NBSIR 75-774

Calibration of Kerr Systems Used to

Measure High Voltage Pulses

Robert E, Hebner, Jr.

Electricity Division

Institute for Basic Standards

National Bureau of Standards

August?. 1975

Final Report on

Sandia Corporation Order No. 51-9312

Sandia Technical Consultant: S. R. Booker, Org. 9532

Sandia Contracting Representative: J. G. Boyes, Org. 4361

Prepared for

Sandia Corporation

BIdg. 894, Kirtland AFB

East Albuquerque, New Mexico 87115

NBSIR 75-774

CALIBRATION OF KERR SYSTEMS USED TO

MEASURE HIGH VOLTAGE PULSES

Robert E. Hebner, Jr.

Electricity Division

Institute for Basic Standards

National Bureau of Standards

August 7, 1975

Final Report on Sandia Corporation Order No. 51-9312

Sandia Technical Consultant: S. R. Booker, Org. 9532

Sandia Contracting Representative: J. G. Boyes, Org. 4361

Prepared for Sandia Corporation

BIdg. 894, Kirtland AFB

East Albuquerque, New Mexico 87115

U.S. DEPARTMENT OF COMMERCE, Rogers C.B. Morton, Secretary

James A. Baker, Mi, Under Secretary

Dr. Betsy Ancker-Johnson, Assistartt Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

\

TABLE OF CONTENTS

I. INTRODUCTION 1

II. CALIBRATION OF DEVICES USED TO MEASURE

HIGH VOLTAGE PULSES 2

A. Introduction 2

B. Divider Uncertainties . . 3

C. Kerr System Uncertainties 6

D. Low Frequency Calibration of a Kerr System 8

1. Introduction 8

2. Direct Voltage Measurements 10

3. Alternating Voltage Measurements 15

a. 60-1000 Hz Experiments 15

b. Measurements at 9,000-20,000 Hz 19

k. Pulse Measurements 20

III. ACKNOWLEDGMENT 2h

IV. REFERENCES 25

APPENDIX 1 "Improved Techniques for the Measurement

of High Voltage Impulses Using the

Electro-optic Kerr Effect" 27

APPENDIX 2 "Electric Field Distributions and Space

Charge Behavior in Nitrobenzene under

Low Frequency Alternating Voltage" Ul
ll
I. Introduction

The purpose of this work is to define, develop and refine techniques

for calibrating pulse voltage measurement systems, particularly those

hased on the electro-optic Kerr effect. The uncertainty of the

calibration is to be no larger than ±0.5^. This calibration is to be

performed at operating voltage levels and not require use of a divider

network.

Substantial progress has been made tovard this goal. The approach

exploits the assumed frequency independence of the Kerr coefficient of

nitrobenzene. Theoretically, the Kerr coefficient should exhibit the

same frequency dependence as the relative permittivity. Measurements

have shown the relative permittivity to be approximately frequency

independent over the frequency range from direct voltage to 10^ Hz.

Recognition of this has prompted speculation that a Kerr system could

be calibrated under high voltage at a convenient frequency—direct or

60 Hz alternating .voltage , for example—and the calibration would be

valid for pulse measurements.

The realization of this calibration approach has been hampered by the

fact that the electric field distribution, in the liquid exhibiting the

electro-optic Kerr effect, is itself frequency dependent. The

frequency dependence of the electric field distribution is caused by

space charge in the birefringent fluid. This space charge, having a finite mobility, reacts to the time-varying applied voltage. The

spatial distribution of the charge carriers, and therefore the spatial

distribution of the electric field, will then depend on a variety of

factors including the natiire of the carriers, the frequency and

magnitude of the applied voltage, the viscosity of the birefringent

fluid, and the geometry of the Kerr cell. Work at the Electrostatics

Laboratory of the National Center for Scientific Research, Grenoble,

France, the National Bureau of Standards, and Sandia Corporation

indicates that the space charge density can be reduced by piirification

of the fluid. It cannot, however, be reduced to such a level that it

becomes an insignificant perturbation under low frequency alternating

voltage.

This report describes the present best comparison of cell calibration

under direct voltage with calibration under low frequency alternating

voltage and calibration under pulsed high voltage. The results under

all three types of waveforms agree to within ±0.5/^. From these results

it can be inferred that it is feasible to use an electro-optic Kerr

system as an independent, and possibly more accurate, device against

which -to calibrate other pulse voltage measurement systems.

In addition to this discussion of Kerr system calibration, the report

contains two appendices presenting topics important for the efficient

operation of a pulse voltage measurement system based on. the electrooptic Kerr effect.
The first appendix to this report contains a discussion of an improved

technique for accumulating and analyzing the data obtained from a Kerr

system. In this technique the voltage signal from the photomultiplier

is digitized and stored using a commercially available transient

recorder. The data is then transmitted to a computer which determines

the voltage as a function of time. Relevant pulse parameters such as peak voltage and risetime are then calculated and displayed. This

permits the immediate and accurate extraction of pulse parameters from

the Kerr response.

The second appendix is a reprint of an article published in the 1973

Annual Report on the Conference on Electrical Insulation and Dielectric

Phenomena. This reprint describes work, partially supported by Sandia

Corporation, directed toward the prediction and control of the space

charge effects in nitrobenzene-filled Kerr cells.

II. Calibration of Devices Used to Measure High Voltage Pulses

A. Introduction

The accurate measurement of high voltage pulses places conflicting

demands on the measurement system. High voltage levels require large

geometry to provide adequate electrical insulation. The fast risetimes

of the pulses—with the attendant wide frequency range of interest —are most accurately measured using a compact, geometrically well-defined

system. As a consequence, measurement systems designed to measure high

voltage pulses represent a compromise between frequency response and

high voltage protection. Accurate measurement systems are, therefore,

generally optimized to faithfully reproduce the waveform of an individual generator rather than designed as wide-range, general-purpose

instruments.-'-

This fact is acknowledged in t^e standard procedures for the

calibration of pulse dividers. Two approaches which permit the

prediction of the response of a measurement system are recognized. One

is a comprehensive approach—both the frequency response and the

voltage dependence of the divider ratio are experimentally determined

so that the magnitude and waveshape of the high voltage pulse can be

calculated from the divider output. A second approach is valid when

the primary interest is in one type of pulse and when the approximate

waveshape and magnitude of the pulse is known. In this case, the

divider to be calibrated is connected in parallel with a measuring

device having a known response. The "unknown" device is then

calibrated against the "known" device as the two are used to measure

the same applied pulse. This second approach has been adopted by NBS

for the calibration of pulse systems submitted by Sandia Corporation.

Part B of this section of the report discusses uncertainties inherent

in the measurement of high voltage pulses using a conventional divider,

while part C discusses the uncertainties when this same measurement is

made using a Kerr system. Drawing on these for background, part D

2
presents the resialts of Kerr system calibration imder direct, lov

frequency alternating and pulsed high voltage.

B, Divider Uncertainties

Determination of the peak value of a high voltage pulse from measured

divider response makes use of the following relationship:

In this equation, "the peak value of the high voltage, a is the

divider ratio and is the measured value of the peak of the

relatively low voltage presented to the input terminals of the

measuring device. In this discussion, an artificial distinction is

being made between the divider and the measuring device. For example, assume that one has a divider connected to a high voltage pulse

generator, an oscilloscope to measure the low voltage output from the

divider, and a cable connecting the two. The value of the divider

ratio which should be used in Eq. 1 will be determined by all three of

these devices. The measured value of the low voltage, V^^, is

determined only by the oscilloscope. The significance of this is that

care must be taken in the assessment of overall measurement uncertainty

if the discrete components of the system are calibrated rather than the

system calibrated as a unit.

From Eq. 1, the uncertainty in the measurement can be expressed

AV /V = ± Aa/a ± AV„/V, (2)

p p II

The quantity AV /V^ is t;v'pically 0.01-0.05. If, however, a suppressed

zero (slidebackj measurement technique is used, its value can be as low

as 0.001. Similarly, Aa/a is typically 0.01-0.05. The factors which

contribute to this uncertainty can be understood from an analysis of

the following published list of the sources of error in pulse

measurements ' :

1. residual inductance in any resistance or capacitance

element

;

2. stray capacitance - (a) from any section of the divider

to ground or a grounded object, (B ) from any section of

the divider to high voltage parts of the supply and test

circuit, and (C) between sections of the divider;

3. impedance drop in the lead from the point at which the

high voltage is to be measured to the high voltage end

of the divider;

h, impedance drop in the ground return lead from the divider

due to either extraneous ground currents flowing in this

lead or to the divider cxirrent

;

3
5. oscillations set up in the divider circuit caused by

capacitance from the divider high voltage terminal to

ground and lead inductance.

Although the first source of error is intrinsic to the divider, the

other four error sources depend upon the arrangement of the • experimental apparatus. It then follows that four of the five sources of error depend upon the experimental set-up and so vill be laboratory

dependent but relatively independent of the divider.

Two implications of this fact should be discussed further. One is that

the use of a calibrated divider does not assure accurate measurement in

the same sense as, for example, the use of a calibrated digital

voltmeter assures accurate measurement of low direct voltage. In the

latter case, user convenience features have been incorporated into the

device which make measurement errors due to undetected operator errors relatively unlikely. In the former case, however, ground cur'rent errors or capacitive coupling between high and low voltage components

can permit consistent, reproducible, but erroneous measurements of the

magnitude and shape of the high voltage pulse. A calibrated pulse

measuring device is most often used to verify that a measurement system

is being used correctly. That is, a calibrated device—a resistor

divider whose ratio is known, for example—is placed in the pulse

generating-measuring circuit under test. Comparison of the high

voltage pulse as measured by the calibrated device and by the system

under test provides a measure of accuracy of the unknown device.

The second implication, which is an extension of the first, is that a program of comparison of measurements among various laboratories can insure that undetected systematic measurement errors have not been

introduced into a measurement system.

As was mentioned previously, the calibration technique consists of

comparing the output of the device under test with the output of

calibrated devices when a high voltage pulse is applied. The two

calibrated devices used by IIBS are a resistor voltage divider and a Kerr system. The possible errors associated with the divider include

the list presented earlier plus any additional uncertainty introduced

by the device used to measure the low voltage signal. The divider is

constructed of counterwound resistors to minimize any residual

inductance. The effects of stray capacitance are kept as small as possible in two ways. First, the resistance of the divider is only 500 fi. This low resistance helps to keep the RC time constant —due

to the divider's resistance and any stray capacitance—short compared

to any time interval during which a significant variation in the

voltage wavefonn occurs, i.e., less than about 100 ns. The second way

to minimize stray capacitance errors is to make measurements only

during a portion of the pu].se when its time rate of change is small.

The applied voltage pulse is an approximately rectangular pulse with

rise and fall times of about 1 ys and a duration of about 10 ys.

Measurements are made near the trailing end of this pulse so that a
"steady-state" condition is attained prior to and during the measurement.

Errors introduced "by induced currents during the measurement can be

made acceptably (i.e., undetectably ) small by appropriate arrangement

of the high and low voltage circuitry. Particular attention is paid to

the grounding procedures. Partial verification that the error is

minimized is obtained in the following manner:

a. the circuit is assembled in exactly the configuration

in which it is to be used;

b. the low voltage output of the divider is shorted to

ground;

c. the pulse generator is fired and the response of the

system is recorded on an oscillogram.

It can be correctly inferred from the first step that any modification

of the high voltage circuit requires a reverification that induced or ground c\arrents are not causing unacceptably large errors. The

sensitivity to geometry can be appreciated by a consideration of the sources of error which can contribute to a non-zero reading under these

conditions.

The first, and in our laboratory, the most common, is the voltage

difference due to the non-zero impedance between various grounds in the

circuit. This phenomenon is sometimes called "ground current error."

The error is indicated as an apparent potential difference between the

input and the ground connection of the oscilloscope. If there is, for

example, a small resistance between the ground connection of the

oscilloscope and the ground connection of the divider, the large

current associated with the high voltage pulse can lead to a significant voltage to be measured at the oscill.oscope. It is selfevident that the magnitude of this voltage is dependent upon the

location of ground connections and the length of the interconnecting

cable between the divider and the oscilloscope.

A second geometry-dependent source of an error voltage is the mutual

inductance in the system. In a Marx-type circuit, such as is used at

NBS to generate voltage pulses, there is a high current pulse as well

as a high voltage pulse. The associated magnetic field induces voltage

pulses in any loops within or adjacent to the high voltage circuit.

The magnitude of this induced voltage is very sensitive to the geometry

of the high voltage circuit. A third geometry dependent effect which

must be . considered is the capacitive coupling among various components

of the circuit. The final error soiarce which could be geometry

dependent is radiated electromagnetic interference. The primary source

of this signal is electrical breakdown, either intentional as in the

operation of the control spark gaps or unintentional such as corona in

the impulse generator at full charging voltage. Although the source of

5
this signal is relatively insensitive to the configuration of the

apparatus, its effect on the measurement can be minimized "by

appropriate placement of sensitive detectors.

To verify that the sum of the errors from all of these sources is

negligible, it is necessary to perform a measurement in a system that

approximates as closely as possible the measurement situation. In this

work, this is accomplished by placing a short circuit in parallel with,

and immediately adjacent to, the low resistance arm of the resistor

divider. The short circuit is contained in a coupler which is used

between the signal cable and the output terminal of the divider.

To determine the errors remaining, the high voltage generator is fired

with the low impedance arm of the divider shorted. The errors are assumed to be sufficiently small if the voltage measured using the

oscilloscope is less than 0.1% of the voltage to be measured under

normal operation.

C. Kerr System Uncertainties

Uncertainties inherent in pulse voltage measurement using the Kerr

effect can conveniently be discussed within the framework of equations

which define the Kerr effect. The Kerr effect is described by the

relationship

n - = ABE^ (3)

where

^2.1(1) index of refraction for light polarized parallel

(perpendicular) to the direction of the applied field E, B is the Kerr

coefficient and A is the wavelength of the monochromatic light

traversing the Kerr cell. Eq. (3) can be used to determine the phase

shift, cf), between the components of the light beam polarized parallel

to and perpendicular to the direction of the applied field:

(}) = 27T BE d2, . (h)

In Eq. (^), L is the length of the path through the applied field. It

is assumed that Eq. (h) can be rewritten

Cj, = TT (V/V f , (5)

where

V = d/(2B£' )' m

(6)

6
and V is the applied voltage. In Eq. 6, it has been assiomed that the

Kerr cell is a parallel-plate capacitor with plate spacing d. The

integral in Eq. has been approximated,

L

be di ^ Bfi,'(V/d), (7)

vhere 2,' is an effective plate length vhich includes the effects of

fringing fields. '

It is appropriate to discuss the physical significance of V which is

named either the "cell constant" or the "half-wave voltage" depending

upon the point of emphasis. Eq. 6 shows the origin of the term "cell

constant". From this expression, it can be seen that the magnitude of

V is determined by the geometry of the cell (d and £') and the Kerr

m

coefficient, B, of the material in the cell. When the cell constant is

known, Eq. 5 can be used to predict the phase shift between

orthogonally polarized components of the light beam upon passage

through the cell when a voltage, V, is applied to that cell.

The term "half-wave voltage" has a slightly different emphasis. From

Eq. 5» it can be seen that when the applied voltage equals V , the

phase shift has a magnitude tt. A phase shift of magnitude tt is

equivalent to a spatial shift of the origin of one of the components by

a distance A/2. Thus V is called a half-wave voltage. m

The cell constant has a further significance. Calibration of a cell

consists of determining the magnitude of V . Because of the

m

configuration of the optical components in a typical Kerr system, the

cell constant corresponds to the smallest voltage which will cause a maximum in the optical transmittance through the system. So

calibration consists of applying a known voltage to the cell, measuring

the phase shift, and using Eq. 5 —in a somewhat more convenient form—to

determine the cell constant.

From Eq. (5) » the uncertainty in voltage measurement can be expressed

as

AV/V = ± ^\/\- (A^/(f.)/2 . (8)

This expression simply states that the uncertainty in voltage measurement is the sum of the uncertainty in the cell's calibration and the

uncertainty in the measurement of the cell's response to the applied

voltage pulse. Previous work^ has shown that for an appropriately

constructed cell and detection system

(A(j)/(}))/2 « 0.01 (9)
The more significant contribution to measurement uncertainty is the ^ uncertainty in cell calibration AV /V . It has also been demonstrated mm

that the cell constant can be determined under pulsed high voltage for

fixed temperature, wavelength and light path through the cell. The

calibration technique is to connect the Kerr cell in parallel with the

divider described above and apply a high voltage pulse to the

combination. The phase shift between the components of the light beam

is measured as is the applied voltage. Eq_. 5 can then be used to

calculate V . If subsequent pulsed high voltage measurements are made . using both ?he divider and now calibrated Kerr cell, it is found that

the results agree to within about 0.1% of the peak voltage value.

Because the estimated uncertainty of the voltage divider measurement is

±1% the uncertainty of the Kerr system calibration is also

approximately ±1^. Direct voltage measurements using the above

approach have also indicated that the uncertainty in the determination

of V is not larger than ±1%. That is to say, AV /V is ±0.01.

m ra m

This procedure, although it has proven to be an effective method of

assuring accurate pulse measurement, is somewhat less than ideal for

two related reasons. One is that although calibration accuracy is

maintained using two independent devices it is established through the

use of a divider alone. Thus the accuracy of the Kerr system

calibration depends on the accuracy of the divider calibration and the

inherent experimental difficulties of divider measurements have been

documented. An independent calibration of a Kerr system would be

desirable to provide additional insurance against undetected systematic

errors in high voltage pulse measurement.

The second point is that simultaneous measurements of the same voltage

pulse using both a divider and a Kerr system have experimentally

demonstrated that the Kerr system offers better measurement precision

than does the divider. Thus an independent calibration of a Kerr

system could result in better measurement accuracy.

An independent—of a pulse divider—calibration of a Kerr system was performed. A discussion of the calibration is the basis for the

following section of this report.

D. Low Frequency Calibration of a Kerr System

1. Introduction

It has long been recognized that one of the potential benefits of a Kerr system is that it should be possible to calibrate a cell at direct

or alternating voltage for use in high voltage pulse measurements. To

understand why this should be possible, it is helpful to review the

nature of voltage measurement using the electro-optic Kerr effect. To

determine voltage from Kerr effect data, the following equation is

used:

I/I = sin^ [ttCv/V f/2] . (10)

8
In this relationship, I is the transmittance of the optical system at a voltage level V, and Vm—the cell constant—is the lowest voltage which

causes a maximum in the transmittance, I^. Calibration of a cell

consists of determining V . Once V is known, Eq. 10 can be used to

m m

relate the optical transmittance to the applied voltage. The cell

constant can be expressed in terms of the cell geometry and the Kerr

coefficient of the birefringent fluid, i.e.,

V = d (2B£' . (11)

m

In Eq. 11, d is the plate spacing, £' is the effective plate length

parallel plate geometry is assumed—and B is the Kerr coefficient. It

follows from this equation that any frequency dependence of the cell

constant would be due to a frequency dependence of either the Kerr

coefficient of the birefringent fluid in the cell or the effective

plate length £ '

.

Quantitatively accurate calculations of the Kerr coefficient of polar

liquids are presently unfeasible because of uncertainties in liquid

structiire. Insight into the sensitivity of the Kerr coefficient to

variations in wavelength, temperature, frequency of the applied

voltage, etc., can, however, be gained from an examination of the

classical expression for the Kerr coefficient of a polar fluid^,

B = up (n^ + 2f (c + (8^ + Q^)/21 nX . (12)

In this equation, n is the index of refraction at the wavelength of the

incident light A, e is relative permittivity of the medium, and p is

the niamber density of the molecules. 8^ and 6^ represent expressions

involving the temperature of the fluid, the static and optical

polar izabilities and the dipole moment of the molecule. Previous

theoretical work has shown that the temperature dependence can be

explicitly expressed in the form

6-^ + 62 = 0^+ (a^/T) + (a^/T^) . (l3)

Recent experimental work^ has verified that the temperature dependence

of the Kerr coefficient of nitrobenzene is well represented by this

quadratic equation. From Eq. 12 it can be inferred that any frequency

dependence of the Kerr coefficient should also manifest itself in the

frequency dependence of the relative permittivity. Measurements "'"^'"''"^ show that the relative permittivity of nitrobenzene is approximately

frequency independent for frequencies between 0 and 10^ Hz. This

suggests that the Kerr coefficient is and hence the cell constant may

9
be frequency independent over the same frequency range.

For the cell constant to loe truely frequency independent, it is also

necessary that Jl' be frequency independent. The quantity Ji' was a constant which permitted s implication of an integral (Eq. 7) "by

assuming that the electric field is uniform and that the effects of any

non-\miformity can be accounted for accurately by adjusting the

"effective" length of the capacitor plates. It has been shown , however, that the space charge density and hence the electric field

distribution are frequency dependent. The "effective" length,

therefore, also depends on frequency. Through careful preparation of

the cell and by judicious choice of the frequency ranges used, it

should be possible to reduce this effect to an acceptably small

pert\irbat ion.

If this be true, it is feasible to calibrate a Kerr system at a number

of discrete frequencies and use the system to measure high voltage

pulses. The remainder of this section will describe efforts to

experimentally verify that the cell constant of a nitrobenzene-filled Kerr

cell is frequency independent over the frequency range from 0 to 20,000

Hz.

2. Direct Voltage Measurements

The circuitry used is shown in Fig. 1. This approach is similar in

principle to the circuit which was previously^ used to determine the

cell constant of a Halowax oil-filled cell under direct voltage. The

apparatus has been improved somewhat by moving the beam splitter so that the light beam is split after it emerges from the Kerr cell rather

than as it comes from the laser. The improvement results because in

this configuration the ratio ^/^^ can be measured directly. The

primary source of attenuation of the light beam is the Kerr cell. In

addition, any voltage dependent source of attenuation, e..g.,

turbulence, is also due to phenomena within the Kerr cell and so will

be appropriately handled by the electronics. The light beam which was

split from the primary beam can be used as a reference signal for the

lock-in amplifiers and as a signal which is proportional to I . A

second lock-in amplifier, using the same reference input, is used to

detect the transmittance of the system, I. Each lock-in amplifier

generates a direct voltage output whose magnitude is proportional to

the root mean square value of the input voltage at the reference

frequency. These direct voltages are measiired using digital

voltmeters. The direct voltage which is proportional to I is used as the reference voltage for the digital voltmeter which measures the

transmittance, I. This meter then displays the ratio ^/^^'

To test the linearity of the system, the electric field was removed,

the analyzer was rotated and the ratio I/I was recorded as a function ' m

of analyzer angle, 0 , in the region +40 <. 9 <. -20 . (An analyzer

angle of +^5 ° is perpendicular to the polarizated light transmitted by

10
11
I

the first polarizer). Following Maithus ' Law, the data were fitted to an expression of the form

For the particular apparatus used, a equalled 0.557 with a standard

deviation of O.O88, Using this result, an estimate of the expected

uncertainty in the measurement of the cell constant can he obtained.

It has been shown that

AVmm/V = ± AV/V/ ± A(J)/2cf) T/ T ,J (15)

where cj) is the phase shift between two orthogonally polarized light

beams upon passage through the Kerr cell and V is the applied voltage.

Because the measurements are performed using direct voltage, it is

anticipated that

AV/V 0.001 < Ac|)/2c|) . (16)

In these measurements, the phase shift is not measured directly. The

measured quantity is the transmittance through the optical system l/l . The relationship between the mcertainty in the measurement of the ^

transmittance and the uncertainty in the determination of the phase

shift is given by^

cos"^ {(-1)''(1-2[I/I ± AI/I ])} - cos ^[(-1)''(1-2I/I )]

, m m m f-i^\

A(j)/(t) = (IT)

niT + cos"-^ [(-1)''(1-2I/I )]

m

In this equation, n is an integer defined by the relationship

(f)/7r = n + a , (18)

where a is the appropriate positive number between 0 and 1.

Assuming (1-2I/I )^ « 1 and that nir > cos"^ [(-l)^ (1-2I/I )], Eq. IT

m m

can be approximated

A(j)/(j) - (2A l/l^)/nTr , (19)

12
so

AV /V ^ (AI/I )/n7T . (20) mm m

Nov if AI/I = 0.088 as indicated above and if n = 10, the iincertainty

in the determination of the cell constant is of order 0.3%, i.e..

AV /V = 0.003 . (21) m m

It should he emphasized that this number is an estimate of the

uncertainty vhich should be attainable due to the measured uncertainty

in the relative transmittance . This is not an estimate of the

uncertainty that would characterize the final data.

To gain some insight into the relative purity of the nitrobenzene, the

resistivity of the cell was measured using high direct voltage. The

electro-polished stainless steel electrodes had approximate dimensions

of k cm width and 12 cm length and an interelectrode spacing (parallel

plate configuration) of 0.5 cm. The measured value of the resistivity

was lO''' 9. ' m at a. field strength of ^0 kV/cm. A photograph of the

transmittance of the Kerr system at hi kV/cm is shown in Fig. 2. It can be seen that the field is approximately uniform between the

electrodes at this field strength. For the indicated applied field

strength, the next dark fringe would represent an increase in the field

strength of less than 10^. To fixrther minimize the effect of electric

field non-uniformities, measurements were taken with the photodet ector

measuring only light from^^he central portion of the interelectrode

region. Previous studies have shown that in this cell the

interelectrode field distortion is a linear function of position, i.e.,

E = ax + b . (22)

The field at the center, E , is ' c

E = a(0.5d) + b (23)

c where d is the interelectrode gap spacing. The applied voltage is

given by

d d

V=f Edx=/ (ax+b)dx (2h) o o = E • d . (25)

c

13
KERR RESPONSE UNDER

HIGH DIRECT VOLTAGE

Fig. 2 Kerr response at an electric field strength of hi kV/cm. The

absence of horizontal fringes indicates an approximately uniform

electric field. This photograph is typical of the field distribution

during the direct voltage calibration of the Kerr cell.

Ih
The implication o? the final expression is that ir. crier -3 neasiire an electric field which is directly proportional zo zhe applied voltage,

neasurenents nust be taken at the center of the in^er electrode region.

In stunmary, cy piir ifying the liquid and by careful attention to

electrode preparation, the non-unifcrni^y of the electric field vas

minimized. The experimental data shov z'r.s.z ~he field variation is' no more than ±3% of i~3 central value. -he effect of any small residual

non-uniformity vas minimized by detecting the light transmitted through

the center of the interelectrode region.

Direct voltage meas-jrements vere made using the apparatus shown in Fig.

At 22.5 °C the meas^ored cell constant vas 5820 V vith a standard

deviation of 0,2% (3- = 0.6%). Tnis is in good agreement \T±th the

predicted uncertainty (Eq.. 2l). It is estimated that the dominant

systematic uncertainty in this measurement was in the determination of

the temperature of the birefringent fluid—the value vas net determined

with any more precision than ±0.5 °C. This would contribute an uncertainty of ±0.23% to the dete2rmination of the cell constant. The

total uncertainty in the measurement is therefore estimated to be

±0.9^.

3. Alternating Voltage Measurements

Measurements were taken over two different frequency ranges: 6O-IOOO Hz

and 9000-20,000 Hz. Because the res-alts of the two sets of

measurements were significantly different, each set "f„-ni]_ '-9 iiscussed . separately.

a. 6O-IOOO Hz Experiments

The measurements over the range of 60 Hz to 1000 Hz were performed

using low resistivity nitrobenzene and these results were not

consistent with results taken at lower and higher frequencies using

nitrobenzene with higher resisti-^/lty . Low resistivity means that

measurement problems due to electric field distortion, fluid motion and

heating will be more severe. These measurements were not included in

the final determii nation of the cell constant but are presented and

discussed for completeness. The resistivity of the cells used was of

order 10 H • m. The Kerr response under direct voltage is shown in

Fig. 3. It was found that the field was approximately xmiform because - the change in field strength necessary to produce the next dark fringe

was of order 2%.

Although the cell had acceptable characteristics "onier direct voltage,

the same was not true under alternating voltage. Tig. k shows the

effect of fluid motion on the optical transmission of the Kerr cell.

To obtain these photographs, linearly polarized light was passed

through the cell, but no crossed polarizer was used. Photographs were

taken at 60, 200, 770 and 912 Hz. Under these applied voltages, the

optical transmission of the Kerr cell is no longer sufficiently well

defined so as to yield usable Kerr effect data.

15
KERR RESPONSE UNDER

HIGH DIRECT VOLTAGE

Fig. 3 The Kerr response under direct voltage in the cell that was used under alternating voltages in the frequency range 6O-IOOO Hz.

Although the field is uniform (non-uniformity of order \% of avera,

value), this is probably due to equal numbers of positive and

negative carriers rather than an absence of space charge.

16
OPTICAL TRANSMITTANCE OF KERR CELL AT SELECTED FREQUENClEb

770 Hz 912 Hz

Fig. h The transmittance of the cell is influenced "by the frequency of

the applied voltage. All of these photos were taken at the same field strength, nominally 12 kV/cm.

IT
To obtain additional information concerning the behavior of the

nitrobenzene under these conditions, the resistance of the cell was measured. Under direct voltage the resistance was calculated from the

measured voltage and current. Under alternating voltage the

measurement process was somewhat more complicated.

The Kerr cell can be represented as a capacitor, C^^, in parallel with a resistor, R„. To determine R , a resistor R and capacitor C are K K. connected in parallel with each other and the combination in series

with the Kerr cell between the Kerr cell and ground. A two-phase

voltmeter was used to measure both the in-phase and quadrature

components of the voltage developed across R and C when a high voltage

signal was applied to the Kerr cell. The low voltage capacitor, C, was

a variable capacitor and at each frequency its value was chosen so that,

the quadrat"ure component as measured by the two-phase voltmeter was

zero. When the quadrature component is zero, '

= RC . (26)

The value of R was measured to be IOO8 Q and assumed to be frequency

independent to within the sensitivity of this experiment. Similarly, C

and the capacitance of the Kerr cell were measured at low voltage and

1000 Hz. The capacitance- of the Kerr cell had measured value, C = 99.7 K

This value was assumed to be independent of both frequency and voltage.

Using these values the resistance of the Kerr cell at various

frequencies was obtained and are listed in Table 1.

Table 1, Resistance of the Kerr Cell as a Function of the Frequency

of the Applied High Voltage.

Frequency (Hz)

0

k6

100

199

h55

Although insufficient data were taken to permit an unambiguous

interpretation of the fluid behavior, a model which invokes particulate

carriers is consistent with the observed behavior. Under direct

voltage the particulate carriers shuttle charges back and forth between

the electrodes. Because of the relatively large number of carriers the

\ in)

8.6 X 10'

3.9 X 10

3.9 X 10

3.7 X 10

3.3 X 10

18
net charge density as determined by the Kerr effect will be small while

the number of positive and negative carriers is large. Therefore under

direct voltage, low resistivity with very small space charge distortion

is observed.

There is also a conditioning effect under direct voltage which can be

explained by assuming that the particulate carriers become trapped on the electrode surfaces. As the number of carriers is decreased, the

current at a given voltage decreases so the resistivity increases.

Under alternating voltage, however, no trapping would occur so the

measured resistivity would be lower. A critical test of the adequacy

of this model is that at some frequency the particulate carriers should

not be able to follow the rapidly changing voltage and the resistance

should begin to increase with increasing voltage. The frequency range

at which this should occur can be theoretically estimated. In a cell

with plate spacing 0.5 cm and at a voltage level of 30,000 volts, the

time required for charge carrier to traverse from one electrode to the

other is of order 8 x 10""^ s."*"-^'"^^ If the carrier is to have an insignificant effect on the conduction process, this time should be very

long compared to one half of the period of the applied voltage. This

condition is satisfied when the frequency is of order 1000 Hz.

Although this calculation is very approximate, it does augur well for

successful operation of the Kerr cell at higher frequencies.

b. Measurements at 9,000-20,000 Hz

To obtain a higher frequency, a series-resonant high voltage system was

constructed. Three air core solenoids were wound. Each solenoid was about 57 cm long and had approximately three hundred turns of #l8 wire.

Each inductor had an inductance of about 0.01 h and could carry about

10 amps continuously with only convective cooling. One of the

inductors was tapped so that a number of inductance values could be

obtained. The voltage and current source was a commercially available

power amplifier having an output rating of 3 kVA. Half-power points

were at about hO Hz and 20,000 Hz. The total resonant circuit

including the Kerr cell had a Q of about 100. To insure that the

applied voltage signal was a sine wave, as would be predicted by the

circuit parameters, an attempt was made to measure the harmonic

distortion at a resonant frequency. The wave analyzer used could

resolve any component which was as large as 0.01^ of the fundamental.

No harmonics could be detected. The frequency of the applied voltage

and the measured cell constant at each frequency are shown in Table 2,

Each of the values of the cell constant listed is the average of

measurements made during at least 8 different half-cycles of the

applied voltage waveform and taken at at least k different voltage

levels. The cell temperature was maintained at 2h °C during these

measurement s

.

19
Table 2. Measured cell constants over the frequency range of

9,000-20,000 Hz.

Frequency

{ nz ) Cell Constant

V vol u S J

9,110 5920

10,7^0 5890

11,U20 5910

12,500 5870

12,610 5870

13,350 5900

16,650 5920

17,610 5910

18,790 5920

19,220 5900

Each determination of the cell constant was made at the peak of a selected half-cycle of the applied sinusoidal high voltage. At each

voltage level, an equal number of measurements were made at positive

and negative half-cycles. To within the sensitivity of the experiment,

no polarity dependence was detected.

The applied high voltage was measured using a capacitor divider and a digital voltmeter. The high voltage element in the capacitor divider

was a three-terminal compressed-gas capacitor with a capacitance value

of IOU.5 pF. The low voltage component was a polystyrene capacitor

having a capacitance of l.OUO yF. The divider ratio was therefore

9952:1. The scale of the digital voltmeter was calibrated (by the

manufacturer) to indicate the true rms value of the signal. The

performance of the digital voltmeter was verified using a true rms meter which incorporated a thermal converter. Because the applied

signal was a very pure sine wave, the peak value of the applied voltage

could be calculated from its rms value.

k. Pulse Measurements

Following these measurements of the cell constant, without use of a pulse divider, the cell was calibrated under pulsed voltage with

respect to a voltage divider. The voltage generat ing-measuring system

was the system described earlier which consisted of a generator capable

of producing an approximately rectangular piilse, with rise and fall

times of about 1 ys and a duration of about 10 ys, and a 500 Q, resistor

20
divider. The low voltage output, of the divider was measured using an oscilloscope operated in a suppressed zero mode. The measured value of

the cell constant was 58UO V at temperature of 22.5 °C. To compare

this value with the value determined under low frequency alternating

voltage at 2k °C, it is necessary to correct for temperature. It has

been previously shown'' that, to within the limits of measurement

accioracy.

8V

V 9T 2B 9T ^ ' ^ m

i.e., the temperature dependence of the cell constant is determined by

the temperature dependence of the Kerr coefficient. From Eq. 6,

V = (—^) V (28)

in?-!--, m^-l-p

1

where the subscripts T^ and T^ correspond to two different

temperatures. Combining Eqs. 12 and 13,

B = Aq + (A^/T) + (A^/T^) . (29)

5 The best available values for the coefficients are

Aq = 2.5^6 X 10 mV

A^ = -1.717 X 10"^ K mV"^

A^ = 3.136 X 10"^ mV"^ .

Using these values in Eq. 28, if the value of V at 22.5 °C is 58I+O V,

, ^ m

the value at 2k °C is 5900 V.

Fig. 5 shows graphically the fluctuation of the measured value of the

cell constant under the various high voltage waveforms that were

21
o>>O

(SilOA)

•H

1>

0)a

pi H

(UO^

(D W^P

ChOO

•HP

•HH

cd

CJ

0)oO

CO •H

?H

03IH

03o

•H

22
I

applied. The significance of these measurements is that they indicate

that a Kerr system can indeed be calibrated at direct or lov frequency

alternating voltage and then be used to calibrate a pulse measurement

system at operating voltage levels. This approach uhen provides

simultaneous, in situ, calibration of the divider ratio and the

measuring device, i.e., the sum of the tvo terms on the right side of

Eq. 2.

23
Acknowledgment

The author would like to acknowledge the contributions of E. C. Cassidy,

J. E. Jones, R. J. Sojka, and M. Zahn, all of whom participated in the

experimental work which served as the basis for the appendices of this

report. In addition, it should be noted that W. A. Bagley provided

technical support during all of the experiments described. Finally

•the author would like to thank M. Misakian for his careful reading of

and comments on the manuscript and J. E. Cunningham and E. D. Sims for

their assistance in the preparation of the manuscript.

2k
References

1) . T. Harada, et al. , "Development of a High Voltage Universal

Divider" Paper No. F 75 560-3 IEEE Power Engineering Society Summer

Meeting, San Francisco, Calif., July 20-25, 19T5.

2) . International Electrotecbnical Commission, High-Voltage Test

Techniques , lEC Puhlication 60, pp. 51-91, (Bureau Central de la

Commission Electrotechnique Internationale, 1, rue de Varembe,

Geneve, Swisse) 19^2.

3) . J. H. Park and K. N. Cones, "Sphere-Gap Volt-Time Curves

Reference Standards for Steep Front Measurements" AIEE Conference

Paper, Reprint No. 57-215, 1957-

k) . E. Kuffel and M. Ahdullah, "High Voltage Engineering" Pergammon

Press, New York, p. 273, 1970.

5) . R. E. Hehner, E. C. Cassidy, R. J. Sojka, "Development and

Analysis of Techniques for Calibration of Kerr Cell Pulse-Voltage

Measiiring Systems VIII" NBSIR 7^-56U, Aug. 197^.

6) . E. C. Cassidy, H. N. Cones, D. C. Wunsch and S. R. Booker,

"Calibration of a Kerr Cell System for High-Voltage Pulse Meas-arements"

IEEE Trans. Instru. Meas . , Vol. IM-17, pp. 313-320, I968.

7) . E. C. Cassidy, W. E. Anderson and S. R. Booker, "Recent Refinements

and Developments in Kerr System Electrical Measurement Techniques",

Vol. IM-21, pp. 50I+-5IO, 1972.

8) . U. Kriiger, R. Pepperl , and U. J. Schmidt, "Electrooptic I'laterials

for Digital Light Beam Deflectors" Proc. IEEE, Vol. 61, pp. 992-1007,

1973.

9) . C. G. Le Fevre and R.J.W. Le Fe^/re, "The Kerr Effect. Its

Measurement and Applications in Chemistry" Rev. Pure Appl. Chem.

,

Vol. 5, pp. 261-318, 1955.

10) . A. von Hippel, "Tables of Dielectric Materials Volume IV"

Technical Report No. 57, Laboratory for Insulation Research,

Massachusetts Institute of Technology, 1953.

11) . G. L. Clark, "Dielectric Properties of Nitrobenzene in the

Region of Anomalous Dispersion" J. Chem. Phys . , Vol. 25, pp. 125-129,

1956.

12) . E. C. Cassidy, R. E. Hebner, M. Zahn, and R. J. Sojka, "Kerr -Effect

Studies of an Insulating Liquid Under Varied High Voltage Conditions"

IEEE Trans. Elec . Insul. EI-9, pp. ^3-56, 197^.

25
13). M. Zahn, C. F. Tsang, and S. Pao, "Transient Electric Field and

Space-Charge Behavior for Unipolar Ion Conduction" J. Appl. Phys.,

Vol. 1+5, pp. 2U32-2UUO, 197^^.

ih) . E. J. Hopfinger and J. P. Gosse, "Charge Transport by SelfGenerated Turbulence in Insulating Liquids Submitted to Unipolar

Injection" Phys. Fluids, Vol. ik , pp. 16TI-I682, 1971.

26
APPErroix 1

improved Techniques for the Measurement of

"oltage Impulses Using the 31ectro-cptic Kerz

Tlie material presented in this appendix is a portion of a preprint of

a talk "by E. E. Hehner, E. C. Cassidy and J. E. Jones at the 19T5

Electrical and Electronic Measurement and T'es* Instr'Jin.ent Conference,

Ottawa, Canada, ?^y 15, 1975.

27
I . INTRODUCTION

Accurate measurement of high voltage pulses is important in a -wide

range of applications. These include pulse testing of power system

equipment-'- '2 , the design and reliability of components used in radar

systems, the design and operation of pulsed lasers3 and the apparatus

used in fusion research^''', and in research and development work such as exploding wire phenomena" and nuclear effects simulation. Conventionally,

these measurements are made using a spark gap and/or a measurement system

that incorporates a high voltage divider.

The procedure used in spark gap measurements and a description of the

resistors in the 500 Q, pulse-voltage divider used in this work have been

published.'^ Descriptions of the performance, reliability, useful range,

and errors characteristic of various types of dividers are available

.

A characteristic common to these systems is that the waveform is obtained

by photographing the oscilloscope deflection produced by the voltage

across the low voltage arm of the divider. The peak value is obtained

either from a photograph as above , or through the use of a peak reading

voltmeter

.

In recent years, an alternative approach to pulse voltage measurement,

based on the electro-optic Kerr effect, has been developed.-'-'''"^-'- The

precision and accuracy of the method have been demonstrated. A

disadvantage of this technique that has been identified^^ is that the

non-linear relationship between the Kerr system transmittance and the

applied voltage makes the data from the Kerr system difficult to

interpret. This paper describes a system which minimizes that

difficulty.

The system uses a transient recorder to digitize and store the Kerr

response. Digitizing the Kerr response offers two advantages over digitizing the low side voltage of the divider directly. The first is

the inherent advantage of optical coupling—protection of the sensitive

electrical apparatus from high voltage or high current surges. Second,

the nonlinearity of the Kerr response may provide a more acciarate

measurement of much of the voltage waveform than would digitizing the

low voltage signal obtained from a very accurate divider. The improved

accuracy can result because the measurement uncertainty introduced

by the digitizer contributes directly to the uncertainty in voltage

measurement when a divider is used, but only indirectly when the

measurement is made using a Kerr system.

The digitized Kerr response is a series of numerals representing the

value of the transmittance of the Kerr system at preselected Instants

during the high voltage pulse. Using a computer, the voltage as a function of time can be calculated.

II. THEORY

If an electric field is applied to a substance the difference between

the index of refraction for light polarized parallel to the applied

28
field, n-j^-j^, and the index, n^^, for light polarized perpendicular to the

applied field is given by the expression

""ll "

""x " TM^ •

In Eq. 1, A is the wavelength of the light, B is the Kerr coefficient of

the material and the electric field is denoted by E. From Eq. 1, it

follows that upon propagation through the material the phase shift, (j), between the component of the light beam polarized parallel to and the

component polarized perpendicular to the applied field is given by

L

(|) = 27T / BE d£ . (2) o

In Eq. 2, L is the length of the optical path through the applied field.

In the most basic arrangement of a Kerr pulse-voltage measurement

system—the arrangement used in all work presented here—light polarized

at an angle of ^5° to the direction of the applied field passes through

the Kerr cell and then impinges upon an analyzer oriented perpendicular

to the original direction of polarization. Under these conditions the

transmittance through the optical system is described by the

relationship^^

I/I^ = sin^ [4>/2], (3)

where I is the instantaneous value of the transmitted light and I denotes the maximum amount of transmitted light.

The Kerr systems used here for voltage measurement were parallel-plate

capacitors. Using this geometry, it is assumed that Eq. 2 can be

rewritten

,

" •

(}) = 2^ BV^£'/d^, ih)

where any modification of the phase shift due to non-uniformity in the

electric field is included in the effective plate length, Defining

V = d (2B£' )~^'^^, (5)

Eq. 3 can be rewritten

m

I/I = sin^ [tt (V/V f/2] . (6) m m

Eq. 6 serves as the basis for operation of a device for measuring high

voltage impulses based on the electro-optic Kerr effect. The quantity —which is the lowest voltage necessary to cause a transmission

maximum in the system—is called the cell constant. The cell constant

29
depends only on cell geometry and on the properties of the birefringent

fluid used in the cell. For the work discussed here, the birefringent

fluid was nitrobenzene which has a Kerr coefficient, B, of

3.2k X

10"-'-^ m/v2 at a temperature of 296 K and a wavelength of 632.8 nm. In most cases, V cannot be determined to sufficient accuracy from

Eq. 5 because of"^uncertainties in the geometrical measurements. The

presently accepted calibration procedure consists of applying -a voltage

pulse of known magnitude to the Kerr cell and determining V from

m

Eq. 6. Once the cell constant is known, Eq. 6 is then used to determine

the magnitude of other pulses.

To evaluate the uncertainty in a voltage measurement. It is convenient

to recognize that from Eqs. 6 and 3, we obtain

V = (^/tt)^/^ V . m

So the voltage measurement uncertainty can be expressed

AV/V = ± (A(j)/2(|)) ± (AVmm/V ) .

Eq. 7 expresses the fact that the uncertainty in the voltage measurement

is the sum of the uncertainty in the measurement of the Kerr system

response and the uncertainty in the Kerr system calibration. The value

of A(f)/(j) is somewhat difficult to express because the phase shift is not

directly measured. The relationship between the phase shift and the

transmittance , which is measured, is given by Eq. 3. This equation can

be used to obtain.

cos"^{(-l)^ (1-2 [(I/I ) ± (AI/I )])} - cos-^[ (-1)^(1-2 (I/I ))]

,,/, m m m

A(t./(t) = — ^

Ntt + cos ^ [(-1) (1-2 (I/I ))] m

In Eq. 8, N is an integer defined by the relationship:

(^/n = N + a

where a is the appropriate positive number between 0 and 1.

The second term in Eq. 7, the uncertainty in the calibration of the Kerr

cell, has been the focus of much of the previous work in the use of the

Kerr system for high voltage pulse measurement."'" The estimated

value for this uncertainty is

AVmm/V = 0.01,

• because present Kerr systems must be calibrated by reference to a resistor divider under pulsed high voltage.

30
III. COMPUTER RECONSTRUCTION OF VOLTAGE WAVEFORM

Previous work has demonstrated that the following procedure is sufficient

on to determine the pulse shape. ^ First a photograph, using a streak

camera, is made of the interelectrode field. This is read, using a microdensitometer to determine the values of I/l at selected times

dixring the voltage pulse. Finally, these values are inserted in Eq. 6

and the voltage as a function of time is calculated.

The work descrihed here removes the photograph from the above process to

obtain immediate information concerning the pulse shape. The operational

procedure using this approach is to detect the light transmitted through

the Kerr system with a photomultiplier . The output from the photodetectcr

is digitized and digital information concerning the transmittance as a function of time is stored in computer memory. The computer can then

reconstruct the voltage waveform, i.e., determine the voltage as a function of time, using Eq. 6. The software concept is to use a main

program to control eight subroutines as shown in Fig. 1. An insight into

the use of the Kerr effect for voltage measurement and into the care that must be taken in computer analysis of data from Kerr systems can be obtained from a study of the opei-ation of each of the subroutines.

The conversion subroutine is a software package made necessary by the

pecularities of the digitizer and computer interface that are used.

The smoothing subroutine fits the digitized data, five data points at a time, to a third order polynomial. This routine minimizes variations in

the data due to electrical noise, non-linear responses of individual

channels in the digitizer or other sources.

The normalization subroutine presents the data in a form that can be

analyzed according to Eq. 6. Mathematically, each transmittance maxima

must be assigned a value of 1 and each minima a value of 0. In practice,

the measured value of the transmittance at each maximum or minimum varies

slightly from extremiom to extremum. This variation can be due to the

bandwidth of the detection system, to slight, short term variations in

the laser output, to variations in the transmittance of the Kerr cell,

or to digitizing errors. These variations are typically no greater than

a few percent of the total difference between a minimum and a maximum.

The normalization routine then sets each maximum to 1 and each minimum to

zero and the intermediate points are adjusted so that they retain the same relative spacing as before normalization. This requires a slightly

different normalizing factor between each maximiom and minimum.

The search and the search parameter subroutines identify the addresses

of the minima and the maxima. The complication in identifying extrema

comes during those portions of the voltage pulse when the relative

transmittance is varying slowly with respect to the digitizing rate.

In this case a number of addresses could correspond to an extremum.

This situation is further complicated by the fact that at these

addresses the signal recorded is not strictly constant but varies in a slight, but unpredictable manner. It is essential that these

31
KERR ANALYSIS PROGRAM

MAIN PROGRAM

CONVERSION

SEARCH PARAMETER

SEARCH

V PEAK

KERR WAVEFORM ANALYSIS

VOLTAGE WAVEFORM ANALYSIS

NORMALIZATION

SMOOTHING

Fig. 1 Outline of software used to convert Kerr data into information

concerning the voltage waveform.

32
oscillations not be identified as extrema. The search subroutine looks

both ahead of and behind a specific point to verify that a true extremum

has been identified. The search parameter subroutine determines from

the responses the number of data points that must be considered.

The V PEAK subroutine then determines the location of the voltage peak

in the Kerr response. In rare cases this point may correspond to a minimum or a maximum. In these rare cases, the normalizing subroutine

handles this portion of the Kerr response correctly. It is much more

likely, however, that the peak corresponds to an intermediate value of

transmittance . The V PEAK subroutine identifies this region and the

normalization of this region of the trace uses p. procedure which is

somewhat different from the procedure used for the remainder of the Kerr

trace.

The Kerr waveform analysis subroutine solves Eq. 6 to determine the

voltage as a function of time.

The final subroutine performs voltage waveform analysis. In addition

to determining the magnitude of the voltage peak and the duration of the

voltage pulse (time between the points at which the voltage is 0.5 V

peak), this subroutine calculates the virtual front time, the virtual

rate of rise of the front, the virtual origin of the impulse, the

virtual time to half-value and the virtual fall time. The virtual

quantities are defined in the appropriate standard.-^

The input parameters and the output summary for a typical voltage pulse

are shown in Table 1. The only input parameter that cannot in principle

be determined by the software is the cell constant. The other four are entered to reduce computation time and to simplify the hardware and

software. The Kerr trace summary gives the extrema, the location of

these extrema, and the phase shift and the voltage at each point. The

time between any two of the extrema can be determined by multiplying

the sample interval by the difference between their location addresses.

The waveform summary provides a convenient synopsis of the waveshape.

To verify the validity of the entire construction process, a photograph

was taken of the pulse using a conventional divider and an oscilloscope.

The pulse shape parameters determined from the reconstructed waveform and

those determined from the divider-oscilloscope agreed to within the

uncertainty imposed by the finite width of the oscilloscope trace.

For example, from the oscillogram the pulse duration was greater than

6.35 ys but less than 6.66 ys. From the computer reconstruction a value

for the pulse duration of 6.U3 ys was calculated. Of course if one wishes

to view the entire waveform, a reconstruction like that shown in Fig. 2 can be obtained.

33

-i:ue3 for Zielec-ric _e5-3, USAS C68.1,

^Ie2";r:r-i3 ^.gineers. Inc., 3^-5 July 1965)

.

op — r: ~ —

'

Zz—-'. S3 ion, High-Voltage lest

. 5'--9'~ v3ureau Central ie la Coinmissd.on

en^e , Svisse) I962.

3. 0. R. Wood III, "Eign-?re 3 5-02-6 3 vol. 62, pp. 355-397, 19T^

h. ^. Skelton, "The Electrical _n~erference Proclez: i:i s'lstzr.

Research.," Zlec'rical ~r.~erferer-ce in lnstr-.:r:en~a~icr. IZZ Tcnf. ?-j."bl.

No. 65, Savcv Place, Icnicn 7r:2R:5i; , pp. 1-5, 19":.

Divider," Rev. Sci. Ins-r., vcl. -2, pp. S2 —52", 19~1.

6. Z. G. :a3 3ii:.-, 5. li—ernan, rC. ?:. :;e-jr:ar-n, "Time Resolved

Electrical Mea3urenen-3 in Righ 3urren- lischarges," Rev. Sci. Inst.,

vol. 31, pp. 210-2lli, 1966.

Steeply Rising Voltage Inp-jZ-es," C. ?.es . 27a- '1. Bur. Si;d3., vol. ooC,

pp. 197-207, 1962.

Resistance Tc l^age Dividers zz eer-Rr :r.- Inpnlse "raves," AIZZ Trans.,

vol. 76, par- 1, pp. 63^-6^c . 19; ~

9. 1. Schvab and J.H.W. Pagel, "rrecisirn ?apaci-ive Vcl-age Divider

for Inp-olse Voltage Measurements," IZZZ Irans . cn 1-^, vcl. ?A£-91,

pp. 2376-2382, 1972.

electronics Zcr Inp-^lse Vclcage ''eas-oremen- s

, " IZZZ Zrans. cn PAS,

vol. PAS-91, pp. 494-5OC, ::arcn April 1972.

11. Z. Sincn and S. 1. leroy, "CcntrilDution to a 3e--er Understanding

cf Inr-ilse Vclta^e ::ea3--Lr ins: Svs-ems," Tf^. Trans. Zcver Ar^^ar. Svs.,
12. F. C. Creed, M.M.C. Collins, Aa. Pedersen, and P. Lausen,

"Evaluating Impulse Measurements—A New Approach," IEEE Trans. Power

Appar. Sys., vol. PAS-91, pp. hS'^-hgh , 1972.

13. F. A. Fisher, "Transient Response of Impulse Voltage Dividers,"

AIEE Trans. Communication and Electronics, vol. 77, part 1, pp. U1I-U2O,

1958.

Ik. W. Zaengl, "The Impulse Voltage Divider With Lead," Bull, d I'A.S.E.,

vol. 61, pp. 1003-1017, 1970.

15. N. R. Hylten-Cavallius and L. Vaughan, "Calibration and Checking

Methods of Rapid High Voltage Impulse Measuring Circuits," IEEE Trans.

Power Appar. Sys., vol. PAS-89, pp. 1393-1^03, Sept. /Oct. 1970.

16. M. M. Brady and K. G. Dedrick, "High-Voltage Pulse Measurement With

A Precision Capacitive Voltage Divider," Rev. Sci. Instr., vol. 33,

pp. 1I42I-II+28, 1962.

17. D. C. Wunsch and A. Erteza, "Kerr Cell Measuring System for High

Voltage Rilses," Rev. Sci. Instr., vol. 35, pp. 816-82O, 196i|.

18. E. C. Cassidy, H. N. Cones, D. C. Wunsch and S. R. Booker,

"Calibration of a Kerr Cell System for High-Voltage Pulse Measurements,"

IEEE Trans, on Instr. and Meas., vol. IM-17 , pp. 313-320, I968.

19. E. C. Cassidy, H. N. Cones, and S. R. Booker, "Development and

Evaluation of Electro-optical High-Voltage Pulse Measurement Techniques,"

IEEE Trans, on Instr. and Meas., vol. IM-19, pp. 395-^02, 1970.

20. E. C. Cassidy, W. E. Anderson, and S. R. Booker, "Recent Refinements

and Developments in Kerr System Electrical Measurement Techniques," IEEE

Trans, on Instr. and Meas., vol. IM-21 , pp. 50U-5IO, 1972.

21. R. E. Hebner and S. R. Booker, "A Portable Kerr System for the

Measurement of High Voltage Pulses" Proc . of 1975 IEEE SOUTHEASTCON

,

vol. 1, pp. 3A-1-1 through 3A-1-5, 1975.

22. A. J. Schwab, "High Voltage Measurement Techniques" MIT Press,

Cambridge, p. 8U, 1972.

23. E. C. Cassidy, R. E. Hebner, M. Zahn, and R. J. Sojka, "Kerr Effect

Studies of an Insulating Liquid Under Varied High-Voltage Conditions"

IEEE Trans. Elec. Insul., vol. EI-9, pp. U3-56, 197^.

2h. R. E. Hebner and E. C. Cassidy, "Measurement of 60 Hz Voltages Using

the Kerr Effect" Rev. Sci. Instr., vol. 1+3, pp. l839-l8i+l, 1972.

36
e 1. Summary of the Kerr response and the waveform of the hi

voltage pulse. This information is calculated, and is

immediately available, for each high voltage pulse.

DATE? 10 April 1975

TIME? 10:i+9

INPUT PARAMETERS

VOLTAGE RANGE? 1.0

SAMPLE INTERVAL? 0.00000001s

MAXIMA OBSERVED? 17

MINIMA OBSERVED? l6

CELL CONSTANT? 33.61+

VOLTAGE WAVEFORM SUMMARY

MAGNITUDE OF VOLTAGE PEAK

VIRTUAL FRONT TIME

VIRTUAL RATE OF RISE OF FRONT

VIRTUAL ORIGIN OF IMPULSE

VIRTUAL TIME TO HALF VALUE

VIRTUAL FALL TIME

DURATION OF IMPULSE

138.158 kV

3.172999E-6 S

h.3'?hl6kE+l kV/S

-3.32i+373E-8 S

7.8U82i+3E-6 S

2.83899'9E-6 S

6.U2.9999E-6 S

37
KERR TRACE SUMMARY

I LOG N VOLTAGE (kV)

1 40 1 3 .14159 33 . d4

0

r-T -1 71 2 6 . 20319 47 . 5741

1

R A 00 3 9 . 4<d4 f 0 50 , 2662

0 100 4 1^ . 5o64 67 . 2o

1

111 111 5 15.1 UOU { 5 . 221

j

0 123 (D

T ft ft )i n<C 10

.

o49d fto ). rinft 02 . 400o

1 TOO 133 / ^;1 . 991^ fto "I 09 . vJU jl

0 145 00 25.1j^f PI cr n ) 1 ft 0 95 . 140

j

1 156 9

oft otIi 0 cfo . I 4:5 lUU . 9'i-U 0 170 lU 31 . 4159 lOb. i f

9

1 105 34 . 55 f 5 111 .5(1

0 1^; if .5991 lib. 5i2

1 1 13 )i n ft )i nv 4U . 04U

(

licl . <cyi

0 2d9 14 1,0 oft 0

0

4 j . 9023 125

.

od9

1 336 15 47.1239 TOO 0 ft

T

130 . 20 f 0 371 1 16 50.2655 ~1 0 1 1 C A 134

.

5dO

956906 427 16 52.9093 T oft T eft IJO.I5O

0

1.0/' 406 16 50.2655 13^ . 560

1 529 15 47.1239 130 , 207

0 598 14 U3.9823 125.869

- 1 640 13 40 .8407 121.291

. 0 659 12 37.6991 116. 532

1 673 11 3U.5575 111.571

0

/' n f- 685 10 3I.UI59 106.379

1 696 9 28.27^+3 100.920

0 707 - 8 25.1327 95.1^83

1 716 7 21.9912 89.0031

0 727 6 18.8I196 82.U008

1 736 5 15.7080 75.2213

0. 7^8 1+ 12.566U 67.28

1 760 3 9.U2I+78 58.2662

0 775 2 6.28319 U7. 57^+1

1 79^+ 1 3.IU159 33.6ii

38
APPENDIX 2

The paper reprinted in this appendix was published in August 197^.

39
1973 Annual Report

Conference on

Electrical Insulation

and

Dielectric Phenomena

Prepared by the CONFERENCE ON ELECTRICAL INSULATION AND

DIELECTRIC PHENOMENA

DIVISION OF ENGINEERING

NATIONAL RESEARCH COUNCIL

NATIONAL ACADEMY OF SCIENCES

WASHINGTON, D.C. 1974

UO
Electric Field Distributions and Space

Charge Behavior in Nitrobenzene under

Low Frequency Alternating Voltage

ROBERT E. KEENER, JR. AND ESTHER C. CASSIDY

National Bureau of Standards, Washington, D.C.

MARKUS ZAHN AND RICHARD SOJKA

University of Florida, Gainesville, Florida

INTRODUCTION

The electro-optic Kerr effect has been used by a number of workers

over the last two decades to measure the electric field distribution

in a variety of liquids and to study the electric field distribution

around solid insulators. Measurements have typically been either

under direct or pulsed high voltage.

It has long been recognized that if one wanted to use the Kerr

effect to measure the electric field distribution due to the geometry

of his electrodes and/or insulator forms he had two choices.

Either he could perform the measurement under pulsed voltage or,

alternatively, could carefully purify his liquid, coat the electrodes

with an appropriate membrane and, if he confined himself to moderate field strengths, could be fairly certain that observed distortions were a result of geometry and not due to a property of the

Kerr fluid itself. If uncoated electrodes or higher field strengths

were used, the electric field in the Kerr liquid would be distorted.

Historically, depending on the materials and their state of purity,

this distortion has been attributed to chemical or electro-chemical

processes either in the bulk or at the electrode surface or to the

presence of suspended particles in the bulk of the field.

It was judged that an understanding of the dynamics of this distortion could lead to more accurate voltage measurement using the
electro-optic Kerr effect and to additional understanding of electrical conductivity and breakdown phenomena in insulating liquids.

We therefore measured the electric field as a function of position

and time under direct and low frequency alternating voltage in a nitrobenzene-filled parallel-plate capacitor.

The data presented here were taken in a cell having nickel electrodes. The nitrobenzene was purified before it was sealed into the

cell. The measured resistivity was of order 10^ - 10^ Q-m.

EXPERIMENTAL RESULTS

The experimental apparatus consists of a nitrobenzene-filled

parallel-plate capacitor, a triggerable pulsed argon laser, crossed

polarizers oriented at + and -45° to the interelectrode field direction, and appropriate photographic equipment for recording of the

transmitted fringe patterns observed when the laser is flashed

during high voltage operation. The laser beam is expanded and

collimated to illuminate the area between and around the test cell

electrodes. During direct voltage studies, the high voltage was

connected to a parallel combination of the test cell and a calibrated

100 MQ resistive divider. For current measurements a microammeter was placed in series with the Kerr cell between the cell

and ground. For ac studies, the power-amplified output of an audio

oscillator supplied a step-up transformer. The transformer's output voltage was applied to one electrode of the cell, the other electrode of the cell being grounded. The rms value of the applied

voltage was measured using a 1000:1 metering tap on the transformer.

The governing equation^ for the analysis of data obtained is

In this expression I is the irradiance of the transmitted light, Ij^

is the maximum irradiance, E is the electric field magnitude,

is the electric field necessary to produce the first maximum in the

transmitted irradiance and the overbar (e.g. , in A) denotes

where L is the geometrical length of the optical path through the

applied field. It should also be noted that the subscripts x, t

(I/Im)x,t = sin:2 [(E/E^)^^t^/2].

L

k2
indicate the time and position at which the data were taken and that

we are assuming a coordinate system in which the light beam propagates in the z-direction, and the x-direction is perpendicular to and

the y-direction parallel to the surfaces of the electrodes. We have

analyzed data only at a specific value of y, the geometric center of

the electrodes.

Figure 1 shows the relative electric field as a function of position

under direct voltage. In order to determine the space charge density a linear fit (least squares) was performed. From the data presented the calculated space charge density ranges from 4 x 10"^ to

14 X 10~8 C/cm^. It is noted that the space charge density observed

here agrees well with similar data obtained, using the electro-optic

Kerr effect, with a chlorobiphenyl as the insulating liquid. ^ In that

case it was postulated "that the space charge. . . is due to the dissociation of the molecule and consists largely of H"*" ions. " Even

though there is good agreement in both magnitude and sign it is

thought that in the present work the generation of the space charge

is dominated by electrode surface rather than fluid bulk phenomena.

This conclusion is based on the behavior under low frequency alternating voltage which will be discussed later in the paper.

Three trends were identified from this and similar data. First,

the net charge was always positive and uniformly distributed in the

bulk. Second, the space charge density decreased as the voltage

level was increased, and, third, the net charge in the liquid was

slightly greater when negative high voltages were applied.

The situation was radically different, however, when alternating

voltage was applied. In Figure 2 is plotted the relative electric

field strength as a function of distance from the high voltage electrode at various instants during the cycle of a 20 kV rms, 60 Hz

applied voltage waveform (plate spacing 0. 5 cm). These data were

taken- by synchronizing a pulsed laser (light pulse width ^ 6 jisec)

with the applied voltage waveform so that the electric field distribution was strobed at a preselected, adjustable time during the

cycle. It can be seen from Figure 2 that as one progresses through

one cycle of the applied voltage (of period T) a field distribution

indicative of homocharge is first produced. ^ Soon after the peak

of the positive half-cycle the field becomes uniform. The field

distribution then inverts and assumes a distribution characteristic

of heterocharge. Figure 3 shows similar observations in the same

cell made at selected instants during the cycle of 16 kV rms applied

voltage at 60 and 120 Hz. In contrast with the previous figure.

^3
RELATIVE DISTANCE FROM HV ELECTRODE (x/d)

FIGURE 1 Typical field distribution data under direct voltage. Photographs from which some of the data were taken are presented in the center of the figure.

there is no longer evidence of an electric field distribution attributable to heterocharge. Note that in this context the words heterocharge and homocharge are used only to describe the relationship

between the polarity of the electrode and the net charge near it. They do not imply any mechanism of charge production of transport.
It was also observed in this work that the electric field distortion

was approximately constant in the range from 60 to 120 Hz, with

measurements being performed at 60, 80, 100, and 120 Hz. At

higher and lower frequencies there was a trend toward reduction in

the curvature in the distributions with limiting cases being a uniform field under short pulse conditions and a field which is approximately a linear function of position under direct voltage.

DISCUSSION

There is qualitative agreement between the data and the assumption

that there are particulate impurities in the system. If particulate

impurities are present they are charged upon contacting an electrode.

Once it leaves the initial electrode, the charge on any particle can

decay due to fluid ohmic conditions. The critical parameter is the

ratio of the electrical relaxation time, e/a, where e is the fluid

permittivity and a its conductivity, to the transport time d/U, where

d is the electrode spacing and U is the average particle velocity.

The ratio of these times is called the electric Reynolds number'^

Re = (e/cr)/(d/U).

RELATIVE ELECTRIC FIELD STRENGTH (F.,-?') FIGURE 2 The electric field distribution at various times during the cycle of. 60 Hz, 20 kV rms, applied voltage. E' is the average value of the field at each instant.

h5
60 Hz 120 Hz

4 -

3 -

-r

1 1 r T 1 1 r

-o— 3/16 T

4 - — 3 X

O

CC

5

4 I- Q 3 ^

1/4 T

3/8 T

U.O

q:»-o

UJ

_l

LlI >

<

_IUJ

CC

-2 p

-3 -

-4 -

-3 I-

-4

-5

- 5/8 T

3/4 T

4 -

-5 J I I L 0 2 0 4 0 6 0 8

-L_ I I L

13/16 T

02 0 4 06 0.8

RELATIVE DISTANCE FROM HV ELECTRODE (x/d)

FIGURE 3 The electric field distributions at corresponding times

during 60 and 120 Hz, 15 kV rms, applied voltage.

If Rg ~ 1, the net charge distribution is the sum of two expontial

distributions. The predicted result is negative charge near the

k6
cathode and positive charge near the anode. This is observed

experimentally in almost all cases. The deviations from this behavior, shown in Figure 2, may be attributable to the voltage dependence of B.Q.

If Rg » 1, the observed behavior can be understood in terms of

the roll cell model used by Felici^ and Thomas. ^ This model assumes that the charge carriers move with the fluid, from electrode

to electrode, with a velocity U. The charge on each carrier is

proportional to the electric field strength at the electrode at the

time that the carrier is in contact with it. This predicts that as

the voltage is increasing in magnitude there will be positive charge

near the positive electrode and negative charge near the negative

electrode. Sometime after the peak the field should become uniform. As the field strength returns toward zero a heterocharge

distribution is predicted. The reason that this heterocharge distribution was not observed in Figure 3 may be that there was insufficient sensitivity at the low voltages.

CONCLUSIONS

It has been shown that the electric field distribution and, consequently, the space charge distribution, in a liquid insulant are different under direct and low frequency alternating voltage and that

both differ from ideal distribution predictable from geometry. It has been recently shown that in commercial insulating liquids the

breakdown is controlled by space charge. 2 For lack of more substantial information, however, authors'^ have obtained the breakdown field strength at 60 Hz in an insulating liquid by measuring

the breakdown voltage and calculating field from the electrode

geometry. It is shown here that even with plane parallel electrodes

the field can differ markedly from the ideal case because the electric field in a liquid insulator is defined by both the electrode geometry and by the space charge dynamics within the fluid.

REFERENCES

1. E. C. Cassidy, W. E. Anderson, and S. R. Booker, IEEE

Trans. Instrum. Meas. IM-21 , 504 (1972).

2. E. A. Cherney and J. D. Cross, IEEE Trans. Elec. Insul.

EI-8, 10 (1973).

hi
3. Z. Croitoru, Progress in Dielectrics , Academic Press, Inc.

,

New York, N. Y. , 1965, Vol. 6, pp. 103-146.

4. H. H. Woodson and J. R. Melcher, Electromechanical

Dynamics, J. Wiley and Sons, Inc., New York, N. Y. , 1968,

Vol. II, Chap. 7, p. 383.

5. N. J. Felici, Direct Current 2, 147 (1971).

6. W. R. L. Thomas, Proc. 4th Int. Conf. on Conduction and

Breakdown in Dielectric Liquids, Dublin, 1972, p. 73.

7. Y. Kawaguchi, H. Murata, and M. Ikeda, IEEE Trans. Power

Appar. Sys. PAS-91 , 9 (1972).

USCOMM-NBS-DC
NBS-1 14A 'REV. 7-73)

Z ^ COMM.

BIBLIOGRAPHIC DATA

SHEET

1. fui<lk:ation or rkport no. 75-llk

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Calibration of Kerr Systems Used to Measure

High Voltage Pulses

5. Publication Date August 7, 1975

6. Pi-rlormin^ Or^anizuuun C uilt7. AUTHORt:

Robert: rleoner, Jr,

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 2IIOU26

11. Contract Grant No. 51-9312

12. Sponsoring Organization Name ana Complete Address fS.'reef. Cicy. State. /CiPj

Sandia Corporation

31dg. 89^^, Kirtland AFB

East Albuquerque, 87115

13. Type of Report & Period

Covered

Final, T-T^ to 6-75

14, Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. -ABSTRACT (A 200-word or less factual summary oI most si^jficant information. If document includes a significant

bibliography or literature survey, mention it here.)

The p\irpose of this vork is to define, develop and refine "techniques for calibrating

pulse voltage measurement systems, particularly those based on the electro-optic Kerr

effect. The approach used exploits the assumed frequency independence of the Kerr

coefficient of nitrobenzene. Theoretically, the Kerr coefficient should exhibit the

same frequency dependence as the relative permittivity. Measurements have shown the

relative permittivity to be approximately frequency independent over the frequency

range from direct voltage to 10^ Hz. The realization of this calibration approach has

been hampered by the fact that the electric field distribution, in the liquid

exhibiting the electro-optic Kerr effect, is itself frequency dependent.

This report describes the present best comparison of cell calibration under direct

voltage vith calibration vinder lov frequency alternating voltage and calibration under

pulsed high voltage. The results under all three types of waveforms agree to within

±0.3%. From these resiilts it can be inferred that it is feasible to use an electrooptic Kerr system as an independent, and possibly more acciirate, device against which

to calibrate other pulse voltage measurement systems.

In addition to this discussion of Kerr system calibration, the report contains two

appendices. One presents an improved technique for analysis of data obtained from a Kerr system and the other discusses space charge in a nitrobenzene-filled Kerr cell.

17. KEY ^"ORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons) Automated measiirements ; dielectrics; dividers; electric fields;

electrical measurement; electro-optics; high voltage measurements; insulating fluids;

Kerr effect; nitrobenzene; pulse measurements; space charge

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