.5 in preference to bayonet type, such asBNC, as they provide more repeatable results. When tightening the screw-typeconnectors, use a torque wrench to avoid over- or under-tightening the connec-tor; then there will be little variation in tightness when another operator takesover.

Using adapters to convert between different families of connectors may beunavoidable, but should be minimized. Adapters should convert directly andshould not be stacked. For example, do not convert from type-N to BNC, andthen BNC to SMA. Use the proper type-N to SMA adapter. Also, be wary of mat-ing between dissimilar connectors. For example, APC-3.5 and SMA look verysimilar but have different mechanical interfaces. The use of a precision adapteror "connection saver" is recommended between APC3.5 and SMA connectors.

There are several kinds of type-N connectors, two of which are the 50-Ω andthe rarer 75-Ω type (which uses a smaller diameter center conductor). A male,75-Ω type-N connector connected to a 50-Ω, female type-N connector will oftenresult in an open circuit because the center-mating pin of a 75-Ω connector issmaller in diameter than the 50-Ω version. If a 50-Ω, male type-N connector isinserted into a 75-Ω, type-N female connector then the male connector willcause irreparable damage to the female connector. This is one reason why 75-Ωtype-N connectors are rare! BNC connectors also come in 50-Ω and 75-Ω vari-eties, but usually mixing the two kinds does not cause damage, although prema-ture wear is possible and the SWR will not be as good as it could be.

The best way to check the performance of cables and adapters is to use a vec-tor network analyzer and record the results for comparison at the next regularaudit of the test station. The ultimate connectors are sexless, meaning there isonly one sex of connector. This means that male-male and female-femaleadapters are never required. Examples of this kind of connector are APC-7 andthe older General Radio 874 connector.

16

Finally, precision connectors should be regularly cleaned and gauged—meas-ured with a special dial gauge to ensure that they have not been mechanicallydamaged. A damaged connector can instantly ruin the mated part.

In summary,

• Select test equipment for lowest SWR.• Keep cable length as short as possible.• Use good quality cables.• Select appropriate connectors.• Keep the connectors clean.• Measure (gauge) the connectors regularly. • Replace faulty, worn, or damaged cables and connectors promptly.• Do not make your own cables for use at high frequencies unless you test

them first.• Minimize the number of adapters.• If possible, use semi-rigid cables for permanently connected cables. • Follow the cable manufacturer's recommendation for minimum bend-radius. • Fix the measurement equipment to the bench if possible (or rack it up).• Do not over-tighten connectors and do not allow them to become loose—use

a torque wrench.• Do not mate dissimilar families, for example APC-3.5 and SMA.• Avoid temperature extremes.

Advanced techniques to improve mismatch uncertaintyWhen the performance of a test arrangement is simply not good enough for thejob, there are a number of techniques that allow an improvement in accuracy.These include adding an attenuator to one end of the transmission line toimprove the test SWR. An isolator component can also reduce reflections froma load. Or, as in the case of the power-splitter method of sensor calibrationdescribed in Fundamentals Part 1, the use of a leveling loop, effectively createsa Zo impedance at the centerpoint of the splitter, with the resulting "generatoroutput impedance" being equivalent to the highly-matched microwave resistorin the second arm of the splitter. [2]

The use of an attenuator (pad) to improve the flatness of a transmission linedepends on the fact that the return loss of the attenuator is better than theoriginal source or load. The attenuator is usually placed at the end of the linewith the worst return loss. Clearly, the generator level will need to be increasedto keep the signal-level constant at the load, which may limit the applicabilityof this method to the mid-range of power levels.

Attenuators are usually broadband devices. In a similar fashion, you can use anisolator to reduce the reflected energy on the line. Isolators are applied at highpower levels, where the economic cost of the power lost in an attenuator wouldbe high, and at very low power levels, where the signal would be masked bythermal noise. They are narrow-band devices and are likely to be more expen-sive than attenuators.

A leveling loop uses low-frequency feedback to improve the effective sourcematch to the line. This requires a two-resistor power splitter or a directionalcoupler. The output of the generator is measured on a power meter and thegenerator is adjusted so that the indicated power is at the level you need. Thistechnique depends on having a power meter that is better matched than thesignal generator, and an accurately matched two-resistor power-splitter ordirectional coupler.

As the measurement frequency increases, so does the importance of maintain-ing a low SWR on the transmission line. You can never completely eliminatemismatch uncertainty, but simple practical measures allow you to keep SWRsto a minimum.

17

Eliminating mismatch uncertainty by measuring source and loadcomplex reflection coefficients and computer correctingAs described in Fundamentals Part 1, Chapter 3, most modern sensor calibration systems utilize a method that all but eliminates the mismatchuncertainties between the signal source and the standard sensor or the sensorunder test. By characterizing the complex reflection coefficient of both thesource and sensor across the frequency range of interest, a software programcan then provide signal transfer corrections using the individual phase/ amplitude of each reflection coefficient at each frequency of calibration.

In critical power measurement applications, the user could resort to this tech-nique, even though it requires extra test runs to characterize the reflectioncoefficient of each source and each load. However, it must be recognized thatthe ordinary power measurements made in production test or R&D labs rely onnon-correction procedures. By simply using power sensors with very low SWR,excellent and usually adequate uncertainties can be realized.

Other sensor uncertaintiesAfter mismatch uncertainty, the second source of error is the imperfect effi-ciency of the power sensor. There are two parameters that define the designefficiency of a sensor, effective efficiency and calibration factor. AlthoughAgilent now furnishes only calibration factor data with its sensors, since bothparameters are still available as measurement services for thermistor sensorsfrom the NIST, they will be reviewed here.

For a power sensor, the power input is the net power delivered to the sensor; itis the incident power minus the reflected power (Pi - Pr). However, not all thatnet input power is dissipated in the sensing element. Some might be radiatedoutside the transmission system or leaked into the instrumentation, some dissipated in the conducting walls of the structure, or in a capacitor compo-nent of the sensor, or a number of other places that are not metered by theinstrumentation. The metered power indicates only the power that is dissipatedinto the power sensing element itself.

For metering, the dissipated high frequency power must go through a conversion process to an equivalent DC or low frequency level. The DC or lowfrequency equivalent is called Psub, for substituted power. There are errorsassociated with the substitution process. In thermistor sensors, for example,errors result from the fact that the spatial distributions of current, power, andresistance within the thermistor element are different for DC and RF power.

18

To accommodate both the usual parasitic losses as well as the DC or low fre-quency substitution problem mentioned, a special term, effective efficiency ηe,has been adopted for power sensors. Effective efficiency is defined by:

Pg is the net power absorbed by the sensor during measurement. Psub is thesubstituted low frequency equivalent for the RF power being measured. Forthermistor sensors Psub is the change in bias power required to bring the ther-mistor back to the same resistance as before the application of RF power. Forthermocouple and diode sensors, Psub is the amount of power from a referencepower source, at a specified frequency, when it yields the same voltage to themetering circuits as Pg. The ηe normally changes with frequency, but changeswith power level are usually negligible.

Effective efficiency is sometimes measured by the manufacturer when calibrat-ing the sensor and furnished in a calibration chart with the product.Sometimes the data is printed on the label of the sensor, or delineated withdots on a label plot of efficiency. It is expressed in percentage and that factoris entered into the power meter by adjusting the analog dial to the appropriatenumber or entered digitally into digital power meters.

Calibration factorThere is another more frequently used term that has been defined for powermeasurements. It combines effective efficiency and mismatch loss and is calledthe calibration factor Kb. The Kb is defined by:

where Pi is the incident power to the sensor. The accurate measurement ofcalibration factor Kb is quite involved and performed mainly by standards laboratories and manufacturers.

The definitions of Kb and ηe can be combined to yield

where ρ is the magnitude of the sensor reflection coefficient. The relationshipon the right, which is found by substituting for Pi and Pg from equations 2-19 and 2-21, shows that Kb is a combination of effective efficiency and mismatch loss.

19

ηe = PsubPg

(Equation 3-4)

Kb = Psub

Pi(Equation 3-5)

Kb = ηePg

Pi(Equation 3-6)= ηe (1 – ρ

2)

20

Most modern power meters have the ability to correct their meter reading bysetting a dial or keying in a digital number to the proper value of Kb. Then Pi isactually read off the meter. Values of Kb for various frequencies are indicatedon each Agilent power sensor (except for the E series sensors, which have thedata stored on EEPROM). When this feature is used, the indicated or meteredpower Pm is (using Equation 2-19):

But the desired quantity is usually not Pi to the sensor but Pgzo, the power thatwould be dissipated in a Zo load. Since PgZo is by definition |bs|2, the ratio ofPgZo to the meter indication is:

The right side of Equation 3-8 is the mismatch uncertainty. Since the use of Kbcorrects for efficiency and mismatch loss, only the mismatch uncertaintyremains. It should be pointed out that there is an additional, unavoidableuncertainty associated with Kb. That uncertainty is due to inaccuracies in themeasurement of Kb by the manufacturer, NIST or standards laboratories andthus the uncertainty of Kb is specified by the calibration supplier.

Power meter instrumentation uncertainties (including sensor)There are a number of uncertainties associated within the electronics of thepower meter. The effect of these errors is to create a difference between Pmand Psub/Kb.

Reference oscillator uncertaintyOpen-loop power measurements, such as those that use thermocouples orsemiconductor diode sensors, require a known source of power to verify and adjust for the sensitivity of the sensor. Many power meters, such as theAgilent EPM and EPM-P, have a stable power reference built in. No matter whatpower reference is used, if it deviates from the expected power output, the calibration adjustment is in error. The uncertainty in the power output fromthe reference oscillator is specified by the manufacturer. Thermistor powermeasurements, being closed-loop and having no need for a reference oscillator,are free of this error.

Agilent has recently made improvements in the uncertainty specifications ofthe 50 MHz reference oscillator in all its power meters. It is now factory set to±0.4 percent and traceable to the National Physical Laboratory of the UK.Expansion of the operating specification includes the following aging character-istics, which are now valid for 2 years:

Accuracy: (for 2 years)±0.5% (23 ±3 °C)±0.6% (25 ±10 °C)±0.9% (0 to 55 °C)

Since the reference oscillator represents a reasonably large portion of the ulti-mate power measurement uncertainty budget, these smaller accuracy numbersin the specification lead to a lower overall measurement uncertainty. Anotherpositive note is that the meters require less downtime in the calibration lab,now having a 2-year calibration cycle.

Pm =PgzoKb

(Equation 3-7)= Pi =|bs|2

|1 – ΓgΓ|2

PgzoPm

(Equation 3-8)= |1 – ΓΓg|2

Reference oscillator mismatch uncertaintyThe reference oscillator has its own reflection coefficient at the operating fre-quency. This source reflection coefficient, together with that from the powersensor, creates its own mismatch uncertainty. Because the reference oscillatorfrequency is low, where the reflection coefficients are small, this uncertainty issmall (approximately ±0.01 dB or ±0.2 percent).

Instrumentation uncertaintyInstrumentation uncertainty is the combination of such factors as meter track-ing errors, circuit nonlinearities, range-changing attenuator inaccuracy, andamplifier gain errors. The accumulated uncertainty is guaranteed by the instru-ment manufacturer to be within a certain limit.

There are other possible sources of uncertainty that are, by nature or design,so small as to be included within the instrumentation uncertainty.

An example of one such error is the thermoelectric voltage that may be intro-duced by temperature gradients within the electronic circuits and interconnect-ing cables. Proper design can minimize such effects by avoiding junctions ofdissimilar metals at the most sensitive levels. Another example is the smalluncertainty which might result from the operator’s interpolation of the meterindication.

Zero setIn any power measurement, the meter must initially be set to zero with no RFpower applied to the sensor. Zero setting is usually accomplished within thepower meter by introducing an offset voltage that forces the meter to read zero,by either analog or digital means. The offset voltage is contaminated by severalsources including sensor and circuit noise. The zero set error is specified bythe manufacturer, especially for the most sensitive range. On higher powerranges, error in zero setting is small in comparison to the signal being meas-ured.

NoiseNoise is also known as short-term stability and it arises from sources withinboth the power sensor and circuitry. One cause of noise is the random motionof free electrons due to the finite temperature of the components. The powerobservation might be made at a time when this random fluctuation produces amaximum indication, or perhaps a minimum. Noise is specified as the changein meter indication over a short time interval (usually one minute) for a con-stant input power, constant temperature, and constant line voltage.

21

DriftThis is also called long-term stability and is mostly sensor induced. It is thechange in meter indication over a long time (usually one hour) for a constantinput power, constant temperature, and constant line voltage. The manufactur-er may state a required warm-up interval. In most cases the drift is actually adrift in the zero setting. This means that for measurements on the upperranges, drift contributes a very small amount to the total uncertainty. On themore sensitive ranges, drift can be reduced to a negligible level by zero settingimmediately prior to making a reading.

Power linearityPower measurement linearity is mostly a characteristic of the sensor. Deviationfrom perfect linearity usually occurs in the higher power range of the sensor.For thermocouple sensors, linearity is negligible except for the top power rangeof +10 to +20 dBm, where the deviation is specified at ±3 percent.

For a typical Agilent 8481D Series diode sensor, the upper power range of –30 to –20 dBm exhibits a specified linearity deviation of ±1 percent.

With their much wider dynamic power range, the Agilent E Series sensorsexhibit somewhat higher deviations from perfect linearity. It is mostly temperature-driven effect and specifications are given for several ranges oftemperature. For example, in the 25 ±5 °C temperature range and the –70 to–10 dBm power range, the typical deviation from linearity is ±2 percent RSS.

[1] Lymer, Anthony, “Improving Measurement Accuracy by Controlling Mismatch Uncertainty.” TechOnLine, September 2002. website: www.techonline.com.

[2] Johnson, Russell A., “Understanding Microwave Power Splitters,” Microwave Journal, December 1975.

22

Calculating total uncertaintyIn Chapter 3, only the individual uncertainties were discussed; now a totaluncertainty must be found. The first descriptions will use the traditional analy-sis for combining the individual uncertainty factors. These are usually termedthe "worst case" and the "RSS (root sum of squares) methods."

Most attention will be devoted to the new international process based on theISO process, to be described below, since the world’s test and measurementcommunities are converting over to a commonly agreed standard method.

Power measurement equationThe purpose of this section is to develop an equation that shows how a powermeter reading, Pm, is related to the power a generator would deliver to a Zoload, Pgzo (Figure 4-1). The equation will show how the individual uncertaintiescontribute to the difference between Pm and Pgzo.

Figure 4-1. Desired power output to be measured is Pgzo , but measurement results in the reading Pm.

Starting from the generator in the lower part of Figure 4-1, the first distinctionis that the generator dissipates power Pg in the power sensor instead of Pgzobecause of mismatch effects. That relationship, from Equation 2-25 is:

The next distinction in Figure 4-1 is that the power sensor converts Pg to theDC or low frequency equivalent, P sub, for eventual metering. However, thisconversion is not perfect due to the fact that effective efficiency, ηe, is less than100 percent. If Pg is replaced by Psub /ηe from Equation 3-4, then Equation 4-1becomes:

The first factor on the right is the mismatch uncertainty term, Mu, discussedpreviously. Mu is also referred to as “gain due to mismatch.” The denominatorof the second factor is the calibration factor Kb from Equation 3-6. Now Equation 4-2 can be written:

The last distinguishing feature of Figure 4-1 is that the meter indication Pm,differs from Psub. There are many possible sources of error in the power meterelectronics that act like improper amplifier gain to the input signal Psub. Theseinclude uncertainty in range changing attenuators and calibration-factor ampli-fiers, imperfections in the metering circuit and other sources totaled as instru-mentation uncertainty. For open-loop power measurements this also includesthose uncertainties associated with the calibration of amplifier gain with apower-reference oscillator. These errors are included in the symbol m for magnification.

IV. Alternative Methods of Combining Power Measurement Uncertainties

(Equation 4-1)|1 – ΓΓg|2

1 – |Γ|2Pgzo =

Pg

(Equation 4-2)1ηe (1 – ρ

2 )Pgzo = |1 – ΓΓg|2 Psub

(Equation 4-3)1Kb

Pgzo = Mu Psub

23

24

There are other uncertainties associated with the electronics that cause devia-tion between Pm and Psub. When Psub is zero, then Pm should be zero.Improper zero setting, zero carryover, drift, and noise are likely contributors toPm not being zero. The meter reading is offset or translated from mPsub by atotal amount t. A general linear equation gives Pm in terms of Psub:

Substituting Equation 4-4 into Equation 4-3 gives the power measurementequation:

In the ideal measurement situation, Mu has the value of one, the mKb productis one, and t is zero. Under ideal conditions, meter reading Pm gives the propervalue of Pgzo.

Table 4-1. Chart of uncertainties for a typical absolute power measurement.

Measurement conditions Pm = 50 µW Full scale (F.S.) = 100 µWρ ≤ 0.091 (SWR ≤1.2) ρg ≤ 0.2 (SWRg ≤1.5)

Kb = 93% ± 3% (worst case), ±1.5% (RSS)

Error Description Worst case values RSS component PgZo max PgZo min (∆X/X)2

Mu (1 ± PgP)2 1.0367 0.9639 (0.0367)2

Kb uncertainty ±3% (w.c.), ±1.5% (RSS) 1.03 0.97 (0.015)2

Components of mRef. osc. unc. ±0.6% (use 2-yr 25 ±10 °C value) 1.006 0.994 (0.006)2

Ref. osc. Mu SWRg = 1.05, SWR, = 1.1 1.002 0.998 (0.002)2

Instrumentation ±0.5% of F.S. 1.01 0.99 (0.01)2

Total m 1.018 0.982

Components of tZero set ±0.5% F.S. (low range) +0.05 µW –0.05 µW (0.001)2

Zero carryover ±0.2% of F.S +0.2 µW –0.2 µW (0.004)2

Noise ±0.025 µW +0.025 µW –0.025 µW (0.0005)2

Total t +0.275 µW –0.275 µW

Expressions oftotal uncertainty

Pgzo max Equation 4-8 55.0421 µWPgzo min Equation 4-9 45.4344 µW∆Pgzo 5.0421 µW –4.5656 µW∆Pgzo /Pm +10.08% –9.13% [0.001837)

= ±4.3%+0.1823 dB

Uncertainty in dB 0.4171 dB –0.4159 dB –0.1903 dB

(Equation 4-5)Mu (Pm – t)

KbmPgzo =

(Equation 4-4)Pm = mPsub + t

1/2

Worst-case uncertaintyOne method of combining uncertainties for power measurements in a worst-case manner is to add them linearly. This situation occurs if all the possiblesources of error were at their extreme values and in such a direction as to addtogether constructively, and therefore achieve the maximum possible deviationbetween Pm and Pgzo. Table 4-1 is a chart of the various error terms for thepower measurement of Figure 4-1. The measurement conditions listed at thetop of Table 4-1 are taken as an example. The conditions and uncertainties list-ed are typical and the calculations are for illustration only. The calculations donot indicate what is possible using the most accurate technique. The descrip-tion of most of the errors is from a manufacturer’s data sheet. Calculations arecarried out to four decimal places because of calculation difficulties with sever-al numbers of almost the same size.

Instrumentation uncertainty, i, is frequently specified in percent of full scale(full scale = Pfs). The contribution to magnification uncertainty is:

The several uncertainties that contribute to the total magnification uncertainty,m, combine like the gain of amplifiers in cascade. The minimum possible valueof m occurs when each of the contributions to m is a minimum. The minimumvalue of m (0.9762) is the product of the individual factors (0.988 * 0.998 * 0.99).The factors that contribute to the total offset uncertainty, t, combine like volt-age generators in series; that is, they add. Once t is found, the contribution indB is calculated from:

The maximum possible value Pgzo using Equation 4-5 and substituting the values of Table 4-1, is:

In Equation 4-8, the deviation of Kbm from the ideal value of one is used to calculate Pgzo max. In the same way, the minimum value of Pgzo is:

25

(Equation 4-6)(1 + i) Pfs

Pmmi =

(Equation 4-7)t

PmtdB = 10 log (1 ± )

(Equation 4-8)Mu max (Pm – tmin)

Kb min mminPgzo max =

= 1.0367 (50 µW + 0.275 µW)

(0.97) (0.9762)= 55.0421 µW = 1.1008 Pm

(Equation 4-9)Mu min (Pm – tmax)

Kb max mmaxPgzo min =

=0.9639 (50 µW – 0.275 µW)

(1.03) (1.0242)

= 45.4344 µW = 0.9087 Pm

26

The uncertainty in Pgzo may be stated in several other ways:

(1) As an absolute differential in power:

(2) As a fractional deviation:

Figure 4-2. Graph of individual contributions to the total worst-case uncertainty.

(3) As a percent of the meter reading:

(4) As dB deviation from the meter reading:

An advantage to this last method of expressing uncertainty is that this numbercan also be found by summing the individual error factors expressed in dB.

Figure 4-2 is a graph of contributions to worst-case uncertainty shows thatmismatch uncertainty is the largest single component of total uncertainty. Thisis typical of most power measurements. Magnification and offset uncertainties,the easiest to evaluate from specifications and often the only uncertaintiesevaluated, contribute less than one-third of the total uncertainty.

RSS uncertainty methodThe worst-case uncertainty is a very conservative approach. A more realisticmethod of combining uncertainties is the root-sum-of-the-squares (RSS)method. The RSS uncertainty is based on the fact that most of the errors ofpower measurement, although systematic and not random, are independent ofeach other. Since they are independent, it is reasonable to combine the individ-ual uncertainties in an RSS manner.

(Equation 4-10)∆Pgzo = Pgzo –Pm = µWmaxmin

+5.0421–4.5656

∆PgzoPm

=

+5.0421–4.5656

50

+0.1008–0.0913= (Equation 4-11)

+0.5

+0.4

+0.3

+0.2

+0.1

0

Magnification

Calibration factor

Mismatch

Instrument

Ref OscOffset

∆PgZo

Pm

∆Pgzo

Pm

+10.08–9.13

= (Equation 4-12)%100 ×

+0.4171–0.4159= (Equation 4-13)dB( )1.1008

0.9087dB = 10 log

Finding the RSS uncertainty requires that each individual uncertainty beexpressed in fractional form. The RSS uncertainty for the power measurementEquation 4-5 is:

Each of the factors of Equation 4-14, if not known directly, is also found by tak-ing the RSS of its several components. Thus:

Where m1, m2, and so forth are the reference oscillator uncertainty, the instru-mentation uncertainty, and so forth of Table 4-1. The extreme right hand col-umn of Table 4-1 shows the components used to find the total RSS uncertainty.The result is ±4.3 percent, which is much less than the worst case uncertaintyof +10.1 percent, –9.1 percent. One characteristic of the RSS method is that thefinal result is always larger than the largest single component of uncertainty.

A new international guide to the expression of uncertainty in measurement (ISO GUM)In recent years, the world’s metrology, standards and quality communities haveauthorized and implemented a new process for calculating and reporting theuncertainties of measurement. The process is based on a standard promulgatedby ISO in Geneva, Switzerland, an adjunct organization of IEC. This process isdocumented in ISO Guide to the Expression of Uncertainty in Measurement,often referred to as the GUM. [1]

The NCSL International (previously National Conference of StandardsLaboratories) in Boulder, CO, cooperating with the ANSI, adopted the ISO doc-ument as a U.S. National Standard, and introduced it in the U.S. as an industrydocument, ANSI/NCSL Z540-2-1996, U.S. Guide to the Expression ofUncertainty in Measurement. [2]

Both of the uncertainty standards operate within a larger metrology context,specified by ISO Guide 25, General Requirements for the Competence ofCalibration and Testing Laboratories. [3] This document was adapted to aU.S. version with the identical title, ANSI/NCSL Z540-1-1994. [4]

Over the last several years, the ISO has replaced ISO Guide 25 with ISO/IEC17025, General Requirements for the Competence of Calibration and TestingLaboratories. [4] It has been promulgated internationally, and achieved consid-erable standing in the test and standards communities.

In the U.S., the ANSI/NCSLI Standards Writing Committee determined thatworld metrology would be best served with a single standard for general labo-ratory requirements. It has adopted the ISO/IEC 17025 document as a U.S.National Standard in cooperation with the American Society of TestingMaterials (ASTM) and the American Society of Quality (ASQ). To meet theneeds of those U.S. users who rely on the older ANSI/NCSL Z-540-1-1994, thatstandard has been officially extended for 5 years.

∆PgzoPgzo

= [( )2+ ( )2

+ ( )2+ ( )2]

1/2∆MuMu

∆KbKb

∆m

m

∆t

Pm

(Equation 4-14)

∆m

m= [( )2

+ ( )2+ • • •]1/2∆m1

m1

∆m2m2

(Equation 4-15)

27

Because of its international scope of operations, Agilent has moved quickly toadopt ISO/IEC 17025 in lieu of its previous commitment to ANSI/NCSL Z-540-1.As a result, most of Agilent’s production and support operations are moving tooffer optional product-specific test data reports compliant to 17025. Agilenthas assigned Option 1A7 to all of its products which meet the ISO 17025-compliant processes. Option 1A7 will assure compliance with 17025 for newproducts shipped from the factory and Agilent will provide for support re-calibrations to the same 17025-compliant processes, data and testing.

Generally, the impact of the ISO GUM is to inject a little more rigor and standardization into the metrology analysis. Traditionally, an uncertainty wasviewed as having two components, namely, a random component and a system-atic component. Random uncertainty presumably arises from unpredictable orstochastic temporal and spatial variations of influence quantities. Systematicuncertainty arises from a recognized effect or an influence that can be quanti-fied.

The ISO GUM groups uncertainty components into two categories based ontheir method of evaluation, Type A and Type B. These categories apply touncertainty, and are not substitutes for the words “random” and “systematic.”Some systematic effects may be obtained by a Type A evaluation while in othercases by a Type B evaluation. Both types of evaluation are based on probabilitydistributions. The uncertainty components resulting from either type are quan-tified by variances or standard deviations.

Briefly, the estimated variance characterizing an uncertainty componentobtained from a Type A evaluation is calculated from a series of repeatedmeasurements and is the familiar statistically estimated variance. Since stan-dards laboratories regularly maintain histories of measured variables data ontheir standards, such data would usually conform to the Type A definition.

For an uncertainty component obtained from a Type B evaluation, the estimat-ed variance, u2, is evaluated using available knowledge. Type B evaluation isobtained from an assumed probability density function based on the belief thatan event will occur, often called subjective probability, and is usually based ona pool of comparatively reliable information. Others might call it “measurementexperience.” Published data sheet specifications from a manufacturer wouldcommonly fit the Type B definition.

Readers who are embarking on computing measurement uncertainties accord-ing to the ISO GUM should recognize that the above-mentioned documents mayseem relatively simple enough in concept, and they are. But for more complexinstrumentation the written specification uncertainties can often depend onmultiple control settings and interacting signal conditions.

Impedance bridges, for example, measure parameters in complex number format. Network and spectrum analyzers have multi-layered specifications.Considerable attention is being expended by test and measurement organiza-tions to define and characterize these important extensions of the basic GUM.[5, 6, 7]

28

Power measurement model for ISO processBeginning with the measurement Equation 4-5, and including power sensor linearity term P,

The determination of m is through the calibration process. During calibration,Pgzo is set to the known power, Pcal. Substituting Pcal for Pgzo and rearrangingEquation 4-16, the equation for m is:

where:

m = power meter gain termMuc = gain due to the mismatch between the sensor and the internal

calibration power sourcePmc = power level indicated by the power meter during calibrationt = power meter zero offsetKc = power sensor calibration factor at the calibration frequencyPcal = power delivered to a Zo load by the power meter calibration output

In equations 4-16 and 4-17, t represents the power meter zero offset.In the glossary of Fundamentals Part I, t is described as the sum of the zeroset value, Zs; zero carryover, Zc; noise, N; and drift, D. However, assuming thezero procedure occurs just prior to calibration, D is zero during calibration,whereas D is non-zero during power meter measurements. To allow t to repre-sent the same quantity in the equation for PgZo and m, the equation for t isdefined as:

where,Zs = power meter zero set valueZc = power meter zero carryover valueN = power meter noise

and the equation for PgZo is redefined as

where D = power meter drift.

29

(Equation 4-16)Mu (Pm – t)PKbm

Pgzo =

(Equation 4-17)Muc (Pmc – t)KcPcal

m =

(Equation 4-18)t = Zs + Zc + N

(Equation 4-19)Mu (Pm – (t+D))

PKbmPgZo =

Equation 4-19 is the measurement equation for a power meter measurement.There are eleven input quantities that ultimately determine the estimated value of Pgzo. These are Mu, Pm, D, Kb from Equation 4-19; Zs, Zc, N fromEquation 4-18; and Muc, Pmc, Kc, and P cal from Equation 4-17. It is possible tocombine equations in order to represent Pgzo in terms of the 11 defined inputquantities. This is a relatively complicated derivation, but the result is theuncertainty in terms of the 11 quantities:

Solving with some nominal values of several input quantities simplifies Equation 4-20,

Mu = 1Muc = 1Pmc = PcalZs = 0Zc = 0N = 0D = 0t = 0m = 1/Kc

The following Table 4-2 summarizes the various uncertainties shown inEquation 4-21.

30

(Equation 4-20)

u2 (Mu)

Mu2u2(Pgzo) = Pgzo

2 [ +u2 (Pm)

(Pm– (t + D))2+

u2 (D)

(Pm– (t + D))2+ u2 (Kb)

Kb2

+u2 (Muc)

Muc2

+u2 (Pmc)

(Pmc– t)2 + u2 (Kc)

Kc2

+u2 (Pcal)

Pcal2

+ ( ( )1

(Pm– (t+D))2+ 1

(Pmc– t)2-

2

KcPcalm(Pm– (t+D))) u2 (Zs) + u2 (Zc) + u2(N)

(Equation 4-21)

u2 (Mu)u2(Pgzo)

Pgzo2

+ u2 (Pm)

Pm2

+ + u2 (Kb)

Kb2

+ u2 (Pmc)

Pmc2

+ u2 (Kc)

Kc2 +

u2 (Pcal)

Pcal2 ( 1

Pm–

1

Pcal)2

(u2(Zs) + u2(Zc) + u2(N))

u2 (D)

Pm2

u2 (Muc)

+

+

u2 (Pl)

Pl2

=

+

]

31

Standard uncertainty of the mismatch modelThe standard uncertainty of the mismatch expression, u(Mu), assuming noknowledge of the phase, depends upon the statistical distribution that bestrepresents the moduli of Γg and Γ.

Combining equations 2-21 and 2-22, the power dissipated in a load whenΓ is not 0 is:

The numerator in Equation 4-22 is known as mismatch loss, and the denomina-torrepresents the mismatch uncertainty:

Mu is the gain or loss due to multiple reflections between the generator andthe load. If both the moduli and phase angles of Γg and Γ are known, Mu canbe precisely determined from Equation 4-23. Generally, an estimate of the moduli exists, but the phase angles of Γg and Γ are not known.

Table 4-2. Standard uncertainties for the Z540-2 process.

Standard uncertainty Source

u(Mu) Mismatch gain uncertainty between the sensor and the generator. The standard uncertainty is dependent upon the reflection coefficients of the sensor and the generator. Refer to the mismatch model. Reflection coefficients may have different distributions as shown in Figure 4-3.

u(Muc) Mismatch gain uncertainty between the sensor and the calibrator output of the power meter. The standard uncertainty is dependent upon the reflection coefficients of the sensor and the calibrator output. Refer to the mismatch model. Note: the calibrator output reflection coefficient is not a specified parameter of the E4418A power meter. AN64-1 suggests ρg = 0.024.

u(Pm) Power meter instrumentation uncertainty.

u(Pmc) Power meter instrumentation uncertainty (during calibration)

u(D) Power meter drift uncertainty.

u(Kb) Sensor calibration factor uncertainty. Typically, the value of the uncertainty is reported along with the calibration factor by the calibration laboratory or the manufacturer.

u(Kc) Sensor calibration factor uncertainty at the frequency of the power meter calibrator output. If the sensor is calibrated relative to the associated calibrator output frequency, Kc = 1 and u(Kc) = 0.

u(P) Power sensor linearity, which is related to power range. Generally negligible on lower ranges but has higher uncertainty at high power levels.

u(Pcal) Calibrator output power level uncertainty.

u(Zs) Power meter zero set uncertainty.

u(Zc) Power meter zero carryover uncertainty.

u(N) Power meter and sensor noise uncertainty.

Pd = Pgzo (Equation 4-22)1 – |Γ|2

|1 – ΓgΓ|2

(Equation 4-23)|1 – Γg Γ|2Mu =

32

Consider two cases:Case (a): Uniform Γ, uniform phase distribution.See Figure 4-3 (a). The moduli of Γg and Γ are each less than a specified value;Γg and Γ each lie within a circle of radius, Γ. Assuming Γg and Γ have equalprobability of lying anywhere within the circle, the standard uncertainty of Muis: (This results in uniform density.)

1u(M u ) = √2

x maximum |Γg| x maximum |Γ|

Case (b): Constant ρ, uniform phase distribution.See Figure 4-3 (b). An estimate of the moduli of Γg and Γ are known; Γg and Γeach lie on a circle of radius Γ. Assuming Γg and Γ have equal probability oflying anywhere on the circle, (equal probability of any phase), the standarduncertainty of Mu is:[8]

u(Mu) = √2 x |Γg|x|Γ|

Figure 4-3. When the reflection coefficients of the generator and load are not known, the user mayestimate probabilities of the mismatch uncertainty according to these two cases: (a) both Γ lieinside the circle with uniform density. (b) both Γ lie on the circle with uniform phase density.

Example of calculation of uncertainty using ISO modelRecognizing that each uncertainty calculation must meet a particular measur-ing requirement, the user will need to structure their calculations for appropri-ate conditions. This following measurement situation reflects some assumedand stated conditions for each of the parameters. The power meter is assumedto be the Agilent E4418B power meter, and the power sensor is assumed to bethe E9300A power sensor.

Measurement conditions for calculation: Unknown CW power, 2 GHz, 50 microwatt level (–13 dBm).

Calculation comments for each parameter:

u(Mu) Uncertainty of mismatch gain between sensor and generator at 2 GHz. Use case (a) and assume generator reflection coefficient specification (from data sheet) is |Γg| = 0.1 (uniform density distribution). Assume the E9300A sensor cal data shows a measured value of |Γ| = 0.1 (uniform distribution of phase).

Use mismatch gain equation of Mu = |1 ± Γg Γ |2

Since each Γ has a different distribution, use a Monte Carlo simulation.

u(Muc) Uncertainty of mismatch gain between sensor and 50 MHz calibratorsource. Use case (a) and assume source reflection coefficient specification (from data sheet) is |Γg| = 0.024. E9300A sensor cal data shows a measured value of |Γ| = 0.1 (uniform distribution of phase). Use mismatch gain equation as above.

Γ Γ

u(Muc) Muc

= =0.024 x 0.1 x 12

0.17% (1–sigma)

u(Mu) Mu

= =0.1 x 0.1 x 12

0.7% (1–sigma)

(a) (b)

33

u(Pm) E4418B power meter instrumentation uncertainty is specified at ± 0.5 percent (rectangular distribution). Use 3 for divisor.

u(Pmc) E4418B power meter uncertainty during calibration. Specified at ±0.5 percent (rectangular distribution).

u(D) E4418B power meter drift uncertainty due to sensor drift. Assume constant temperature, measurement taken one hour after calibration. From data sheet E9300A sensors are ±150pW(rectangular distribution).

u(Kb) E9300A power sensor calibration factor uncertainty at 2 GHz. From the calibration certificate, specification is ±1.7 percent(Gaussian distribution, 2-sigma).

u(Kc) E9300A power sensor cal factor uncertainty at 50 MHz is assumed to be 0 since it is referred to the internal calibration source.

u(Pl) E9300A power sensor linearity uncertainty. For the 100 µW assumed range, this is specified for 25 ±10 °C as ±3 percent(assume Gaussian distribution is 2−sigma).

u(Pcal) 50 MHz calibrator power reference output uncertainty is specified at0.6 percent, RSS, for 2 years (25 ±10 °C). Gaussian distribution is 2-sigma. (new specification)

u(Zs) E4418B power meter zero set uncertainty is specified at ±500pW(rectangular distribution).

1Pm

=– =x– 0.0005% (1–sigma)u (Zs)1

Pcal

500 x 10–12

50 x 10–6 31

10–3

1

u(Pcal)Pcal

= = 0.3% (2–sigma)0.0062

u(P1)P1

= = 1.5% (1–sigma)0.032

u(Kc)Kc

= 0

u(Kb)Kb

= = 0.85% (1–sigma)0.0172

u(D)Pm

= =x 0.017% (1–sigma)150 x 10–12

50 x 10–6 31

u(Pmc)Pmc

= = 0.3% (1–sigma)0.0053

u(Pm)Pm

= = 0.3% (1–sigma)0.0053

u(Zc) E4418B power meter zero carryover is included in the overall instrument uncertainty specification, since there are no ranges as such in this meter. For other power meters this would need to be considered.

u(N) E4418B power meter noise uncertainty is ±700 pW and negligible at the 50 mW power level.

Using the above comments, Table 4-3 summarizes the various uncertainty fac-tors. Each factor is normalized to a one sigma value. In the case of a data sheetspecification, the divisor factor used to convert to one sigma is square root ofthree. These sigma values are added in RSS fashion and then multiplied withthe coverage factor. The coverage factor is a guard band number, typically twois used, but experience and knowledge of the measurement process allows forthe user to establish any other value.

34

Symbol Source of uncertainty Value ±% Probability distribution Divisor D(Kx)

Mu Mismatch gain between |Γg| = 0.1 |Γg| - uniform density (1) 0.7%generator and sensor |Γs| = 0.1 |Γs| - uniform phase

Muc Mismatch gain between |Γg| = 0.024 |Γg| - uniform density (1) 0.17%calibration source and sensor |Γs| = 0.1 |Γs| - uniform phase

Pm Power meter instrumentation 0.5% rectangular √ 3 0.29%

Pmc Power meter instrumentation 0.5% rectangular √ 3 0.29% during calibration

D Power meter drift ±150 pW rectangular √ 3 0.017%

Kb Sensor calibration factor 1.7% Gaussian 2 0.85%

Kc Sensor calibration factor at 50 MHz 0 rectangular — 0

Pl Power sensor linearity 3.0% Gaussian 2 1.5%

Pcal Calibrator output power 0.6% Gaussian 2 0.3%

Zs Power meter zero set ±500 pW rectangular √ 3 0.0005%

Zc Power meter zero carryover 0 rectangular √ 3 0

N Power meter and sensor noise ±700 pW rectangular √ 3 0.0007%

Combined uncertainty—RSSed 1.94%

Expanded uncertainty Coverage factor K = 2 3.88%

Table 4-3. Worksheet for uncertainties calculation using ISO process.

(1) Monte Carlo simulation

1Pm

=– =x– 0.0007% (1–sigma)u (N) 1Pcal

700 x 10–12

50 x 10–6 31

10–3

1

1Pm

=– 0u (Zc)1

Pcal

35

[1] "ISO Guide to the Expression of Uncertainty in Measurement," International Organization for Standardization, Geneva, Switzerland, ISBN 92-67-10188-9, 1995.

[2] “U.S. Guide to the Expression of Uncertainty in Measurement,” ANSI/NCSL Z540-2-1996, NCSL International, Boulder, CO.

[3] ISO Guide 2, “General Requirements for the Competence of Calibration and Testing Laboratories,” ISO Guide 25, International Organization for Standardization, Geneva, Switzerland. This same title now applies toISO/IEC EN 17025.

[4] “General Requirements for the Competence of Calibration and Testing Laboratories,”ANSI/NCSL Z540-1-1994, NCSL International, Boulder, CO.

[5] Moens, Jon C. “Software Technology to Support Measurement Uncertainty for Complex Electronic Test Equipment,”NCSLI 2002 San Diego Conference, NCSL International, Boulder, CO.

[6] Kasuga, Makoto, “Adapting The ISO GUM For A Practical Approach To Uncertainty Calculation Of Complex Numbers,” NCSLI 2002 San Diego Conference, NCSL International, Boulder, CO.

[7] Abell, David and Moens, Jon C., "Meeting ISO 17025 Requirements for Complex Electronic Test Equipment," Cal Lab Magazine, Oct/Dec, 2002.

[8] Harris, I.A., and Warner, F.L., “Re-examination of Mismatch Uncertainty when Measuring Microwave Power and Attenuation,” Proceedings of the British IEE, Vol. 128, pp 35-41, Feb 1981.

General References

NAMAS NIS 3003, “The Expression of Uncertainty and confidence in Measurement for Calibrations,” Edition 8,NAMAS Executive, National Physical Laboratory, Teddington, TW11 0LW, England, 1995.

B. N. Taylor and C. E. Kuyatt, “Guidelines for Evaluating and Expressing the Uncertainty of NIST MeasurementResults,” NIST Technical Note 1297, National Institute of Standards and Technology.

NCSL Recommended Practice RP-12, “Determining and Reporting Measurement Uncertainties,” National Conference of Standards Laboratories.

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AgilentFundamentals of RF and MicrowavePower Measurements (Part 4)

Application Note 1449-4

An Overview of Agilent Instrumentation forRF/Microwave Power Measurements

2

I. Introduction ........................................................................................ 3

II. A Review of Various Power MeasuringInstrumentation ................................................................................ 4

Instrument alternatives for measuring RF/microwave power ............ 4Types of superheterodyne instruments for measuring power ............ 5Power measurement considerations for superheterodyne

instruments .............................................................................................. 6Power measurement considerations for test-set-type instruments .... 8

III. Power Sensor/Meter Methods and Comparisons ....................................................................................... 9

Accuracy vs. power level ........................................................................... 9Frequency range and SWR (reflection coefficient)............................... 12Waveguide sensor calibration ................................................................... 13Speed of response at low signal levels .................................................... 13Automated power measurement .............................................................. 14Susceptibility to overload.......................................................................... 14Signal waveform effects ............................................................................. 16Computed data and analyzer software package.................................... 17

IV. Capabilities Overview of Agilent Sensors and Power Meters.......................................................................... 18

An applications overview of Agilent power sensors ............................. 18A capabilities overview of Agilent power meters .................................. 19

Fundamentals of RF and Microwave PowerMeasurements Part 1: Introduction to Power, History, Definitions, International Standards, andTraceability, AN 1449-1, literature number 5988-9213EN

Part 1 introduces the historical basis for power measurements, and providesdefinitions for average, peak, and complex modulations. This applicationnote overviews various sensor technologies needed for the diversity of testsignals. It describes the hierarchy of international power traceability, yield-ing comparison to national standards at worldwide National MeasurementInstitutes (NMIs) like the U.S. National Institute of Standards andTechnology. Finally, the theory and practice of power sensor comparisonprocedures are examined with regard to transferring calibration factors anduncertainties. A glossary is included which serves all four parts.

Part 2: Power Sensors and Instrumentation, AN 1449-2, literature number 5988-9214EN

Part 2 presents all the viable sensor technologies required to exploit theusers’ wide range of unknown modulations and signals under test. Itexplains the sensor technologies, and how they came to be to meet certainmeasurement needs. Sensor choices range from the venerable thermistor tothe innovative thermocouple to more recent improvements in diode sensors.In particular, clever variations of diode combinations are presented, whichachieve ultra-wide dynamic range and square-law detection for complexmodulations. New instrumentation technologies, which are underpinnedwith powerful computational processors, achieve new data performance.

Table of Contents

For user convenience, Agilent’sFundamentals of RF andMicrowave Power Measurements,application note 64-1, literaturenumber 5965-6330E, has beenupdated and segmented into fourtechnical subject groupings. The following abstracts explain how thetotal field of power measurementfundamentals is now presented.

3

Part 3: Power Measurement Uncertainty per International GuidesAN 1449-3, literature number 5988-9215EN

Part 3 discusses the all-important theory and practice of expressing measure-ment uncertainty, mismatch considerations, signal flowgraphs, ISO 17025, andexamples of typical calculations. Considerable detail is shown on the ISO17025, Guide for the Expression of Measurement Uncertainties, has becomethe international standard for determining operating specifications. Agilenthas transitioned from ANSI/NCSL Z540-1-1994 to ISO 17025.

Part 4: An Overview of Agilent Instrumentation for RF/Microwave Power Measurements,AN 1449-4, literature number 5988-9216EN

Part 4 overviews various instrumentation for measuring RF and microwavepower, including spectrum analyzers, microwave receivers, network analyzers,and the most accurate method, power sensors/meters. It begins with theunknown signal, of arbitrary modulation format, and draws application-oriented comparisons for selection of the best instrumentation technology andproducts.

Most of the note is devoted to the most accurate method, power meters andsensors. It includes comprehensive selection guides, frequency coverages, con-trasting accuracy and dynamic performance to pulsed and complex digital mod-ulations. These are especially crucial now with the advances in wirelesscommunications formats and their statistical measurement needs.

The purpose of the new series of Fundamentals of RF and Microwave PowerMeasurements application notes, which were leveraged from former note 64-1, is

1) Retain tutorial information about historical and fundamental considerations of RF/microwave power measurements and technology which tend to remain timeless.

2) Provide current information on new meter and sensor technology.

3) Present the latest modern power measurement techniques and test equipment that represents the current state-of-the-art.

Fundamentals Part 4, Chapter 2 presents an overview of various instrumenta-tion for measuring RF and microwave power. Those methods include spectrumanalyzers, microwave receivers, vector signal analyzers, and wireless and cellu-lar test sets, among others. Naturally, it also includes the most accuratemethod, power sensors and meters. It begins with the unknown signal of arbi-trary modulation format and draws application-oriented comparisons for selec-tion of the best instrumentation and technology.

Chapter 3 reviews other applications and measurement considerations ofpower sensors and meters not covered in the technology presentations ofFundamentals Part 2. These include such matters as susceptibility to overload,automated data functionality, etc.

Chapter 4 provides an overview of the entire line of Agilent sensors andmeters. It includes a functionality chart for compatibility of sensors withmeters. Some early sensor technologies like thermocouples work with allAgilent meters, while new peak and average sensors are only compatible withthe EPM-P meter. Signal application charts and frequency and power rangecapabilities are all presented in tabular format.

Note: In this application note, numerous technical references will be made tothe other published parts of the series. For brevity, we will use the formatFundamentals Part X. This should insure that you can quickly locate the con-cept in the other publication. Brief abstracts for the four-part series are provid-ed on the inside front cover.

Fundamentals of RF andMicrowave PowerMeasurements, continued

I. Introduction

4

Instrument alternatives for measuring RF/microwave powerIngenuity has dominated the inventive progress of RF/microwave power meas-urements. One clever method mentioned in Fundamentals Part 1, was theWorld War II (WWII) legend of Russell Varian drilling a tiny hole in his experi-mental klystron cavity and using a fluorescent screen to indicate whether theoscillation was on or off. Other non-instrument methods followed, such as the“water-load” calorimeter, which threaded a glass tube diagonally through a rectangular waveguide. By measuring the heat rise and flow rate of the waterstream, the transmitter power could be computed. That method served both asa high-power termination for the tube as well as a power measuring process.

Serious power measuring instrumentation came out of the WWII developmentsof radar, countermeasures and communications system demands. Crystaldetectors furnished a crude method of indicating and metering power, butsince they were fragile, the high power signals required precision attenuationbefore applying to the sensor. Bolometers, which utilized tiny power-absorbingelements, terminated the unknown power and heated up. By monitoring orsensing the heat buildup, highly accurate measurements could be realized onunknown power over wide frequency ranges.

Microwave superheterodyne-type receivers were always capable of sensingRF/microwave power because their inherent purpose was the detection anddisplay of power versus frequency. Some called them “frequency-domain oscil-loscopes.” While most such receivers were used for system purposes, somewere used for research and instrumentation. The main advantage of usingsuperheterodyne-type instruments was and is the ability to obtain power over aspecified and tuned bandwidth, whereas power sensors measure total poweracross their entire specified frequency range.

Early spectrum analyzers were basically uncalibrated for absolute power. Anunknown signal under test could be measured by comparison with a knownpower from a calibrated signal generator, where the microwave receiver wasused only as a comparison sensor. The calibrated reference signal generator signal would be adjusted to be equal to the unknown.

II. A Review of Various Power Measuring Instrumentation

Types of superheterodyne instruments for measuring powerIn 1964, Agilent introduced the HP 851/8551 as the first “power-calibrated”spectrum analyzer, available as a commercial product. This offered a consider-able advance in frequency and power characterization of unknown signals.While we look back now at such relatively crude instruments with relativelypoor accuracy specifications, they were the wonders of their time.

Enormous progress has been made in improved accuracy and functionality inthe intervening years. Spectrum analyzers have gained digital precision in bothfrequency and power level because of sophisticated digital signal processing(DSP) microcircuitry and more precise components such as highly-linear ampli-fiers. Meantime, a number of other types of instrumentation have also beenconfigured to make excellent measurements of power levels, not just for simplemodulated signals, but for all of the new modulation formats common to themodern communications and wireless systems.

Here is a list of typical instrument types, based on a superheterodyne blockdiagram, that are designed to make signal power measurements:

• spectrum analyzers• vector signal analyzers• calibrated microwave test receivers• other instruments

Another variety of instrumentation for signal power measurements is the popu-lar and ubiquitous wireless, cellular, and communications test sets. For thepurposes of this application note, a test set is considered to contain an array oftest functions that can characterize a complete operating communications system, both transmitter and receiver. It provides precision calibrated andadjustable test signals with system-specific modulation formats to test the system's receiver portion, and it contains power measurement capability tocharacterize the performance of the system's transmitter.

A typical wireless test set would be the Agilent E5515C mainframe and E1962Btest application software. For the most precise power measurement, such a testset uses directional bridges at its input to feed the power to a thermal powerdetector as well as a “fast power detector.” Other portions of the test set feature demodulation downconversion and measurement downconversion,which utilize the superheterodyne processes.

5

6

Power measurement considerations for superheterodyne instruments [1]As with most things in life, a required measurement of a system's output powercomes with predictable tradeoffs. Simply stated, the power sensor/power metermethod always offers the best measurement accuracy, but it measures all thepower at the input to the sensor - it is not frequency-selective. Further, thepower meter method measures true average power, even of complex digitalmodulation formats, some of which look like noise. Even peak power sensors,which are based on detection curves ranging from square law to linear, are dig-itally compensated to present full averaging of power. Power meter instrumen-tation now also provide time-selective measurements, meaning the user can settime gates for bracketing the time period over which a power measurement ismade.

Superheterodyne-type instruments, on the other hand, offer versatile frequencyselectivity, as well as considerable flexibility on the measurement of signalpower, also including all the newer and complex modulation formats. In fact,one of the main reasons that superheterodyne-type instruments are selected isto provide a selectable bandwidth for a power measurement. A typical require-ment would be for measuring integrated channel power in the presence ofother system channel power.

Since their block diagrams are typically double or triple downconversion, thereare important measurement considerations of resolution bandwidth, types offinal detection and, more-importantly, the particular DSP algorithms used tofurnish output data for the power level. [2]

Figure 2-1 shows a block diagram of a typical modern spectrum analyzer. Theunknown signal receives a user-set attenuation, usually has some pre-selectionfiltering, then gets downconverted to an IF (intermediate frequency) amplifier.Modern analyzers are designed with less and less IF amplification and moreand more powerful DSP microcircuits further forward in the IF signal path.Those DSPs can now sample the IF signals and their modulation envelope withextremely high sampling rates.

Figure 2-1. Block diagram of a typical traditional superheterodyne spectrum analyzer.

Whatever signal conditioning strategy is used, the end result is a display pres-entation of the modulation envelope of the signal under test. It should be notedthat this is all carried out as linear detection, meaning the display is a voltage-related parameter. Logarithmic amplifiers or logarithmic data processing, asshown in Figure 2-1, converts the display to a dB display at the user command.Such display formats are especially useful for ultra-wide dynamic amplituderanges, for example 10 dB per division.

Pre-selectoror low pass

filter

Crystalreference

LogAmp

RF inputattenuator

MixerIF filter

Detector

Videofilter

Localoscillator

Sweepgenerator

IF gain

Inputsignal

CRT display

7

To measure power, consider the CW power spectrum of Figure 2-2(a). The display is produced by sweeping frequency (horizontal scale) across the CWunknown power. If the resolution bandwidth (RBW) set by the user is widerthan the spectral components of the unknown CW, then the highest point onthe display will represent the true CW power.

Figure 2-2. A spectrum analyzer's resolution bandwidth setting can be adequate for a single CWpower measurement (a), but for digitally modulated signals it is either inadequate (b) or erroneouslyadds power in from the adjacent channel (c).

Now, consider an unknown signal as in Figure 2-2(b), which is a QAM (quadra-ture-amplitude-modulation) format with an 8 MHz bandwidth. This is consider-ably wider than the filter’s RBW of 3 MHz, and therefore cannot integrate allthe 8 MHz power.

If you select a RBW setting that is larger than the unknown signal, will thatintegrate the unknown broadband signal format? Well, no, because the RBW filter is Gaussian shape, and while it may be wide enough to enclose theunknown signal at its –3 dB points, out at the noise floor of the RBW, its widthwill enclose a lot of noise as well as perhaps other adjacent channels of power.This is shown in Figure 2-2(c) as a QAM signal of 2 MHz bandwidth, easilyenclosed by the 3 MHz RBW of the analyzer, but also allowing in unwantedsideband channels and noise.

3-MHzRBW

Power

Frequency sweep

2-MHz QAMsignals

3-MHzRBW

Power

Frequency sweep

8-MHz QAMsignal

Frequency sweep

CW signal

Power

RBW

(a)

(c)

(b)

8

The upshot of this analysis is that the measurement needs to be made with anarrower RBW, such that the skirts of its filter are steep and help define theskirts of the power spectrum of the unknown signal under test. Powerful soft-ware computation routines of modern analyzers take all this into considera-tion, realizing that the user simply wants to measure the integrated “channelpower” of a wireless channel, for example 8 MHz, and reject the channel powerof the adjacent channel which is also on the air.

The analyzer performs this task internally by using the proper RBW settings,and making corrections for what is called the equivalent noise power band-width (ENPBW) using a correction factor for Agilent ESA analyzers of 1.128.The internal computations for pre-set channels can also be pre-determinedsince the performance parameters for industry standard wireless formats areknown, for example CDMA, TDMA, etc. Suffice to say that instrumentation ana-lyzers based on the superheterodyne principle have powerful characterizationcapabilities, and generally can provide channel power readings with accuracieson the order of ±1 dB or less.

When considering the tradeoffs in specifying power instrumentation, a lot willdepend on the needs of the measurement requirement and the condition of theunknown signal. Is it accompanied by multiple channels? Is the lowest uncer-tainty required? Does the unknown signal format contain time-domain charac-teristics that need to be time-selectively sorted out by the Agilent EPM-P andP-Series gated power capabilities?

Power measurement considerations for test-set-type instrumentsA modern wireless test set provides two paths for measuring unknown power.The first was mentioned above, whereby the unknown signal is directionally-bridged off right at the input terminal and applied to either a thermal detectoror a peak detector. This assures that the best possible accuracy is maintainedfor characterizing the unknown. Actual performance specifications are quotedin considerable detail for various frequency bands and power levels. For a general ballpark figure, specified uncertainties range from ±4.2 percent to ±7.5 percent (typical ±3.0 percent). Such specifications, of course, state only the instrument performance, other uncertainties such as mismatch and powerreference details would have to be computed for given measurement environ-ments and requirements. Specifications differ for the thermal detector and thepeak detector.

The other power measurement function of test sets is the “tuned channel powermeasurement.” This is the one that utilizes the complete superheterodynedownconversion signal chain, such that it measures and computes “channelpower,” by rejecting adjacent channel power in operating systems. Typicalmeasurement uncertainty for such system signal characterization is stated inthe ± 1 dB ranges. Calibrating against a known power level signal furnishedfrom within the test set enhances accuracy for this function. Again, additionaluncertainties would need to be considered for mismatch and other additives.

[1] Mill, Alistair, Measuring Digital Carrier Power with a Spectrum Analyzer, Test & Measurement World Europe, April/May 2000.

[2] Agilent Technologies, Spectrum Analyzer Basics, Agilent Application Note 150, literature number 5952-0292.

9

Assume that the user’s power measurement requirements have been analyzed.The outcome of that analysis shows that power sensor/meter is the preferredmethod. All of the previous discussion in Fundamentals Part 2 on sensor andmeter technology still leaves choices for which power meter and sensor willprovide the best or fastest or most accurate solution. As was seen, each averageor peak and average sensor and meter technology has some advantages overthe others, yet there is an optimum choice, and that is the purpose for thischapter.

Factors such as cost, frequency range, the range of power levels to be meas-ured, the importance of processing and capturing data, accuracy, speed ofmeasurement, and the skill of the personnel involved take on varying degreesof importance in different situations. This chapter compares the measurementsystems from several aspects to aid in the decision-making process for anyapplication. At the end, a signal applications chart profiles sensors best suitedfor particular modulation formats. Other charts briefly overview the measure-ment capabilities of the sensor and power meter families now available fromAgilent.

Accuracy vs. power levelThis comparison of power measuring systems demonstrates the measurementuncertainty and power range of several equipment selections. The EPM Seriespower meters and E Series sensors are emphasized, although several existingsensors are included. The EPM-P meters and E9320A peak and average sensorswere not included in this comparison exercise since they require other consid-erations outlined in Fundamentals Part 2, Chapter V.

Figure 3-1 shows plots of the root-sum-of-squares (RSS) uncertainty whenmeasuring power for a common condition at various levels from –70 to +20 dBm.The measurement conditions were assumed for a CW signal at 2 GHz and asource SWR of 1.15, and data sheet specifications.

The three parts of this figure show a comparison of three common combina-tions of power meter and sensor:

a) Agilent 432A analog power meter plus 8478B thermistor sensor.

b) Agilent E4418B digital power meter plus 8481A thermocouple and 8484D diode sensor.

c) Agilent E4418B digital power meter plus E4412A extended dynamic range power sensor.

The data for Figure 3-1 was computed using a commercially-availablemathematics simulation software product called MathCad. To present theseoperating performances under typical present-day conditions, the ISO uncer-tainty combining process of Fundamentals Part 3 was used for the MathCadcalculations. Results are approximate, although they are entirely suitable forthese comparison purposes.

The reason for presenting these overall measurement uncertainties in this for-mat is that, as far as the user is concerned, there is little need to know whetherthe sensor works on the diode principle or on the thermocouple principle. Withthe introduction of the new extended-range PDB diode sensors, a singleE4412A sensor can achieve the –70 to +20 dBm power range, which previouslyrequired a combination of diode and thermocouple sensors.

III. Power Sensor/ Meter Methods andComparisons

10

The top graph of Figure 3-1 describes the thermistor sensor/meter combinationand is shown mostly for reference. With the decreasing applications of thermis-tor-type sensors, the primary need for understanding their theory and practiceis that they are used as power transfer devices for metrology round robins.They also find use in transferring a power reference from a higher-accuracyechelon or national standards labs to operating labs. In the DC substitutionprocess, 432 instrumentation error is substantially reduced because the substi-tution DC power can be measured with precision digital voltmeters.

A comparison of the top two graphs of Figure 3-1, (a) and (b), shows that theuncertainties of the thermocouple and diode-based systems (b) are somewhatless than the thermistor-based systems (a). At this 2 GHz calculation frequency,the thermocouple and diode sensors have the better SWR (see Figure 3-2), butthe thermistor system, being a DC substitution system, does not require apower reference oscillator and its small added uncertainty. These two effectstend to offset each other for this application. The significant advantage of theE4418B power meter measurement is the performance flexibility of being ableto use the large installed base of all the other Agilent family of thermocoupleand diode sensors.

The third graph of Figure 3-1, (c), for the E4418B power meter and E4412Aextended dynamic range sensor, immediately shows that even with the sensor’swide dynamic measurement range from –70 to +20 dBm, it provides approxi-mately equivalent uncertainties. The dashed portion of the E Series sensorcurve (0 to +20 dBm) represents nominal high-power cal factor uncertainty lim-itations imposed by the sensor calibration system. Refer to the latest sensortechnical specifications to determine actual uncertainties for your particular application.

Figure 3-1. RSS uncertainty vs. dynamic power range from data sheet specs for source SWR = 1.15(ρs =0.07) and f = 2 GHz: (a) Analog thermistor mount system(432A plus 8478B). (b) E4418B digitalpower meter system using 8481D diode and 8481A thermocouple sensors. (c) E4418B digital powermeter and E4412A PDB extended-range sensor. RSS-combining method is the same as used inFundamentals Part 3.

20

15

10

0-70 -60 -50 -40 -30 -20 0-10

5

Power dBm

Uncertainty %

(b)

20

15

10

0-70 -60 -50 -40 -30 -20 0-10

5

Power dBm

Uncertainty %

20

15

10

0-70 -60 -50 -40 -30 -20 0-10 +10 +20

5

Power dBm

Uncertainty %

(a)

(c)

8481A8481D

+10 +20

+10 +20

11

While most modern power meter designs have utilized digital architectures,analog-based meters, such as the 432A, are still available. Analog meter meas-urements are limited by the mechanical meter movement of the instrument thatrequires uncertainty to be stated in percent of full scale. Thus, at the low endof each range, the uncertainty becomes quite large when expressed as a per-cent of the reading. Digital systems are free of those problems and, with properdesign and an adequate digital display resolution, provide better accuracy.

The instrumentation accuracy for a digital meter is specified as a percent ofthe reading instead of as a percent of full scale. This means that at the point ofeach range change, there is not a big change in uncertainty for the digitalmeter. This effect can be seen in the max-min excursions of the sawtooth-likecurves of the analog meter shown in Figure 3-1 (a). For this reason, the digitalpower meter does not need as many ranges; each digital range covers 10 dBwith little change in accuracy across the range.

One application advantage attributed to analog meters is the “tweaking” functions where an operator must adjust some test component for optimum ormaximum power. Digital displays are notoriously difficult to interpret for “maximizing or minimizing” readings, so the display of the E4418B powermeter features an analog scale in graphic display format, which provides forthe “virtual-peaking” function.

It should be recognized that the accuracy calculations of Figure 3-1 are basedon specification values. Such specifications are strongly dependent on the manufacturers’ strategy for setting up their specification budget process. Somepublished specifications are conservative, some are less so. Manufacturers needto have a good production yield of products for the whole family of specifica-tions, so this often leads to a policy of writing specifications that have generous“guard bands” and thus are more conservative.

Further, a particular measurement configuration is likely to be close to onespecification limit, but easily meet another specification; a second systemmight reverse the roles. By using the new ISO uncertainty-combining method,this takes advantage of the random relationship among specifications and theuncertainties tend to be smaller, yet realistic.

A second reason to observe is that the Figure 3-1 calculations are done for oneparticular frequency (2 GHz) and one particular source SWR (1.15). A differentfrequency and different source match would give a different overall uncertain-ty. Sources frequently have larger reflection coefficient values that would raisethe overall uncertainty due to usually-dominant mismatch effects.

12

Frequency range and SWR (reflection coefficient)All three types of power sensors have models that cover a frequency range from10 MHz to 18 GHz, some higher, with coaxial inputs. A special version of thethermistor mount operates down to 1 MHz (see Fundamentals Part 2) and the8482A/B/H thermocouple power sensors operate down to 100 kHz. The effec-tive efficiency at each frequency is correctable with the Calibration Factor dialor keyboard of the power meter, so that parameter is not particularly critical indeciding on a measurement system.

In most analyses, the sensor’s SWR performance is most important becausemismatch uncertainty usually contributes the largest source of error, asdescribed in Fundamentals Part 3. Figure 3-2 shows a comparison of the speci-fication limits for the SWR of a thermistor mount, a thermocouple power sensor,an 8481D PDB diode power sensor, as well as the E Series power sensors.

It should be recognized that published SWR specifications are usually conserva-tive and that actual performance is often substantially better, yielding loweruncertainty in practice. That fact argues for a preferred practice that measuresactual source SWR for situations where highest accuracy is important.

These graphs indicate that over the bulk of the frequency range, the thermo-couple and diode sensors have a considerably-lower SWR than the thermistorsensor. It also shows that the E4412A sensor, even with its superior dynamicrange, still provides a satisfactory SWR.

Figure 3-2. A comparison of specified SWR limits for the 8478B thermistor mount, 8481A thermocouple power sensor, 8481D PDB power sensor, and E4412A PDB sensor.

8481A thermocouple

1.7

1.6

1.5

1.4

1.3

1.2

1.1

10 MHz

4

30

2

50 100 MHz 1 GHz 2 4 10 GHz

8478B thermistor 8481D diode

E4412A diode

30 50

30 GHz

12.4

8478B

1812.4

E4412A

8481A

8481D

Frequency

SWR

13

Waveguide sensor calibrationPower measurements in waveguide present several special considerations.Waveguide thermocouple and diode sensors must have the usual 50 MHz refer-ence oscillator to adjust for calibration factor from one sensor to another. Sucha low-frequency signal cannot propagate in a waveguide mode. Agilent wave-guide thermocouple sensors (26.5 to 50.0 GHz) and waveguide diode sensors(26.5 to 110 GHz) all utilize a special 50 MHz coaxial injection port that appliesthe reference oscillator output to the sensor element in parallel to the usualwaveguide input. This permits the meter-sensor system to be calibrated at theirwaveguide operating frequencies.

Speed of response at low signal levelsTo measure the lowest power ranges with optimum accuracy, power meters aredesigned with a highly-filtered, narrow bandwidth compared to most otherelectronic circuits. Narrow band circuits are necessary to pass the desiredpower-indicating signal but reject the noise that would obscure the very weaksignal. Narrow bandwidth leads to the long response time. For heat respondingpower sensors, like the thermistor and thermocouple, response time is also lim-ited by the heating and cooling time constants of the heat sensing element.

The typical thermistor power measurement has a 35 ms time constant and 0 to 99 percent response time of about five time constants or 0.175 s. Thepower meters for thermocouple and PDB sensors have 0 to 99 percent responsetimes of 0.1 to 10 s, depending on the range of the power meter. The more sensitive ranges require more averaging and hence longer settling times.

For manual measurements, the speed of response is seldom a problem. By thetime the observer turns on the RF power and is ready to take data, the powermeter has almost always reached a steady reading.

For analog systems applications, where rapid data acquisition is required, orwhere the power meter output is being used to control other instruments, thepower meter acts like a low pass filter. The equivalent cutoff frequency of thefilter has a period roughly the same as the 0 to 99 percent response time. Forsignals where the signal power changes too rapidly for the power meter torespond, the power meter averages the changing power. When a power meter isbeing used to level the output of a signal generator whose frequency is beingswept, the speed of the frequency sweep may have to be reduced to allow thepower meter time to respond to the power level changes.

There is no clear-cut advantage with regard to speed of one power measure-ment system over another. In some power ranges one system is faster, and inother ranges another system is faster. If response time is critical, manufactur-ers’ data sheets should be compared for the particular application.

14

Automated power measurementRecognizing that a large percentage of digital power meters are used in produc-tion test and in automated systems, it is reasonable to assume that digitizingmeasurement speed is critical in at least some of those applications. Digitalpower meters programmed for automatic operation gather data rapidly andwith minimum errors. The data can be processed and analyzed according toprogrammed instructions, and the system can be operated with little processattention. Even in a manual mode, digital indications are less prone to thehuman error of misinterpreting the meter scale and using wrong range multi-pliers. In the case of power measurement, there are additional advantages toautomatic systems. Successive data points can be compared mathematically toassure that the power measurement has reached steady state and multiple suc-cessive readings can be averaged to statistically reduce the effects of noise.

The Agilent EPM Series power meters have been optimized for maximum digi-tizing speed. Since its architecture is totally DSP-based, and it is married to anew E Series diode sensors, circuit decisions were made to increase the digitiz-ing speed to maximum. For example, output filtering on the sensor is smaller,which provides faster response. On the lower power ranges, this smaller filter-ing might cause an increase in measurement noise, but the power meter itselfprovides for digital averaging up to 1,024 readings to minimize noise effects.The meter is specified to provide up to 20 readings per second and 40 per second in the X2 mode. The specification for the FAST range in the free-runtrigger mode, using the binary output format, is 200 readings per second. Forthat function, circuit settling times are 5 mS for the top 70 dB power ranges.

Agilent’s EPM-P power meters have advanced their measurement data outputspeed another step. Their peak and average power sensors have a wider videobandwidth, and their DSP-based circuitry is designed for 20 megasamples persecond (Msa/s) data sampling in the analog-to-digital converter section. SeeFundamentals Part 2, Chapter V for complete details.

This permits data outputs up to 1000 corrected readings per second, which can be ideal for certain production test situations. Further, because they caninternally compute combined parameters like peak-to-average ratio on the fly,important production test requirements are easier to meet.

Agilent P-Series power meters have the fastest measurement speed of 1500 cor-rected readings/second, which is ideal for manufacturing applications. There isan EEPROM in the sensor that stores the 4-D calibration model. This model isgenerated in the factory during the calibration process by measuring the inputpower, frequency, temperature, and output voltage. While performing normalmeasurements, this model evaluates the current temperature and input fre-quency to determine the correction factor. It does not require the meter to per-form interpolation of calibration factors and linearity curves. Therefore, thisresults in quick and more accurate measurements.

Susceptibility to overloadThe maximum RF power that may be applied to any power sensor is limited inthree ways. The first limit is an average power rating. Too much average powerusually causes damage because of excessive accumulated heat. The second limitis the total energy in a pulse. If the pulse power is too high for even a veryshort time, in spite of the average power being low, the pulses might cause atemporary hot spot somewhere in the sensor. Damage occurs before the heathas time to disperse to the rest of the sensor. The third limit is peak envelopepower. This limit is usually determined by voltage breakdown phenomena thatdamages sensor components.

Overload limits are usually stated on the manufacturer’s data sheet. None ofthe three limits should be exceeded. The power limits of any sensor may bemoved upward by adding an attenuator to pre-absorb the bulk of the power.Then the power limits are likely to be dictated by the attenuator characteris-tics, which, being a passive component, are often fairly rugged and forgiving.

Table 3-1 shows that the 8481H power sensor, which consists of a 20-dB attenu-ator integrated with a thermocouple sensor element, excels in resistance tooverload. One characteristic, which might be important but not obvious fromthe chart, is the ratio of maximum average power to the largest measurablepower. The 8481D PDB sensor can absorb 100 mW (+20 dBm) of average power,yet the high end of its measurement range is 10 µW (–20 dBm). This means thatthe PDB diode is forgiving in situations where the power level is accidentallyset too high. A mistake of 10 dB in setting a source output attenuator, during ameasuring routine will merely cause an off-scale reading for the 8481D. Thesame mistake might damage the other sensors. Excessive power is, by far, theprimary cause of power sensor failure.

The diode-stack-attenuator-diode stack topology of the Agilent E9300A averagepower sensors provides a maximum average power specification of 316 mW(+25 dBm) and peak power specification of 2 W (+33 dBm) for less than a 10 µSduration. These specifications allow the E9300A sensors to handle the largecrest factors typical of the newest signal formats, such as W-CDMA and orthog-onal frequency division multiplexing (OFDM), while still maximizing thedynamic range.

Although intended for handling pulsed signals, peak and average sensors, typi-fied by the E9320A sensor, are not necessarily more immune to overload limits.In fact, it might be argued that the user needs to exert even more caution whenusing pulsed power signals, especially if the actual peak power is unknown.One simple way to do this is to insert a step attenuator between the unknownpulsed power and the peak and average sensor and set in an appropriateamount of attenuation. Since peak and average sensors have an excellentdynamic range, the meter will indicate some peak power on the high sensitivityranges. At that point, the user can determine whether the test signal peakpower will do damage to the sensor.

15

Table 3-1. Overload characteristics for various types of power sensors.

8478B 8481A 8481H 8481D E4412A E9300A E9320A N1921A/22AThermistor Thermo- Thermo- Diode Extended- Two-path Peak and Peak and sensor couple couple sensor range diode diode sensor average average

sensor sensor sensor diode sensor diode sensor

Maximum average power 30 mW 300 mW 3.5 W 100 mW 200 mW 316 mW 200 mW 200 mW

Maximum

energy per pulse 10 W • µS 30 W • µS 100 W • µS See Footnote 1 See Footnote 1 See Footnote 1 See Footnote 1 See Footnote 1

Peak power 200 mW 15 W 100 W 100 mW 200 mW 2 W (< 10 µS) 1 W (< 10 µS) 1 W (< 1 µs)

1. Diode device response is so fast, device cannot average out high-energy pulses

16

Signal waveform effectsWhile the waveform considerations were fully covered in Fundamentals Part 2,Chapter IV, it is well to consider the waveform factor as a differentiator for thevarious meters and sensor technology. Briefly, the thermistor is a totally heat-based sensor and therefore the thermistor sensors handle any input waveformwith any arbitrary crest factor, that is, they are true square law sensing ele-ments.

Thermocouple sensors are full square law sensing for the same reason, butthermocouples operate beyond the thermistor high power limit of 10 mW, allthe way to 100 mW and 3 W for the 848X H-models, which have the integratedfixed pads. The 8481B features a 25-watt external characterized attenuator andoperates from 10 MHz to 18 GHz for medium power applications.

PDB-diode-based sensors of the 8481D family feature full square-law perform-ance because their operating power range is limited to a top level of –20 dBm,thus restricting their meter indications to the square-law range of diodes. Theuser should assure that peak power excursions do not exceed –20 dBm.

The E Series diode sensors (E441XA CW, E9300 average and E9320 peak andaverage) require simple attenuation to their input signal characteristics. CWsignals may be applied all the way from –70 to +20 dBm with confidence andaccuracy, using the E441XA sensors.

E932X peak and average sensors are intended for characterizing the power ofcomplex modulation formats. Thus their main purpose is to high-speed samplethe detected power envelope and compute various types of power parameters.When used with their companion EPM-P power meter, the 20 Msa/s data sampling rates permit fast data acquisition and combined parameter outputs,such as peak-to-average power ratios for specified time-gated periods asdefined by wireless system specifications.

The N1921/22A peak and average power sensors, when used with theN1911/12A power meters, provide up to 30 MHz of video bandwidth. They areintended to measure output power and timing parameters of fast radar pulsesand wide bandwidth wireless signal formats such as W-CDMA, WLAN, OFDM,WiMAX, and others ranging from -35 to 20 dBm.

17

Computed data and analyzer software packageAs fully described in Chapter V of Fundamentals Part 2, the design strategy forthe EPM-P power meters includes highly-versatile user-selectable data compu-tation and display features. Gated data features the ability to set specific gateperiods for time-selective power periods, and then combine several data pointsinto more desired system parameters such as peak-to-average power ratios.

The EPM-P power meters support the innovative and powerful Agilent VEEanalyzer software package, which places the meters totally in the control of theuser’s PC or laptop. This VEE software package is available free of charge.[1] It operates via the GPIB, and provides the statistical, power, frequency, andtime measurements that are required for CDMA and TDMA signal formats. TheCD-ROM package includes a VEE installation program.

The statistical package includes the ability to capture

1. cumulative distribution function (CDF)2. complementary CDF (CCDF or 1-CDF)3. probability density function (PDF)

These are crucial diagnostic parameters for system signals like CDMA formats.For example, analyzing such power distribution computations can reveal how apower amplifier may be distorting a broadband signal that it is transmitting. Ora baseband DSP signal designer can completely specify the power distributioncharacteristics to the associated RF subsystem designers.

For traditional pulse work, the analysis package also includes a powerful pulsecharacterization routine. It computes and displays the following power parame-ters: pulse top, pulse base, distal, mesial, proximal, peak, average, peak/averageratio, burst average, and duty cycle. It does the same for these time and fre-quency parameters: rise time, fall time, pulse repetition frequency (PRF), pulserepetition interval (PRI), pulse width and off time. All of these pulsed powerparameters were originally defined with the 1990 introduction of the Agilent8990A peak power analyzer, and are described in Chapter II of FundamentalsPart 1.

[1] CD-ROM: EPM and EPM-P Series Power Meters, part number E4416-90032.

This CD-ROM contains the power meters and sensors Learnware (User’s Guides, Programming Guides, OperatingGuides and Service Manuals). The CD-ROM also contains technical specifications, data sheets, product overviews,configuration guides, application and product notes, as well as power meter tutorials, analyzer software for the EPM-Ppower meters, IVI-COM drivers, IntuiLink toolbar for the EPM power meters and VXIplug&play drivers for the EPMpower meters.

This versatile CD-ROM package is shipped free with every EPM and EPM-P series power meter. Most of the information is also available at www.agilent.com/find/powermeters.

18

An applications overview of Agilent sensorsIn general, power sensors are designed to match user signal formats and modu-lation types. Similarly, power meters are designed to match the user’s testingconfigurations and measurement data requirements. Thus, it is the user’sresponsibility to understand the test signals in detail, the technology interac-tion with the sensor capabilities, and combine those results with the optimumpower meter to match the data output needs of the test combination.

Table 4-1 presents an overview of the most common signal formats in variousindustry segments and suggests appropriate sensor technologies that can characterize them. (Since Agilent thermistor sensor/meter technology is almostuniquely metrology-and traceability-based, they are not included in Table 4-1.)

IV. Capabilities Overview of AgilentSensors and PowerMeters

Table 4-1. Agilent sensor vs. signals applications chart.

Signal characteristics > CW Modulated

CW Pulse/ Pulse/ AM/FM Wireless standardsaveraged profiled

Typical Metrology Radar/ Radar/ Mobile TDMA cdmaOne W-CDMA 802.11a/blgapplication lab navigation navigation radio GSM Bluetooth™ cdma2000 MCPAexamples > EDGE HiperLan2

NADC WiMAXIDEN

Thermocouple • • • • • • •sensors Avg. only Avg. only Avg. only Avg. only

Diode • • • • • • •sensors Avg. only Avg. only Avg. only Avg. only

Diode sensors • FM onlycompensated forextended range

Two-path • • • • • • •diode-stack sensors Avg. only Avg. only Avg. only Avg. only

Peak and average • • • • • • • •diode sensors (30 MHz) (30 MHz) (300 kHz) (1.5 MHz) (5 MHz) (30 MHz)(video BW)1 time-gated peak, avg, peak, avg, peak, avg,

peak/avg peak/avg peak/avg

1. The video bandwidth is sometimes referred to as the modulation bandwidth.

Sens

or te

chno

logy

19

A capabilities overview of Agilent power metersOnce the signal and modulation format leads you to the best sensor choice, thepower meter decision is straightforward. Table 4-2 compares the performanceof Agilent’s present power meter line of products. Generally the Agilent EPM,EPM-P, and new P-Series power meters are completely backward compatiblewith all diode and thermocouple sensors. This includes sensors of a vintagefrom several decades back. So, the power meter decision becomes mostly a mat-ter of single vs. dual channel capability. The VXI power meter (E1416A) wouldbe chosen for installations which use the plug-in instrumentation concept.

Table 4-2. Agilent’s family of power meters

Agilent model Name RemarksPeak and average power meters P-SeriesN1911A Single-channel Digital, programmable, peak, and average measure-

ments, uses N1921/22A sensors. Perform accurate and repeatable power, time, and statistical measure-ments up to 300 MHz (video bandwidth). 100 Msamples/sec. Continuous sampling.

N1912A Dual-channel Two channel version of N1911A. Measures and computes parameters between the two sensors.

Peak and average power meters EPM-P seriesE4416A Single-channel Digital, programmable, peak and average measure-

ments, uses E9320 series sensors. Innovative time-gated pulse-power measurements. 20 Msamples/sec.

E4417A Dual-channel Two-channel version of E4416A, plus measures andcomputes parameters between the two sensors.

Averaging power meters EPM seriesE4418B Single-channel Digital, programmable, uses E-series and 8480 series

sensors, reads EEPROM-stored sensor calibration factors of E-series sensors.

E4419B Dual-channel Two-channel version of E4418B, plus measures and computes parameters between the two sensors.

System power meterE1416A VXI power meter Has functional performance features of previous

model 437B; uses all 8480-series sensors

Thermistor power meter432A Thermistor power meter DC-substitution, balanced-bridge technology, ideal for

reference power transfers

Table 4-3 presents a compatibility chart for combinations of sensors andmeters.

20

Table 4-3. Agilent power meter/sensor compatibility chart

Agilent power meters

Type > P-Series EPM-P series EPM series System power Thermistorpeak, average, peak, average and averaging meter power meterand time gating time gating E4418B single Ch E1416A VXI 432A

Agilent N1911A single Ch E4416A single Ch E4419B dual Chpower sensors N1912A dual Ch E4417A dual Ch

Thermocouple8480A/B/H-family • • • • •R/Q8486A W/G(11 models)

Diode8480D-family8486A/D-W/ • • • • •G-family(7 models)

Diode sensors with extended range • • • •E4412A/13A(2 models)

Two-path-diode-stack • • • •E9300 family(7 models)

Peak and average sensors • •E9320 family(6 models)

Thermistor sensors478 coaxial •486 waveguide(6 models)

Peak andaveragesensor •N1921A/22A30 MHz videobandwidth(2 models)

Finally, the last user-selection step is to decide on the specific power sensor,which matches the signal format, power dynamic range and frequency range ofthe application. The technology considerations of Fundamentals Part 2 mightbe consulted for more detail on performance and functionality. The five chartsof Table 4-4 classify the various sensor technologies and their frequency andpower level coverage.

21

Table 4-4. Agilent’s five families of power sensors

Thermocouple sensors

Diode sensors

Extended range diode sensors

Thermocouple sensors

25 W, 0 to +44 dBm

3 W, –10 to +35 dBm

100 mW, –30 to +20 dBm

8482B

8482H

8481B

8481H

8481A

8483A .75 Ω

8485AOption 33

W/G

8487A

Q8486A

Frequency100 kHz 10 MHz 50 100 500 MHz 1 GHz 2 4.2 18.0 26.5 33 40 50 75 110 GHz

8482A

W/G

Sensor family

8480 series

Technology

Thermocouple

Max. dynamic range

50 dB

Frequency range1

100 kHz to 50 GHz

Power range1 Signal type Max. measurementspeed (rdgs/sec)

–30 to +44 dBm All signal types,unlimited bandwidth

40 (x2 mode)

R8486A

Diode sensors

10 µW, –70 to –20 dBm

Frequency100 kHz 10 MHz 50 100 500 MHz 1 GHz 2 4.2 18.0 26.5 33 40 50 75 110 GHz

8481D8485D

Option 33

8487D

R8486DQ8486D

W8486A

–30 to +20dBmW/G

W/GW/G

–30 to+20dBm

V8486AW/G

Sensor family

8480 series

Technology

Diode

Max. dynamic range

50 dB

Frequency range1

10 MHz to 110 GHz

Power range1 Signal type Max. measurementspeed (rdgs/sec)

–70 to –20 dBm All signal types,unlimited bandwidth

40 (x2 mode)

100 mW, –70 to +20 dBm

Frequency100 kHz 10 MHz 50 100 500 MHz 1 GHz 2 4.2 18.0 26.5 33 40 50 75 110 GHz

E4412A

E4413A

Sensor family

E-series: CWE4412AE4413A

Technology

Single diode pair

Max. dynamic range

90 dB

Frequency range1

10 MHz to 26.5 GHz

Power range1 Signal type Max. measurementspeed (rdgs/sec)

–70 to +20 dBm CW only 200 (fast mode)

100 mW, –70 to +20 dBm

Extended dynamicrange diode sensors

Option H33

1. Sensor dependent

22

Two-path diode stack sensors

100 mW, –60 to +20 dBm

Frequency

9 kHz 100 kHz 10 50 MHz 100 MHz 500 1 GHz 6 18.0 26.5 33 40 50 GHz

E9300A

E9301A

Sensor family

E-series: average powersensors E9300

Technology

Diode-attenuator-diode

Max. dynamic range

80 dB

Frequency range1

9 kHz to 18 GHz

Power range1 Signal type Max. measurementspeed (rdgs/sec)

–60 to +44 dBm All signal typesunlimited bandwidth

200 (fast mode)

100 mW, –60 to +20 dBm

Two path diode stack sensors

25 W, –30 to +44 dBm

25 W, –30 to +44 dBm

1 W, –50 to +30 dBm

1 W, –50 to +30 dBm

100 mW, –60 to +20 dBm

1 MHz

E9304A

E9300H

E9301H

E9300B

E9301B

24.0

Option H24

Option H18

1 W, –50 to +30 dBm

1 W, –50 to +30 dBm

E9300A Option H25

E9304A Option H19

1. Sensor dependent

23

100 mW, Avg. only: –65/60/60 to +20 dBm Normal –50/45/40 to +20 dBm

100 mW, Avg. only: –65/60/60 to +20 dBm Normal –50/45/40 to +20 dBm

100 mW, –35 to +20 dBm

Frequency

100 kHz 10 50 MHz 100 MHz 500 1 GHz 6 18.0 26.5 33 40 50 GHz

E9321A 300 kHz

E9322A 1.5 MHz

Sensor family

E9320-series2

peak and averageE9321/22/23AE9325/26/27A

N1921/22A3

peak and average sensors

Technology

Single diodepair, two-path

Single diode pair built-in voltage reference for internal zero andcalibration

Max. dynamic range

85 dB

55 dB

Frequency range1

50 MHz to 18 GHz

50 MHz to 40 GHz

Power range1 Signal type Max. measurementspeed (rdgs/sec)

–65 to +20 dBm CW, avg, peak,pk/avg, TDMA,W-CDMA

Up to 1000

–35 to +20 dBm CW, avg, peak,pk/avg, TDMA,W-CDMA, radar

Up to 1500

1 MHz

E9323A 5 MHz

E9325A 300 kHz

E9326A 1.5 MHz

E9327A 5 MHz

N1921A 30 MHz

N1922A 30 MHz

Peak and average sensors

1. Sensor dependent2. Peak and average sensors must be used with an E9288A, B, or C sensor cable, and only operate with the E4416A/17A power meters3. E9320 Series sensors, when used with the E4416A/17A power meters, must be used with E9288A/B/C sensor cables. When used with the N1911A/12A power meters,

they must be used with the N1917A/B/C sensor cables.

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