NBSIR 77-1317

Calibration of High-Voltage

Pulse Measurement Systems

Based on the Kerr Effect

Robert E. Hebner, Jr. and Martin Misakian

Electricity Division

Institute for Basic Standards

National Bureau of Standards

September 16, 1977

Final Report on

Sandia Corporation Order No. 02-8994

Sandia Technical Consultant: S. R. Booker, 9532

Sandia Laboratories Buyer: John G. Boyes

Prepared for Sandia Corporation

Bldg. 894, Kirtland AFB

East Albuquerque, New Mexico 87115

NBSIR 77-1317

CALIBRATION OF HIGH-VOLTAGE

PULSE MEASUREMENT SYSTEMS

BASED ON THE KERR EFFECT

Robert E. Hebner, Jr. and Martin Misakian

Electricity Division

Institute for Basic Standards

National Bureau of Standards

September 16, 1977

Final Report on

Sandia Corporation Order No. 02-8994

Sandia Technical Consultant: S. R. Booker, 9532

Sandia Laboratories Buyer: John G. Boyes

Prepared for Sandia Corporation

Bldg. 894, Kirtland AFB

East Albuquerque, New Mexico 871 15

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Dr. Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director
,,

.

'

. ,

r- •/., • •
Executive Summary

High voltage pulse measurements have been performed using systems based on

the electro-optic Kerr effect for a number of years. In certain applications,

these systems permit state-of-the-art measurements (uncertainties - ±1%).

Because the precision of the measurement can be significantly better than the

accuracy, an investigation of techniques to improve the calibration of the

system--and, thus, to advance the state of the art in pulse measurement--was

I undertaken.

I The investigation focused on two areas. One was the experimental

determination of correction factors which would account for differences in

environmental factors between the calibration of the system and its use. These

measurements yielded accurate corrections for variations in temperature and

quantitative evidence of the magnitude of the wavelength dependence of a Kerr

system's response.

The second was further study into the feasibility of calibrating the Kerr

system at a number of discrete frequencies and using this calibration for pulse

measurement. Thi s -approach was not completely successful, but did suggest

more feasible alternatives. It was concluded that electrohydrodynamic effects

in nitrobenzene introduce errors which are sufficiently large that no significant

increase in accuracy is possible. Preliminary investigations into another fluid,

however, suggest that the problems may be minimized by a judicious choice of the

electro-optic material. It should also be emphasized that electrohydrodynamic

phenomena are only evident under the application of a steady-state voltage. They,

therefore, introduce errors during single frequency calibration but do not degrade

the performance of the system under pulsed voltage.

TABLE OF CONTENTS

I. INTRODUCTION 1

II. FACTORS WHICH INFLUENCE THE CELL CONSTANT 2

1 1. A FACTORS WHICH INFLUENCE THE PLATE SPACING 3

II.A.l TEMPERATURE 3

II.

FACTORS WHICH INFLUENCE THE KERR COEFFICIENT 4

II.B.l GENERAL 4

II. B.

WAVELENGTH 5 II.B.3 TEMPERATURE 8

II. B.FREQUENCY 13

II.

C

FACTORS WHICH INFLUENCE THE EFFECTIVE LENGTH 16

II.C.l GENERAL 16

II.C.2 TEMPERATURE 19

II. C.

3

FREQUENCY 20

1 1 . C. 3.

a

GENERAL 20

1 1 .C. 3.

b

MEASUREMENTS IN NITROBENZENE 20

II.C.3.C MEASUREMENTS IN CHLORINATED BIPHENYLS ... 22

III. PHASE SHIFT MEASUREMENT 27

IV. ACKNOWLEDGMENTS 31

V. REFERENCES 32

I. INTRODUCTION

High voltage pulse measurements with uncertainties of order 1% have become

routine using the electro-optic Kerr effect. Because the precision of the

measurements is more than an order of magnitude greater than the accuracy, it

should be possible to improve the accuracy of the measurement.

This report discusses the limitations on calibration techniques and

Kerr cell operation, both of which contribute to the measurement uncertainty.

It is anticipated that the fundamental limitations are sufficiently well defined

by this report that it provides guidance in the selection of specific research

and development activities to improve the accuracy of pulse voltage measurement

using the Kerr effect.

To accomplish a calibration of high-voltage pulse measuring systems, two

techniques are recognized J One is a comparison technique while the other

|| requires a more fundamental analysis of error sources. The comparison technique

is not suitable for this application. The primary reason is that there is no

I known (standard) system which has better accuracy than a Kerr system. For

example, consider the most common measuring system, a voltage divider-oscilloscope

combination. The calibration of this system could consist of

-- determination of scale factors of oscilloscope;

-- determination of the positional dependence of oscilloscope

scale factors;

-- measurement of system's step (frequency) response;

-- low voltage determination of divider ratio;

-- test for a voltage coefficient of the divider.

Uncertainties in these determinations limit the best high voltage measurement

systems to uncertainties of about 1% (with much larger uncertainties being common).

As a consequence, Kerr system accuracy cannot be improved by comparison with a
- 2

-

pulse divider system. It is, therefore, necessary to perform a more fundamental

calibration. l

To identify the factors which influence the accuracy of Kerr system a

measurements, it is helpful to note that the uncertainty in voltage measurement {Hi

can be expressed as

AV

AVm A<j> V_ -

2<*»

( 1 ) m

In this equation, Vm

is the cell constant and cp is the optical phase shift. The

remainder of this report is an analysis and a quantification of these error terms, a'

In Section II, the definition of the cell constant and errors in its determination

are discussed. The errors associated with phase shift measurements are discussed

in Section III.

II. FACTORS WHICH INFLUENCE THE CELL CONSTANT

The phase shift, <t>, between two orthogonally polarized components of a

linearly polarized light beam, upon passage through the Kerr system, is given by

the expression

2tt / BE a£ . o

( 2 )

In Eq. 2, B is the Kerr coefficient of the optically active material, E is

the applied electric field, and z is a spatial coordinate in the direction of light

beam propagation. For voltage measurement it is assumed that Eq. 2 can be

rewri tten

= TT (V/V )' m

( 3 )

where the cell constant, V , is defined as m
V ( 4 ) = d (2B£ 1 )~

l* m

In Eq. 4, the assumption is made that the Kerr cell is a paral lei -pi ate structure

with d being the spacing between the plates. In addition, it is assumed that

any electric field non-uniformity can be accounted for by the effective plate

length £ '

.

Calibration of a Kerr cell consists of a determination of V . The values m

of d, B, and £' are not independently known with sufficient accuracy to permit

Vmto be calculated using Eq. 4. The technique which is used is to apply a known

voltage to a Kerr cell, measure the phase shift, and using Eq. 3, calculate V .

This value of Vm

is then used to measure unknown voltages. As pointed out above,

if pulsed voltages are used in the determination of V , no improvement in

accuracy is possible. Attempts have been made, therefore, to calibrate the

cell at a number of discrete frequencies--where improved accuracy is possible--and

to apply this calibration to the extent permitted by the frequency response

of the Kerr system.

The technique is valid to the extent that differences between experimental

conditions during calibration and during measurement do not change the value of

V . The remainder of this section will be devoted to a discussion of those

mfactors which could modify the value of the cell constant, V . As suggested

by Eq. 4, these factors will be considered in terms of their impact on the

plate spacing, the Kerr coefficient, and the effective length of the parallel

plates.

1 1. A FACTORS WHICH INFLUENCE THE PLATE SPACING

II. A. 1 TEMPERATURE

In evaluating the effects of temperature on plate spacing, it is convenient

to take the partial derivative of Eq. 4, with respect to temperature. This
-4-

yields

1 m _ 1 3d 1 3B 1 3£‘

( 5 ) V 3T d 3T 2B 3T 2fc' 3T m

The term containing the spacing, d, is in the form of a coefficient of

linear expansion. Because the Kerr cell is constructed of glass and metal,

it would be expected that

Because the cells are used near room temperature, and because an inaccuracy

of 0.1% in the determination of Vm

is acceptable, the variation of the plate

spacing with temperature is negligible. The second term in Eq. 5 is discussed

in Section II. B. 3 and the third in Section II. C. 2.

No other reasonable, non-catastrophic variation in experimental conditions

has been identified which could yield a significant variation in the plate

spacing.

II.B FACTORS WHICH INFLUENCE THE KERR COEFFICIENT

II.B.l GENERAL

It is widely recognized that the understanding of liquid structure is not

sufficiently advanced to permit the calculation of the Kerr coefficient in

nitrobenzene with the necessary accuracy to be useful in pulse measurement. The

classical expression for the Kerr coefficient of a polar fluid is valuable in that

it provides a means of identifying those parameters which may cause a variation

3

in the Kerr coefficient. This expression is of the form

( 6 )

B = np

o (n^ + 2)^ (e + 2)^ (0-j + 0 2

) / 2 7 nA (7)
-5-

where p is the number density of the molecules, n is the index of refraction

of the light beam at a wavelength A, e is the dielectric constant of the

material, and and represent expressions involving the temperature of

the fluid, the static and optical polarizabilities and the dipole moment of

the molecules.

The variations which have been investigated are the dependence of the

Kerr coefficient on the wavelength of the incident light, on the frequency of

the applied voltage, and upon the temperature of the material. These will be

discussed in detail in the following sections.

II.B.2 WAVELENGTH

From Eq. 7, it can be seen that the Kerr coefficient, and thus the cell

constant, has an explicit dependence on the wavelength. As shown in Fig. 1,

measurements of the wavelength dependence have been made at a number of

laboratories, including NBS. The data exhibit approximately a A variation.

In addition, more careful examination of the NBS data indicates dispersion

in the index of refraction may also be significant. Fig. 2 shows a plot of the

product Ba vs a. This drawing reflects the fact that BA may change by as much

as 11 over the wavelength range from about 475 - 625 nm.

4

Elementary analysis indicates that some variation should occur. There is

5 strong absorption in nitrobenzene for wavelengths shorter than about 400 nm.

From Kramers-Kronig relationships, a wavelength dependent absorption should

lead to a wavelength dependence in the index of refraction. From Eq. 7,

therefore, it is reasonable to expect a wavelength dependence of Ba.

The significance of this variation on Kerr system calibration is twofold.

From Fig. 2, it can be inferred that over visible wavelengths

1 3 ( BA

(BTT 3 X ^ -5 x 10 /nm . ( 8 )
5

0x10 - 6 - O - / / / / /

'? /

org5 <| M

iLl CO

LlI £ / / /

// t /

//

// /

//

//

o5

X/ / /

// // co T3 " / / / t / / < / ® / / / 7 /" 7

<j / 7 1 u / m • < / / / / / / tf / / / /

,d o / 5 53 / / / / / / / /

/3 / / / / / OO

h- oo

CD / a 1 1 1 \ n o

S- >> QJ -M ^

<D

•«~ <D XI

TO 4-> >

4-

<o

O E CL) o os_ r: 4- 4-> o ro c o 4-> CD 00

CO TDCOE

4— qj o xz

CO

uu =3

a o 0

s~ JC s. i- 4—) C

cd r— rt ro

r~

CL) 4-> rc -C co C

4-) xz

a

4->

C 4- a O 00 c

a>

CL> 4->

O

O r3 •«- cz o

CD •ra "O -o C

O

ccC 0

a> •r—

X o Q_ 4- in CD "O

00

sM 94

ro

Z2. o 1O 1O X X X . O o o CD ro C\J Ll_
7

-

o

o

CD

£

c

o

in <?*> in X

h~

CD

LlJ _l

Ll!

>

<

o 5

o

in

CD c\J o

u ££9 IV 3R1VA lAJOdd N0I1VIA3Q % )

C\J

cn \*a

Variation

of

the

product

of

the

Kerr

coefficient

and

the

wavelength

with

a

change

in

wavelength.

The

open

circles

represent

measured

values.

The

imprecision

of

the

measurement

is

less

than

]%.

These

data

emphasize

the

fact

that

the

product

BA

is.

wavelength

dependent.
If the light source used for Kerr effect measurement is a laser, the linewidth is

sufficiently narrow that dispersion effects are negligible. If, however, the

cell constant is determined at one wavelength, there is no way to accurately

calculate the cell constant at a significantly different wavelength. This is

to say, reliable data concerning the dispersion of the Kerr effect over a wide

range of wavelengths are not available. This is not generally a problem as the

use of a variety of lasers is not common practice.

II.B.3 TEMPERATURE

The temperature dependence of the Kerr coefficient of nitrobenzene has been

redetermined during this contract period. Previous measurements have indicated

that over the range of normal room temperatures

Hr* 10

' 2/k • (9)

For a nitrobenzene-filled Kerr cell, therefore, the term (Eq. 5) containing the

Kerr coefficient is the only significant contribution to the temperature dependence

of the cell constant. This is a fortunate situation because this variation is

a fundamental property of the nitrobenzene and not an "accidental" property

which is unique to each Kerr cell. As a practical matter, this means that given

the temperature dependence of the Kerr coefficient of nitrobenzene, the cell

constant of any nitrobenzene-filled Kerr cell can be corrected for temperature

changes. From Eqs. 4 and 5, this simple relationship between the values of the

cell constants at two temperatures T-j and T^ is

W* [B{T2

)/B< T

i)] Vm

(T

2

) ( 10 )
-9-

The temperature dependence of B is determined by measuring the cell constant

-2

of a given cell as a function of temperature and noting that V is proportional

-2

to B; a plot of Vm versus temperature indicates the relative change in B with

temperature. The absolute variation in B(T) can be obtained by normalizing

the data at a specific temperature to a previously measured value of B. This

approach has been employed previously6

and is used in the present set of

measurements

It should be noted in Eq. 10 that the only dependence on the Kerr coefficient

is its ratio at two different temperatures. Therefore, any errors introduced by

the normalization do not affect the accuracy of the correction of the value of

the cell constant.

The glass cell used to determine the temperature dependence of B was

cylindrical, approximately 7 cm long and 2 cm in diameter. The parallel-plate

electrodes were about 5.8 cm long, 1.3 cm wide, and spaced about 0.3 cm apart.

A calibrated copper-constantan thermocouple was inserted into a hollow electrode

support to measure the nitrobenzene temperature. The cell with its electrical

connections was totally immersed in an oil bath which could be cooled or heated

over a temperature range of approximately 280 K to 340 K. Temperature

measurements in the oil bath immediately adjacent to the cell, using a second

thermocouple (chromel -alumel ) , revealed no temperature gradients in excess of

0.1 K between the interior of the cell and any of the selected points shown in

Fig. 3. The nitrobenzene temperature measurements are believed to be accurate

to within ±0.1 K; this represents a substantial improvement over previous

work

6 ’ 7 (±0.5% of the measured value).

At elevated temperatures, measurements of Vm were made by first heating the

oil bath; cell constant data were then obtained as the bath cooled. An analogous

procedure was followed to obtain results below room temperature. Data were
- 10 -

Fig. 3 Apparatus used in the determination of the temperature dependence of the

Kerr coefficient of nitrobenzene. To insure that the thermocouple in the

grounded electrode was measuring the temperature of the interelectrode

nitrobenzene, the Kerr coefficient was not measured until temperature

measurements at 1, 2, 3, and 4 agreed with measurements inside the grounded

electrode to within 0.1 K. I
- 11 -

col lected from 285 K to 337 K.

Redundant systems of voltage measurement were used to determine the cell

constant V . The peak value of the applied high voltage pulses measured with

a standard Kerr cell at room temperature and a calibrated resistor divider were

averaged to determine a single value. Differences between the two measurements

were typically near 0.5%. A helium-neon laser (632.8 nm) was used as the light

source

.

6 8 9

Experimental evidence 5 as well as a theoretical model using a classical

statistical mechanical approach suggest that the temperature dependence of the

electro-optic Kerr coefficient has the functional form

B (T) = + a-j/T + o^/T2

, (11)

where the a's are constants. This relationship has been adequate to describe the

behavior of B for nitrobenzene in earlier NBS studies and is employed again in

the present work.

Fig. 4 shows the experimental results normalized to the previously measured

value, B = 3.26 x 10~ 12

± 6% mV"

2

, at 295.6 K and 632.8 nm. The curve in Fig. 4

is a least squares fit to the data. This fit yields the following values for

the constants in Eq. 11:

a = 6.556 x 10" 12

mV

-2

o

a-, = -5.610 x 10' 9 K mV"

2 (12)

a

? = 1.379 x 10' 6

K

2 mV'

2

. f . . -15

The residual standard deviation for the fit is 9.423 x 10

Although the above values are different by factors of 2.3 to 4 from earlier

results over a more limited temperature range, the calculated values of B over a

coronon temperature interval agree to within 2.8%. Because of improvement in

experimental technique, the more recent values are considered to be more reliable.
KERR

COEFFICIENT

B(

X

lo'

2

m/

V*)

TEMPERATURE (K)

Pi q 4 Plot of the temperature dependence of the Kerr coefficient of nitrobenzene.

The solid circles represent data points. The measurement imprecision

is of order the dot size. The magnitude of the Kerr coefficient was determined by normalization to previous data5 at one point. The reference

data had an uncertainty of ± 6 %.
-13-

As has been noted previously, the above constants are appropriate for

interpolating over the temperature range of the data (285 K to 337 K);

extrapolation beyond this range may introduce substantial error.

II. B. 4 FREQUENCY

From Eq. 7, it can be inferred that any dependence of the Kerr coefficient

on the frequency of the applied voltage is due to the frequency dependence of

the dielectric constant, e. Measurement of the frequency dependence^ of c

9 shows a flat response for frequencies below about 10 Hz, Fig. 5. This frequency

i ndependence served as one of the early justifications for the development of Kerr

systems for the measurement of high voltage pulses. It permits calibration of

a system at one or a number of discrete frequencies and subsequent use of this

calibration for pulse measurements. This is appealing because, in general,

single frequency, high voltage measurements are more accurate than high voltage

pulse measurements by one or more orders of magnitude.

A direct method to verify that the cell constant is indeed frequency independent

is to apply high voltages over the frequency range of interest and measure the cell

2 constant. An attempt was previously made to perform such a measurement and the

results are summarized in Fig. 6.

These results are promising but not definitive because of the limited number

of frequencies over which data were taken. The fundamental limitation to the

extension of these data is the electrohydrodynamic phenomena for a certain range

of low frequencies which result from the presence of space charge in nitrobenzene.

These phenomena are discussed in more detail in Section II.C.3.b.

The present status, therefore, is that frequency independence cannot be fully

verified because electrohydrodynamic effects at low frequencies prevent measurement

of the cell constant. These effects, however, only complicate calibration; they

have not caused an identified error in the measurement of microsecond duration.

high voltage pulses.
- 14 -

CU

CT) 03

4-> CU

i— 1/3 O r- > 3

a.

-o

cu cu

•r- +->

> <tJ CL i~ Q- =3 <0 U

U

at <T3 x:

+J co

4— 4— O

T3

>> cu

(_) +-> C -r- <D O

3

CT CL

O) X

s- cu

in

cu

N

4->C0

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' CU 4-> C 3

CU O > Nl _Q C ra o CU .a 5 O O

i— J LU 4-> QJ Z>

•<- JZl c O

c

n

4- CU LU O -r-O

cr

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CUE

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cn A±IAI±±llNU3d 3AllV"l3d
15

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to

<u

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to

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s- • t(_ CU 4- Xj O -r-tO >> «

4-> QJ <u 4- 2 <u

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(O +-> to r- >> i— to

d)o si- c a)

QJ ^>

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+-> <o C S- (O -Q

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a> r— +-> i— lO

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4-> 4-O

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to +-> c

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aj co

+-> CT) aj 3 Q tO

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CO
-16-

II.C FACTORS WHICH INFLUENCE THE EFFECTIVE LENGTH

II.C.l GENERAL

I i Care must be taken to distinguish between two different phenomena which

influence the value of the effective length. Recall from Eqs. 1-3, the effective

length, £' , is defined

4> = 2tt / BE

2 d£ = 2ttB£' (V/d)

2

. (13)

o

The first phenomenon is geometrical in nature.^ The Kerr cells used in this

study are parall el -pi ate capacitors. The light beam passes between the plates,

not only through the uniform field area but also through the fringing fields at

the ends of the plates. The effect of this is shown in Fig. 7. It should be

noted that in Fig. 7 the experimentally derived electric field distribution is

asymmetric about the midplane. This is attributed to the perturbing effects

of nearby grounded objects.

The second phenomenon which influences a' can be more significant and is

more difficult to discuss rigorously. To understand this effect, it should be

noted that in Eq. 13, the electric field has been replaced by the voltage divided

by the spacing. If space charge exists, the field distribution is not uniform.

So the effective length must also account for the field non-uniformity caused by

space charge. An example of such distortion is shown in Fig. 8.

So the value of the effective length is a function of position with the

positional dependence influenced both by cell geometry and space charge. For

pulse measurements, space charge is negligible and compensation for variations

due to geometry is made by confining the light beam to a single path.

However, these effects become troublesome when uncertainties less than 1 % are

requi red.
(NORMALIZED

EFFECTIVE

LENGTH)"'

-17-

I.OO0.96

0.92 -

0.88

0. 84 -

0.25 0.50 0.75

x/d

g. 7 Effect of fringing field. This plot shows calculated (dashed lines) and

measured (solid dots) values of = 0 . 5/

^

x / d ’ where x is a variable

along a central path between the electrodes and d is the plate spacing. It can be seen that the effective length for a parallel plate system is shortest

for a point one half way (x/d = 0.5) between the electrodes. The calculated

curve is symmetrical about the center while the measured points are assymmetrical due to nearby grounded objects.
RELATIVE

FIELD

STRENGTH

(E/E

2.8 §- V= 77,280 volts

it*- (E m d) = 45, 330 volts

DISTANCE FROM ANODE (

x

/d)

Fig. 8 Effect of space charge. Under direct voltage the effect of fringing

fields is dominated by the effect of space charge. The quantity Ed

is Vm

as defined in Eq. 4.

- 18 -

ELECTRODE
-19-

II.C.2 TEMPERATURE

The effect of temperature on the geometric contribution to the effective

length is negligible. For square-ended electrodes of thickness y, spacing d and

1

length i and for a central path,

£' = £ + ( d/7T ) [1 + y/d In (1 + d/y ) ] . (14)

It should be noted that recent work by Thacher has extended this type of

analysis to include non-central paths and has found the same general dependence

on spacing and length.

Because i' is only a function of geometry,

JT = 10~ 5 /K . (15)

From Eq. 5, it can be seen that this term does not make a significant contribution

to the variation in the cell constant.

In addition to the direct effect on geometric length, temperature variations

can also change the value of the effective length by changing the space charge

distribution. The effect of a temperature change is to modify the mobility of

the charge carriers in the fluid. Theoretical consideration of simplified physical

models indicates that the electric field distribution does depend on the mobility.

Experimental confirmation has been obtained using a mixture of pentachlorobi phenyl

and trichlorobenzene. As the temperature of the mixture was increased from 0 °C

to 60 °C, the central field strength, under direct voltage, decreased by more than

20%. Of course, the applied voltage remained constant.

In nitrobenzene-filled Kerr cells, space charge has been found to be

negligible if the voltage is applied for times shorter than about 100 ys.

Under pulse conditions, therefore, no space charge distortion exists. Under

steady-state condi tions--for example, during a single frequency cal ibrati on--space
- 20 -

charge distortion does exist. Because of the finite resistivity of the

nitrobenzene, there can be significant self-heating during steady-state voltage

application. This can lead to the temperature dependent change in the field

distortion discussed above. In extreme cases, electrical breakdown could result.

II. C. 3 FREQUENCY

1 1 . C . 3 . a GENERAL

From Eq. 14, it would be expected that the geometric contribution to the

effective length would be frequency independent. Data such as that shown in

Fig. 6 confirm this expectation.

The effect of frequency on the space charge distribution, however, is

significant. Three main sources of space charge production have long been

recognized. These are molecular-level processes in the bulk (e.g., dissociation,

chemical interactions, etc.), molecular-level processes at the interface between

the liquid and the electrode and suspended particles in the fluid. Once the

charge carriers have been produced, their trajectory depends on the applied voltage

and presumably on the coupling to the neutral fluid. This electrohydrodynamic

phenomenon is in turn dependent on the geometry of the cell. In the present

state of understanding, space charge dynamics cannot be calculated with precision.

An experimental measurement of the space charge distortion is, therefore, necessary.

These measurements have been performed in a variety of liquids under direct and

selected low frequency alternating voltages. This report will focus on results

obtained in nitrobenzene, but measurements taken using a chlorinated biphenyl

will also be discussed to emphasize the role of the fluid in space charge distortion

1 1 . C. 3. b MEASUREMENTS IN NITROBENZENE

The basic behavior of nitrobenzene is summarized in Figs. 9, 10, and 11. The

first point, which is emphasized by Fig. 9, is that the electric field distribution
PULSED VOLTAGE

Fig. 9

r»usT£ "tx- » <.u.> <•'«* °< <«'>/

- 21 -
- 22 -

or, equivalently, the space charge distribution, does, indeed, depend on the

frequency of the applied voltage. Under pulsed voltage the field between the

1

3

plates is calculable from electrostatics. The absence of interelectrode fringes

in the central region indicates a uniform field. The other two photos at dc

and 60 Hz indicate interelectrode fringes with very different distributions.

This implies that the space charge distribution is frequency dependent. This

dependence is shown more quantitatively in Fig. 10. In this figure, it can

14 be seen that for the voltage levels and geometry used in this study, the

space charge density has a broad maximum in the frequency range between 60 and

90 Hz. The reduction in the space charge density as the frequency is increased

above 60 Hz suggests that the effect of space charge may be minimized at somewhat

higher frequencies. At higher frequencies, however, a different phenomenon

2 dominates as is shown in Fig. 11. From these photographs, it is apparent that

the optical transmission of the cell is profoundly affected by high voltage in

the audio frequency range. Within the purification limits attainable with the

MBS nitrobenzene purification system (resistivity % 10 ft • m) this behavior

could not be substantially modified by cell purification.

For this reason, further related studies on the time evolution of space

1

5

charge were undertaken using a chlorinated biphenyl as the Kerr fluid. This

liquid was selected because it has a relatively large Kerr coefficient, was

commercially available, and because of its widespread use as a high voltage

insulating liquid. Since the study was initiated, polychlorinated biphenyls

were identified as being environmentally harmful and further Kerr work was

terminated at NBS. The completed study does, however, provide further information

concerning space charge dynamics in a fluid other than nitrobenzene.

II.C.3.C MEASUREMENTS IN CHLORINATED BIPHENYLS

The measurements of space charge dynamics in a chlorinated biphenyl were
- 23 -

J</

‘A1ISN3Q 39dVH0 30VdS 030003^

O

z

LU

O

UJ

cr

The

space

charge

density

as

a

function

of

frequency.

The

reduced

space

charge

density

p

r

is

a

dimensionless

number

which

is

proportional

to

the

space

charge

density

p.

The

equation

relating

these

two

is

p

=

(d

Ve\L)

p.
-24-

OPT I CAL TRANSMITTANCE OF KERR CELL AT SELECTED FREQUENCIES

60 Hz 200 Hz

770 Hz 912 Hz

Fig. 11 Optical transmittance of a Kerr cell at selected frequencies,

frequencies above a few hundred hertz, the optical distortion

sufficiently severe that no Kerr measurements are possible.

At

is
-25-

made using a "pulsed" 60 Hz voltage source. Specifically, the power source was

capable of providing a preselected, integral number of half-cycles of a 60 Hz

waveform at high voltage. These measurements are summarized in Fig. 12.

The filtration of the fluid was accomplished in the same way that nitrobenzene

is filtered. Specifically, the liquid was drawn under vacuum through an

approximately 28-cm-long column of activated alumina and micrometer-sized filters

with a mechanical pump. The double filtration referred to in Fig. 12 consisted

of drawing the same sample of fluid through the same column twice. Measurements

were made in a tetrafl uoroethyl ene cell having Rogowski profile electrodes.

From Fig. 12, it can be inferred that the space charge is due to contaminants

which can be removed by filtration. The upper photographs also show the temporal

evolution of the space charge and thus the electric field distribution. It can be

seen that the field is uniform until about the fifth half-cycle; the distortion

comes to equilibrium during the interval from about the fifth to eleventh half-cycle

and remains stable after about the eleventh half-cycle.

It is interesting to compare this temporal behavior with related experimental

1 c studies. Dakin, Studniarz, and Hummert have investigated the breakdown

strength of transformer oil as a function of the number of cycles of 60 Hz voltage

which was applied. They found the breakdown strength to be higher and less

variable if fewer cycles are applied. They observed that there was a definite

relationship between the duration of voltage application and breakdown strength

and postulated that this relationship was due to space charge. The present study

{

demonstrates the analogous temporal dependence for the space charge distortion.

In addition, previous work in nitrobenzene^ had shown that at 60 Hz the

space charge did not respond to the instantaneous value of the applied voltage.

In this study, it is also apparent that the time necessary for the space charge

to respond to a change in the applied voltage is long compared to a cycle of

a 60 Hz waveform.
Fig.

12

Kerr

response

in

chlorinated

biphenyls.

The

upper

sequence

of

photos

shows

the

evolution

of

the

electric

field

distribution

during

the

first

few

cycles

of

a

60

Hz

waveform

after

a

single

filtration

cycle.

Interelectrode

field

distortion

due

to

space

charge

is

negligible

until

about

the

fifth

half

cycle.

The

lower

photos

show

that

after

double

filtration,

space

charge

remains

negligible

for

arbitrarily

long

times.
-27-

With a second filtration, the net space charge density in the chlorinated

biphenyl becomes negligibly small. This indicates, of course, that the space

charge is not an intrinsic property of the fluid.

These preliminary results suggest that in a fluid other than nitrobenzene

single frequency measurements may be possible. Because of the preliminary

success in this fluid coupled with the lack of success in reducing the space

charge density to an acceptable level in nitrobenzene, investigation of

alternative fluids to nitrobenzene appears to be a reasonable goal for future

research

It should be acknowledged, however, that the gradients in the index of

refraction which yield the transmittance shown in Fig. 11 may not result solely

from the space charge density. The volume force can be expressed as the sum

of two termsj'

7

F v

= pE + p m

V (eZ $T] ’ (16) m

where p is the charge density, p m the mass density, E the electric field, e Q

permittivity of vacuum, and k the relative permittivity of the fluid. The

second term takes into account the interaction between the field and liquid

structure. It has not been demonstrated that this second term is negligible.

III. PHASE SHIFT MEASUREMENT

The second fundamental contribution to error in the measurement of voltage

is the error in phase shift measurement. In most previous work the Kerr system

was designed so that this error was sufficiently small to be negligible.

Minimization of this error source has been possible because of the nonlinearity

of the Kerr response. The conventional detection scheme uses a polarizer to

convert the phase shift (Eq. 3) between the components of the light beam to a
-28-

variation in transmitted intensity. If the incident light is polarized at an

angle of 45° to the field direction and the second polarizer is oriented so that

its transmission axis is orthogonal to that of the first, the phase shift is

related to the transmittance by the expression

In Eq. 17, I is the optical transmittance of the system. Combining Eqs. 17 and 2

yields

An analysis of this equation shows that for V £ 5 Vm

, a 1% change in the applied

voltage will cause nearly a 100% change in the transmittance of the cell.

As a consequence, accurate voltage measurements can be performed with very

modest requirements on the measurement of the relative transmittance, I/I .

Typical systems have resolution of 0. 1-0.2 I/I . So in a well designed system,

1 g the voltage resolution is typically of order 0.1% of the applied voltage.

The possible change from nitrobenzene as the Kerr fluid and the general

need to perform measurements in a variety of materials with smaller Kerr

coefficients have generated the desire to perform accurate measurements in the

voltage range V < 5 V . This requires a more accurate determination of the

relative transmittance of the system, or, more fundamentally, of the optical

phase shift.

A technique which has been recommended as a way to attain better accuracy

than is obtainable using crossed polarizers has been discussed in the literature.

This approach replaces the second polarizer with an interferometer as shown in

Fig. 13. The operational principles have been discussed previously. For this

I = I sin 2 U/2) . m

(17)

I = I sin

2 0/2 (V/V) 2

] . m m

(18)
- 29 -

CU -C

II

c:cu

cu

a) X3 ocuto

13

<uN

03O

a.

CUCnc

l/l

03

T3

03

a>

COc

i-cu

cuEo

s-<u

S-a>

atE • CU i_

4->

O

to 4-> >3 U

CO CU

4-> c cu O -O

•rO 4-> -t-> o o

cu jc -t-> o.

a> o cu XT O 4->

t- T3

+->

C

CU 03 EO

i_ rcu aj

«+- c_> 5-

(U S-

-t-> s*. c cu •—

3wC

cn
-30-

device, the transmitted intensity is given by the relationship 20

( 19 )

where <f>, I, and I have the same meanings as above and 6, the phase shift

introduced by the interferometer, is given by

The angle 0 is defined in Fig. 13.

Eq. 19 predicts that in the absence of an electric field (<}> = 0), a

conventional i nterferometric fringe pattern results. For <f> =(= 0, the fringes

are shifted or, equivalently, the intensity at single point on the detector is

changed

.

It should be emphasized that interferometric detection offers no inherent

increase in sensitivity when compared to a crossed polarizer detection scheme.

This point can be demonstrated by considering the variation of the intensity at

one point on the detection plane as the electric field is varied. It is assumed

that the point is on a dark fringe when the electric field is equal to zero.

This implies

6 = ~~ cos 0 . A

( 20 )

6 = (2n + 1) tt , n = 0,1,2,.... ( 21 )

Combining Eqs . 19 and 21 yields

1 = I m

sin 2 4/2) ( 22 )
-31-

which is identical to Eq. 17 which describes the transmittance of a crossed

polarizer system.

So an interferometric detection scheme can be conceived as a crossed

polarizer detector with the initial (E = 0) transmittance a function of position.

The approach does offer advantages in the situation where V £ V . In this case,

the background or interference fringe pattern makes the determination of I

convenient whereas it is impossible with a crossed polarizer detector.

21 There are additional detection techniques applicable to the measurement

of very small phase shifts that may be valuable in applications for which

V < 0.5 V . The conclusions of this discussion are summarized in Table 1. m

Table 1. Range Of Voltages For Which Various Detection Schemes May Have Value

Relative Voltage, V/V

m Detection Method

> 5 Crossed Polarizers

0.5 ^ 5 Crossed Polarizers

Interferometer

<0.5 Interferometer

Small Phase Shift

Techniques

It should be emphasized that factors of cost and convenience, as well as the

possibility of accepting reduced accuracy can provide justification for using a

less than ideal detection method.

IV. ACKNOWLEDGMENTS

The authors would like to thank W. A. Bagley for help in the experimental

phase of this investigation and J. C. Palla for assistance in the preparation of

the manuscript.
-32-

V. REFERENCES

1. IEEE Standard, IEEE 4 "High Voltage Test Techniques," in press.

2. R. E. Hebner, "Calibration of Kerr Systems Used to Measure High Voltage

Pulses," NBS Report, NBSIR 75-774, 1975.

3. C. G. Le Fevre and R.J.W. Le Fevre, "The Kerr Effect. Its Measurement and

Applications in Chemistry," Rev. Pure Appl . Chem. , vol . 5, pp. 261-318, 1955.

4. E. Frederico and C. Houssier, "Electric Dichroism and Electric Birefringence,"

Oxford: Clarendon Press, 1973, pp. 1-59.

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

Pulses," Rev. Sci. Instrum., vol. 35, pp. 816-820, 1964.

6. R. E. Hebner, E. C. Cassidy, and R. J. Sojka, "Development and Analysis of

Techniques for Calibration of Kerr Cell Pulse-Voltage Measuring Systems VIII,"

National Bureau of Standards Report, NBSIR 74-564, 1974.

7. R. E. Hebner, E. C. Cassidy, and R. J. Sojka, "Kerr Coefficients of Nitrobenzene

and Water," NBS Report, NBSIR 74-544, 1974.

8. F. Gabler and P. Sokob, "Die Temperaturabhanzigkeit Des Kerreffektes Am

Nitrobenzol ," Zeitschr. Tech. Physik, vol. 6, pp. 197-201, 1936.

9. A. D. Buckingham and R. E. Raab, "A Molecular Theory of the Electro-optic Kerr

Effect in Liquids," J. Chem. Soc., pp. 2341-2351, 1957.

10. G. L. Clark, "Dielectric Properties of Nitrobenzene in the Region of

Anomalous Dispersion," J. Chem. Phys., vol. 25, pp. 125-219, 1956.

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

Developments in Kerr System Electrical Measurement Techniques," IEEE Trans.

Instrum. Meas., vol. IM- 21, pp . 504-510, 1972.

12. L. Chaumont, "Recherches Experimentales sur le Phenomene Electro-optique

de Kerr et sur les Methods Servant a 1' Etude de la Lumiere Polarisee

El 1 iptiquement, " Ann. de Phys., vol. 5, pp. 17-78, 1916.

13. P. D. Thacher, "Optical Effects of Fringing Fields in Kerr Cells," IEEE Trans.

Elec. Insul., vol. E

I - 1 1 , pp. 40-50, 1976.

14. E. C. Cassidy, et. al., "Kerr Effect Studies of an Insulating Liquid Under

Varied High Voltage Conditions," IEEE Trans. Elec. Insul., vol. EI-9,

pp. 43-56, 1974.

15. M. Misakian and R. E. Hebner, "Kerr Coefficients of Polychlorinated Biphenyls

and Chlorinated Naphthalene," J. Appl. Phys., vol. 47, pp. 4052-4055, 1976.

16. T. W. Dakin, S. A. Studniarz, and G. T. Hummert, "Dielectric Breakdown of

Insulation Materials on the Front of Cycle and a Small Number of Cycles of

60 Hz Voltage," 1972 Annual Report Conference on Elec. Insul. and Dielectric

Phenomena, National Academy of Sciences, Washington, D.C., 1973.
-33-

17. W.K.H. Panofsky and M. Phillips, "Classical Electricity and Magnetism,"

2nd Edition, Addison-Wesley: Reading, MA, pp. 107-111, 1962.

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

of High Voltage Pulses," in Proc. IEEE Southeastcon , vol . 1, pp. 3A-1-1 to

3A-1-5, 1975.

19. J. E. Thompson, M. Kristiansen, and M. 0. Hagler, "Optical Measurement of

High Electric and Magnetic Fields," IEEE Trans. Instrum. Meas., vol. IM-25,

pp. 1-7, 1976.

20. J. E. Thompson, "Optical Measurements of High Electric and Magnetic Fields,"

thesis submitted to the Department of Electrical Engineering, Texas Tech

University, Lubbock, Texas 79409.

21. See, for example, C. E. Hill and H. House, "The Problems in Using the Kerr

Electro-optic Effect to Measure the Field Distribution in Non-polar Liquids,"

in Phenomenes De Conduction Dans Les Liquids Isolants, National Center for

Scientific Research: Paris, pp. 465-481, 1968.

22. E. C. Cassidy, et. al .

,

"Development and Analysis of Techniques for Calibration

of Kerr Cell Pulse-Voltage Measuring Systems VII," National Bureau of Standards

Report, NBSIR 73-403, 1973.
N BS-1 1 4 A (REV 7-7 3)

U .S. DEPT . OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. IM MLR A 1 ION OR REPORT NO. NBSIR 77-1317

2. Gov 't Ae< ess ion No.3. Kcc i y irn

t

' s Ai i c *. i <

«

n \m .

4. M I'Ll AND SUBTITLE

Calibration of High-Voltage Pulse Measurement Systems

Based on the Kerr Effect

5. 1 'iild it .ir ion 1 Lit e

6. Performing Org.im /.it ion ( od<

7. All II OR ( SI Robert E. Hebner, Jr. and Martin Misakian

8. Performing Ore.. in. Report No.

9. PI K FOR MING ORGANIZATION N AML AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project 1 ask Work Unit No. J 2110136

1 1 . ( out rat t Grant No. . Sandia No. 02-8994

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP) Sandia Corporation

Bldg. 894, Kirtland AFB

East Albuquerque, N.M. 87115

13. Type of Report K: Period Covered

Final July 75-0ct. 77

14. Sponsoring Agency < title

15. SI PPI.I MI N I AKY NOTES

16. ABS! KA( I (A 200-word or less (actual summary of most significant information. If document includes a significant

bibliography or I iterature survey, mention it here.)

High voltage pulse measurements have been performed using systems based on the electrooptic Kerr effect for a number of years. These systems permit state-of-the-art

measurements (uncertainties - ±1%). Because the precision of the measurement can be

significantly better than the accuracy, an investigation of techniques to improve the

calibration of the system was undertaken.

The investigation focused on two areas. One was the experimental determination of

correction factors which would account for differences in environmental factors between

the calibration of the system and its use. These measurements yielded accurate

corrections for variations in temperature and quantitative evidence of the magnitude of

the wavelength dependence of a Kerr system's response. The second was further study

into the feasibility of calibrating the Kerr system at a number of discrete frequencies

and using this cal ibration for pulse measurement.

17. K 1 Y WORDS (six to twelve entries; alphabetic at order; capitali ze only the first letter of the first key word unless a proper name; separated by semicolons

)

Calibration; dielectrics; dividers; electric fields; electro-optics; high voltage

measurement; insulating fluids; Kerr effect; nitrobenzene; pulse measurement;

space charge

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