a controllable phase coherent pulsed rf signal generator for microwave network analyzer measurements

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 47, NO. 12, DECEMBER 1999 2605

A Controllable Phase Coherent Pulsed RF SignalGenerator for Microwave Network

Analyzer MeasurementsPhilip Vael and Yves Rolain,Senior Member, IEEE

Abstract—In this paper, a method is proposed to build aphase coherent modulated radio-frequency (RF) signal with highmodulation depth, which can be used as an excitation signalfor nonlinear pulsed-RF network analyzer measurements. Thesource consist of an RF carrier modulated by an arbitrarywaveform generator whose sampling clock is phase coherent tothe carrier. A software feedback technique is used to eliminatespurious modulation harmonics and to correct the amplitude andphase distortions in the IF signal path. This technique allowsto create a modulated excitation signal with a known modu-lation spectrum (in amplitude and phase). Such a “controlledmodulation” signal is required to fully characterize a device-under-test under noncontinuous wave (modulated or pulsed) testconditions with a sampling downconvertor. The measurement ofa controlled pulsed-RF spectrum shows the obtained performance(the modulation bandwidth is limited to 4 MHz at this moment).

Index Terms—Microwave measurements, nonlinearities, non-linear systems, pulse measurements, pulse modulation, signalgenerators, spectral analysis.

I. INTRODUCTION

T HE measurement capabilities of recently developed vec-torial nonlinear microwave network analyzers [1], [2]

allow to characterize the nonlinear behavior of microwavecomponents and systemsunder continuous wave excitation.Thereto, simultaneous absolute measurement of transmittedand reflected waves at the input and output of the device-under-test (DUT) in both amplitude and phase is required.

Today, there is also a need to characterize microwavecomponentsunder noncontinuous wave excitations(modulatedor pulsed-RF signals). In this paper, a possible extension of thenonlinear microwave network analyzer toward noncontinuouswave excitations is proposed. Thereto, an adaptive setup thatgenerates and measures a phase coherent modulated RF exci-tation signal is used. When information of both the modulation(envelope) and carrier signal is wanted simultaneous fromthe measurement data, a phase coherent signal is needed(i.e., the phase relation between the carrier and modulationharmonics is independent of time). The measurement is doneby a downconvertor that uses the “harmonic mixing” principle,

Manuscript received March 26, 1999; revised July 12, 1999. This workwas supported by the Flemish Institute for the Improvement of the Scientific-Technological Research in Industry (IWT) under a grant, and by the BelgiumFederal Government under Grant IUAP 4.2.

The authors are with the Electrical Measurement Department, Vrije Uni-versiteit Brussel, 1050 Brussels, Belgium.

Publisher Item Identifier S 0018-9480(99)08462-8.

which makes a low-frequency copy of the input signal. Thismeans that the amplitude and phase relation of the spectralcomponents of the input signal remains the same.

To ensure phase coherency, three devices in the generatorsetup of Fig. 1 need a reference clock, namely, the frac-tional_N synthesizer, the analog-to-digital convertor (ADC)and the arbitrary waveform generator (AWG). A first possi-bility is to use the 10-MHz reference clock of the microwavesource as a reference clock for all three devices. A secondpossibility consists of using a frequency-divided carrier as areference signal for all three devices. Combinations of the twoformer cases were also investigated. The 10-MHz referenceclock of the microwave source is fed to the fractional_Nand ADC, while the AWG gets the frequency-divided carrierreference clock. To compare the three different setups, a mea-surement of the obtained spectrum is performed. Both short-and long-term drift are considered. To correct for the amplitudeand phase distortions in the signal path, a software feedbacktechnique is used [4]. This allows to create a modulatedexcitation signal with a modulation spectrum known bothin amplitude and phase. Verification of the generated phasecoherent modulated RF signal relies on the measurement of theobtained signal by a calibrated digital sampling oscilloscope(DSO) [5], which is independent of the adaptive measurementsetup.

II. M EASUREMENT SETUP

The proposed setup shown in Fig. 1, which is a part of avectorial nonlinear network analyzer, can be divided in twoblocks. The signal generator (see top of Fig. 1) generatesthe phase coherent modulated RF signal. The RF carrier atfrequency is generated by a microwave synthesizer (HP83650B). The modulation signal is fed as a sampled datastream to a VXI-based AWG (type HP E1445) and has alimited bandwidth of 20 MHz because the maximum samplingclock frequency of the AWG is 40 MHz. The RF signal andthe modulation signal are then combined by a mixer (typeZEM-4300). The microwave source is set to produce a carrieroutput level of 7 dBm at the LO port of the mixer. TheRF output signal is then amplified by an MAR-2 amplifier(device of MiniCircuits with gain of 12 dB). The output of theamplifier is filtered by a low-pass filter (type TTE- J3627, with

MHz), to remove all the higher harmonics ofthe RF signal and spurious mixing products. The output of thefilter is the requested modulated RF signal.

0018–9480/99$10.00 1999 IEEE

2606 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 47, NO. 12, DECEMBER 1999

Fig. 1. Setup to generate and measure a phase coherent modulated RF signal.

The second block is the measurement setup required tocharacterize and control the signal. It contains four differentcomponents: the fractional_N synthesizer, the downconvertor,a VXI-based ADC (type HP E1437), and a computer (NationalInstruments’ PCI-MXI 8000) connected via the VXI–MXIinterface. The modulated signal (hereafter “signal under test”)described earlier, is connected to the input of the harmonicmixing downconvertor (type HP 85120-1250), which makes alow-frequency copy of the input signal. The downconvertedsignal is digitized by the HP E1437 ADC. The trigger signalfor the ADC is generated by the AWG, which gives a markerout signal at the start of each modulation period. The measureddata is then transferred into a computer for further processingto the MATLAB environment.

To ensure a phase coherent relationship between andthe modulation spectra, the sampling clock of the AWG isobtained by direct division of the carrier frequency . The

prescaler has a fixed division factor of 64. Hence, the sampleclock becomes

(1)

The sampling frequency requested for downconversion isgenerated by a fractional_N synthesizer, whose reference clockinput is connected to the 10-MHz reference signal of themicrowave synthesizer. The sampling frequency of the ADC isalso the 10-MHz reference clock of the microwave synthesizer.This possibility, to ensure phase coherency, is shown in thesetup of Fig. 1, and is known as “10 MHz_PRES&RFG.”

A second possibility consists of using a frequency-dividedcarrier as a reference signal for the AWG, fractional_N syn-thesizer, and ADC. Since the reference clock frequency for thefractional_N synthesizer has to be 10 MHz and the prescalerhas a fixed division factor of 128, only an RF frequency of1.28 GHz can be used in this setup. This possible setup is

VAEL AND ROLAIN: CONTROLLABLE PHASE COHERENT PULSED RF SIGNAL GENERATOR 2607

TABLE ISHORT- AND LONG-TERM EFFECTS

TABLE IIRELATIVE VALUES OF MULTISINE EXAMPLE 1

known as “10 MHz_PRES” because the reference clock is theRF frequency divided by a prescaler.

A third possibility consists of using the 10-MHz refer-ence clock of the microwave source for the AWG, frac-tional_N synthesizer, and ADC. This possibility is known as“10 MHz_RFG” because the 10-MHz reference clock of theRF generator is used.

III. M EASUREMENT PRINCIPLE

The goal of the measurement principle is to set and verifythe relative amplitudes and relative phases of the modulationsignal relative to the first spectral modulation component.A software feedback loop will be used to set the spectralcomponents of the modulation to the requested values, despitethe nonidealities of the hardware. Therefore, the followingassumptions on the measurement setup must be made.

1) The downconvertor board introduces only a linear phasedistortions in the frequency band of the modulated RFsignal.

2) The delay introduced in the signal path has to remainstable over time.

3) The filter is a linear time-invariant (LTI) system.4) The MAR-2 amplifier is working in the linear region of

operation.

The advantage of the software feedback control is that thelinear dynamic response of the filter and amplifier can becompensated by the adaptation of the signal loaded into theAWG by the following steps.

Step 1: Specify the required modulation signal first.Suppose that this modulation signal is a baseband

multisine, whose sampled data representation is

(2)

where is the number of sines, the amplitude,and the phase of the th sine. The phases ofthese sinusoids can be determined by use of theSchroder equation to reduce the crest factor [4]

(3)

Step 2: To remove leakage in the measurement, the con-straint that an integer number of periods of themodulation fit exactly in the acquisition windowis imposed.

Step 3: The calculated modulation waveform is loaded intothe AWG and the modulated RF signal is measured.

Step 4: After conversion to the spectral domain, the relativeamplitudes and phases of thespectral modulation components relative to the firstone are calculated for the upper sideband of themeasured data

(4)

(5)


TABLE IIIRELATIVE AMPLITUDES AND PHASES OF THESPECTRAL MODULATION COMPONENTSBETWEEN THE MEASURED AND SPECIFIED MODULATION SIGNAL FOR THE

TWO ITERATIONS. m: MEASURED, o: DESIRED

Fig. 2. Multsine with four sinusoids andfmod = 99 kHz.

where is the frequency of the carrier andthe fundamental frequency of the modulation com-ponents.

The compensation (superscript) for the relative differenceof the spectral modulation components is done by the linesof [3]

(6)

with

(7)

where stands for the specified modulation signal,for thenew modulation signal, is the iteration index, and is themeasured signal. According to the given scheme, there is nocompensation in Step 1.

The new modulation signal, which will be loaded into theAWG, is then calculated by (2) with the new values for theamplitudes and phases of the modulation signal.

Before the envelope signal can be reconstructed from themeasured data, a linear phase delay has to be compensatedfor every frequency component of the modulation signal.Therefore, a delay is fitted on the measured data. The slope

Fig. 3. Measured signal after compensation (top) and associated amplitudespectrum (bottom).

of this function is the constant phase delay and has to becompensated by the following equation:

(8)

Step 5: The compensation will be stopped when somefigure-of-merit is met. Here, the following criteriaare selected:

Allowed Phase Error

(9)

Allowed Phase Error

(10)

Whenever (9) and (10) are not met, the modulation wave-form must be reloaded into the AWG and a new cycle starts(i.e., go back to Step 3). When both (9) and (10) are met, thenthe modulation signal is realized with sufficient accuracy andthe process is stopped.

IV. EXPERIMENTAL RESULTS

The three different setups that generate and measure aphase coherent modulated RF signal are tested and compared.For these measurements, a phase coherent modulated RFsignal that consist of a carrier with 1.28-GHz RF frequency,a multisine with four sines, and a fundamental modulation


Fig. 4. Reconstructed and specified modulation signal (top) and error signal(bottom).

Fig. 5. Measured phase coherent pulsed RF signal (top) and associatedamplitude spectrum (bottom).

Fig. 6. Pulsed signal as modulation signal.

frequency of 99 kHz was generated and measured. The meanand standard deviation of the amplitude and phase between thecarrier and first modulation component are given in Table I.

Fig. 7. Reconstructed and specified modulation (top) and error signal (bot-tom).

Fig. 8. Linear phase contribution of the spectral components.

Fig. 9. Amplitude error of spectral modulation components.

On the left-hand side of Table I, short-term effects are shown(in minutes). Thereto, 20 successive measurements are taken.On the right-hand side of Table I, the long-term effects areshown. Thereto, a pause of 1 min is included between themeasurements. From these long-term effects, it is seen that thesmallest standard deviation of the phase difference is given by


Fig. 10. Illustration on how the DSO measures.

TABLE IVPHASE VALUES OF THE SPECTRAL MODULATION COMPONENTS FOR THESPECIFIED AND MEASURED PHASE COHERENT MODULATED RF SIGNAL

the setup “10 MHz_PRES&RFG.” For the other setups, thevalue lays in the same range and is approximately 0.05. Thestandard deviation of the amplitude difference of all setupslays in the range of approximately67 dBm. For the short-term effects, it can be seen that the setup “10 MHz_PRES” hasthe smallest value of all three setups for the standard deviationof the phase difference, which is about 0.0346, and for theamplitude difference, about 67.806 dBm. This means thatmeasurements done in a short time has the best accuracywith the setup “10 MHz_PRES.” In the experiments thatfollow, the setup “10 MHz_PRES&RFG” (shown in Fig. 1)is used because this setup gives us the best accuracy withlong measurement times.

In the first example, a phase coherent modulated RF signalconsisting of a carrier with a RF frequency of 1.28 GHz, amodulation multisine with four sinusoids, and a fundamentalmodulation frequency of 99 kHz (see Fig. 2) is chosen.

The ideal and measured relative amplitudes and phases forthe spectral components relative to the first spec-tral modulation component are given in Table II. This phasecoherent modulated RF signal (see Fig. 3) is generated andmeasured by the setup of Fig. 1. Compensation is stoppedwhen the amplitude error is smaller than 1% and the phaseerror is smaller than 3. The stopcriteria was met after twoiterations (values of the relative amplitudes and phases aftereach iteration are given in Table III). The envelope signal,


Fig. 11. Multisine with five sinusoids andfmod = 100 kHz.

Fig. 12. Measured signal after compensation (top) and associated amplitudespectrum (bottom).

which is reconstructed from the measured signal, is shownin Fig. 4. The error between the specified and reconstructedmodulation signal is also shown in Fig. 4. From this figure,it is seen that the reconstructed modulation signal matchesthe specification with sufficient accuracy within two iterations.The relative phases are all smaller than 0.03even if onlyan error smaller than 3was asked in the stop criteria. Therelative amplitudes are below 1% without compensation andare smaller than 0.13% after two iterations.

In the second example, a pulse with a limited numberof spectral contributions (70 frequency components) at afundamental modulation frequency of 30 kHz and a duty cycleof 10% is generated. The measured phase coherent modulatedRF signal is shown in Fig. 5 and the ideal envelope is shownin Fig. 6. The RF signal frequency is 1 GHz. For the spectralmodulation components, a phase error smaller than 8and anamplitude error smaller than 4% was reached. The envelopesignal, which is reconstructed from this measured signal, isshown in Fig. 7. The error between the specified and recon-structed modulation signal is also shown in Fig. 7. In Fig. 8,the linear phase contribution, which has to be compensatedfor the modulation signal, is shown. The allowed amplitude

and phase errors for the spectral modulation components weremet after two iterations. Since the phase loses significancewhen the amplitude is low, the compensation is only donefor the spectral modulation components whose amplitude ishigher than 50 dBm. This means that the zeros of the pulsespectrum are not compensated. From Fig. 5, it can be seenthat the upper sideband contains seven frequency componentsbelow 50 dBm. A maximum amplitude error of 3.715% isobtained at component number 11. These amplitude errorscan be found in Fig. 9. The measured modulated RF signalis shown in Fig. 5.

V. VERIFICATION OF EXPERIMENTAL RESULTS

For the verification of the experimental results, a totallyindependent measurement setup is used. The phase coherentmodulated RF signal, which is generated and compensatedby the principle described above, will be measured with acalibrated DSO (type HP54120T) [5]. The goal is to comparethe amplitude and phase values of the spectral componentsof the measured signal with the setup of Fig. 1 and withthe DSO.

To measure the amplitude modulation of the phase coherentmodulated RF signal, the DSO will be triggered on themodulation signal by the AWG, which produces a triggersignal each time the modulation period starts. The length ofthe acquisition window (at least one modulation period long) isspecified by the user that contains 1024 sample points. Whenthe DSO receives a trigger signal, a trace of 1024 sample pointsis measured. Since the acquisition window contains an integernumber of the modulation period and the carrier frequency isnot harmonically related to the modulation frequency, i.e.,

(11)

the acquisition window will not be harmonically related to thecarrier frequency. Therefore, the DSO will measure anothervoltage value of the modulated carrier at each acquisitionwindow (see Fig. 10).

Now, to determine the amplitude modulation of the modu-lated RF signal, many measurements have to be taken and thestandard deviation (12) of the voltage at each sampled datapoint for all measured traces has to be calculated as follows:

(12)

In this verification, the phase coherent modulated RF signalconsist of a carrier with an RF frequency of 1010.010 101 MHzand a multisine containing five sinusoids with a fundamentalmodulation frequency of 100 kHz. The modulation signal isshown in Fig. 11. This signal is generated and compensatedwith the setup of Fig. 1. The compensation is stopped whenthe amplitude error is smaller than 1% and the phase error issmaller than 4. The result is shown in Fig. 12. The errorsignal between the reconstructed and specified modulationsignal is displayed in Fig. 13.


Fig. 13. Reconstructed and specified modulation signal (top) and error signal(bottom).

Fig. 14. Standard deviation of measured sample points with the digitalsampling scope.

The generated signal is then measured eight times withthe calibrated DSO. Each measurement consist of 512 tracesof 1024 sample points. For each measurement, the standarddeviation is calculated and shown for measurement number 1in Fig. 14. The phase values of the spectral modulation com-ponents are determined for each measurement. The mean andstandard deviation of the phase values are given in Table IV.From this table, a little phase residual of approximately 4can be seen for the spectral modulation components number1 and 5 for the measurement result of the DSO and themeasurement result of the technique described in this paper.For the spectral modulation components 2, 3, and 4 is the phaseresidual approximately 3. When the uncertainty regions forthe spectral modulation components 2, 3, and 4 of the DSOmeasurement are taken into account, the phase values of thespecified modulation signal lays within that uncertainty region

of about 4 , which means that the generated modulated RFsignal is synthesized with sufficient accuracy.

VI. CONCLUSIONS

The measurement results allow to conclude that an arbitraryphase coherent modulated RF signal can be generated andmeasured. To minimize spectral errors in amplitude and phase,a software feedback technique is used (this means that theexcitation signal at the input port of the DUT has a knownamplitude and phase spectrum, where the user is free to specifyany kind of modulation signal in either the time or frequencydomain with a modulation bandwidth limited to 20 MHz inthe proposed setup). The verification results allow to concludethat the arbitrary phase coherent modulated RF signal realizedwith the described technique has sufficient accuracy.

REFERENCES

[1] J. Verspecht, P. Debie, A. Barel, and L. Martens, “Accurate on-wafermeasurement of phase and amplitude of the spectral components ofincident and scattered voltage waves at the signal ports of a nonlinearmicrowave device,” inIEEE MTT-S Int. Microwave Symp. Dig., Orlando,FL, May 1995, pp. 1029–1032.

[2] T. Van den Broeck and J. Verspecht, “Calibrated vectorial nonlinear-network analyzers,” inIEEE MTT-S Int. Microwave Symp. Dig., SanDiego, CA, 1994, pp. 1069–1072.

[3] F. Louage, J. Schoukens, and Y. Rolain, ‘Generation of computer con-trolled estimations and its applications to the detection and measurementof harmonic distortions,” inIEEE IMTC, Hamamatsu, Japan, May 1994,pp. 1385–1388.

[4] M. R. Schroeder, “Synthesis of low peak factor signals and binarysequences with low autocorrelation,”IEEE Trans. Inform. Theory, vol.IT-16, pp. 85–89, Jan. 1970.

[5] A. Barel and Y. Rolain, “A microwave multisine with known phasefor the calibration of narrow-band nonlinear vectorial network analyzermeasurements,” inIEEE MTT-S Int. Microwave Symp. Dig., Baltimore,MD, 1998, vol. 3, pp. 1491–1494.

Philip Vael received the elektrotechnical engineer-ing degree from the Vrije Universiteit Brussel,Brussels, Belgium, in 1997.

He then joined the Electrical MeasurementDepartment (ELEC), Vrije Universiteit Brussel,as an IWT Reseacher, where he is involvedwith a pulsed RF network analyzer for nonlinearmicrowave circuits and systems. His main researchinterests are optical-fiber communications andnonlinear microwave measurement techniques.

Yves Rolain (M’90–SM’96) is currently with theElectrical Measurement Department (ELEC), VrijeUniversiteit Brussel, Brussels, Belgium. His mainresearch interests are nonlinear microwave measure-ment techniques, applied digital signal processing,parameter estimation/system identification, and bio-logical agriculture.

a controllable phase coherent pulsed rf signal generator for microwave network analyzer measurements

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