electronics measurement devices basics

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University of Wisconsin-MadisonCollege of Letters and Science

Department of Communicative Disorders

A Poor Man's Tour of Basic Electronic Measurement Devices

Michael R. Chial, Ph.D. 1999

INTRODUCTION

This material is designed to familiarize you with devices commonly used to measure signals expressed asvoltages. The signals themselves can represent almost anything--speech waves, noise, simple tones, gated auditorytest signals, etc. You will make the best use of your time if you (1) scan this Tour, paying particular attention tothe section on entry level skills, (2) study the content notes, and finally (3) work through the separate problem set.Spend time with the instruments discussed in this Tour to insure you can identify controls and functions. If youhave trouble using these devices in later work, review this material.

ENTRY LEVEL SKILLS

Prior to using this Tour, you should be able to do each of the following:

(1) Correctly distinguish between wave form and spectral representations of simple and complex signals;correctly state the quantities and units of graphical representations of these things.

(2) Correctly use metric system prefixes to convert quantities expressed by one prefix to another (e.g., frommilliseconds to seconds and vice-versa).

(3) Correctly state and explain the relation between frequency and period of simple periodic waves; correctlycompute either, given the other.

(4) Correctly state and explain the general equation for a sinusoidal function:

Y = A sin

(5) Correctly state, explain and use common equations for the decibel:

LW = 10 log (Wm/Wr)

LI = 10 log (Im/Ir)

Lp = 20 log (pm/pr)

Lps = Lp - 10 log (fm/fr)

Lp = Lps + 10 log (fm/fr)

(6) Correctly state and describe Ohm's law for DC signal systems, including units of measurement forelectrical voltage, current, and resistance.

V = I * R

(7) Correctly distinguish between DC and AC signals.(8) Correctly describe the relations among resistance (R), capacitive reactance (XC), and inductive reactance

(XL) as contributors to total impedance (Z) in AC signal systems.

Z = (R)2 + (2fL - 1/2fC)2

(9) Correctly identify the characteristics of stimuli used in auditory research and clinical practice.(10) Correctly identify characteristics of measurement systems.(11) Correctly distinguish between emission and transmission models of measurement.(12) Correctly state general safety rules for electronic measurement.


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If you cannot meet these competencies, consult one or more of the following references:

Chial, M. (1998). A Poor Mans Tour of Basic Electricity and Electronics.Chial, M. (1998). A Poor Mans Tour of Basic Electronic Measurement Systems.Chial, M. (1998). A Poor Mans Tour of Physical Quantities and Units.Speaks, C. (1999). Introduction to Sound, 3rd ed. San Diego, CA: Singular Publishing Group, Inc.

INSTRUCTIONAL OBJECTIVES

When you finish this material, you should be able to do each of the following correctly and withoutassistance.

(1) State the functions of volt-ohm-milliameter (VOM) operated in voltage, decibel, or resistance modes.(2) Identify the purposes of the controls of an analog VOM.(3) Identify the purposes of the controls of a digital VOM.(4) State the functions of a VOM used to check the continuity of a transmission path.(5) Calculate voltages and resistances displayed via an analog VOM.(6) State the cautions to be observed when using analog VOMs.(7) State the cautions to be observed when using digital VOMs.(8) State the functions of a frequency-period-event counter (EPUT).

(9) Identify the purposes of the controls of an EPUT.(10) State the cautions to be observed when using an EPUT.(11) State 4 signal characteristics that can be measured with a dual-channel, triggered oscilloscope.(12) Identify the purposes of amplitude sensitivity, time-base sensitivity, trigger sensitivity, and position

controls of an oscilloscope.(13) Calculate amplitude, period, and phase-angle difference displayed via an oscilloscope.(14) State the cautions to be observed when using an oscilloscope.(15) Identify the names and "sex" of connectors commonly used with laboratory equipment.(16) State 3 major problems common to electronic connectors and cables.

I. Introduction

A. Electronic measurement devices can be thought of as machines that solve equations within narrowly definedlimits. For reasons of economy, most such devices solve more than one general type of equation, orproduce data that can be used to calculate more than one result or outcome.

B. Measurement systems may consist of one or several individual instruments, but virtually all exhibit thefollowing functional components.

1. A primary sensing component that "acquires" the signal to be measured.

2. A conversion component that changes the quantity or variable measured into whatever quantity is

internally required by the instrument.

3. A scaling or manipulation component that accommodates differences in the size of the quantity or

variable measured.

4. A data transmission component that modifies the internal "image" of the quantity or variable for

eventual display.

5. A data presentation component that displays the result of the measurement.


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For example, a sound level meter includes a microphone (sensing component), an internal microphoneamplifier (conversion component), sensitivity controls, filters, and decibel-calculators (scaling andmanipulation components), circuits that prepare results for display (data transmission components), and ameter movement or numerical panel to display results (data presentation component). Sound level metersare simply specialized voltmeters.

C. Characteristics of measurement systems. Measurement is the act of assigning numbers (or other symbols)

to events. Measurement systems may be dedicated to particular tasks, very general tasks, or somecombination of the two extremes. Regardless, virtually all measurement systems exhibit the followingfeatures.

1. Sensitivity: the size (amplitude) of the smallest signal to which a measurement system can respond.

2. Noise floor: the amplitude response of a measurement system when no input signal is present.

3. Distortion level: the amplitude of the largest signal to which a measurement system can respond

without unacceptable amplitude non-linearity.

4. Dynamic range: the amplitude difference (usually expressed in decibels) between noise floor and

distortion level of a measurement system.

5. Signal-to-Noise ratio (S/N) : the difference (usually expressed in decibels) between noise floor and

any signal amplitude below the distortion level of a measurement system.

6. Frequency response: the variation in sensitivity or level (usually expressed in decibels) of a

measurement system as a function of frequency; also may include the variation in phase (usuallyexpressed in degrees) as a function of frequency.

7. Transient response: the variation in sensitivity or level (usually expressed in decibels) of a measurement

system as a function of changes in amplitude or amplitude envelope.

8. Precision: the size of the smallest change in a signal characteristic that can be measured or produced

with a system; typically, a property of an instrument, but also may be a property of a procedure.

9. Accuracy: the validity of measurement possible with a system; influenced by the precision of ameasurement system, plus how the system is used by an operator.

10. Repeatability: the consistency with which a measurement system produces the same results at different

times, or as used by different operators.

11. Robustness: the extent to which the results of using a measurement system are immune to operator

errors.

12. Efficiency: the rate at which important results can be produced by a measurement system, typically

defined in terms of time-to-task completion; influenced by all of the above.

13. Utility: the overall merit of a measurement system for a given application; may be defined in terms

of a benefit-cost ratio; influenced by all of the above.

D. Measurement systems also consist of rules of procedure (recipes of use) that range from simple tocomplicated depending upon the nature of the phenomena to be measured and the instruments or devicesrequired to accomplish measurement. For complex problems (e.g., calibration of tape recorders,audiometers, acoustic immittance devices), rules of procedure are detailed in measurement standards such asthose published by the American National Standards Institute. Some specialized measurement instrumentsincorporate rules of procedure into their design. For more routine problems (e.g., measuring batteryvoltages or features of simple signals), rules of procedure are less formally codified. Whether general-purpose measurement devices such as voltmeters, event counters and oscilloscopes are used effectively orineffectively depends upon what the user knows about the basic function and rules of procedure pertaining to


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that class of device. Many of these rules have the goal of avoiding reactive measurement, that is,influencing the thing measured by the act of measurement.

II. Analog Volt-Ohm-Milliameter (VOM)

A. Function. The analog VOM is capable of measuring potential difference (DC voltage or AC voltage),

resistance, or DC current. Each quantity can be measured in various ranges, from small to large.Measurement is accomplished by manually positioning test leads on a test object, or at test points. Resultsare displayed by a needle that moves left to right in front of a meter face on which is printed severalmeasurement scales. Better quality VOMs have narrow mirrored strips on the face of the display meter toincrease the precision with which needle position can be read. The deflection of the indicator needle isproportional to the amount of current flowing through the coil of the meter mechanism. These ammetercoils are rated in terms of "Ohms/Volt"--higher is better. Because this display system is essentially analog(as opposed to digital), such meters are called analog meters. Most such meters also use internal circuitsdesigned with analog components. Some offer a "continuity check" mode with an audible signal displaywhen resistance is very low (i.e., electrical continuity exits). VOMs require electrical power to operate,either batteries or AC power (e.g., 110 Volts), depending upon design.

B. Limits of Function . Analog VOMs respond to steady-state DC and AC signals, and to signals that change

very slowly. AC voltage and current are measured as "averages" of the instantaneous values of one-halfcycle: the average equals 0.637 times the peak value of a sinusoidal wave. Display scales are usuallycalibrated (graphically) to show root-mean-square (RMS) average readings: RMS equals 0.707 times thepeak value of a sinusoidal wave. The difference between average and RMS values is accommodated byamplification. The purpose of all this is to display AC signals as their DC equivalent, that is, a DC valuethat dissipates the same amount of heat in a resistor as the original AC signal. Most meters that display(rather than calculate) RMS voltages or currents are accurate only for sinusoidal signals. Most analogVOMs also offer a decibel display option on the face of the meter, but again, these are accurate only forsinusoidal signals. Thus, most analog VOMs are "RMS responding" devices, not "true RMS" meters.Some analog VOMs give "true RMS" measurements which differ from "RMS-responding" in that circuitsare included to calculate RMS values, rather than average values. For this reason, true RMS meters givemore accurate results for complex (non-sinusoidal) signals.

Other limits of function involve sensitivity and dynamic range: most inexpensive VOMs cannot reliably

measure voltages smaller than about 0.1 Volt. More expensive units equipped with multi-stage inputamplifiers can measure signals in the milli voltrange.

C. Computations.

1. The analog VOM solves Ohm's law. This is done through internal electronic components selected bythe position of function and range switches, and by selection of test lead ports. For example, Ohm'slaw states that voltage equals current times resistance:

V = I * R

The resistance of the meter coil is known (to the designer, anyway). The user selects a voltagesensitivity setting with the range switch, thus identifying an exact resistance inside the meter. Themilliameter current flow-needle displacement relationship is a constant. Thus, the meter face is

calibrated (marked) to display voltage. Similar calculations are done by the meter to measure resistanceand current. Resistance measurements use a calibrated voltage source (a battery) built into the meter:

R = V / I

where V is a known voltage, I is the current flowing through the meter, and R is the combination ofrange resistors internal to the meter, plus the resistance being measured.


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2. Decibel display option. This computation is accomplished graphically by carefully printing a decibelscale on the face of the meter. Thus, the following equation is solved graphically, rather than throughcircuitry.

Lv = 20 log (Vm/Vr)

where Vm is measured voltage and Vr is a reference voltage. Both are average or RMS values--they

could be peak-to-peak, it really isn't important as long as they are the same. Vr is ultimately defined as

equal to some DC voltage. In some cases the magnitude of Vr can be adjusted by the user, but most

often it is preset to equal 0.775 Volts. In other words, the meter reads 0 dB when Vm equals 0.775

Volts. This value is selected because it is equal to 1 milliWatt in a 600-Ohm line, convenient becausevirtually all professional audio equipment uses 600 ohmsas the standard electrical impedance forinternal circuitry. It also is conveniently equal to 0 VU (volume units) on a standard VU-meter, suchas those found in tape recorders and audiometers. This practice is so common that resulting decibelmeasurements are designated as "dBm" values.

3. Continuity check option. Some analog VOMs offer an audible check of electrical continuity. This isactually a variation of resistance measurement: if measured resistance is less than a specified amount(say, 300 Ohms), an audible tone is produced; if measured resistance is greater than the specified

amount, the result is interpreted as an open circuit and no tone is displayed. The continuity checkoption is most useful for checking the integrity of cables and connectors.

D. Controls . Virtually all VOMs include the following controls. Many combine the range selector and mode

switches into a single control. Some VOMs have controls in addition to those noted below.

1. The power switch turns the VOM on and off.

2. The function (mode) switch sets the meter to measure voltage, resistance, current, or some other signalparameter.

3. The range selector switch adjusts the sensitivity of the VOM. More sensitive (smaller numbers) meanssmaller values can be measured; less sensitive (bigger numbers) means larger values can be measured.Always begin measurements by adjusting the meter to be least sensitive. Increase sensitivity as needed

to make a measurement.

4. The zero-adjust (continuous) control lets the user calibrate the meter for voltage and currentmeasurements. If this is not done properly, measurements will be invalid.

5. The Ohms-adjust (continuous) control lets the user calibrate the meter for resistance measurements. Ifthis is not done properly, measurements will be invalid.

E. Display Scales and Measurement .

1. With the VOM turned ON, set the zero-adjust knob so the needle is directly over the "0" of the DCscale at the left of the meter face. With the VOM turned ON, the range selector set to "Ohms," and thetest leads touching each other, set the ohmsadjust knob so the needle rests on the "0" of the ohms scale

at the right of the meter face.

2. Voltage and resistance measurements are made by positioning the test probes so as to put the test objectin parallel with the VOM. Probe polarity is important when measuring voltage, but not whenmeasuring resistance.

3. Current measurements are made by positioning the test probes so as to put the thing tested in serieswith the VOM. In this case the current of the device being tested flows through the VOM. Test probepolarity is important.


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4. Voltage measurements are read by

a. setting the sensitivity switch,

b. noting the left-most digit of the sensitivity switch setting (usually 3 or 1),

c. choosing a meter face scale whose full-scale deflection value matches that found in b,

d. viewing the needle deflection, and

e. mentally shifting the decimal point of the value shown by the needle to reflect the significant digitsof b.

5. By careful reading of the position of the needle, is is possible to interpolate values between the graduatedmarks of the meter face. More precise measurements are possible by using the mirrored band tominimize parallax errors. More accurate measurements are possible when the needle is deflected to atleast half of full scale.

6. Resistance measurements are read very much like voltage measurements. However, most VOMs haveresistance scales printed on meter faces in a direction opposite that of voltage and current: largerresistances are toward the left. The user still must set, note , choose , view , and shift .

7. Current measurements are read in essentially the same manner as voltage measurements. The user stillmust set, note , choose , view , and shift .

8. A simple and practical use of VOMs is to check the electrical continuity of cables and connectors. Thisis done with no external power or signals applied to the cables. The VOM is adjusted to measureresistance and the test probes are placed on the contacts of the cable or connectors to verify thatcontinuity exits where it should and is absent when it should be absent. Shorts occur when there is

undesired continuity (low resistance); opens occur when there is undesired discontinuity (high

resistance).

F. Cautions of Use include those intended to protect the user from harm, those intended to protect the meter

from harm, and those intended to produce consistent and valid measurements.

1. DO start all measurements by using the Ohms-adjust and zero-adjust controls.2. DO attach the meter test leads to the proper ports for the measurement you wish to make.3. DO observe proper test lead polarity when making measurements of voltage or current.

4. DO start all voltage and current measurements with the least sensitive range setting.5. DO adjust the range selector to a position that produces a needle deflection that is at least half of full

scale.6. DO avoid parallax reading errors by viewing the meter such that the needle forms a single line with its

reflection on the mirror of the meter face.7. DO use extreme care when measuring high voltages: remember the "one hand in pocket" rule.8. DO NOT let your fingers touch the tips of the test probes when making measurements.9. DO NOT try to measure current with the meter set to measure resistance.10. DO NOT try to measure AC voltage or current with the meter set to DC mode.

III. Digital Volt-Ohm-Milliameter (VOM)

A. Function . The typical digital VOM is capable of measuring potential difference (DC voltage or AC

voltage), resistance, or DC current. Each quantity can be measured in various ranges, from small to large.Digital VOMs may be able to measure other quantities such as frequency, relative levels (i.e., decibels),conductance, and capacitance. Measurement is accomplished by manually positioning test leads on a testobject, or at test points. Results are displayed as numbers by means of light-emitting diodes or liquidcrystal displays. Such displays also may show status information and serve as function or mode selectors.Some digital VOMs also function as hand calculators. Some offer a "continuity check" mode with anaudible signal display when resistance is very low (i.e., electrical continuity exits). VOMs require electricalpower to operate, either batteries or AC power (e.g., 110 Volts), depending upon design. Digital VOMsare digital in the sense that results are displayed as numbers, rather than by a needle. This simplifiesoperation, thereby increasing efficiency. Better digital VOMs display more digits. Some such meters (not


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all) also are digital in the sense that some or all of the operations performed by the meter are accomplishedwith digital integrated circuits, including self-calibration. These are "true" digital VOMs, rather than"digital read-out" VOMs which display results in digital form, but perform calculations with analogcircuits. Many "true" digital VOMs include an "auto-ranging" feature by which the position of a decimalpoint is computed by the meter.

B. Limits of Function . Digital VOMs are limited in function in the same manner as analog VOMs. However,

certain options (such as true RMS amplitude) are common. Some digital VOMs can perform additionalmeasurements (e.g., frequency counting, conductance). Digital VOMs tend to have greater sensitivity andwider dynamic ranges than analog VOMs.

C. Computations .

1. The "true" digital VOM solves Ohm's law, but in a manner different from an analog VOM. The analogsignals (current flow or voltage) are digitally sampled, then converted into numerical values forcalculation. Results are shown in numerical form, rather than by the position of a needle.

2. "True RMS" computations are made by internal circuit operations on sampled signals. The calculationperformed is as follows:

VRMS = vi=12 + vi=22 + vi=32 + . . . + v i=n2Nwhere the symbol vdesignates instantaneous voltage amplitude and the subscript i denotes a particularsample (from the first (1) to the last (n).

3. Decibel measurement option. Some digital VOMs contain circuits that calculate decibel values asindicated above. Results are displayed numerically. The reference voltage may be 0.775 volt (for dBmmeasurements) or 1.0 volts (for dBv measurements). Most meters that perform such calculations

allow the user to declare an arbitrary voltage input to the meter as the reference for the decibel equation.That reference value may be stored for later use, even after the meter is turned off. Like all decibelmeasurements, these are meaningful only in relatrive terms, i.e., in the context of the reference voltage.

4. Frequency option. Some digital VOMs also measure AC signal frequency. This is done by firstmeasuring the period of some number of cycles, then calculating the reciprocal of that value:

F = 1 / T

Results are displayed numerically.

D. Controls. Like analog VOMs, digital VOMs have sensitivity (range) and function selectors. Unlike, analog

VOMs, most digital VOMs automatically calibrate electrical zero and infinite resistance. Thus, mostdigital VOMs lack "Zero Adjust" and "ohmsAdjust" controls.

1. The power switch turns the VOM on and off.

2. The function (mode) switch sets the meter to measure voltage, resistance, current, or some other signal

parameter.

3. The range selector switch adjusts the sensitivity of the VOM. More sensitive (smaller numbers) meanssmaller values can be measured; less sensitive (bigger numbers) means larger values can be measured.Always begin measurements by adjusting the meter to be least sensitive. Increase sensitivity as needed

to make a measurement.

4. Other controls may be present to allow setting of voltages for relative decibel measurements, or toperform self-tests, or to change display modes (e.g., volts vs. decibels).


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E. Display Scales and Measurement.

1. Function switches should be adjusted before the VOM is turned on. Test probes should be inserted inthe ports appropriate to the measurements to be taken. If the digital VOM performs self-tests when themeter is turned on, the results of these should be noted.

2. Most digital VOMs display special symbols to indicate whether the meter is set to be more sensitive

than it should be. Similarly, most digital VOMs employ special symbols (e.g., a flashing, rather thansteady, display) to indicate that a voltage or current is too small to be measured (i.e., below the noisefloor of the meter).

3. Voltage and resistance measurements are made by positioning the test probes so as to put the test objectin parallel with the VOM. Test probe polarity is important when measuring voltage, but not whenmeasuring resistance. Polarity of measured voltage is designated by algebraic sign (+ or - ).

4. Current measurements are made by positioning the test probes so as to put the thing tested in serieswith the VOM. In this case the current of the device being tested flows through the VOM. Test probepolarity is important. Polarity of measured current usually is displayed by algebraic sign (+ or -).

5. Voltage, current, and resistance measurements are read by noting the number displayed by the meter.Because there is no needle, measurement is simplified and interpolation is unnecessary. However, forsome digital VOMs, it is still necessary to note the sensitivity setting of the meter and interpret themagnitude of the result accordingly.

6. A simple and practical use of VOMs is to check the electrical continuity of cables and connectors. Thisis done with no external power or signals applied to the cables. The VOM is adjusted to measureresistance and the test probes are placed on the contacts of the cable or connectors to verify thatcontinuity exits where it should and is absent when it should be absent. Shorts occur when there is

undesired continuity (low resistance); opens occur when there is undesired discontinuity (high

resistance).

F. Cautions of Use include those intended to protect the user from harm, those intended to protect the meter

from harm, and those intended to produce consistent and valid measurements.

1. DO observe the results of any self-tests to verify proper performance.2. DO attach the meter test leads to the proper ports for the measurement you wish to make.3. DO observe proper test lead polarity when making measurements of voltage or current.4. DO start all voltage and current measurements with the least sensitive range setting.5. DO watch for the over-range indication. Adjust sensitivity accordingly to insure accuracy.6. DO use extreme care when measuring high voltages: remember the "one hand in pocket" rule.7. DO calibrate the meter properly when making decibel measurements.8. DO NOT let your fingers touch the tips of the test probes when making measurements.9. DO NOT try to measure current with the meter set to measure resistance.10. DO NOT try to measure the frequency of large AC voltage signals (e.g., 120 volts).

IV. Event-Per-Unit Time (EPUT) Counter

A. Function . Event-per-unit time meters (EPUTs) are devices which measure the period and frequency ofsimple wave forms (sine, triangular, square) and electronic pulses. Thus, they measure AC signals. ManyEPUTs are equipped with two main signal input channels (A and B) and can measure the time intervalbetween pairs of pulses or the period ratios of two simple wave forms. Most also offer a "totalize" functionby which periods or pulses are counted, beginning with some external trigger signal and ending with aseparate trigger signal. Trigger channels accommodate control signals, rather than measurement signals.Each quantity can be measured in various ranges, from small to large.


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Measurements are based upon averages taken over a number of individual signal periods. Results are shownnumerically (i.e., digitally) by means of light-emitting diodes, liquid crystal displays, or (in older units)electoluminescent "numetron" displays based upon vacuum-tube technology. Such displays also may showself-test and status information. Better EPUTS display more digits. Most offer automatic positioning of adecimal point. Older EPUTs use analog circuits to sample input signal and calculate results; many newerdevices of this type use digital circuits and techniques. In either case, because EPUTs display numericalresults, they offer advantages in ease of use similar to digital VOMs.

B. Limits of Function . EPUTS are designed for use with repetitive sinusoids and pulses, and with simple

repetitive signals such as square waves. Some cannot reliably measure triangular waves because such wavescontain too much relative energy at frequencies above the fundamental. Most EPUTs cannot reliablymeasure the period or frequency of simple signals that are asymmetrical; nor can they reliably measure thefundamental frequency of complex signals. EPUTs vary in their ability to measure very fast pulses. Mostgive errors if they are adjusted to be too sensitive (i.e., the input signal voltage is too large). As with otherdigital display devices, the least-significant (right-hand) digit usually is less accurate than more significantdigits.

C. Computations . In the event-counting mode, the EPUT simply counts the number of events occurring

between manual or external control trigger pulses. In the period mode, the EPUT averages individualperiods:

Taverage = {ti

N

i = 1

N }where individual periods ti are summed from the first (i = 1) to the last (n), then divided by the number of

samples (N). In the frequency mode, the EPUT finds the reciprocal of the average period.

Faverage = 1 / Taverage

D. Controls . Almost all dual-channel EPUTs contain the following controls.

1. The power switch turns the EPUT on and off.

2. The function (mode) switch sets the EPUT to measure frequency (channel A or B), period (channel A orB), period ratio (between channels A and B), or interval (between channels A and B).

3. The range selector switch adjusts the number of digits displayed, the position of the decimal point, andthe time base of the device. Typical frequency ranges are from 1 Hz to 10 MegaHz in a "1, 10, 100"sequence; period ranges are from microseconds to seconds.

4. The sensitivity switch is a step attenuator that allows measurement of large and small voltage signals.Ranges are usually in a "1, 10, 100" sequence. Begin measurements by adjusting the EPUT to be least

sensitive. Increase sensitivity as needed to make a measurement.

5. The periods/sample switch controls how many cycles form the basis for averaging. Values typicallyrange from 1-1000 periods/sample in decade steps (i.e., x10, x100).

6. The display time switch (usually a continuous control) adjusts how long a result is shown before beingupdated. Display times range from 1 sec to infinite (frozen).

7. The reset switch (usually, a push button) stops the current measurement and sets the display to zero.


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1. Function switches should be adjusted before the EPUT is turned on. The sensitivity initially should beadjusted to the least sensitive position. Period/sample and display time switches should be adjusted tomid-scale positions. Signal cables should be attached to the ports appropriate to the measurements tobe taken. Results of any self-tests should be noted.

2. The sensitivity switch should be adjusted to make the meter more sensitive until a reading appears.

3. The position of the range selector switch should be adjusted to display 3-4 significant (non-zero) digits.This position should be noted. Read the numerical value displayed by the EPUT, noting the positionof the decimal point. Multiply the value of the range selector switch by the displayed value. Forexample, if the range selector is set to "kHz" and the displayed value is "00.510," the result is 0.510kHz or 510 Hz.

F. Cautions of Use . These are intended to protect the user and the EPUT from harm, and to produce consistent

and valid measurements.

1. DO observe the results of any self-tests to verify proper performance.2. DO attach test leads to the proper ports for the measurement you wish to make.3. DO start all measurements with the least sensitive amplitude range setting.4. DO adjust input sensitivity to insure accuracy.

V. Oscilloscope

A. Function . The oscilloscope is an extremely flexible measurement tool, largely because it allows direct

visualization of signals. Scopes are capable of quantitative measurement of DC and AC voltage, the period(hence, frequency) of simple wave forms, frequency ratios, phase angle differences, and signal duration.Because they allow visual monitoring of signals, scopes also permit a qualitative assessment of otherinstruments and system.

Oscilloscopes display signals on a cathode-ray tube (CRT), the basic operation of which is important tounderstanding what scopes do. The following figure is a simplified illustration of a CRT. Negatively-

charged electrons are emitted by a cathode at the rear of thick glass tube from which air has been removed.These electrons are formed into a beam, focused and accelerated by positively-charged, tubular anodes. Thebeam position is controlled by two sets of plates, the electronic charge of which can be controlled bycircuitry. One set of plates control the vertical position of the beam (the Y-axis); another set controls thehorizontal position (the X-axis). The inside front surface of the tube is coated with a phosphorous materialthat emits light when struck by electrons.

Cathode

Focusing

Anode

Accelerating

Anode

Vertical

Control Plate

Horizontal

Control Plates

Phosphor

Coating

Calibrated Viewing

Grid

Y-axis

(Vertical)

X-axis

(Horizontal)

Electron

Beam


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A signal to be measured is connected to the vertical control plates through an amplifier system. Thehorizontal plates are controlled by internal circuits that cause the image to sweep across the screen fromright to left. The user controls the sensitivity of the vertical channel and the sweep rate of the horizontalchannel. The front surface of the CRT is faced with a transparent plate with lines on the horizontal andvertical axes. These lines are usually calibrated in centimeters and tenths (or fifths) of a centimeter.Distance measurements can be made using the viewing grid and landmarks of the displayed signal. Thesedistance measurements can be converted into units of voltage and time by noting the sensitivity settings of

the vertical and horizontal channels.

Oscilloscopes are available in various configurations, including single, dual, and multiple vertical, (i.e.,voltage) channels. Some scopes are dual-beam devices with two cathodes (also called "electron guns") inthe CRT; others are dual-channel devices with a single CRT cathode and ancillary circuits that alternatesweeps between two channels, or time-share ("chop") a single electron beam between two Y-axis inputs.

Many measurements with scopes require only one channel; some (e.g., frequency-ratio and phasemeasurements) require two vertical channels that can be precisely matched in voltage sensitivity. Scopesalso differ in band-width (units with higher cut-off frequencies are more expensive, but not necessarily betterfor measurement of audio frequencies; high band-width scopes are needed to display signals such as thehorizontal scan rate of television or very fast transient signals). Storage scopes are capable of capturing and

retaining information displayed on the screen. Older scopes of this type accomplish storage with long-persistence phosphors in the CRT tube; newer storage scopes use digital techniques to sample and holdvoltage information. Still others are designed to monitor special signals (e.g., video vector scopes), or toperform special calculations on signals (e.g., sampling digital scopes that accept time-varying wave forms,then compute and display spectra).

B. Limits of Function . Except for band-width and numbers of input channels, most scope limitations relate to

how they are used, rather than design. Misuse can be avoided by remembering that displayed images are theresult of two independent things: (1) the signal itself, and (2) choices made by the user about how to viewthe image. In other words, the operator can change the appearance of the signal without changing the signalitself.

C. Computations . In a sense, the oscilloscope accomplishes a translation of "back and forth" voltage change to

a rectilinear display. The coordinates of this display are amplitude (Y or vertical axis) and time (X orhorizontal axis). An example of the equations solved by this device is the familiar sinusoidal function:

Y = A sin

where Y is deflection on the Y-axis.

D. Controls . Most dual-channel, triggered-sweep scopes contain the following controls. Some of these may

be combined to reduce the number of knobs and buttons.

1. The power switch turns the scope on and off.

2. The beam intensity (continuous) control that adjusts the brightness of the image. Adjust to acomfortably visible level.

3. The beam focus (continuous) control that adjusts the sharpness of the image. Adjust to minimum beam

width.

4. Y-axis (amplitude or vertical channel) controls. (Dual-channel and dual-beam scopes have two sets ofthese, designated Y1 and Y2.)

a. The coupling switch (one or more push buttons) controls selection of AC signals only (i.e., andDC component is blocked with a high pass filter) or DC signals (i.e., no low frequency blockingso both AC and DC signals are passed for measurement). A third option, "GND," connects theinput to electrical ground so no signal is presented to the vertical channel. The result is a flat line


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image. GND coupling is used in conjunction with the Vertical Position control to center thescope image prior to measurement.

b. The vertical sensitivity control adjusts the gain of an input amplifier, allowing measurement ofsignals ranging from large to small. This is a stepped with values calibrated in different units ofvoltage per centimeter. Steps are in a "1, 2, 5" sequence, usually ranging from 10 Volts/cm to100 microVolts/cm. Adjusting this control modifies the apparent amplitude (height) of the signal.

c. The vertical calibration control is a continuously variable control. When set to the "CAL"

position, Y-axis settings are accurate as indicated by the vertical sensitivity control. Sometimesthis control is used in uncalibrated positions to simplify X-axis (time) measurements.

d. The vertical position control allows the image to be moved up and down in continuous increments.It is used to position the image relative to the calibrated viewing grid, thus simplifyingmeasurements of distance between image landmarks.

5. X-axis (time-base or horizontal channel) controls. (Most dual-channel scopes have only one set ofhorizontal axis controls; some dual-beam scopes have two). The X-axis usually is time; for somemeasurements the X-axis can be adjusted to respond to amplitude.

a. The horizontal sensitivity control an internal sweep oscillator allowing measurement of signalsranging from long to short. This is a stepped with values calibrated in different units of time percentimeter. Steps are in a "1, 2, 5" sequence, usually ranging from 1 sec/cm to 10 microsec/cm.Adjusting this control modifies the apparent width (duration) of the signal.

b. The horizontal calibration control is a continuously variable control. When set to the "CAL"position, X-axis settings are accurate as indicated by the horizontal sensitivity control. Sometimesthis control is used in uncalibrated positions to simplify Y-axis (amplitude) measurements.

c. On most scopes, the horizontal channel also can be used as an amplitude channel. This mode ofoperation is invoked by a push-button selector, or by special positions of the horizontal sensitivitycontrol. In this mode, horizontal sensitivity and calibration controls operate in the same manneras similar controls for the vertical channel. However, here the input signal causes side-to-side,rather than up-and-down deflection of the electron beam.

d. The horizontal position control allows the image to be moved from left to right in continuousincrements. It is used to position the image relative to the calibrated viewing grid, thussimplifying measurements of distance between image landmarks.

e. The trigger controls determine when a signal image is displayed on the screen. Images are tracedfrom left to right across the screen.

(1.) The trigger selector determines which signal, and which phase of that signal (positive ornegative), initiates a sweep. Options include the Y-axis signal (internally routed to this partof the scope), an external signal, a line (frequency) signal that produces 60 sweep-starts persecond, and a "GND" position that connects the external input port of the trigger circuit toground.

(2.) The trigger sensitivity control sets the threshold voltage of the trigger circuit.(3.) When correctly adjusted, these controls produce visually stable images that do not appear to

"walk" across the screen from left to right. An exception to this "proper" display occurs whenthe horizontal sensitivity control is set to a large value (e.g., 1 sec/cm). In such a case, theimage should seem to move from left to right.


1. Oscilloscopes typically have one input port for each vertical (Y-axis) channel and one input port for thehorizontal (X-axis) channel. The Y-axis input channels are used for display and measurement of waveforms or other time-varying signals. The X-axis input channel is used for either an external triggersweep signal, or for an X-axis amplitude signal.

2. Amplitude Measurement. A voltage is presented to a Y-axis channel. Vertical coupling and sensitivitycontrols are adjusted and noted. The Y-axis vertical calibration control should be set to the "CAL"position because this is the dimension of measurement. For repetitive signals, the time-basesensitivity is adjusted to display a convenient number of cycles, and the X-axis trigger polarity andsensitivity controls are adjusted to give a stable trace on the screen. The vertical sensitivity controlshould be adjusted to produce a trace that is one-half (or more) as tall as the calibrated viewing grid.


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The horizontal position control is adjusted to place the image at a convenient location relative to thecalibrated viewing grid. Peak-Peak amplitude is measured by:

a. reading the Y-axis sensitivity setting in Volts/cm,

b. counting the number of cm (and fractions thereof) between the top and bottom peaks (or other

landmark) of the signal displayed on the screen, andc. multiplying the Y-axis sensitivity setting (in Volts/cm) by the counted deflection (in cm). The

result is given in Volts, Peak-Peak. Peak voltage is one half the Peak-Peak voltage. For sinewaves (only) RMS amplitude can be calculated by:

VRMS = VP x 0.707

VRMS = VP-P x 0.353

d. For example, in the following figure the Peak-Peak amplitude of a sine wave is 5 cm. If thevertical sensitivity control were set to 2 volts/cm (CAL), then VP-P = 10 volts and VRMS = 3.53

Volts.

X-axis (time)

Y-axis(amplitude)

5 cm

3. Period and Duration Measurement. A voltage is presented to a Y-axis channel. Vertical coupling and

sensitivity controls are adjusted and noted. The X-axis horizontal calibration control should be set tothe "CAL" position because this is the dimension of measurement. For repetitive signals, the time-base sensitivity is adjusted to display 1-3 cycles, and the X-axis trigger polarity and sensitivity controlsare adjusted to give a stable trace on the screen. The vertical sensitivity control should be adjusted toproduce a trace that is one-half (or more) as tall as the calibrated viewing grid. The horizontal positioncontrol is adjusted to place the image at a convenient location relative to the calibrated viewing grid.Period is measured by:

a. reading the X-axis sensitivity setting in sec/cm,

b. counting the number of cm (and fractions thereof) between successive peaks (or other landmark) of

the signal displayed on the screen, andc. multiplying the X-axis sensitivity setting (in sec/cm) by the counted deflection (in cm). The result

is given in units of time per period. Frequency can be calculated by:

F = 1/T

d. For example, in the following figure the distance between successive positive peaks of a triangularwave is 6 cm. If the time-base sensitivity were set to 1 msec/cm (CAL), then the period is 6 msecand the frequency is 166.7 Hz.


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X-axis (time)

Y-axis(amplitude)

cm

4. Phase Angle Measurement: Wave Form Method. Here the goal is to measure the difference in phasebetween two signals of the same frequency, for example the input and output signals of a filter oramplifier. If the signals are sine waves, measurement can be made in two ways. The Y-time or wave

form method requires a dual-channel or dual-beam scope and is really just a variation of periodmeasurement. We assume a scope with one horizontal channel.

a. AC couple the Y1 and Y2 vertical channels. Connect the reference signal to Y1 and the comparison

signal to Y2. Use the vertical sensitivity and calibration controls to produce identical Peak-Peak

images of the two waves.b. Adjust the horizontal axis trigger system to sweep from the reference signal. Set the trigger level

control to give a stable image. Set the horizontal sensitivity to show 1-3 cycles of the referencesignal (fewer displayed cycles will give more precise results).

c. Adjust the horizontal calibration control so one complete cycle of the reference signal occupiessome convenient number of centimeters on the calibrated viewing grid. The total number ofdegrees in a cycle (360) will be evenly divided across this distance, in units of degrees/cm. This iscalled a "scale factor."

d. Measure the distance between identical points of the reference and comparison waves.e. Multiply the measured distance by the scale factor. The result is the phase shift between the twosignals.

f. NOTE: this method requires phase-matched vertical amplifiers. It is accurate only for phase shiftsof less than 360.

g. For example, in the following figure Y1 is the reference signal and Y2 is the comparison signal.

One cycle of the reference signal equals 4 cm; thus each cm corresponds to 90 degrees. Thehorizontal distance between the positive peak of the reference signal and the positive peak of thecomparison signal equals 1 cm. When this distance is multiplied by the scale factor (4 cm/360 x 1cm), the result is 90 degrees.


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X-axis (time)

Y-axis(amplitude)

1 cm

Y1

Y2

5. Phase Angle Measurement: Lissajous Method. The other method for phase measurement uses

Lissajous figures formed by the scope when (1) the reference signal is presented to the Y-axis and (2)the comparison signal is presented to the X-axis operated in amplitude mode. Lissajous figuremeasurement requires more elaborate set-up than duration measurement, but it is still straightforward.

a. Place the X-axis in amplitude mode and route the comparison signal to the external input port ofthis channel. The reference signal should be routed to the Y-axis channel.

b. Ground couple both the X-axis and the Y-axis. Use the vertical and horizontal position controls toplace the resulting dot in the exact center of the display screen.

c. AC couple the X-axis input (leave the Y-axis ground coupled). A horizontal line will result. Usethe X-axis sensitivity and calibration controls so this line is a convenient length (say, 5 or 6 cm).Note this length.

d. AC couple the Y-axis and ground couple the X-axis. A vertical line will result. Use the Y-axissensitivity and calibration controls to produce a line exactly the same length as in the last step.

e. Now AC couple the X-axis. The result will be a figure somewhat like the following.

90 or 270 0 or 360180

f. The signal should be symmetrically centered vertically and horizontally on the calibrated viewinggrid. Note that the figure crosses the major vertical grid line at two points, one above the majorhorizontal grid line and one below major horizontal grid line. Measure this distance. Call it A.Now measure the distance between the top and bottom of the figure. Call this distance B.

g. The ratio A/B equals the sine of the phase angle difference between the two waves. Solve for phaseangle by

= arcsin A/B

Remember, "arcsin" means "inverse sine".h. NOTE: this method requires phase-matched vertical and horizontal amplifiers. The equation given

above works only for phase shifts between 0 and 90 degrees, i.e., in Cartesian quadrant I. Forlarger shifts, use the Y-time method to determine the quadrant of the shift, solve the equationabove, then calculate an "equivalent" acute angle in quadrant I.


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in quad. II, "equivalent" angle = 180 degrees - in quad. III, "equivalent" angle = 180 degreesin quad. IV, "equivalent" angle = 360 degrees -

i. For example, in the following Lissajous figure B = 6 cm and A = 5 cm. The the ratio A/B equals0.833 and the phase angle is 56 degrees.

X-axis (amplitude)

Y-axis(amplitude)

A B

6. Signal Monitoring. A common use of scopes is simply to visually monitor one or more signals,without any particular interest in quantitative measurement.

F. Cautions of Use . As with other electronic measurement devices, these cautions protect the user and the

oscilloscope from harm, as well as promote consistent and valid measurements.

1. DO allow adequate warm-up time before taking measurements (usually 5-10 minutes).2. DO set up the scope before attempting measurements by using the GND-coupling, beam-position, and

beam-intensity controls to give a straight-line (no input) trace that is crisp and centered.3. DO begin measurements by adjusting the scope to consistent sensitivity settings for the time-base and

the Y-axis. Good starting values for audio signals are 1 msec/cm (time-base) and 5 Volts/cm (Y-axis).

4. DO begin measurements with the continuously variable sensitivity controls for vertical and horizontalchannels in their calibrated ("CAL") positions.

5. DO position the signal image properly for the observations you wish to make. For time-domainmeasurements of signal period, adjust the time-base to show 1-3 waves. For voltage measurements,adjust the vertical channel sensitivity to fill one-half or more of the screen. Once the time-base andvertical sensitivities are adjusted, the position controls can be used to move the image.

6. DO minimize parallax reading errors by measuring deflections from "dead ahead," not from an angle.7. DO NOT damage the phosphor of the CRT by using very bright intensity settings, or by displaying

stabilized signals for long durations.

VI. Cables, connectors and adaptors.

A. Function. Cables carry electrical signals from one device to another. Such signals may be AC or DC; they

may serve functions of control or communication, or they may carry the information of primary interest inmeasurement. Connectors are the mechanical means by which cables are attached to devices or other cables.Adaptors are specialized connectors that changing from one type or configuration of connector to another.

When cables and connectors interconnect points, those points are electrically identical, even though they

may be physically separated.

Cables, connectors, and adapters have one, two or more electrical conductors. Multiples conductors areelectrically isolated from each other by insulating material. Most commonly, connectors have twoconductors of different polarity: a signal positive or "high" conductor, and a signal ground , negative or


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"low" conductor. In audio work, it is common to use three conductors, where the third is a neutral shield,sometimes called a system or instrument ground with the purpose of isolating the cable from stray

electromagnetic radiation produced by instruments, transducers, motors, lighting fixtures, etc. Anothercommon three-conductor cable system is used for stereo applications (two signal lines, right and left, sharea sole signal ground). Co-axial cable is so called because it contains two or more conductors that share acommon "axis," i.e., the conductors are physically joined and parallel to each other.

Connectors are of two forms: male , with protruding contacts; and female , with recessed contacts. Maleconnectors also are called "plugs"; female connectors also are called "jacks." Connectors exist in a largenumber of physical configurations or designs, usually distinguished by abbreviations based upon the namesof the companies that originally developed the design (e.,g., "GR" connectors developed by the GeneralRadio Corporation). Finally, some configurations of connectors also differ in physical size (diameter).

B. Limits of Function. Ideally, cables are electronically transparent, having no effect on the signals they

conduct. Practically, the electrical conductors (usually copper) offer some small resistance and some smallcapacitance. For very long cables, these resistances and reactances contribute to potential differences(voltage drops) between the two ends of a cable. This amounts to an attenuation of signal level (note: thedecibel originally was devised as a way to measure loss of signal level in cables; cable is rated inattenuation per unit length, e.g., dB/100 meters). These effects can be ignored in audio work if cables are 5-10 meters in length. In other applications (e.g., those involving very small amplitude electrophysiologic

signals), cable length may be critical. Larger diameter conductors generally offer less resistance thansmaller diameter conductors (cable conductors are rated in wire gauge and whether stranded or solid).Separation of co-axial conductors via insulation creates capacitance between the two conductors. Cablecapacitance also is influenced by the surface areas of conductors (greater area produces greater capacitance).These effect usually can be ignored, except for frequencies (and band widths) well above the audio range. Incritical applications, the effects of cable resistance and capacitance can be solved through the use of fiber-optic transmission systems that transmit coherent light through optical conductors. Fiber-optic methodsalso are suitable in cases where large numbers of signals must be transmitted through a small number ofcable assemblies, or in cases where security of transmission is important.

"Ground loops" are undesired signal paths that may occur when cables with three or more conductors (e.g.,microphones wired with a third conductor serving as an instrument ground) are incorrectly integrated withthe instruments they connect. When an instrument ground or "shield" conductor is present, it should beconnected to a real-earth ground or chassis ground at only one physical location.

C. Computations . Cables and connectors are not considered to perform calculations, but they do accomplish a

sort of logical operation. Except for minimal resistance and capacitance effects (which amount to asubtraction of signal energy), cables can be thought of as performing an equivalence operation:

EA = EB

where V represents voltage and where A and B denote physically different points or positions.

D. Configurations of connectors . Connectors are designed to be attached to the ends of cables, or to the panels

of instruments (the latter are called "bulkhead" connectors). In almost all cases, the connectors on cables aremale, while bulkhead (instrument panel) connectors are female. Connectors are attached to cables bystripping off insulation and soldering, or (for some types of connectors) with crimping tools designed forspecific types of connector. Some connectors are mechanically pre-polarized, i.e., designed so that correct

mechanical connection automatically produces proper signal connection (i.e., positive-to-positive andnegative-to-negative). The following connectors (all male) are common in laboratory practice.


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BNC

Alligator

Phone

RCA

(Phono)GR

Cannon

1. "GR" (for General Radio Corporation) connectors, also called "banana" plugs because of appearance.

Most often these are built in pairs (thus, "dual-banana"), but they also are available as single-conductorconnectors. GR plugs may carry labels to designate which contact is signal ground, but they are notmechanically pre-polarized. Most GR connectors are both male and female. GR connector contacts are

silver in color; the insulated housing may be black or some other color. Most VOMs are equipped

with female GR connectors.

2. "Phone" connectors originally were developed by the Bell System in the days of manual telephone

switchboards. Today they are used to connect microphones to other equipment, and to connectearphones to amplifiers, stereo pre-amplifiers, and audiometers. Phone connectors may be two-conductor (one channel) or three-conductor (two channel or stereo) devices. In the one-channel form,the tip of the plug is one conductor (signal) and the shaft is the other (signal ground). In the two-channel form, a ring is added near the tip to accommodate an additional conductor. Two sizes arecommon (for both mono and stereo plugs): 1/4-inch diameter and 1/8-inch diameter.

3. "BNC" (for Berkeley Nucleonics Corporation) connectors are two-conductor devices. The male

conductor has a rotating outer shell containing slots that mechanically latch to pins on the neck ofthe female connector. BNC connectors are mechanically pre-polarized and usually silver in color. Athin center pin is for signal; the outer portion of the connector is signal ground. Most electronic test

instruments are equipped with female BNC connectors.

4. "Cannon" connectors are three-conductor devices used exclusively with microphones. This connector

uses conductors numbered 1 (signal), 2 (signal ground), and 3 (shield or instrument ground). Cannonconnectors are common in professional recording applications where it is important to eliminatespurious electromagnetic noise.

5. "Alligator clips" are spring-loaded connectors with gripping teeth used for temporary connection between

test equipment and electronic components. One-conductor, non-polarized connectors, they are availablein several sizes.

6. "RCA" (for Radio Corporation of America) connectors are two-conductor devices, also called "phono"

(for phonograph) connectors. Because these are very commonly used with home-entertainment stereogear, RCA cable assemblies often contain two sets of conductors. RCA connectors are pre-polarizedand available in various colors.

E. Configurations of adapters. These devices convert the form or function (or both) of dissimilar connectors so

as to allow complete signal paths. Like connectors, they are designated in terms of sex, size, andconfiguration. Another purpose of adapters is to allow splitting or branching of signals. Some examplesof the many types of adapters are:

1. Female BNC-to-male 1/4-inch phone.

2. Female BNC-to-male RCA.


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3. Male BNC (1)-to-female BNC (2), or "T."

4. Female BNC-to-female BNC.

5. Female BNC-to-GR.

F. Common problems with cables, connectors and adapters include the following. The first is a deviceproblem; the remaining are usually user problems.

1. "Open" conductors (e.g., due to broken wires, bad solder joints, or broken contacts) that prevent acomplete signal path.

2. "Shorted" conductors (e.g., due to bad insulation, poor soldering work, or incorrect connection) thatcreate a signal path where there should be none.

3. Routing problems that result in signals not being present at desired locations.

4. Incorrect connection of adapters or of non-polarized connectors resulting in mismatched signal polarities.

5. In applications involving cables with three or more conductors (e.g., microphones), the instrumentground conductor should be "tied to ground" at only one point. If more points are used, ground loopscan occur and cables can become antennas that pick up stray electromagnetic radiation.

G. Cautions of Use.

1. DO think through how you want to route signals from one device to another.2. DO pay attention to the polarity of connectors that are not mechanically pre-polarized.3. DO plan the proper mating of connectors and adaptors (size, sex, and type).4. DO keep cable lengths as short as possible.5. DO learn wiring conventions for connectors and adaptors.6. DO check suspect cables with a VOM continuity checker.7. DO mark and set aside cables (or connectors or adapters) that do not function correctly.8. DO NOT pull or jerk connectors and cables.

9. DO NOT force connectors into place.10. DO NOT jerk connectors loose from equipment.11. DO NOT drag equipment by pulling cables.

SELECTED REFERENCES

Ballou, G., Editor. (1987) Handbook for Sound Engineers. Indianapolis, IN: Howard W. Sams & Co.Cudahy, E. (1988). Introduction to Instrumentation in Speech and Hearing. Baltimore, MD: Williams and

Wilkins Co.Curtis, J., and Schultz, M. (1986). Basic Laboratory Instrumentation for Speech and Hearing. Boston, MA:

Little, Brown and Co.Grob, B. (1977). Basic Electronics, 4th Ed. New York, NY: McGraw-Hill Book Co.Lenk, J. (1969). Handbook of Practical Electronic Tests and Measurements. Englewood Cliffs, NJ: Prentice-

Hall, Inc.Lenk, J. (1968). Handbook of Oscilloscopes: Theory and Application. Englewood Cliffs, NJ: Prentice-Hall,Inc.

Lenk, J. (1971). Handbook of Electronic Test Equipment. Englewood Cliffs, NJ: Prentice-Hall, Inc.Radio Shack. (1972). Electronics Data Book. Fort Worth, TX: Radio Shack, Inc.

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