IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-15, NO. 4, DECEMBER, 1966

Refinements in Precision KilovoltPulse Measurements

W. R. FOWKES, MEMBER, IEEE, AND R. M. ROWE, MEMBER, IEEE

Abstract-This paper describes techniques for reducing errors en-countered in measuring the amplitude of 100-300 kV pulses whichare a few microseconds in length. The accuracy to which such mea-surements can be made depends, for the most part, on how preciselythe behavior of the voltage dividing network is known. Problems dueto stray reactances, temperature, voltage effects, dielectric and di-mensional instabilities, losses, improper terminations, and externalcircuitry are dealt with, with particular emphasis on capacitive volt-age dividers. Also described briefly are an ultrastable laboratorystandard divider, calibration techniques, and measuring instrumen-tation.

I. INTRODUCTIONTv HE FUNDAMENTAL techniques used today for

measuring high voltage pulses to be delivered tohigh power radio frequency tubes were established

two decades ago. In general, these techniques haveserved adequately, although those who have workedwith high power pulse modulators have had to overcomecertain problems in order to improve the accuracy of thepulse measurement. We find, however, that remarkablylittle progress has been made in some areas and somespecial programs now demand accuracies exceeding thepresent state-of-the-art. This paper presents some of theneeded refinements in the accurate measurement ofpulses from 100-300 kV, which are a few microsecondsin length and are delivered by line-type pulse modu-lators. The techniques described may apply as well tohard tube pulsers with similar pulse specifications.

Stimulated by the discussions last year at the HighPulse Voltage Seminar at the National Bureau ofStandards in Washington, D. C., and by our laboratory'sneeds, these measurement problems have been investi-gated in an effort to extend the accuracy to +0.1 per-cent or better. The purpose of this paper is to examineknown sources of error in the measurement of high pulsevoltages to determine more precisely what the kilovoltreally is. The sources of error will be examined quanti-tatively where possible.The standard approach to the high voltage pulse

measurement problem is to reduce the amplitude of thepulse while still retaining the initial character so that itcan be measured accurately by conventional low voltageinstruments of reasonably well-known precision. This

Manuscript received June 23, 1966. This work was supported bythe U. S. Atomic Energy Commission, and was presented at the 1966Conference on Precision Electromagnetic Measurements, Boulder,Colo.

The authors are with the Stanford Linear Accelerator Center,Stanford, Calif.

reduction is accomplished with a voltage dividing net-work which usually has negligible loading effect on thepulse modulator output; it should be carefully designedtaking into consideration voltage and temperatureeffects, stability with time, and transient response overa wide range of frequencies.The present state-of-the-art allows the measurement of

short, high voltage pulses to accuracies of from one tothree percent [1]. Most of the uncertainty in these mea-surements lies in the inability to predict the exactresponse of the dividing network to the high voltagepulse.

II. TYPES OF HIGH VOLTAGE PULSEDIVIDING NETWORKS

The basice pulse voltage dividing network is the RCdivider shown in Fig. l(a). Special cases of this generalform are the pure resistive and the pure capacitive di-viders. The former is used primarily for measuring dcand low-frequency and the latter for microsecond pulsemeasurements.The pure resistive divider high-frequency response is

usually quite poor due to the distributed capacity withinthe resistor, stray capacity to other parts of the circuit,inherent inductance, and the shunting effect of theviewing cable; all resulting in pulse waveform distortionsignificantly affecting a precision measurement. Theeffects of distributed and stray capacity are less signifi-cant in the low resistance divider but this is limited toapplications where the additional power absorbed doesnot adversely affect the pulse modulator performance.Care must be taken here to insure that the temperaturecoefficients of the resistors are uniform and the powerhandling ratings are conservative. Another advantageis that the bottomside resistor can be made equal to thecharacteristic impedance of the viewing cable wheretermination problems and distortion are minimum.Many of the above disadvantages are minimized in

the RC divider. In theory, the time constants RIC, andR2C2 of each section, when equal, result in a uniformresponse at all frequencies. In practice, however, thedistributed capacity in the topside resistor is difficult tocompensate for so that the result is equivalent to asection which has the same RC time constant as thebottom section. As in other dividers, the topside resistormust be well shielded to eliminate stray capacity toother parts of the circuit.

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The pure capacity divider is probably the mostpopular for short, high voltage pulses [1] and the em-phasis of this paper will be on this device. The schematicis shown in Fig. 1(b). The problems of distributed ca-pacity, stray capacity and power absorption are vir-tually eliminated. The capacity divider can be designedto work at very high voltages, occupy relatively littlespace, and can be made stable and relatively unaffectedby its environment, making it a suitable choice for alaboratory standard for dividing down pulse voltages.The main disadvantages are that its very low-fre-

quency response drops off and that since it is virtuallya pure reactance, it tends to form a resonant circuit withthe inductance of connecting leads which can result inhigh-frequency ringing on the leading portion of fastrising voltage pulses [2 ].The voltage division ratio of the pure capacity voltage

divider may be anywhere from 500 to 1-10 000 to 1.This demands that the topside capacitor withstandvirtually the full voltage of the pulse and be smallenough to have negligible reactive loading effect on thepulse modulator output. Vacuum capacitors are suitablefor voltages up to 100 kV or so, but problems with fieldemission have been experienced and to eliminate themwould perhaps necessitate an unusually large designphysically. High voltage capacitors, using solid insu-lators such as epoxy as a dielectric material, havealso been used. Perhaps most common for use above 100kV is the divider which uses transformer oil for thedielectric in the topside capacitor, which typically hasa value of 1 to 10 picofarads. Usually the bottom or lowvoltage capacitor is a silver-mica type having a valueof 0.001 to 0.05 microfarad.The earlier designs of this type were quite arbitrary

in the choice of electrode geometry for the topside ca-pacitor, emphasizing primarily voltage breakdownstrength and careful shielding from stray capacity. Thecoaxial capacity divider, using guard rings, as shown inFig. 2, was suggested by Dedrick [3], and perhapsothers, a decade or so ago. This divider has two mainadvantages over the earlier type. First, its topsidecapacity could be calculated and built easily to withinone percent [4]. Second, its capacitance value is vir-tually insensitive to geometrical misalignment or elec-trode deformation [3]- [5].The most common problem with the oil-type capacity

dividers is the sensitivity of the topside capacitor valueto changes in oil temperature which may typically be0.06 percent per degree centigrade, making them nor-mally unsatisfactory for precision high voltage measure-ments where the oil temperature is likely to vary.

III. DEVELOPMENT OF A LABORATORY STANDARD

An ultra-stable capacity divider usable to 300 kVwas designed and built at Stanford by Brady and Ded-rick [3]-[5] in 1960. Extreme care was taken in its

(a)

(b)

Fig. 1. Typical high voltage pulse divider networks. (a)Compensated RC divider. (b) Pure capacity divider.

Fig. 2. Coaxial capacitive divider with guard electrodes.

design to make the division ratio essentially independentof voltage, temperature, position, and time over a wideband of frequencies. The temperature independencewas achieved by providing uniform properties in bothcapacitors. Dow-Corning 200 silicone electrical grade oilis used for the dielectric in both C1 and C2 and brasselectrodes are used throughout. A cutaway section isshown in Fig. 3.The division ratio remains unchanged due to changes

in physical dimensions caused by temperature varia-tions, since each electrode capacity change with tem-perature goes as the expansion coefficient of brass. Sincethe same oil is used for the dielectric in each capacitor,the division ratio remains unchanged with changes indielectric constant due to temperature. The topsidecapacitor is a coaxial configuration which has a radiiratio of e which, it can be shown, provides the maximumratio of capacity to electric field. This obviously allowsthe optimum package size for a given capacity andvoltage rating. The bottomside capacitor is made up of50 annular rings separated by 0.050 inch. The capacitiesof the topside and bottomside capacitors are nominally8 pf and 8000 pf, respectively, giving a division ratio ofapproximately 1000 to 1. Errors due to ellipticity orlack of concentricity of circular electrodes are second-order, but nevertheless considered and known [5].

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT

Fig. 3. Brady capacitive divider standard.

IV. PRECISION CALIBRATION

After the high pulse voltage seminar mentioned earlierit was decided to use the Brady capacitive divider as a

laboratory standard at SLAC after a suitable calibrationwas performed. It w7as of course desirable to calibratethis standard as w-ell as other dividers under pulsed highvoltage conditions.At present the best certified high voltage pulse stan-

dard calibration service is at the National Bureau ofStandards. The Brady capacitive divider was calibratedat NBS at 20, 60, and 100 kV using a 12.5 microsecondpulse. The uncertainty in this calibration is + 1.0percent.

It was decided to make a precision calibration underlov voltage conditions and then carefully examine thepossible deviations w-hich might exist when translatingto the high voltage pulse conditions. One calibrationmethod used was to carefully measure the ratio of ca-

pacity divider impedances at 1000 Hz on a precisionbridge using a cascaded pair of ratio transformers, eachhaving a division accuracy of one part in 106. Thebridge circuit is shown in Fig. 4. The outer shield andone terminal of the bottomside capacitor of the dividerbeing calibrated are common and normally at groundpotential. It can be seen from the bridge circuit sche-

matic that this ground is incompatible with the bridgeground thereby making it necessary to "float" the di-vider being calibrated inside a shielded cubicle.Without going into the mathematics of the bridge

balancing equations, it should be pointed out that cor-rections must be made for stray capacities within thebridge and for lead inductances where critical. Precisionphase balance in the bridge is accomplished with thedecade resistance box in series with the divider. Withcare and appropriate corrections, this calibration canbe made to better than 50 ppm. However, this calibra-tion applies necessarily at only the voltage, temperature,and frequency at which it is made.A second calibration is made using the bridge circuit

in Fig. 5. This method lacks the precision of the firstmethod but does have two advantages. First, it is lessunwieldy and can be used to calibrate dividers whilethey are in place in the pulse transformer tank since theshielded cubicle is not required. Secondly, the calibra-tion may be performed at any frequency up to 100 kHzwhile the ratio transformer bridge accuracy drops offabove 1 kHz. This circuit is similar to a Schering bridgeexcept that all arms of this bridge are primarily capaci-ties. Two General Radio precision standard capacitors,one fixed and one variable, are balanced with the ca-pacity divider undergoing calibration. Care must betaken to minimize the inductance of the leads connect-ing the bridge components where coax is not used. Theinductance inherent in the components must be knownand corrected for. Proper phase balance is achieved byadjusting Rn, the decade resistance box, along with thevariable capacitor to achieve a good null. The topsidecapacitor is a GR 1422-CD precision variable capacitorstandard which has two sections which can be set from0.05 to 1.10 pF and from 0.5 to 11.0 pF, respectively.The bottomside standard capacitor is one of theGR-1402 series. Three different values have been used,0.001, 0.005, or 0.01 pF depending on the divisionratio of the divider being calibrated. The value is chosenwhich allows the variable topside capacitor to operatenear its full-scale setting for minimum uncertainty. Forgreater accuracy, it is planned to have both standardcapacitors fixed and one of them "trimmed" to balancethe bridge with a precision variable capacitor. At pres-ent, the largest single source of error with the presentcapacitor bridge is the uncertainty in the variable ca-pacitor setting which is about 0.1 percent [6].At first this bridge was used for calibrations without

the quadrature balancing resistor R. and the null wasquite broad and difficult to set, thereby limiting therepeatability to about 0.15 percent. This is due pri-marily to the finite resistance to each input of the dif-ferential amplifier rather than to the dissipation factorloss in any of the capacitors. The exception, of course,occurs when a symmetrical situation exists when R2C2=R4C4, eliminating the need for Rn.

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of the dielectric medium. The change in capacity with

temperature is then given approximately by

C(T) = (p + a)AT + 2pa(AT)2.CIO

ig. 4. Ratio transformer bridge for 0.005 percenit calibration.

r_DECADE r- DECADE

RESISTOR I R R -.--RESISTORnji

L1J

I~3

Fig. 5. Precision capacitor bridge for 0.2 percent calibration.

V. BEHAVIOR UJNDER HIGH VOLTAGE PULSE CONDITIONS

A capacity divider can be calibrated at a particular

voltage, temperature, and frequency. The division ratio

under these conditions can be known to within ±+0.01percent. Let us now examine many of the possible devia-

tions from the measured division ratio which may exist

under pulsed high voltage conditions.

A. Temperature and Dimensional Stability

Small changes in the geometry of a capacity voltage

divider will normally occur with environmental tem-

perature changes due to thermal expansion of the elec-

trodes, insulator supports, etc. This discussion will be

confined to capacity dividers which have a coaxial con-

figuration for the topside capacitor since most of the

capacity voltage dividers at SLAC are of this type.

For a divider which has guard electrodes the topside

capacity is given by [41]

C =

In (bla)(1)

For a vacuum coaxial capacitor p =0 and the capacityis affected only by expansion in the longitudinal dimen-sion. A capacitor with transformer oil between theelectrodes is primarily governed by p rather than a.

The p term varies with type and manufacturer but istypically -3 X 10-4 to -1 X 10-3 per degree centrigrade.a is typically 2 X 10- per degree centrigrade for brassor aluminum.The changes in the bottomside capacitor due to tem-

perature changes may not be so easy to predict. If thebottomside capacitor is the silver-mica type, the capac-

ity temperature coefficient may be as high as + 3 X 10-4per degree centigrade but is usually unspecified. Thiswould govern the ratio of a divider with a vacuum

capacitor but would be relatively insignificant com-

pared with the oil temperature coefficient in an oildielectric capacitor. 'This points out one obvious ad-vantage of the vacuuim capacity divider over the oilcapacity divider.

In the stable laboratory standard (Fig. 3) the capacityof the bottomside capacitor is approximately

NErEOA

C2 =

d(4)

where A is the effective area of the plates, d is the spac-

ing per gap, and N is the number of gaps. The area ofcourse goes with temperature as [5]

A(T) = Ao(l + aAT)2

and the gap goes as

d(T) = do(l + aAT).

(5)

(6)

Therefore, the capacity of the bottomside capacitor goes

with temperature as

C2(T) = 6'20(1 + pAT)(l + aAT) (7)

where e, is the relative dielectric constant between theinner and outer electrodes; eo is the permittivity of freespace; a and b are the radii of the inner and outer elec-trodes, respectively, and I is the effective length of theouter electrode which is sometimes called the signal ring.This length includes the effect of the fringing fields inthe vicinity of the gap next to each guard electrode. Ifthe electrodes are made of the same material, then theradii ratio will remain constant with thermal expansionand the capacity can be expressed as

C1(T) = C1o(1 + pAT)(1 + aAT) (2)

where a is the thermal coefficient of expansion of theelectrode material and p is the temperature coefficient

and

AC2(T) = (p + a)zAT + 2pa(AT)2,C20

(8)

making the ratio of capacities in the Brady dividerindependent of the oil and electrode temperature [51.The effect of unequal temperature coefficients is most

evident in the voltage divider which uses transformeroil for the dielectric C1 and a small paper or mica ca-

pacitor for C2. This can cause errors in the pulse mea-

surement of 2 to 4 percent since oil temperature varia-tions of 400 C are not uncommon.

The effect of temperature on a commercial capacitydivider of this type was measured using a variation of

RATIOTRANSFORMERS

(3)

1966 287

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT

the precision capacitor bridge described earlier andshown in Fig. 6. The divider was placed in transformeroil which was circulated and carefully temperature con-trolled from 20 to 80 degrees centigrade while the divi-sion ratio was measured as a function of temperature.The silver-mica bottomside capacitor was then removedand replaced by a General Radio precision standardcapacitor of approximately the same value, but whichwas placed in a constant temperature environment whilethe test was repeated, varying only the temperature ofthe topside capacitor. The results indicated that thetopside capacitor (oil dielectric) accounts for most ofthe division ratio change with temperature. The entiredivider has a temperature coefficient of 556 ppm/°C,while the topside capacitor has a coefficient of 614ppm/°C indicating that the temperature coefficient forC2 was much smaller and opposite in sign to that for Cl.The accuracy of high voltage pulse measurements,

using the commercial divider which has an oil-coaxialtopside capacitor and a silver-mica bottomside capacitorunder varying temperature conditions, can be improvedconsiderably by a temperature compensating technique.Capacitors with unusually large temperature coefficientsare available and can be used to "trim" the bottomsidecapacitor in such a way as to allow nearly identicalcapacity changes with temperature, thereby keeping afairly uniform division ratio. To compensate the dividerin this manner, the trimming capacitor must be

C (a2 -a C2 (9)(al - at)

where a. is the temperature coefficient of C.. The divi-sion ratio will be altered, of course, and the new divisionratio becomes

C,K = (10)

Cl + C2'

where C2'= C2+ Ct. It should be mentioned at this pointalso that this compensation relationship does not holdwhere the viewing cable capacity is significant. As dis-cussed later, the quasi-steady-state division ratio is

C, C1 ~~~~~(11)Cl+ C2 + Cc

where C, is the capacity of the viewing cable. If thecable temperature is assumed to remain relatively con-stant the temperature term a2 in (9) must be replacedby a2', which is given by

I C2°t2 = °Z2y

C2 + Cc(12)

and C2 in (11) must be replaced by C2' to express thedivision ratio of the temperature compensated dividercorrectly.

Figure 6 shows the effect of compensation on thedivider on which the temperature coefficient measure-

ments were made. Before compensation the division

@a)rr~)

-bx

(2

0

z0(I)

0ccc

LL

2.25

2.00

1 75

1.50

1.25

1.00

0.75

0.50

025

0

-0.25

-0.50

-0.75

C, Ct

C1 =1.29pF (a) -540 PPM /OC- C2 =5600 pF (o) +35 PPM /°(- Ct =900 pF ( -5100 PPM /a

:(Oil): (Mica)DC (Ceramic) 1~~~~~~

IJUNCOMPENSA TED-- DIVIDER

COMPENSATED DIV/DER

16 40 50 60OIL TEMPERATURE °C

f _

70 80

Fig. 6. Temperature behavior of a commercial divider using oil andmica dielectrics for Ci and C2, respectively, and the results oftemperature compensation with a "trimming" capacitor.

ratio changed approximately 3 percent over a 60°Ctemperature range. After compensation the divisionratio deviation was about +0.1 percent over the sametemperature interval. The trimming capacitor Ct hadan average temperature coefficient of approximately-5 X10-3/°C. There is an error in the capacity dividerwhich has been temperature compensated withoutallowing for the cable, or in the divider which has equaltemperature coefficients for C1 and C2 such as in theBrady Standard. The error due to temperature with thecable present is given by

(13)

This effect obviously can be minimized by keeping theratio C,/C2 as small as possible. For a 20 foot length ofRG58A/U coax and a change in oil temperature of20°C, the change in division ratio of the Brady capaci-tive divider is -0.1 percent.One unique advantage of the coaxial capacitor, which

has guard rings in addition to the signal ring, is that itscapacity is relatively insensitive to misalignment of thetwo electrodes compared with the parallel plate geome-

try [4]. The most likely misalignment problem with a

coaxial capacitor would be skewed conductor axis. Thisproblem, being too difficult to solve analytically, can besolved intuitively by examining the case where the twoelectrodes are not concentric. Referring to Fig. 7(a) itcan be shown [4] that for small deviations from con-

centricity the change in capacity is approximately

AC a

C~0

LIn 1-- (14)

where = b/a. For a coaxial capacitor which has = e

a 5 percent misalignment results in a capacity changeof only 0.04 percent.Another dimensional change which might occur is

warping of the outer conductor or signal electrode.

AK a,C,AT(-(T) -

Ko C1 + C2 + Cc

H~~~~ Tr

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(a) (b)

Fig. 7. Coaxial geometry irregularities.

Referring to Fig. 7(b), it can be shown [4] that thechange in capacity of a coaxial condenser, whose outerelectrode has been distorted into an ellipse is givenapproximately by

AC (k/b)2 5 21C lno~Lf[ 4 (15)

where h is the deformation, and o-= b/a. For a deforma-tion of one percent, where o-=e, the change in capacityis 0.012 percent.

B. Frequency Response

The data supplied by transformer oil manufacturersindicates that the dielectric constant of most oils isrelatively independent of frequency [7 ] between 20 and100°C although exact figures over the bandwidth ofinterest are not readily available. Bridge measurementsin our laboratory at room temperature indicate that thechange in capacity from 1 kHz to 100 kHz is less thanone part in 1000.

Because the capacity divider is a pure reactance ittends to form a resonant circuit with the length of wireconnecting the topside capacitor to the high voltageterminal [2]. With a moderate amount of care this doesnot present a problem unless the pulse to be measuredhas an extremely short rise time. A 10-inch length oflarge diameter wire, say 8 inch diameter copper tubinghas a self inductance of about 0.3 ,h, having a reactanceat 1 MHz of about 2 ohms compared with a total reac-tance of a capacity divider with a 5 pf topside capacitorof about 30 kilohms at the same frequency.The frequency response of three different types of

coaxial dividers was measured in two ways. First, thedivision ratio was carefully measured on the capacitancebridge as a function of frequency from 1 kHz to 100kHz. At the higher frequencies the residual inductancesof the precision standard capacitors and the dielectricchanges have a small effect that is known and is cor-rected for. Second, the response of each divider was thenmeasured from 50 kHz to 50 MHz using a constantamplitude sine wave generator and two RF voltmeters;one to insure that the input voltage to the high voltageterminal remained constant, and the other to monitorthe output of the divider. All three dividers were flat towithin 0.2 percent from 1 kHz to 100 kHz. Above 1 mHz

FREQENCY IN Hz

Fig. 8. Frequency response of capacitive dividers.

each exhibited similar resonances as shown in the re-sponse curves of two of these dividers in Fig. 8. Someresonances were observed which turned out to be causedby harmonics in the signal generator and were disre-garded and are not shown on the response curves. Thedip occurs at about 13 MHz on the Brady capacitivedivider and at about 23 MHz on a commercial divider.Because of the relatively large values of C2, the bottom-side capacitors in each case, it would only take a fewhundredths of a microhenry to form a series resonantcircuit to cause the dip at these frequencies. The peakwhich occurs at the higher frequency can have high Q'sbut is not serious for high voltage pulses with normalrise times.At this writing it is not clear exactly what the equiva-

lent circuit inductance values are or how they are dis-tributed although it is believed that the first dip is dueto the series "self resonance" in the bottom-side capaci-tor. It is not apparent why the dip occurs at such a lowfrequency in the Brady capacitive divider since C2 hasvery low residual inductance by virtue of its design.

C. Voltage Effects

A 1000 ohm non-inductive resistive divider/dummyload combination was built; one purpose being to in-vestigate possible voltage effects on the capacity dividerpulse voltage measurement. It was hoped that a re-sistance divider of this type could be built with uniformvoltage and temperature coefficients and suitable fre-quency response which could handle 50 MW peakpower, 12 kW average power with adequate oil cooling.Unfortunately, the inductance of the 0.2 ohm bottom-side resistor affects the frequency response to the pointwhere a precision measurement cannot be made forcomparison with the capacitive divider measurement.The resistive divider at NBS in Washington, D. C., isprobably the best suited for this investigation. At thiswriting, the authors are attempting to improve the re-sponse so that this comparison can be made. It has beenassumed that the voltage coefficient of the divider oil islinear and the ratio of capacities in the Brady capacitivedivider is independent of voltage.

2891966

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT

D. The Viewing Cable

Quantitative information on the effect of the viewingcable on the precision high voltage pulse measurementis for the most part nonexistent except for the effectof the added capacity presented to the system by thecable. This has the obvious effect of increasing the effec-tive division ratio of the divider and it is a simple matterto include the cable as part of the divider when makingbridge measurements of its ratio and to include itsknown capacity in division ratio calculations.There are other effects that should be mentioned. It

is generally known that when the divider is purelycapacitive, the output end of the viewing cable cannotbe terminated in its own characteristic impedance with-out differentiating the pulse beyond recognition. Theuniversally accepted method around this problem is toinsert a series termination Rm=Zo between the inputend of the cable and the capacity divider output asshown in Fig. l(b). It is assumed that the input im-pedance to the oscilloscope is essentially an open circuit.At the higher frequencies the reactance of the bottom-side capacitor in the divider is sufficiently low so thatmost of the pulse that is reflected from the open circuitend of the transmission line is absorbed by Rm. It hasbeen found that the common 2 watt carbon resistormakes an adequately non-inductive termination.There is a problem of transient cable loading, which is

generally overlooked. This occurs when the length of thetransmission line is such that the transit time of the sig-nal is a significant fraction of the pulse width or thecapacity of the cable is an appreciable portion of thebottomside capacitor in the capacity voltage dividingnetwork. When either or both of these conditions exist,waveform distortion occurs which cannot be overlookedif an accurate measurement is desired.When the high voltage pulse is applied to the capacity

voltage divider, C1 and C2 assume their appropriate volt-ages. However, the impedance seen across C2 initially isRm+Zo. As the divided voltage pulse enters the cableit is further divided by Zo/(Rm+Zo) and as the signalpropagates along the cable the voltage across C2 dropswith a time constant (Rm+Zo)(Ci+C2). Assuming thatthe load at the viewing end of the cable has essentiallyinfinite impedance, the voltage doubles at the scopeand the wave is reflected essentially unchanged backtoward the capacity voltage divider; arriving at suchtime that the voltage across C2 has dropped to

ClV2 Voe72L/vp(Rm+Zo) (C1+C2) (16)

C1 + C2

where vp is the velocity of propagation and I is the cablelength. It is assumed the 21/vp is less than the pulsewidth To, that Rm-=Zo, and that the transmission lineis ideal. Therefore

I T,CC - = -~-- ' ~ 1(17)

VpZO zo

where C, is the capacity of the cable and T1 is the one-way cable transit time. If C,/C2<<1 then after one downand back transit or cable filling time, 2Ti,

V2 - V3 1+Co1Cl + C2 + CC

(18)

This is the familiar expression for the division ratio ofa capacitive divider which has significant cable capacityadded to it. It is, however, only an approximation dur-ing the transient filling time of the cable and exactlyexpresses the divided down voltage value after severalreflections have occurred within the cable. It is impor-tant that the measuring point be made far enough fromthe leading edge so that a quasi-steady-state level isreached when the cable is uniformly charged to thesame potential as the final voltage across the bottomsidecapacitor C2.

Figure 9 shows the measured effect of transient cableloading on a 225 kV pulse which was divided nominally5000 to 1 with a divider having C1 = 1.2 pF and C2 = 6000pF. The pulse has a rise time of 0.5 microsecond. Itis seen that initially the pulse is divided down byCl/(Cl+ C2). Each reflection will contribute to thecharge adjustment along the cable; the nth reflectionhaving the form

(I -2nT1)nV3 e-

- nE(t-n2Tl)/Irnthr Tnn!

(19)

As the number of reflections approaches infinity (18)becomes exact. The cable lengths are abnormally longmerely to illustrate this effect. It is important to re-member, however, that the early part of the pulse willalways be distorted by the transient loading effect. Theextent depends on the cable length and for a precisionmeasurement a selected point at least ten transit timesfrom the leading edge of the pulse should be sufficient.The distortion caused by cable high-frequency disper-sion or dielectric loss is difficult to predict. For frequen-cies which primarily contribute to the flat portion ofthe pulse the effect is considered negligible.Another form of distortion is caused by the finite

resistance shunting the viewing end of the cable result-ing in pulse droop. This causes the voltage across C2 andCc to droop with a time constant Ri(C2+C,+-Cj), whereRi and Ci are the input resistance and capacity to thescope. The error is greater the further the measurementis made from the leading edge. For the other reasonsdiscussed it is generally still desirable to choose a pointon the pulse for the measurement well away from theleading edge since the high-frequency errors are not sowell known. The error due to the droop is given approxi-mately by

AVV R(+c+C)(20)V Ri(C2w+ Cc + Ci)

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FOWKES AND ROWE: PRECISION KILOVOLT PULSE MEASUREMENTS

clI vV02LJC):D

Jc-0-2

LLJ(I)

c-

LLI0

C)

Fig. 9. Transient cable laoding effect when cable lengths are ex-cessive. 72 and r3 are the reflection coefficients at each end of theviewing cable.

where T, is the time from leading edge selected for themeasurement. For this approximation an ideal stepfunction is assumed. For the capacity divider mentionedabove and an oscilloscope input resistance of one meg-ohm, this error is about 0.017 percent per microsecondreferred to the leading edge.

VI. MEASUREMENT OF THE REDUCED VOLTAGE PULSE

Once the high voltage pulse has been reduced andpassed by the dividing network the uncertainty in themeasurement is typically an order of magnitude betterthan that of the divider itself. Divided pulse voltagesmay be measured with pulse voltmeters of either theslideback or direct peak reading type. For precisionmeasurements, however, there are intrinsic drawbacksto these pulse voltmeters, and oscilloscope voltage com-parator methods are preferred. Here the divided downpulse amplitude is compared with a dc voltage and fedinto the high gain differential amplifier and the differ-ence displayed on an oscilloscope. Such a circuit foroscilloscope presentation is provided in the Tektronixtypes "Z" or "W" oscilloscope preamplifiers. Care mustbe taken to insure that the equipment has been carefullycalibrated so that the comparator voltage is accuratelyknown. This depends on the comparator voltage powersupply stability and the uncertainty in the comparatorvoltage dividing potentiometer. Also contributing to theuncertainty are the limited resolution of the video dis-play and the common mode rejection capability of thedifferential amplifier. When using a good voltage com-parator differential amplifier oscilloscope the resolutionuncertainty is typically 0.01 percent for measuring apulse 50 volts in amplitude. The common mode rejec-tion capability in the Tektronix unit is about three partsin 105. This particular unit is known to experiencesevere instability when the rate of rise of the voltagepulse exceeds six volts per nanosecond. Care should betaken to insure a true response of the amplifier to thewaveform to be measured, and to insure that its leadingedge does not have a rise time approaching the criticalspecification. There is some uncertainty in the input

attenuator to the differential amplifier. Where possible,the reduced pulse should be fed directly into the com-parator circuit, i.e., when the input attenuator is in thezero attenuation position thereby eliminating any un-certainty in the attenuator divider ratio.

For more precise measurements the "Z" or "W" pre-amplifier is used only as a differential comparatorwhereby an external (Ic comparator voltage, monitoredby a precision dc voltmeter, is compared with the pulsevoltage. Similar precautions mlust be taken with thismethod also, but the uncertainty in the comparatorvoltage is limited only to the uncertainty in the externalprecision voltmeter. The overall uncertainty in thismeasurement, apart from that in the dividing network,is determined by the resolution of the video display, thecommon mode rejection capability of the differentialamplifier, and the accuracy to which the external com-parator voltage can be measured with the precision dcmeter. This can be malde typically to 0.05 percent usinga Fluke differential voltmeter.When circumstances require rapid, routine pulse volt-

age measurements, oscilloscope methods may be im-practical. At this facility where data must be taken on246 klystron modulator systems which are operatingsimultaneously, the pulse voltmeter has the advantagethat it can be made portable or that it may provide asuitable analog signal for feeding operating conditionsinto a computer; but at the expense of at least two ordersof magnitude in accuracy.

Peak reading pulse voltmeters, in addition to normalmeter errors, are subject to errors introduced when theduty cycle is short. For the simplified peak-above-zerocircuit in Fig. 10 the error due to the short duty cycle isgiven approximately by

L\V / DRm -1_V(1_ Rd) (21)

where Rd iS the equivalent resistance of the peak readingdiode, Rm is the resistance of the metering circuit, andD is the duty cycle. It is therefore desirable to have ashigh impedance metering circuit as possible. It is in-teresting to note that the value of the peak readingcapacitor, Cp, does not affect the division ratio whenloading a capacity divider once a steady-state conditionis reached.

In addition to the intrinsic duty cycle dependenterror, there is an error due to the shunt capacity of thepeak reading diode that is given approximately by

AV-- _ CdlCpV

(22)

and also by irregularities in the pulse waveform whichmay exceed the portion of the pulse which is of primaryinterest. An example is a small amount of overshoot onthe leading edge of an otherwise flat pulse waveform.

In view of these problems the pulse voltmeters shouldnot warrant consideration for precision pulse measure-

1966 291

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT

Cd

THIGH

INPUTCpt Rm IMPEDANCEINPUT' METERING

CIRCUIT

PEAK ABOVEZERO CIRCUIT

Fig. 10. Typical peak reading circuit.

ments but rather should be limited to applicationswhere quick voltage measurements of the order of 5-10percent are adequate.

VII. CONCLUSIONMost of the error in a high voltage pulse measurement

is due to the uncertainty in the voltage dividing net-work. Using the described capacitive divider standard,which has been calibrated on a precision ratio trans-former bridge and the oscilloscope voltage comparatormethod, the overall uncertainty is about + 0.2 percent.

This paper has been limited primarily to improve-ments in capacity divider techniques in order to accom-

modate our laboratory's needs. It is hoped that thiswork will encourage others to improve these methodsand perhaps supply new techniques in the field of highvoltage pulse measurements. X-ray hardness and elec-tron momentum methods perhaps could be applied toprecision high voltage measurements. Electrical break-down in gases has also been suggested. Low voltagebridge techniques are presently adequate for their pur-

pose but the need exists for a high voltage bridge forpulse divider standardization, extended perhaps to1 MV.

ACKNOWLEDGMENTThe authors wish to express their thanks to Dr. J. V.

Lebacqz, J. H. Jasberg, and R. J. Alatheson for theirvaluable advice and suggestions in this effort, to theSLAC staff for their cooperation, and for the encourage-ment given by V. G. Price.

REFERENCES[1] Minutes of 1965 NBS High Pulse Voltage Seminar.[2] G. N. Glasoe and J. V. Lebacqz, Pulse Generators, M.I.T. Rad.

Lab. Ser., vol. 5. New York: McGraw-Hill, 1948, Appendix A.[3] K. Dedrick, "Measurement of high voltage pulses with the co-

axial voltage divider, " Stanford University, Stanford, Calif., MLRept. 556, November 1958.

[4] M. M. Brady and K. G. Dedrick, "High voltage pulse measure-ment with a precision capacitive voltage divider," Rev. Sci.Instr., vol. 33, pp. 1421-1428, December, 1962.

[5] M. M. Brady, "350 kilovolt pulse voltage divider," StanfordUniversity, Stanford, Calif., M Rept. 247, January 1961.

[6] W. R. Fowkes, "Low voltage calibration voltage dividers,"Stanford Linear Accelerator Center, Stanford, Calif., InternalRept., June 1965.

[7] F. M. Clark, Insulating Materials for Design and EngineeringPractice. New York: Wiley, 1962, pp. 161-169.

[8] P. A. Pearson, "Pulsers for the stanford linear electron acceler-ator," Stanford Microwave Lab., Stanford Univ., Calif., Rept.173, November 1952.

[9] McGregor et al., "New apparatus at the national bureau ofstandards for absolute capacitance measurement," in PrecisionMeasurement and Calibration, NBS Handbook 77, vol. I, pp.297-304, February 1961.

[10] D. L. Hillhouse and H. W. Kline, "A ratio transformer bridge forstandardization of inductors and capacitors," IRE Trans. onInstrumentation, vol. 1-9, pp. 251-257, September 1960.

[11] J. F. Hersh, "A close look at connection errors in capacitancemeasurements," Gen. Radio Exper., July 1959.

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