IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-17, NO. 4, DECEMBER 1968

REFERENCES[11 R. W. Anderson, "S-parameter techniques for faster, more ac-

curate network design," Hewlett-Packard J., vol. 18, February1967.

[2] R. A. Hackborn, 'An automatic network analyzer system,"Microwave J., vol. 11, May 1968.

[31 K. Kurokawa, "Power waves and the scattering matrix," IEEETrans. Microwave Theory and Techniques, vol. MTT-13, pp.194-202, March 1965.

[4] F. Weinert, "Scattering parameters speed design of high fre-quency transistor circuits," Electronics, vol. 39, September 5,1966.

[5] G. E. Bodway, "Two port power flow analysis using generalizedscattering parameters," Microwave J., vol. 10, May 1967.

[6] -, "Circuit design and characterization of transistors bymeans of three port scattering parameters," Microwave J., vol.11, May 1968.[71 W. H. Froehner, "Quick amplifier design with scattering param-eters," Electronics, vol. 40, October 16, 1967.[8] R. W. Anderson and 0. T. Dennison, "An advanced new net-work analyzer for sweep-measuring amplitude and phase from 0.1to 12.4 GHz," Hewlett-Packard J., vol. 18, February 1967.[9] "Network analysis at microwave frequencies," ApplicationNote 92, Hewlett-Packard Co., Palo Alto, Calif., May 1968.[10] K. B. Magleby, "A computer for instrumentation systems,"Hewlett-Packard J., vol. 18, March 1967.[11] D. M. Kerns and R. W. Beatty, Basic Theory of WaveguideJunctions and Introductory Microwave Network Analysis, Inter-nat'l series of monographs in electromagnetic waves, vol. 13.New York: Pergamon, 1967.

Calibration of a Kerr Cell System for High-VoltagePulse Measurements

ESTHER CHRISTMAS CASSIDY, SENIOR MEMBER, IEEE, HAROLD N. CONES, SENIOR MEMBER,IEEE, DONALD C. WUNSCH, STUDENT MEMBER, IEEE, AND STANLEY R. BOOKER, MEMBER, IEEE

Abstract-Several techniques for calibration of an electrooptical(Kerr cell) high-voltage pulse measuring system are described. In-dependent calibrations, without reference to pulse divider measure-ments, are achieved by application of a direct bias voltage to theKerr cell. After calibration, experiments with voltages as high as 100kV demonstrate reasonable agreement (to within 1 percent) be-tween simultaneous Kerr cell and calibrated pulse divider measure-ments.

I. INTRODUCTIONJVi/1ANY normally optically isotropic liquids ex-

hibit birefringence when subjected to an elec-trostatic field. When polarized light is passed

between two electrodes immersed in a vessel containingsuch a liquid, application of a high voltage alters thestate of polarization of the light. If the vessel is installedbetween crossed polarizers, the applied voltage, ineffect, causes modulation or gating of the light. Devices(Kerr cells) utilizing this phenomenon, the so-calledKerr electrooptical effect [I], are often used as ultra-high-speed optical shutters and laser Q-switches.

In 1963, Ettinger and Venezia [2] developed a pulse

Manuscript received June 26, 1968. This paper was presented atthe 1968 Conference on Precision Electromagnetic Measurements,Boulder, Colo. This work was supported in part by the U. S. AtomicEnergy Commission through the Sandia Corporation, Albuquerque,N. Mex.

E. C. Cassidy and H. N. Cones are with the National Bureau ofStandards, Washington, D. C.

D. G. Wunsch and S. R. Booker are with the Sandia Corporation,Albuquerque, N. M.

voltage measuring system based on the Kerr effect.More recently, a much improved system for measure-ment of pulses between 30 and 100 kV was described byWunsch and Erteza [3 ]. These systems, particularly thelatter, offer unique advantages over more conventionalresistive and/or capacitive divider techniques of high-voltage pulse measurement, including the following:1) measurement resolution increases with the magnitudeof the applied voltage; 2) the system has a linear fre-quency response to about 100 MHz; and 3) the measur-ing circuit is electrically isolated from the highvoltagecircuit, thus avoiding sources of error [4] that are char-acteristic of divider techniques.To date, most pulse voltage measurements are made

by use of calibrated resistive or capacitive dividers.Calibration is achieved either by low-voltage measure-ments (and extrapolation to high voltages) or by com-parison at high voltage with a standard divider (whichwas itself calibrated at low voltages). The dividing ratioat higher voltages is, therefore, always somewhat un-certain. The present work reports development andevaluation of several methods for calibrating a Kerr cellsystem, similar to that described in [3], for measure-ment of pulses with peak amplitudes as high as 100 kV.Techniques that permit calibration without reference tocalibrated divider measurements are emphasized, inas-much as they provide an independent check of dividermethods, thus adding considerably to our confidence inthe accuracy of high-voltage pulse measurements.

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II. THE KERR CELL DESIGN AND LIQUIDSince Kerr cells suitable for high-voltage pulse mea-

surements are not commercially available, and sincecalibration techniques depend upon cell constructionand the purity of its liquid, some discussion of theseaspects of the present system is required. The cells aresimilar in design to those described by Zarem et al. [5 ].Glass to Kovar seals are used for insertion of the elec-trodes (parallel nickel plates; dimensions =0.2 cm by1.5 cm by 10 cm; interelectrode distances dr0.25 to0.75 cm) into the cell. The cell used for measurement ofvoltages in excess of 60 kV was encapsulated (except forits windows) in silicone rubber compound to preventexternal flashover. It should be noted, however, thatexposure to such high field strengths is not recom-mended because of the increased probability of internalcorona or flashover. These hazards should be avoidedby using cells of greater interelectrode distance athigher voltages.

Because of its large Kerr constant and relatively highdielectric strength, nitrobenzene is used in the Kerrcells. In order to reduce space charge effects and mini-mize the probability of electrical breakdown in the cell,nitrobenzene of higher purity than is available commer-cially is necessary. Further purification is achieved bypassing nitrobenzene (under vacuum) through a chro-matographic column of neutral alumina directly intothe cell. Initial quantities of the processed nitrobenzeneare used to wash the cell and are then discarded untilmeasurements of the current passed by the cell uponapplication of direct voltage indicate that adequatepurification has been achieved. The following criteriawere found helpful in this procedure. 1) When purity isnot adequate, the conduction is ohmic, and the currentis relatively large and independent of the time intervalbetween voltage applications. 2) When purity is satis-factory, the conduction is nonohmic; the peak currentis smaller and strongly dependent upon the time intervalbetween voltage applications; and the current, after afew minutes of high-voltage conditioning, remains stableat a relatively low level (

CASSIDY et al.: KERR CELL SYSTEM FOR HIGH-VOLTAGE PULSE MEASUREMENTS

3 5 7 9 11 13 15 17

DC BIAS CIRCUIT

Fig. 2. The Kerr electrooptical system.

the cell by the positive pulse. This bias voltage servesseveral purposes: 1) it reduces the danger of internalarcing by conditioning the cell for application of highvoltage; 2) it increases the sensitivity of the Kerr system(more oscillations of the transmitted intensity are pro-duced by a given pulse voltage); and 3) it enables cali-bration of the system without reference to pulse dividermeasurements.When voltage is applied across the cell electrodes, the

state of polarization of the beam is altered (the Kerreffect), thus causing variations in the intensity of thetransmitted light. The intensity I at any instant is de-pendent upon the strength E of the electric field imposedby the applied voltage as follows [3], [5]:

(1/Im) = sin2- (/Em)2, (2)2where Im is the maximum intensity transmitted by thesystem and Em is the field strength required to producethe first transmission maximum. The relative intensity(I/Im) of the transmitted beam as a function of relativefield strength (E/Em), as computed by use of (2), isshown graphically in Fig. 3. Maximum transmission willoccur when (F/Em) = 1, -3, a/5, etc., and minimumtransmission will occur when (F/Em) = 0, V2, V4, etc.Thus the relative strength (F/Em) of the field im-

posed by an applied voltage may be determined from atime-resolved oscilloscope record of the photomulti-plier's response to the modulated beam intensity asfollows. If the relative intensity is increasing at theinstant of measurement,

r 2 n(F/Em) = + - arc sin (I/Im)']X (3)

where n is the number of maxima and minima traced bythe waveform prior to the instant of measurement and(I/Im) is the relative intensity of the beam at the instantof measurement. If (1/Im) is decreasing at the instant ofmeasurement,

F ~~~2(F/Em) = + 1) - - arc sin (I/II,.) (4)7rIThe applied voltage V is determined from this ratio(F/Em) by use of the following equation:

V = (E/E.)(Emd), (5)

' 1.00

z 0.75zw

z

I 0.5CI

w 0.25

0Jw 0.0

o. 0.5 l0 1.5 20 Z5 3.0 3.5 4.0RELATIVE ELECTRIC FIELD STRENGTH (E/Em)

Fig. 3. Relative transmitted light intensity as a function of relativefield strength with numerical values assigned to successive maximaand minima.

where the product (Ed) of the field strength Em re-quired to produce maximum transmission and the inter-electrode distance d is the cell constant. Determinationof this quantity (Emd) constitutes calibration of thesystem. In the present work, calibrations of a cell withrelatively small interelectrode spacing (-0.25 cm) wereachieved by the methods described in Section IV. Inthis case, the field imposed by an applied voltage wasassumed to be uniform, since little evidence of fielddistortion was observed. However, two cells with greaterelectrode spacing (0.75 cm) exhibited significant fielddistortion effects when direct bias voltage was appliedto the cell. In these cases, effective calibrations wereachieved by the techniques described in Section VI.

Tracings from typical oscilloscope records are shownin Fig. 4. The top trace vs [see (1)] gives the dividermeasurement of the peak amplitude of the pulse. Theother traces show (1/Im) as a function of time over thelatter portion of the pulse, including the peakamplitudepoint and the trailing edge. Numerical values (n) areassigned to successive maxima and minima as indicatedpreviously. These are counted from right to left for con-venience, since the peak amplitude (the selected pointof measurement) of the applied pulse occurred just priorto the trailing edge. It should be noted that the valueassigned to the first intensity peak (on the right of therecord) is affected by the bias voltage. When the cell isbiased to the first, second, or third transmission mini-mum, this peak is indicative of n = 3, 5, or 7, respec-tively. The traces were obtained with no bias voltageapplied (second trace) and with applied direct biasvoltages that produced the first transmission maximum,the first minimum, and the third minimum (third,fourth, and fifth traces, respectively). The higher valuesof n prior to the peak of the pulse (n = 19, 22, 33) dem-onstrate the increased sensitivity of the system at higherbias levels.Superimposed pulse divider measurements are com-

pared with superimposed Kerr system results (obtainedwith another Kerr system) in Fig. 5. The peak ampli-tude of the superimposed pulses differed by 0.1 percent(peak amplitudes in the top records 142 300 volts and142 450 volts) and by 1 percent (peak amplitudes inthe bottom records 142 300 volts and 143 800 volts).

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, DECEMBER 1968

I I 9 7 5 3 n 8~~ ~~ ~~~ BIAS:

7 ZERO

19 5 3=n

II,

TIME~ ~ ~ ~ ~ ~ A

m/\ X M A N S~~~~~~~~IT MIN

9 7=n

Im\A A:0fi11h02ARSA ~3RD MIN10 12 14 16 18

TIME-iis

Fig. 4. Calibrated pulse divider (top) and Kerr system measure-ments of peak amplitude of a high-voltage pulse. Cell constant(Emd) = 2776 volts.

DOUBLE TRACES

The superior measurement resolution afforded by theKerr cell system, as compared to that obtained withconventional pulse divider techniques, is evident; in-dications of the peak amplitude differences are notdetectable in the divider records, whereas sizable differ-ences are noted in the Kerr cell records.

IV. CALIBRATION WITH A UNIFORM FIELDAs stated above, assumption of a uniform interelec-

trode field distribution did not introduce serious errorwhen Kerr cells having relatively small (-0.25 cm)electrode spacing, filled with highly purified nitro-benzene, were used. In such cases, several straight-forward methods of calibration were found to be valid,including the following.

A. Pulse Divider TechniquesIf no bias voltage is applied, the cell constant (Emd)

may be obtained quite simply from simultaneous cali-brated divider and Kerr system measurements by use ofthe following equation:

(6)(E,d) = VD(E/Em)where VD is the divider measurement derived from (1)and (E/Em) is derived from the photomultiplier recordof n and (I/I.) using (3) or (4). Accuracy in the calibra-tion is limited only by the accuracy of the calibrateddivider ratio and by error in reading of (1/Im) from theoscilloscope record. In the present work, it is estimatedthat these errors did not exceed 1 percent.

If a bias voltage is applied to the cell, (Emd) may bedetermined from the following equation:

( VD + VBIAS(EIE,n) (7)

DIFFERENCE IN PEAK AMPLITUDE 0.1%

DIFFERENCE IN PEAK AMPLITUDE 1.0%

Fig. 5. Superimposed pulse divider and Kerr system measure-ments. Peak amplitudes: 142 300 and 142 450 volts (top), and142 300 and 143 800 volts (bottom).

In the present work, the direct voltage VBIAS, which wasmeasured to within 0.01 percent by use of a resistivedivider, was adjusted until the first, second, or thirdtransmission minimum was observed visually. The firstpeak of the pulse-induced photomultiplier record wasthus indicative of n = 3, 5, or 7, respectively, and (E/Em)was the total relative field strength imposed by thepulse and bias voltages. Values of (E.md) determined inthis way are subject to the same errors as in the previouscase, the principal limitation in both cases being theirdependence upon the calibrated pulse divider measure-ments.

B. Two-Pulse TechniqueReference to pulse divider measurements may be

avoided by applying two identical pulses (vl=v2) to thecell while it is biased first at one and then at anothervoltage. The total voltages across the cell are thus

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CASSIDY et al.: KERR CELL SYSTEM FOR HIGH-VOLTAGE PULSE MEASUREMENTS

V1 = V1 + VBIAS 1 and V2 = V2 + VBIAS 2, (8)and the cell constant may be written

(Ev,d) VBIAS 1 VBIAS 2 (9)(El/Em) - (E2/Em)

with all parameters measured as in Section IV-A andwith the added advantage that pulse divider measure-ments are not required. Significant errors may beaverted by making every feasible effort to satisfy thefollowing criteria: 1) the pulses applied must be identi-cal, and 2) factors contributing to error in the difference[(EI/Em) - (E2/Em) ] must be minimized. To achieve thelatter, the oscilloscope's vertical amplifier may be ad-justed to yield maximum deflection for Im on the oscillo-scope screen, VBIAS I may be made as high as is feasiblewith a given cell, and VBIAS 2 may be made as low asfeasible (zero if no bias is desired for conditioning pur-poses). In the present work, values of (Emd) obtained bythis method for a cell that exhibited little evidence ofnonuniformity in its field distribution differed frompulse divider calibrations by about 2 percent.

C. Detection and Measurement of Bias at MinimumFinally, if the field distribution is uniform, indepen-

dent calibration may be achieved by adjusting the biasvoltage until the first, second, or third transmissionminimum (n = 2, 4, or 6) is observed or detected photo-electrically. The cell constant is then calculated from

(Emd) = Vmin (10)(Emin/Em)where Vmin is the bias voltage at which the minimum isobserved, and, from (3), (Emiin/Em) = V/2, V/4, or V6.Minimum, rather than maximum, transmission pointswere selected for detection, because perception of themaximum intensity of a high-intensity source is moredifficult. Minimum transmission points, on the otherhand, were detected reproducibly to within 0.1 percent.Values of (Emd) for the cell with d~0.25 cm, as deter-mined by this method, deviated from pulse divider cali-brations by less than 1 percent. This method was pre-ferred because it does not require reference to pulsedivider measurements.

V. FIELD NONUNIFORMITYUnfortunately, calibrations of cells with greater inter-

electrode spacing (-0.75 cm) showed significant errorswhen calibrated by the foregoing methods. Applicationof a direct bias voltage produced distortion in the elec-tric field distributions, probably because it caused ionicimpurities in the nitrobenzene to collect near the elec-trodes. Experiments were therefore performed with cellsdesigned for use at higher voltages to investigate theextent of field distortion.

7NzE

0.80.80

d0.840.89

E/Emin = l.O 1..1257///////// /7///CATHODEFig. 6. Profile of the electric field distribution over the interelectrode

area (end view, d zO0.75 cm).

In the first of these experiments, a pinhole-aperture,collimating lens and beam-expanding telescope, whichexpanded the 2-mm diameter beam to a collimated50-mm beam, were attached to the laser source, thuscausing the beam to cover the entire interelectrode area.The pinhole-aperture provided a smooth Gaussian inten-sity profile across the collimated beam. The image of theelectrodes silhouetted by the transmitted beam wasobserved on and photographed from a ground-glassscreen placed between the negative lens and the photo-multiplier tube. Upon application of voltages near thatrequired for the first transmission minimum, dark re-gions of low and near-zero transmission were evident incontrast to regions of relatively high transmission, thusindicating variations in the electric field intensity. Theregion of near-zero transmission, where (I/fm 0) and(E/Em) - N/2, first appeared as a narrow dark bandparallel to the surface of the cathode. As the appliedvoltage was increased, the band grew in area, bowed outin the center, and moved toward the anode. At anygiven voltage, the pattern was stable. Fig. 6 is a mapshowing the profile of the field distribution as tracedfrom enlarged projections of the previous photographs.The relative local field intensities (E/Emin) were derivedfrom the changes in voltage required for given shifts inthe transmission pattern. The results demonstrate sig-nificant nonuniformity in the field strength.

In a second series of experiments, the direct voltageVmin, which produced the first transmission minimum,was measured with the laser beam passed along variouspaths between the plates. A micrometer coupled with aspring-loaded base, as shown in Fig. 7, was used foradjustment and measurement of the position of eachpath. Results showing Vmin as a function of distance areplotted in Fig. 8. Significant distortion of the electricfield distribution is evident. Extrapolation of the curveto the electrodes suggests that even greater distortionexists near the electrodes. The following techniques weredevised for calibration in the presence of these field dis-tortion effects.

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IEEE TRANSACrIONS ON INSTRUMENTATION AND MEASUREMENT, DECEMBER 1968

Fig. 7. Kerr cell (interelectrode distance - 0.75 cm) installed in micrometer-driven, spring-loaded base.

ANODE CATHODE;7 3

4~~~~~~

45 16 %

2 3 4 5 6 7DISTANCE BETWEEN PLATES-rmm

Fig. 8. Measurements of bias voltages that produce minimumtransmission along different paths in the cell of Figs. 6 and 7.

VI. CALIBRATION WITH A NONUNIFORMFIELD DISTRIBUTION

A. Pulse Divider TechniqueIn cases where application of a direct bias voltage

imposed a nonuniform field distribution, calibration wasachieved by reference to pulse divider measurements asfollows. The bias was adjusted until the first transmis-sion minimum was detected. At this point, the relativefield strength along the selected light path was (Emin/Em)= V2. A measured pulse voltage VD was then applied tothe biased cell. Since experiments indicated that thefield imposed by a short pulse (duration t 10 ,us) is uni-form, n and (IIIm) were measured from the photomulti-plier record, and (EIEm) was determined by use of (3)or (4). The cell constant (Emd) was determined from thefollowing equation:

(E.d) = VD(EIEm) - (Emi./Em)

percent) and by error in the detection of the transmis-sion minimum (about 0.1 percent). The error in (E/Em)will be negligible if the amplitude of the applied pulse issuch that n> 10.

B. Calibration from Measurements of Direct Voltages thatProduce Minimum TransmissionThe cell constant (Emd) was also derived from mea-

surements (see Fig. 8) of the direct voltages that pro-duced the first transmission minimum along paths atdifferent distances from one of the electrodes of the cell.Several assumptions were made as follows: 1) that thecell constant does not vary significantly with limitedchanges in time, temperature, or applied voltage, and2) that the field strength at any point between the elec-trodes is proportional to the applied voltage. (Experi-ments performed over periods of several months withseveral different sealed and conditioned cells indicatedthat these assumptions are reasonable.) On this basis,the field distribution was determined, by a methodsimilar to that used for plotting Fig. 6, from the mea-surements in Fig. 8. The relative field strength (E/Emin)as a function of distance, when the voltage V4 thatproduced minimum transmission along path 4 (of Fig. 8)was applied to the cell, is shown by the curve in Fig. 9.The relative strength (E'/Emin) of the uniform field thatV4 would impose, as determined from this curve bynumerical integration, is shown by the horizontalstraight line. The cell constant (Emd) was then deter-mined from the following equation:

(11)(Rind) = (id) ( Ein) V/ (12)

Measurement of the bias voltage was not required.Calibrations in this manner are limited only by inac-

curacies in the pulse divider measurement (less than 1Calibration results obtained in this manner differedfrom divider calibrations by about 2 percent. With

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CASSIDY et al.: KERR CELL SYSTEM FOR HIGH-VOLTAGE PULSE MEASUREMENTS

TABLE IPULSE MEASUREMENT EXPERIMENTS

Pulse Dmvider Kerr System Results after Beam Expander CalibrationMeasurementsVD Beam Path (Emd) VK(volts) (approximate) n (I/Im) (volts) (volts) (percent)

Cell 136 320 near anode 21 0.05 11 170 36 420 +0.236 290 center 21 0.17 11 170 36 270

-0.0436 320 near cathode 21 0.14 11 170 36 310-0.05

Cell 218 470 center 10 0.86 9 890 18 450

-0.136 310 near anode 25 0.29 9 950 36 310-0.0136 910 center 26 0.69 9 870 36 970 +0.236 290 near cathode 25 0.33 9 980 36 400 +0.355 090 center 48 0.41 9 890 54 850-0.473 560 center 77 0.09 9 970 73 960 +0.591 980 center 114 0.09 9 970 92 280 +0.3

* Deviation of Kerr system measurement vK from voltage divider measurement VD, the latter being obtained as described in Section VI-A.

' 1.05z

o~~~~~~~~~~~~~/mmL 1.00

0-%

1 2 3 4 5 6 7DISTANCE BETWEEN PLATES- mm

Fig. 9. Relative electric field intensity as a function of inter-electrode distance.

higher-purity nitrobenzene and more accurate determi-nation of the field distribution (from measurements ofVmjn in the regions very close to the electrodes), weanticipate that independent calibrations to within about1 percent should be feasible by this method.

C. Beam Expander MethodThe foregoing analysis led to the realization that

(EBid) might be determined with relative ease and per-haps greater accuracy if the diameter of the laser beamwere enlarged so that the laser radiation fell upon theentire interelectrode distance. In this case, the relativeradiant flux transmitted over the interelectrode distanceshould be indicative of the average intensity of the non-uniform field. To test this idea, a beam-expanding tele-scope was attached to the laser source so that an ex-panded beam (diameter 50 mm) was directed betweenthe plates of the cell. A mask with a rectangular slot oflength slightly greater than the interelectrode distanceand width 2 mm was placed in the optical path to reduce

errors from field distortion over the width of the elec-trodes. The bias voltage that minimized the transmittedflux was then measured. The cell constant (Emd) wasdetermined by substituting this measured bias voltagefor Vmin in (10). Calibrations of two cells with 0.75-cminterelectrode distance differed from divider calibrationsby less than 1 percent, in spite of variations as large as10 percent (from the average) in local field intensitiesacross the interelectrode distances.

After calibration, the beam expander and pinholeaperture were removed from the system, and pulsemeasurements were made using the two calibrated cellswith the beam passed along various paths between theelectrodes. In each experiment, direct voltage (notmeasured) was applied to bias the cell to the first trans-mission minimum. The Kerr system "pulse measure-ments Vk" were then obtained by use of the followingequation:

VK = (E/Em) (Emd) -Vmin (13)where (B/Em) was determined from the photomultiplierrecord as before and Vmin was the bias voltage thatminimized the radiant flux transmitted by the systemduring calibration. Deviations of VK from VD did notexceed 1 percent. Results are given in Table I.

VII. SUMMARY AND CONCLUSIONSSeveral techniques for calibration of a Kerr electro-

optical pulse measurement system, under both uniformand nonuniform field conditions, have been describedand evaluated. Independent calibrations (without refer-ence to pulse divider measurements) were achieved byapplication and measurement of a direct bias voltageaccording to Section IV-B or C (under uniform fieldconditions) and Section VI-B or C (under nonuniformfield conditions).

Experiments demonstrated that the electric fielddistribution is often significantly nonuniform, particu-

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-17, NO. 4, DECEMBER 1968

larly in cells of greater interelectrode distance (requiredfor higher-voltage measurements). Greater convenienceand higher accuracy were afforded by the beam ex-pander method (Section VI-C). After calibration bythis method, pulses peaking at up to 100 kV were mea-sured with accuracies comparable to those obtainedusing conventional pulse divider techniques. With fur-ther refinements, it is anticipated that such calibrations,accurate to within +0.5 percent, will be feasible forsystems capable of time-resolved measurements ofpulses as high as 300 kV.

ACKNOWLEDGMENTThe authors thank Drs. F. R. Kotter and H. E.

Radford for helpful discussion and suggestions, R. P.Chase and W. A. Bagley for assistance in purification of

the nitrobenzene, and C. V. Kurtz and M. C. King forassistance in preparation of the manuscript.

REFERENCES[1] J. Kerr, "A new relation between electricity and light: Dielec-

trified media birefringent," Phil. Mag., vol. 50, pp. 337-348 and446-458, 1875.[2] S. Y. Ettinger and A. C. Venezia, 'High voltage pulse measure-ment system based on Kerr effect," Rev. Sci. Instr., vol. 34, p.221, 1963.

[3] D. C. Wunsch and A. Erteza, "Kerr cell measuring system forhigh voltage pulses," Rev. Sci. Instr., vol. 35, p. 816, 1964.[4] J. H. Park and H. N. Cones, "Sphere-gap volt-time curves.Reference standards for steep front measurements," AIEE Conf.Paper 57-215, 1957.[5] A. M. Zarem, F. R. Marshall, and F. L. Poole, "An electro-opticalshutter for photographic purposes," Elec. Engr., vol. 68, p. 283,1949.

[6] J. H. Park and H. N. Cones, "Spark-gap flashover measurementsfor steeply rising voltage impulses," J. Research NBS, vol. 66C,p. 200, 1962.

A Novel Technique for Measuring Pulse-Train JitterABRAHAM SINGER, MEMBER, IEEE, I. S. FRIEDBERG, MEMBER, IEEE,

EINAR NAESS, SENIOR MEMBER, IEEE, AND CLYDE D. HARDIN, SENIOR MEMBER, IEEE

Abstract-A quantitative definition of pulse-train jitter is de-veloped. The definition surmounts the two main shortcomings of theexisting definitions, viz., 1) it permits an absolute evaluation of jitterand 2) it is independent of the jitter character. The developmentconsists of showing mathematically that information on each type ofjitter-jitter in pulse repetition rate, width, and height-is stored in alinear fashion in the AM sidebands of one or more harmonics of themean pulse train and that pulse-train jitter may consequently be de-fined as the ratio of the AM power associated with a convenient har-monic to the power in that harmonic. The definition is valid for pulsetrains of low duty factor (e.g.,