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HCP/T-6010/E1

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AC TRANSMISSION

UNE FIELD MEASUREMENTS

WORK PERFORMED UNDER CONTRACT

EA 77 A 01 6010 AO 181

Kotter, F. R., Misakian, M., AC transmission

line field measurements, Energy Technol.

HCP/T-6010/E1, 82 pages (U.S. Department of

Energy, Division of Electric Energy Systems,

Washington, DC Nov. 1977).

2- / ^ 211

miR-77-/3!,

.

y/f - f —y? - /??&

DIVISION OF ELECTRIC ENERGY SYSTEMS
NOTICE

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o£ any information, apparatus, products or process disclosed in this

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HCP/T-6010/E1

DISTRIBUTION CATEGORY UC-97a

AC TRANSMISSION

LINE FIELD MEASUREMENTS

F. RALPH HOTTER

MARTIN MISAKIAN

INSTITUTE FOR BASIC STANDARDS

NATIONAL BUREAU OF STANDARDS

WASHINGTON, D.C. 20234

PUBLICATION DATE: NOVEMBER 1977

PREPARED FOR THE

U.S. DEPARTMENT OF ENERGY

ASSISTANT SECRETARY FOR ENERGY TECHNOLOGY

DIVISION OF ELECTRIC ENERGY SYSTEMS

WASHINGTON, D C., 20545

WORK PERFORMED UNDER CONTRACT NO.

EA 77-A-01 6010 AO 18 1
AC TRANSMISSION LINE FIELD MEASUREMENTS

Contract No. EA-77-A-01-6010-A0 18-1

NBS PROJECT No. 2110416

Prepared for

Department of Energy

Electric Energy Systems Division

Washington, D.C. 20545

Prepared by

F. Ralph Kotter

Martin Misakian

Institute for Basic Standards

National Bureau of Standards

Washington, D.C. 20234

September 30, 1977
Contents

Page

I. Introduction and Summary 1

II. Electric Field Meters 5

A. Instrumentation and Theory of Operation 5

B. Parameters Influencing Instrument Performance 7

1. Laboratory Studies 7 (a) Temperature and Humidity Effects 7 (b) The Effect of Electrical Leakage Along the Handle 8

(c) Meter Balance 9

(d) Meter Orientation 9

(e) The Influence of Ambient Magnetic Field 10

(f) Waveform Considerations 11 (g) Measurement of Non-uniform E-fields 13

2. Field Studies 17

(a) Effect of Proximity of the Observer 17

(b) Comparison of U.S. and Soviet E-field 19

Measurement Procedures

C. Calibration of Electric Field Meters 23

1. Introduction 23

2. Finite Size of Plates and Fringing Fields 24

3. Modification of Fringing Fields, Compensating 25

Procedures and Generation of a Calibration Field

4. Parallel-Plate Calibration Structures 34

5. Current Injection Calibration 35

III. Magnetic Field Measurements 40

A. Instrument Performance 40

B. Calibration of Magnetic Field Meters 41

Appendix A. Current Induced in Conducting Sphere by Quasistatic 46

Electric Field From Point Charge

Appendix B. The Electric Field Between Parallel Plates— One 49

Plate Grounded

(i) Perturbation of Surface Charge Density By 49

Field Meter

(ii) Perturbation of Surface Charge Density By 57

Nearby Ground Planes

(iii) Effectiveness of Guard Rings For Reducing 62

External Perturbations

( i v

)

Parallel Plates With Guard Rings 65

Appendix C. Ground Referenced Electric Field Meters 71

Appendix D. Miniature Electric Field Probe 75

Notes and References 78

I . Introduction and Summary

The concern in recent years over the environmental effects of electric and

magnetic fields from high voltage transmission lines has also focused attention

on the accuracy of measurements of these fields. This research effort has had

several objectives: (1) to evaluate the instrumentation available for measuring

the near fields of ac transmission lines; (2) to evaluate and suggest criteria

for calibration; (3) to evaluate field-use procedures; (4) to establish a

calibration service at NBS for these instruments; and (5) to document the

results of this study in a form useful as a guide for all concerned with such

measurements

.

A portion of the material presented in this report has been contributed

to an IEEE Working Group Report, "Measurement of Electric and Magnetic Fields

From Alternating Current Power Lines," presented at the 1977 Summer Power

Meeting.

The instrumentation study has been limited primarily to two ac electric

field (E-field) meters commercially available in the United States. One of

these has a magnetic field probe accessory which has also been evaluated.

Laboratory studies (II.B.l) of parameters influencing the performance of

a small sample of E-field meters are summarized in Table I.

This unit is also designed to measure space potential, induced short circuit

current, and induced open circuit voltage. These functions were not evaluated.
9

Table I

Performance Evaluation of Several

E-Field Meters

Parameter

Temperature

(temperature

coefficients)

Relative Humidity

(change from 20 to 95%)

Handle Leakage

Frequency

Type A

Field Meter

Type B Field Meter

0.1-0.2%/°c( a ) 0. l-0.2%/°C

0.4%/°C

(a)

< 1 %

(c)

Waveform

Ambient Magnetic

Field

Not likely to be a source of error(d)

Independent of

frequency over

the power frequency range

Sensitive to harmonic

distortion. Maximum

error is less than 1/3

the % distortion.

Negligible influence

<l%(a)

<3%(b)

A potential

source of error

Indication is

function of

frequency

Quite sensitive to

harmonic distortion.

Maximum error can be

approximately the same as the % distortion,

Negligible influence

(a) v 'two instruments tested

^one instrument tested gave these values--indicating a possibly defective unit

( c

)

'one of the two instruments tested initially exhibited a much larger effect

but this disappeared with subsequent use ^surface contamination of the yoke is a potential source of error under conditio;

of high humidity
-3-

Yet another parameter, the observer's proximity, has also been studied in

the field under EHV lines. It has been found that in making measurements at a

height of one meter above the ground, a standing observer can perturb (reduce)

the field measurement by 5 % when 1.4 to 2.1 m away from the field meter

(Section II.B.2.a).

The proximity effects of the observer when U.S. field meters with short

j handles are used to measure E-fields at a height of 1.8 m (attempted simulation

[ of reported Soviet practice, circa 1972) are highly variable (Section II.B.2.b).

Simulation results were found to be dependent on such factors as the orientation

of the observer's hand and arm relative to the meter, probe (sensing electrode)

geometry, the angle of meter handle with respect to the vertical, and location

relative to transmission lines. The proximity effects produced significant

enhancements in the field measurement (> 20%) for all configurations examined.

Experimental verification is provided of theoretical studies which show

that the field meters, although designed for use in uniform fields, can under

certain conditions be used to within an accuracy of approximately 7% in

!

non-uniform fields which vary as much as 30% over the major dimension of the

meter (Section II.B.l.g).

Details of extensive model and full-scale studies of parallel-plate

electrode structures for the calibration of E-field meters are presented

(Section II. C and Appendix B). The investigations consider the effects of

guard rings, guard bands, method of energizing the plates, nearby ground planes

(walls, floor), as well as the field meter itself on the field between the plates.

These studies have led to the conclusion that 1.5 x 1.5 meter plates separated

by 0.75 meter without guard rings or 1 x 1 meter plates separated by 0.75 meter

v and equipped with four properly voltage-graded guard rings can be satisfactory

for calibration of the field meters studied with an accuracy of better than 2%.
-4-

Calibrations of ac field meters to an accuracy of 1% are now available from the

National Bureau of Standards.

The relative merits of several current-injection "calibration" circuits

are explored (Section II. C. 5). Different circuits are recommended for use with

the two field meters studied and precautions in their use outlined which, if

followed, make this a valuable and convenient technique for frequent calibration

checks

.

Results describing the performance of the magnetic field probe referred to

above are presented, as well as an analysis of the accuracy to be expected from

the use of simple multiturn rectangular loops for the calibration of such meters

(Section III).
-5-

II . Electric Field Meters

A. Instrumentation and Theory of Operation

The two commercially available electric field meters currently available in

the U.S. are of the so called "free body" type. That is, both are self-contained

units with sensing electrodes which are integral with the battery-operated circuits

I and read-out devices; the meters are introduced into the electric field (E-field)

to be measured at the end of an insulating rod and have no connection to ground

except possibly via the observer holding the handle. Sketches illustrating their

approximate geometry are shown in Figure la; the side dimensions range from

'v 7 cm to ^ 20 cm. It should be noted that ground referenced meters have also

been devised [1,2] but that they can be used only under special conditions

described in Appendix C.

j

I

(a) Geometries of commercial

U.S. E-field meters.

(b) Spherical E-field

probe

.

Fi gure 1

.

Briefly the theory of operation of free-body meters can be understood by

considering an uncharged conducting free body with two halves introduced into

a uniform field E . o The charge induced on one of the halves is
- 6

-

Q = / D • dA (1)

S/2

-> -> where D is the electric displacement and dA is an area element on half of the

body with total surface area S. The case of a sphere divided into hemispheres

by a plane normal to the electric field (Figure lb) yields the result that [3]

Q

= 3n a e E o o

( 2 )

where a is the radius of the sphere and e Q

is the permittivity of free space.

For less symmetric geometries (Figure la), the result can be expressed as

Q

= k e E oon (3)

where k is a constant dependent on geometry. If the electric field has a sinusoidej

dependence, e.g., E q

sin wt, the charge, given by Eq. 3, oscillates between the twc

halves and the current is

I = m = dtk a) e E cos o>t . 0 0

It should be noted that the uniform E-field direction serves as an alignment

axis for the field probe. The constant k can be thought of as a field meter

constant and is determined by calibration.

One of the commercial E-field meters, designated Type A, is designed to

determine E Q by measuring a quantity proportional to the charges induced on the

sensing electrodes; the other, designated Type B, is designed to determine E Q by

measuring a quantity proportional to the current between the electrodes. In both

types the analog meter, while calibrated to read the rms value of a sinusoidal

signal, actually responds to the average value of the rectified signal. Thus the
-7-

presence of harmonics in the electric field being measured introduces an error

which depends on the phase relationships of the harmonic components to the

fundamental as well as on their magnitudes. Furthermore, the signal processing

techniques used in the two instruments differ in their sensitivities to the

harmonic components in the field waveform. The significance of these differences

is discussed in Section II.B.l.f.

B. Parameters Influencing Instrument Performance

j| 1 . Laboratory Studies

(a) Temperature and Humidity Effects

Studies have been made of the influence of temperature and relative humidity

on the analog output of the ac field measuring instruments. In addition to the

two instruments purchased for this study, three others, obtained on loan, were

studied.

The behavior of three (one of Type A and two of Type B) of the instruments

was very similar--wi th a calibration midway in the temperature range between 0 and

40 °C (32 and 110 °F), each could be used over that complete range with a maximum

uncertainty due to temperature of less than ±5%. (Temperature coefficients were

of the order of 1 or 2 parts in 10^/°C). The influence of relative humidity over

the range from about 20% to 95% was less than 1%. The results obtained with the

fourth meter (Type B) were somewhat erratic; however, the influence of both

temperature and relative humidity was significantly greater for this instrument

than for the others. The meter indication at 40 °C differed from that at 0 °C

by about 17% (a temperature coefficient in excess of 0.4%/°C) and, while the

scatter in the data was large, the indication was that a change in relative

humidity at constant temperature from 50 to 95% changed the meter indication

about 3%. The fifth meter (Type A) initially exhibited an extreme sensitivity

to high relative humidity; however, this behavior was relatively short lived and
- 8 -

the subsequent behavior was essentially identical with that of the first three

i mentioned above.

(b) The Effect of Electrical Leakage Along the Handle

The effect of electrical leakage along the supporting handles has been

studied in a semi-quantitative way by introducing multi-megohm resistors of

known magnitude in a conducting path along the handle to ground. The interpretatio

of the results is not exactly straightforward since the effect of the resistive

leakage has not been rigorously separated from the contribution of the stray

if

{If

%

if

ini

capacitances; however, the results are believed adequate for the present purpose.

The two instruments which are currently commercially available differ in a

significant way with respect to susceptibility to error from a leakage path to

tki

1

ground along the handle. In the Type B meter the section of the meter case to

which the handle is connected is an active member of the field-sensing arrangement.

In the Type A meter the handle is connected directly to the meter case, but both

sensing elements are isolated to some extent from it.

Electrical leakage along the handle is not a source of error in Type A meters.

In fact, in normal use the meter case can be tied directly to ground without

introducing more than a few percent error. However, under high humidity conditions

surface contamination of the yoke which connects the handle to the meter can

introduce significant error as a result of the field distortion produced.

For the Type B meter, electrical leakage along the handle can be a significant

source of error. It appears that an effective leakage resistance to ground of the

order of 10^ ohms introduces an error of several percent. Measurements in an

environmental chamber of the resistance between contacts placed about 1 meter

apart on one handle gave a value of about 10^ ohms when the relative humidity

ril

is

lit

ji

li

k

it was about 90%. This result should be accepted only as an indication of the

possible existence of a problem since the surface conductivity of an insulating

’iii
material is usually strongly voltage dependent and, of course, greatly influenced

by contamination of the surface resulting from even only ordinary handling.

As has been pointed out by the designer of this meter, the effect of

electrical leakage along the handle is not the same with the handle connected to

the upper electrode as with it connected to the lower electrode. Thus in use,

3

I if the meter movement is well balanced and its reading is the same when it is

l inverted as when in the normal position, it may be assumed that electrical

leakage to ground along the handle is introducing negligible error. However,

I

! this test can be applied only if the handle length is sufficient to eliminate

the perturbing effect of the observer in both orientations of the meter. In

general, the perturbation can be expected to be somewhat larger with the meter

in the inverted position (see Section II.B.l.d).

(c) Meter Balance

l The question of mechanical balance of the meter movement is important. If

a meter is not sufficiently well balanced it must be used in the same orientation

with respect to the vertical as existed when it was calibrated. Of the five

instruments so far tested, four were quite satisfactorily balanced, but the zero

( position of the fifth changed by as much as a full division as the orientation

with respect to the vertical was varied.

(d) Meter Orientation

With field meters having geometrically symmetric sensing electrodes, a

Tiaximum reading is obtained when the meter is so oriented that the field is

aligned with the meter axis--def ined as the line passing through the centers of

the two electrodes. The meter reading is then expected to follow a cosine law

vith respect to the angle between the field and the meter axis. However, the

nounting of the indicating meter on the upper electrode and the handle-mounting

jracket on the lower electrode of the Type B field meter introduce a significant
- 10 -

asymmetry. The maximum reading is obtained with the top of the front surface

of the Type B meter tipped toward the observer about 15 degrees with respect to

the field vector. The reading in this position is about 4% greater than when the

meter is aligned with the field. If the vertical geometric axis of the field

meter coincides with the field vector both during calibration and in use, this

anomaly can be ignored except as it imposes a requirement for somewhat greater

care in maintaining correct orientation during both calibration and use. An

error will be introduced in attempting to use this meter to measure the vertical

component of the field if a significant horizontal component in the direction

of the handle exists. For this reason it appears that measurements with it in

the vicinity of transmission lines should be made with the handle of the field

meter parallel to the line. This same orientation should be used with any field

meter when measurements of the maximum E-field are being sought because there are

no field components parallel to the transmission line direction. Exceptions to

this are locations near towers and other field perturbing objects.

(e) The Influence of Ambient Magnetic Field

_5 Using a set of Helmholtz coils, a 60 Hz magnetic field of 1.2 x 10 tesla

(0.120 gauss) was impressed on one of the instruments when set as for use in

measuring an electric field. The test was repeated with several scale readings

and for several orientations of the meter relative to the magnetic field vector.

Similar tests were made with each of the five instruments referred to above. No

significant influence of the magnetic field at this level was detected with any ol

the meters.

Tests using one field meter of Type A and one of Type B were repeated at

field values near 1.1 x 10

- ^ tesla (1.1 gauss). This is well in excess of values

likely to be encountered near transmission lines. Negligible effects were observe

witn a Type A meter on the most sensitive E-field range (5 kV/m full scale).
- 11 -

Perturbations of a few percent on the 1 x 100 V/m scale of the Type B meter were

evident, but negligible effects on the higher ranges were observed. The

orientation of the meters with respect to the B-field direction was varied during

each of the tests without significant effect.

( f ) Waveform Considerations

While both Type A and Type B field meters are calibrated to read the rms

value of a 60 Hz sinusoidal waveform, the analog meters actually respond to the

average value of the rectified signal. The presence of harmonic components in the

electric field waveform introduces errors which depend on both the magnitudes of

the harmonic components and their phase relationships to the fundamental. Figure 2

shows the calculated measurement errors which are introduced when selected harmonic

components are present. The calculation assumes that the harmonics are in phase

with the fundamental, a condition which leads to maximum measurement errors [4].

The percent error for the even harmonics are actually negative in sign but are

presented on the same graph for the reader's convenience.

The measurement errors for the Type A meter, a charge sensing device (Eq. 3),

can be determined directly from the curves shown.

There are additional considerations which enter into the calculations in the

case of the Type B field meter. As noted in Section II. A, this device responds

to the current induced (Eq. 4) between its sensing electrodes. The current

results from the capacitive coupling between the transmission line and the field

meter and between the field meter and ground. Since these admittances are

directly proportional to frequency, the amplitude of each harmonic component of

current induced between the sensing plates of the field meter relative to the

amplitude of the fundamental is increased by the order of the harmonic, e.g.,

by a factor of 3 for the third harmonic, a factor of 5 for the fifth harmonic,

etc. An RC network introduced in the signal processing portion of the Type B
- 12 -

field meter modifies the relative amplitudes and phase relationships of the harmon:

components; however, since the network is not the same for all models it is not

possible to calculate error curves which apply to all Type B instruments. The

curve shown in Figure 2 indicates the calculated percent error for the third

harmonic if the RC network is ignored.

HARMONIC DISTORTION (%)

ip

L III

Figure 2, Maximum rms value errors due to selected harmonic components for Type A

and B meters. The even harmonic percent errors are actually negative in

sign. The error curve for the Type B meter does not include the effect

of the RC network (see text).

The following experimental data obtained with voltage waveforms having measured

harmonic distortion (but with unknown phase relationships between fundamental and

harmonic components) provide confirmation that the curves of Figure 2 provide an

indication of the error which may be encountered.

a
-13-

n

Error in Field Measurement

Harmonic Content

of Impressed Waveform

** 3rd 5th 7th 9th 11th 13th

0.1 <.l <.l <.l <.l <.l

51 .5 .2 .1 <.l

*

Type A Field Meter

%

^

0

0.7

0.5

Type B Field Meter

Model Purchased 7/75

%

'VO

Type B Field Meter

Model Purchased 7/77

l

^0

4.7

2.5

1 .8 3.6

The amplitudes of the harmonic components were the same for the two tests but the

phase relationships were different (but not known for either). In all cases the

contribution from even-harmonic components was negligible.

Under normal operating conditions in most locations under transmission lines

the harmonic content in the electric field waveform is probably in the range of

1-2% or less; however, close to large industrial loads it may reach 10% [5] and

thus may introduce significant errors in field strength measurements.

(g) Measurement of Non-uniform E-fields

A thesis by Lothar Wilhelmy of Stuttgart University [6] describes the design

and operation of an electric field probe which can be used in nonuniform as well as

uniform electric fields. The magnitude and direction can be measured even in the

presence of rapid field fluctuations. The device is considerably more complicated

and expensive to fabricate than the commercially available U.S. meters.

Although designed for measurements of near-uniform fields, the U.S. meters

may have application in some relatively non-uniform field situations as the

following theoretical analysis suggests. The current induced in a spherical

I E-field probe in a non-uniform quasistatic field generated by a point charge is

given by (in the absence of nearby ground planes)

I - 37Ta 2

to E (iot) [1 - + (t) “ •••] 24 v d' (5)
-14-

where

E (wt) - 4«

0

d

2

9

a is the radius of the spherical probe and d is the distance between the point

charge Q(wt) and the probe center. This result is given without derivation in

a paper "Electrical Field Measurement in the Vicinity of HV Equipment and

Assessment of Its Bio-Physiological Perturbing Effects" by C. Mihaileanu et. al .

,

presented at the 1976 CIGRE Meeting (Paper 36-08). A derivation of Equation 5

is given in Appendix A.

The current induced in a spherical E-field probe in a uniform quasistatic

field, E q

(cot), is given by [see Eq. 4]

I - 3-rra^ 0) e QE q(u)t) . (6)

Comparison of Equations 5 and 6 shows that the induced current for the nonuniform field case is the same as that produced by a uniform field of magnitude

E o

= Q/4 tte o

d if the terms in (a/d) can be neglected. Thus the induced current

at a point in the highly non-uniform field produced by a point charge is nearly

the same as that produced by a uniform field of equal magnitude if d is sufficient!

large. For example, if a/d = 0.1, the difference in induced current (E-field

measurement) produced by a uniform and highly non-uniform field is less than 1%;

the change in E-field magnitude over the dimensions of the sphere is

| aE/E

|

= 4 a/d = 0.4 (40°/).

The "effective" radius of commercially available E-field meters, which have

rectangular geometries, can be estimated as half of the largest diagonal dimension.

It would, therefore, appear that these instruments can be used with slightly

reduced accuracy in regions where the field nonuniformities approximate that of
-15-

the field of a point charge at a distance of five times the major dimension of

the field meter.

To examine this theoretical prediction, a non-uniform field was produced

by energizing an aluminum sphere (15.2 cm diam.) suspended 2 m above a concrete

floor. The experimental arrangement is shown in part in Figure 3. The E-field

at several locations below the sphere was measured with ^ 3% accuracy using a

miniature E-field probe developed at NBS (Appendix D). The field was also

measured using both types of comnercial meters. The E-field values measured with

the various devices are plotted in Figure 4 as a function of distance from the

sphere's center and field meter center. All the instruments were calibrated in

a uniform field between parallel plates (Section II. C. 3). No corrections have

been made for temperature differences at the time of calibration and during the

non-uniform field measurements (this could lower the datum points of Type A and B

meters by ^ 1% to 2%). Errors in reading the analog output of the commercial

meters during the experiment are estimated to be less than % 3%.

Figure 3. Experimental arrangement for generating a non-uniform electric field.
-16-

0.8 0.9 1.0 l.l DISTANCE FROM SPHERE CENTER (m)

Figure 4. Within experimental uncertainty, the field measurements obtained with

the large field meters agree with those observed with the miniature

field probe. The solid curve has been drawn to pass through the points

measured with the miniature probe.

n

The non-uniform field departed significantly from that expected for a point

charge over an infinite ground plane because, as modeling experiments showed,

contributions to the field occurred from the unshielded lead which energized the

sphere.

The data of Figure 4 confirm the theoretical expectation that, within

experimental uncertainty, relatively large commercial E-field meters which are

calibrated in uniform fields can also be used to measure non-uniform fields

29% change over dimensions of Type B meter) with introduction of small error.
-17-

The theoretical and experimental results have been obtained under the

constraint that the meter is aligned with a single-phase E-field. It should

be noted that the asymmetry associated with the Type B field meter (II.B.l.d)

imposes a requirement for particular care in interpreting the results obtained

with it in non-uniform field situations.

2. Field Studies

(a) Effect of Proximity of the Observer

Limited studies of the proximity effect of the observer were conducted under

the "C" line at the Apple Grove, West Virginia EHV test facility and under an

operating 500 kV line near Urbana, Maryland. The meters, with handles attached,

were supported on a glass tube and read with the aid of field glasses from a

distance of approximately 7 meters by one observer as another observer stood at

measured distances from the instrument.

The extent and nature of the field distortion introduced depends on many

variables in addition to the horizontal distance between the meter and the

observer, i.e., (a) the detailed geometry of the transmission line; (b) the

relative positions of the line, meter, and observer; (c) how well the observer

is grounded; (d) the effective height of the "ground plane"; (e) the height

of the observer; and (f) the height of the field meter above the ground. Table II

provides an indication of the influence of some of these parameters on measurements

under the 500 kV line.

Comparisons of the perturbation caused by wel 1 -insul ated observer with those

caused by one who was well grounded revealed that the effect was noticeably

larger for the grounded observer at distances where the perturbation was significant.

The data reported here were taken with the "observer" wearing conducting shoes and

holding a wire attached to a 40 cm metal rod driven into the ground. Thus from

this aspect they represent a worst case situation.
-18-

TABLE II

Effect of Proximity of Six-foot Observer

(field meter one meter above ground)

Meter

Meter

Location

Handle Orientation

Relative to

Transmission Line

A Under outer

conductor

Parallel

11 li Perpendicular,

toward outside

ll ll Perpendicular,

toward center line

B

ll Parallel

II ll Perpendicular,

toward outside

II ll Perpendicular,

toward center line

II Under center

conductor

Paral 1 el

II ll Perpendicular

Observer proximity effects which result in an error of opposi

considered in the next section.

Approximate

Meter-Observer

Distance Resulting

in -5% Error

(m)

2.0

2.1

1.8

1.4

2.0

1.4

1.5

1 .4

sign are
-19-

It was found that the proximity effect of the observer is significantly

different for the two types of field meters as Table II and Figures 5 and 6 show.

These data, which are representative of the data obtained with other configurations,

were obtained with the field meter under the center conductor and with its handle

oriented in a direction perpendicular to the line. The area was covered with

grass about 10 cm high and was reasonably flat with only a slight slope.

The results shown in Figures 5 and 6 indicate that the error introduced by

the proximity of the observer could be reduced by specifying a height above

ground for field measurements greater than one meter. Unfortunately, the optimum

height is not the same for the two field meters. It appears to be about 1.5 meters

for the Type A and 1.2 meters for the Type B.

An explanation for the differences between the proximity effects with the two

field meters is to be found in the geometric asymmetry in the Type B field meter

sensing electrodes (see Section II.B.l.d). While this departure from symmetry

imposes the necessity for the precautions mentioned in Sections II.B.l.b and

II.B.l.d, it does result in a reduction in the perturbing effect of the observer

for a range of field meter heights.

(b) Comparison of U.S. and Soviet E-field Measurement Procedures

Electric field measurements in the U.S.S.R. have been made at a height

of 1.8 meters [7] using a field meter with a 25 cm handle [8,9]. Field measurements

in the U.S. are normally made at a height of 1 m with considerably longer

handles 1 m to % 3 m) . Interest, first generated in 1975 [10], has recently

focused on obtaining a relationship between E-field values measured in the

two countries. Attempts at simulation of the Soviet measurement technique

have been made in the U.S. by holding, 1.8 m high with outstretched arm,

commercial U.S. meters with a shortened grip on the handle. The field values

obtained in this fashion are compared with values obtained at the same location
-20-

10.0

O 0 __-o " *“*'

.—

"O O - 8 --— - D — h” . n

- < - °"

ffl l.4m o'"

n m '' 3 -ic.o -

I- /

l.Om * tua. “20.0 * 1 1 1 1 1 1 i 1 0 1.0 2.0 3.0 4.0 5.0

DISTANCE OF OBSERVER FROM TYPE A METER (m)

Figure 5. Proximity effect of six foot observer for Type A Field Meter at heights

of 1.0, 1.4, and 1.6 m.

1.6m o. o_ .o-— 'Os' ' ~o— o - 8

"

-- o _ - --

<

l.4m ^

l.Om *

J i I i L

DISTANCE OF OBSERVER FROM TYPE B METER (m)

Figure 6. Proximity effect of six foot observer for Type B Field Meter at heights

of 1.0, 1.2, and 1.4 m. The two sets of data for the 1.0 m height give

an indication of the reproducibility of the results. The proximity

effect of bystanders positioned in directions other than along the

handle will introduce greater perturbations for the 1 m height.
- 21 -

1 m above the ground with a long handle. The ratio of the two values has been

found by a number of observers to range from approximately 1.2 to 1.8 depending

on the geometry of the meter-observer-transmission line combination and the choice

of commercial meter (Type A and Type B).

Such measurements were repeated under a 500 kV transmission line near

Urbana, Maryland using both Type A and Type B meters. At a location of about

3.5 m outside the outer phase conductor (near maximum E-field) the ratio of the

"Soviet" E-field value (short handle - 1.8 m) to U.S. E-field value (long

handle - 1 m) was found to be about 1.8 using a Type B meter and 1.4 using a

Type A meter. The ratios changed to about 1.7 and 1.3 respectively when the

location was changed to about 14 meters outside the outer phase conductor. It

should be noted that the principal cause of the observed differences (1.8 m vs. 1 m)

is the perturbation introduced by proximity of the observer rather than differences

in elevation above the ground.

The lack of agreement between ratios obtained with Type A and Type B meters

has a qualitative explanation which raises questions regarding the accuracy of

such simulation experiments. As noted above, the enhanced field value at

1.8 m is primarily due to the proximity of the observer and his hand. The

observer may be regarded as a nearly grounded object which concentrates the field

and it is this enhanced field the meter "sees." Depending on the geometry of the

hand-handle combination relative to the sensing plates, the geometry of the

meter sensing electrodes (i.e., flat plates or "hemispheres"), the relative

position of the transmission lines and perhaps other parameters (e.g., closeness

of meter to body, height of observer) the enhancement (and ratio) will be

different. Figure 7 shows the approximate geometries of the Soviet meter [8,9]

and the two U.S. meters; arrows indicate field sensing surfaces. Marked differences

can readily be seen which, when taken with the asymmetry characterizing the Type B
(Figures are not scale drawings)

meter (see Section II.B.l.d), can provide an explanation for the observed results.

The above observations were confirmed qualitatively by suspending U.S.

field meters in a parallel plate E-field and bringing a grounded aluminum foil

"hand" to within 25 cm of the meter. The enhancement in field reading was found

to depend on direction of approach and choice of field meter.

The lack of documentation providing details of the Soviet measurements

(e.g., closeness of meter to body, orientation of body with respect to signal

source, height of observer, etc.) as well as the lack of availability of the

appropriate Soviet meter makes any comparison of measurement techniques difficult.

What seems certain from the above comments is that the measurements made using the

Soviet technique will be significantly larger than U.S. measurements because of

proximity effects. (The reader should note also that the proximity effect of the

observer can decrease the field reading when the meter is held at the lowered

height of 1 m. See Section II.B.2.a). Because different ratios are obtained with

the same field meter at different locations relative to the transmission line, the

ratio will have a range of values (presumably this would be true even if the Soviet

field meter were used). It is also perhaps noteworthy that the quoted [9] accuracy

of the Russian field meter is ±20%.
-23-

C. Calibration of Electric Field Meters

1 . Introduction

Calibrations of ac electric field meters have been made in quasi-static

(60 Hz) uniform fields of known (rms) magnitude. A uniform field has been chosen

because it resembles the transmission line fields usually encountered near ground

level. (Measurements of transmission line fields are usually performed at a height

of 1 meter). The small non-uniformities which actually exist in transmission line

fields near ground level are not expected to influence the E-field measurement in

light of the discussion of Section II.B.l.g.

Two methods of calibration have been used: (1) A uniform field is established

under an energized line and the current through a guarded electrode of known area

(see "one meter square panel" Appendix C) placed at ground level is measured to

determine the field value. The field meter to be calibrated is supported at a

distance of ^ 1 m above the electrode. The field at the instrument is assumed to

be the same as that at the electrode. (2) The field meter is inserted into the

space between two parallel-plate electrodes having a known separation and a voltage

applied between them. The field is assumed uniform over a volume large compared

with the dimensions of the instrument prior to its insertion.

While sometimes improperly referred to as an alternative method of calibration,

the current injection technique described in Section II.C.5 provides a calibration

of the signal processing circuits of the field meters and thus serves as a very

useful calibration check.

Since it is believed that the convenience offered by the paral lei -plate

calibration technique relative to the "one square meter panel" method will lead

to its adoption by most users of field meters, a rather extensive theoretical and
-24-

experimental study has been made of factors which influence the accuracy

obtainable with this method.

2. Finite Size of Plates and Fringing Fields

Uniform field regions of known magnitude and direction can be created with

parallel plates provided that the spacing of the plates, relative to the plate

dimensions, is sufficiently small. The uniform field value E q

is given by V/t

where V is the applied voltage and t is the plate spacing.

While many texts have treated the problem of semi-infinite plates theoretically

a recent Sandia report by P. D. Thacher [11] has presented the results in perhaps

the most graphic form. In common with earlier analytical treatments, the problem

is solved by utilizing the theory of functions of a complex variable [12]. The

details of the conformal mapping which permits the problem's solution are not

presented here. They are provided in the references cited.

The results of Thacher's calculation are shown in Figure 8 with the author's

kind permission. Illustrated are contours of equal field intensity relative to

2 2 2 the uniform value squared, E = V /t . Only one electrode is shown with the

midplane of the electrodes corresponding to the bottom of the figure. The

coordinates u

1 and v' are shown in the inset. The magnitude of the relative

electric field is found by taking the square root of the numbers shown. It should

be noted that the field direction is not explicitly shown. It can be assumed,

however, that when the field magnitude is nearly equal to the uniform value, the

direction will be approximately normal to the plates.

Using the results of Figure 8, the magnitude of the electric field at either

plate surface and the midplane can be plotted as a function of distance from the

plate edge. This is shown in Figure 9 with numerical values [11] shown in Table III.

Thus given a plate spacing t, one can determine how large the plates must be in

order to have field uniformity to a specified degree. For the idealized case of
-25-

no nearby planes or objects, these results could be used to design a finite-sized

parallel plate structure. A linear superposition of the edge effects (nonuniformities) due to opposite edges of the plates can be made at the center when

the perturbations are less than approximately 0.5%.

Figure 8. Contours of equal field intensity. Only one electrode is shown, with

the bottom of the diagram corresponding to the midline between electrodes.

Values of u' and v'are normalized by the electrode separation t. Numbers

beside the lines give the field squared relative to V^/t^, the value well

in from the edge of the electrodes.

3. Modification of Fringing Fields, Compensating Procedures and Generation

of a Calibration Field

As noted in the previous section, the theoretical results presented for the

design of a parallel plate calibration structure are valid in the absence of nearby

ground planes (walls, floor, etc.) and other perturbing objects. The degree of
-26-

«* U'/t NORMALIZED

DISTANCE FROM EDGE

Figure 9. Variation of normalized electric field strength at plate surfaces and

midplane as function of normalized distance from plate edge.

modification of the theoretically predicted E-field will depend on the geometry of

HI

these surfaces as well as the method used to energize the parallel plates. The two

methods commonly used to apply a voltage to the plates are (a) "balanced" arrangemen

in which a grounded center- tapped transformer is employed to provide voltages on

the two plates equal in magnitude but 180° out of phase, and (b) "single-ended"

arrangement in which one plate is grounded. The balanced scheme was chosen as the

better arrangement because modeling experiments demonstrated that there was a greate

l degree of immunity from the perturbing influences of nearby ground planes. Signific

departures from idealized surface E-field predictions (Table III) were evident using

a single-ended arrangement, even when the nearby ground planes were several plate

spacings away. Details of the modeling measurements are presented in Appendix B.

The effectiveness of guard rings in reducing the perturbation and creating a

larger region of uniform field is also examined in Appendix B; guard bands are

discussed later in this section.
- 27 -

Table III

MIDPLANE

u'/t m m O

- 0.0698 0.836

- 0.1621 0.894

- 0.2965 0.948

- 0.4177 0.974

- 0.6821 0.994

- 0.7934 0.997

PLATE SURFACE

- 0.7954 1.002

- 0.6861 1.005

- 0.4376 1.025

- 0.2431 1 .095

- 0.1624 1.183

- 0.1230 1 .265

- 0.0991 1.341

- 0.0829 1.414

- 0.0452 1.732

- 0.0307 2.000

- 0.0185 2.449
-28-

Using the results of the previous section, it can be shown that, in the absence

of external perturbations, the E-field between parallel plates 3 m x 3 m x 1 m

spacing can reach values that are within a few tenths of a percent of the uniform

value V/t. A structure of this size was constructed for purposes of investigation

and is shown in Figure 10. Both plates consist of nine tightly stretched aluminum

screens, 1 m x 1 m, mounted on an aluminum frame. The top plate is suspended

from the ceiling with electrically isolated chains and turnbuckles; the bottom

oi

di

K'

I

a plate is mounted on wooden tables about 1 m above the floor. The nearest wall

is located about 1.5 m away. The plate flatness and spacing was adjusted to reduce

the uncertainty in plate spacing to less than 'v 0.5%.

The power supply consists of a low distortion oscillator-amplifier combination

supplying two transformers with primary windings in parallel, and secondary windings

in series "center-tapped" to ground. The total harmonic content of the transformer

r

0

1

a

o

Figure 10. Large parallel plates with 1 m separation. Each plate consists of nine

1 m x 1 m tightly stretched aluminum window screens mounted on an aluminum frame.
-29-

output voltage is less than 1%. As a safety measure, three-megohm current limiting

resistors are placed in series with the output of each transformer. The voltage

difference across the plates is measured with a calibrated electrostatic voltmeter

with an error less than ^ ±0.2%. The system remained corona free during the

measurements described below.

Measurements of the vertical and horizontal E-field profiles were made with

a Type B field meter. The meter was inserted into the field with 'a dielectric

rod, 2 m long, which was mounted on a wooden frame. Readings of the analog

output were made with a cathetometer aligned to reduce parallax; differences of

less than 1% could be discerned. Figure 11 shows the vertical E-field component

as a function of height near the center of the plates. The horizontal profile

of the vertical E-field at a number of heights above the bottom plate are shown

in Figure 12. The inset in Figure 12 compares the horizontal profile at a height

of 50 cm with the predictions of Section II. C. 2 ignoring superposition of fringing

fields. The field values in Figure 11 and the inset of Figure 12 have been

normalized with respect to the value measured at the center of the parallel plates.

The data of both figures indicate that a substantial region of nearly uniform

field exists between the plates. The vertical profile shows that, within

experimental error (£ 1%), E is constant from % 30 cm to ^ 70 cm above the bottom

plate. The increase in field values at distances closer to the plates can be

attributed to interaction between the meter and surface charge distributions on

the plates (Appendix B.i). Thus it can be assumed that E remains constant along

the entire vertical path. Since the potential difference V must equal the line

integral

t -> t V = /

E • d£ = E / d£ = Et,

o o
-30-

VERTICAL E-FIELD PROFILE

HEIGHT ABOVE BOTTOM

PLATE (m)

Figure 11. Within experimental uncertainty, a region of nearly constant E-field is

observed from ^ 30 cm to ^ 70 cm above the bottom plate.

it is possible to conclude that E is within ^ 1% of the uniform value V/t and

that a structure 3 m x 3 m x 1 m will generate a nearly uniform field.

This conclusion regarding field uniformity was confirmed with a second

independent experiment employing guard bands. Both guard bands and rings

(Appendix B.iii) have been used to enlarge the region of uniform field between

parallel plates. Guard bands have been used extensively in the past for calibration

of x-ray beams, and, consequently, the relevant theory and experimental verification

can be found in the literature [13].

The spacing of the large parallel plate structure was increased to 1.2 m and

_3 aluminum foil 3.8 x 10 cm thick) bands 14 cm and 28 cm wide were wrapped

around the perimeter as shown in Figure 13. Bakelite tubes at the corners and maskinc
-31-

PLATE

EDGE

-1.5m

3.1

HORIZONTAL E-FIELD PROFILE

CENTER

-I.Om -0.5m 0 0.5 m

PLATE

EDGE

I.Om 1.5 m

3.0 -

• • • •

• •

E 2.9 - >

UJ

o o

o o

2.8 -

o o O o i%I l 4 | 4 4 $ 8

cA

2.7 -

2.6

a HEIGHT ABOVE BOTTOM PLATE (cm) * °

d> *15

0

o

LlI s

UJ 0.8

Figure 12. The horizontal profile of the vertical E-field measured at several

heights above the bottom plate. The inset compares experimental

observations of the normalized field at 50 cm with the theoretical

predictions for semi-infinite plates. The presence of ground planes

less than two plate spacings away from the apparatus and the

superposition of fringing fields do not significantly perturb the

field from ^ -0.75 m to +0.75 m.

tape at intermediate points were used to support the bands. A resistor divider

of four 5-megohm resistors was used to grade the potentials applied to the bands.

The spacing between adjacent bands was nominally 2 cm which is sufficiently large

to avoid corona and sufficiently small for application of the experimentally

confirmed theory [13]. The bottom plate was grounded to allow deployment of a

current-sensing probe on the bottom plate. The earlier concern regarding the

perturbing influence of nearby ground planes when using the single-ended arrangement
-32-

was not applicable in the present case because of the large electrical isolation

provided by the bands. Such a banded structure is expected to generate a large

volume of uniform field [13].

Figure 13. Large parallel plates with guard bands. E-field meters are introduced

into the field via the "window" in the band structure. The inset is

a schematic view of resistor divider and electrical connections.

The current-sensing probe consisted of an aluminum covered 0.15 cm thick

plastic disc 16.5 cm in diameter. An isolated circular segment, 8.5 cm in

diameter, in the center made up the current sensing surface.

Measurement of the induced current (see Appendix B.i) permitted determination

of the E-field along the bottom plate to within an accuracy of ±0.2%.

Values of the E-field along the surface of the bottom plate are shown in

Figure 14. The data have been normalized with respect to the uniform field value
-33-

V/t. The lack of symmetry is due in large part to an opening in the band

structure (Figure 13). The results show that a uniform field does exist across

much of the bottom plate surface confirming our expectations; it can be inferred

that this field extends nearly vertically to the top plate [13].

The earlier conclusions regarding the field uniformity of the unbanded

3 m x 3 m x 1 m structure were confirmed with the banded structure (3 m x 3 m x 1.2 m)

in the following way. E-field measurements were first made at the* center of structure

with both types of field meters. The bands were then removed and the same voltage

difference was applied to the plates using a balanced arrangement. The E-field

measurements were repeated. No measurable differences could be seen in the field

values indicating a uniform field for both configurations. Reducing the plate

spacing from 1.2 to 1 m increases the lateral region of field uniformity.

Having constructed a relatively large apparatus which generated a uniform

E-field, the question of building a smaller more easily fabricated system for

calibration purposes was addressed. With the goal of producing a field which was

within 2% of the uniform field value V/t, several parallel plate structures were

examined.

PLATE DISTANCE (m) PLATE

EDGE EDGE

Figure 14. The E-field along the bottom plate is within 1% of the uniform value,

V/t, over an extended region. The lack of symmetry at the left is

largely due to the "window" in the band structure.
-34-

Facilitating this study was the development of a miniature E-field probe.

Because of its small size, it could be used to map the field profiles over large

regions without significant perturbation of the surface charge distributions.

Some details of the probe and its operation are given in Appendix D.

4. Parallel-Plate Calibration Structures

An initial design consideration is the minimum plate spacing which can be

used without introducing serious feedback effects because of surface charge

perturbations. The data of Figure 11 indicate that the spacing must be at least

0.75 m to avoid measurable effects. Because the data were obtained with a Type B

meter 19 cm vertical dimension), a 0.75 m spacing will also be adequate for the

Type A meters which are smaller. Using this spacing, a number of parallel plate

systems were examined with the miniature field probe. It was found that a parallel

plate system 1 m x 1 m x 0.75 m with four equally-spaced guard rings contained

3

a central 20 x 20 x 20 cm volume in which the E-field value remained constant to

within ^ 0.6%. The magnitude of the vertical E-field at the center of the structure

was about 1% less than the uniform value, V/t. The balanced voltage arrangement

and adequate current limiting resistors were again employed; the bottom plate was

^ 0.8 m above the floor.

The system was tested as a calibration facility by comparing measured E-field

values at the center of this structure with values measured in the larger

3 m x 3 m x 0.75 m apparatus for the same V/t. Both commercial meters were used

for the comparison. The Type A meter readings were 'v 1.0-1. 7% less in the smaller

guarded structure. The Type B meter readings appeared to be ^ 0.0-0. 6% less

in the guarded structure. Thus, both meters read values that are within 2% of the

uniform field value V/t. The lowered readings in the smaller guarded structure

are compatible with the fact that the field at the center is less than V/t by

^ 1 %.
-35-

A second calibration system without guard rings and having greater accuracy

was characterized from modeling experiments. Examination of a 1 m x 1 m x 0.5 m

3

structure with the miniature probe revealed a central 20 x 20 x 20 cm volume in

which the field value did not differ from V/t by more than % 0.3%. This result

was not affected when two metal grounded "walls" (metal fences) were brought to

within 0.25 m of the plates on opposite sides of the structure. If the model is

scaled upward in size to 0.75 m spacing to eliminate measurable feedback effects,

the above results indicate that a structure 1.5 m x 1.5 m x 0.75 m will provide a

usable calibration field which is well within 1% of the uniform field V/t.

The perturbations due to nearby walls (floor) will not be significant if they are

half the plate spacing or more away from the plates.

Briefly summarizing the characteristics of the calibration facilities described

above, we have:

Wal 1 /Floor

Applied Voltage Dimensions Guard Rings Error Distance

Balanced- to-ground 1 x 1 x 0.75 m 4 < 2% 0.4 m

Balanced- to- ground 1.5 x 1.5 x 0.75 m 0 < 1% > 0.4 m

5. Current Injection Calibration

The field meters being studied can be considered current measuring devices

which in use are capacitively coupled to a high voltage source and to ground.

(As indicated in Section II. A, the Type A field meter measures the charge on

the sensing electrodes; however, since this is accomplished by integrating the

current, the concept of "current injection" is appropriate for both types). The

two functions, current measurement and capacitance coupling, are independent

parameters and may be treated separately. The capacitance coupling is a function
-36-

of the total geometry and is influenced, of course, by the proximity of other

objects (grounded, floating, or connected to the high voltage source) as well as

by the meter's location with respect to the high-voltage lines and the ground

plane and by the geometry of the meter itself.

The current injection "calibration" procedure, hereafter referred to as a

"current calibration," provides a convenient method of monitoring the current

measurement parameter and determining a correction factor to be applied to the

meter readings in the event that it changes with time.

The Type B meter is provided with an input jack for a current calibration.

Insertion of a plug into the jack connects the two sensing electrode structures

together to provide a shield. A current injection circuit, such as shown in

Figure 15, which permits this shield to be grounded during the calibration

eliminates the problem of interference from stray fields normally encountered in

a laboratory, e.g., from fluorescent lights, unshielded power raceways, extension

cords, etc.

Figure 15

VM is a precision voltmeter and Z a known impedance, large compared with

the input impedance of the field meter.

The manufacturer 1 s instruction manual for the Type B meter gives 193 x 10

amperes/(vol t/meter) as the design value for the current sensitivity. Choice of
-37-

the series impedance, of course, determines the voltage required to obtain full

scale deflection on a given range. The input impedance of the Type B meter (of

the order of 1000 Q, for the ranges of interest) may be neglected if the series

impedance selected is 10^ ohms or larger.

Current calibration of the Type A meter is accomplished by attaching leads

to the sensing plates. During calibration the meter is in its normal operating

condition and thus responds to stray ambient fields. The interference of stray

fields proved to be least when the current limiting impedances were introduced

in a balanced configuration as shown in Figure 16,

Figure 16

Use of a voltage supply which was balanced to ground did not further

reduce the influence of stray fields.

An indication of the magnitude of interfering ambient fields may be obtained

by changing the phase relationship between the calibrating and interfering signals.

This may be done by interchanging the lead connections to the sensing plates of

the meter being calibrated or by reversing connections to the power supply. If

the calibrating voltage required for a given meter reading is the same for the

two arrangements, the interfering signal is negligibly small. If a small difference
-38-

exists, the average of the two voltage values is that which would be required in

the absence of i nterference

.

The manufacturer's instruction manual for the Type A meter implies a value

-12

of 100.8 x 10 ampere-meter/vol t for the current sensitivity. Choice of

impedance values and supply voltages are dictated by convenience except for the

4 limitations imposed by the input impedance of the meter—of the order of 10 ohms.

Examples of suitable impedance values for current calibrations of the meter

ranges of greatest interest are given in the following table:

Type A Field Meter

Range

kV/m

5

10

25

Impedance

(in each arm)

(ohms

)

1.5 x 10

6

5 x 10 6

Approximate Voltage

Full-Scale Deflection

(volts)

1.5

5

1.5 x 10 6 3

5 x 10 6 10

1.5 x 10 6 7.5

5 x 106 25

Type B Field Meter

lanqe Impedance

Approximate Voltage

Full Scale Deflection

kV/m (ohms

)

(volts)

3 10 6 0.6

10 7 6

10 10 6 1.9

10 7 19

30 10 6

6

10 7 60

As indicated in the text, resistors as series impedance elements in general are preferred. However, if the source voltage has negligible harmonic distortion

capacitors may be used instead.
-39-

Since the current calibration is intended only to monitor the stability of

the current measuring circuit by periodic calibration, the values of the impedances

need not be known with high accuracy. It is essential only that they be stable.

Thus, verification of the stability of the resistors used may be accomplished by dc

measurements, and the stability of the capacitors used may be determined by

measurements at 1 kHz— although in each case the values thus measured may differ

from those which exist at the frequency of use, 60 Hz.

Special shielding of the impedances is not required unless the values selected

differ by orders of magnitude from those given in the tables.

Care must be taken to insure that the calibrating voltage waveform closely

approximates a sine wave. As discussed in Section II.B.l.f, the percentage error

in the calibration resulting from a non-si nusoidal voltage waveform under certain

circumstances may be as large as the percent harmonic distortion existing in that

voltage. In general, iron-core transformers, being non-linear devices, are

sources of waveform distortions. The design of the adjustable voltage supply

for use in current injection calibrations should be examined carefully and checked

experimentally, if feasible, to assure its adequacy with respect to the requirement

of low distortion.

In view of these waveform considerations there is some advantage in using

resistors rather than capacitors as the series impedance elements in the circuits

of Figures 15 and 16. Since the admittance of a capacitor increases with increasing

frequency, the error contribution of the harmonic components of the source waveform

is larger with a capacitor than with a resistor.
-40-

III. Magnetic Field Measurements

An accessory is available from the manufacturer of the Type B electric field

meter which extends its use to the measurement of 60 Hz magnetic fields. An

adapter is provided to convert the field meter to a voltmeter mode. The probe

is an electrostatically shielded multiturn loop.

A. Instrument Performance

A magnetic field measuring instrument of the type described above was used to

measure the 60 Hz magnetic field (B-field) at the center of a calibrated 1.5 meter

Helmholtz coil. Prior to the ac measurements, a dc field was generated and found

to be uniform to within 0.2% over the volume of the field probe. This was determined

by nearly nulling the earth's magnetic field and measuring the field variations

over the volume of the probe to be calibrated with a sensitive magnetometer.

The errors in the measurement of fields over the range of 7 x 10"^ to

1.9 x 10" 4 tesla (0.007 to 1.9 gauss) using this particular instrument were as

indicated in Figure 17.

The influence of ambient electric fields on the operation of the magnetic

field probe was examined in a field near 5.3 kV/m using the parallel plate structure

described in Appendix B.i. A Helmholtz coil, with its axis parallel to the

E-field direction, was placed between the parallel plates. Measurements of the

background 60 Hz B-fields near the center of the parallel plate Helmholtz coil

system with and without the E-field showed an increase in the B-field reading

of about 0.15 milligauss in the presence of the E-field. This result was

independent of whether the Type B E-field meter and adapter were in or out of the

E-field, and independent of the orientation of the probe relative to the E-field.

The small perturbation of the B-field reading due to the E-field could also be seen

on the more sensitive ranges of the meter [1 10”^ tesla (0.01 gauss) full scale)

when a small B-field was applied with the Helmholtz coils; however, it could
-41-

_ r not be resolved on the higher meter ranges (1 10 tesla (0.100 gauss) full scale)

when the magnitude of the B-field was increased. These results indicate that

there was no serious inadequacy in the electrostatic shielding.

I Error

8

7 -

6

5

-•

a

y .

'V

4 ' 1-

u

2 5 10

_t) 2

Flux Density (Tesla)

Figure 17. Magnetic field measurement errors using a Type B electric field meter,

magnetic field probe and adapter. The uncertainties indicated in the errors result from measurement uncertainties in the 60 Hz calibrating

field.

Because the probe signal is dependent on the magnetic field frequency

(Faraday's Law), the discussion pertaining to the response of the Type B electric

field meter to field harmonics (Section II.B.l.f) is again applicable when

magnetic fields are measured.

B. Calibration of Magnetic Field Meters

Calibration of a magnetic field probe is typically done by introducing the

probe into a nearly uniform magnetic field of known magnitude and direction.

Helmholtz coils have frequently been employed to generate such fields, but the
- 42-

more simply constructed single loop (of many turns) with rectangular geometry has

also been used. The simplicity in construction is at the expense of reduced field

uniformity, but sufficient accuracy is readily obtained. The z-component of the

magnetic field produced by a rectangular loop of dimensions 2a x 2b is given by

the expression [14]

where

4

a-1

(-1)“ d.

r [r +(-l)“

+1

C ] a a a

C a

r (r +d ) a a a

N = number of turns

(7)

C-j = -C^ = a+x

^2

= ~^3 = a_x

d-j = d

2 = b+y

d

3

= d

4

= y-b

r

l ^(a+x)

2 + (b+y)

2 + z 2

r

2

= /

(a-x)

2 + (b+y)2 + z

2

r

3

= /

(a-x)

2 + (b-y)

2 + z 2

r 4

= ^(a+x)

2 + (b-y)2 + z

2

I is the current, is the magnetic permeability of air and the coordinates x, y,

and z are shown in Figure 18. The conductors in the current loop are assumed to be

of small cross section. It is noted for purposes of reference that
-43-

B

z (0,0,0) = y Q

I N v^/ua for a square loop of side dimension 2a. Equation 7 has

been used to calculate the field values at and near the center of a rectangular

loop of dimensions 5 m x 0.53 m. The percent departure from the central magnetic

field value at nearby points in the plane of the loop and 3 cm above the plane

of the loop are plotted in Figure 19. A similar plot is shown in Figure 20 for

a square loop having dimensions 1 m x 1 m. Also shown in Figures 19 and 20 is an

approximate outline (actual size) of the magnetic field probe. Examination of the

two figures indicates that the square loop, with a smaller cross sectional area,

provides a more uniform field.

Z

Figure 18. Coordinate system for current loop generating magnetic field B

z>

It should be noted that an error in centering a 12 cm diameter sensing coil

of 2 cm in any of the three orthogonal directions introduces an error of less than

V/o in the calibration. Any uncertainty in the effective loop dimensions is

reflected as the same percent error in the magnetic field produced.
-44-

y

Figure 19. Percentage departure of B

z from B

z (0,0,0) for positions in the plane

of a rectangular current loop 5 m x 0.53 m and 3 cm above or below

the plane (brackets)

.
-45-

y

Figure 20. Percentage departure of B z from B

z (0,0,0) for positions in the plane

of a square current loop 1 m x 1 m and 3 cm above or below the

plane (brackets).
-46-

Appendix A

Current Induced in Conducting Sphere by

Quasistatic Electric Field From Point Charge

The electric potential, U, at points exterior to an uncharged spherical

conductor of radius a in the vicinity of a point charge q(cot) can be shown to be,

using the method of images [15]

U (r,0,<f»,o)t)

1 4«

0

[.a. + al . si]

L r n r 0 r

J (Al)

where

r, = y 2 , ,2 Z Z ~

1 r + d - 2 rd cos 6

r

2 ^ + b^ - 2 rb cos e

q

= q sin wt = q (cot)

q' = - (a/d) q

b = a

2 /d

and d is the distance between the point charge and the center of the sphere;

q (cot) is assumed to have a quasistatic time dependence. The geometry of the

problem is shown in Figure Al

.
-47-

To determine the induced current, the surface charge density a is first found

from the relation

o = - e

_9U, o 3r 1 r=a

(A2)

The total induced charge Q on the hemisphere facing the point charge can then be

calculated using Equation A2 and differentiation with respect to time will yield

the current. Details of the algebra are briefly presented below.

Differentiating Equation A1 with respect to r and setting r = a yields

9U

3r r=a

q 1 r 1 - (a/d)

2

4 " c o ad

(1 + (a/d)

2

- 2 ( a/d ) cos e)

3/2

(A3)

It is convenient to rewrite Equation A3 as

8r

(1 + s' - 2s cos e 3/2

1 ] r=a

( A4)
-48-

where

E q/47re M od

2

and s = a/d. The surface charge density is, therefore.

a ‘of £ 0 - S^)

(1 + s 2

- 2s cos e)

3//2

- 1]

2 The radical can be expanded in powers of (s - 2s cos e) which is less than one;

4

for purposes of this derivation only terms of order s or less need be retained.

Performing the term by term integration of the expanded a over the surface of the

top hemisphere leads to

2tt tt/2 ^ Q = / / a a sin 9 de d<j> o o

= 3tt£ o Ea

2

[1 - (7/12) s 2 + ^ s 4 + ...] . ( A5

)

The current which flows between isolated hemispheres is given by

1 = ft

= 3 t,£ o“

E a? [1

2 4

-L ( i) + II (!) ] 12 ^d ; 24 V "* J (A6)

It should be noted that Equation A6 has been derived for the case when the

hemispheres are aligned with the E-field direction.
-49-

Appendix B

The Electric Field Between Parallel Plates

--One Plate Grounded

While conceptually the calibration procedure of introducing a field meter,

at the end of an insulating rod, between electrically energized parallel plates

seems straightforward, the following effects must be considered in order to

establish a well defined E-field: (i) perturbation of the surface charge density

on the plates, a, by the field meter, and (ii) perturbation of o by nearby ground

planes. These effects are now considered in some detail both theoretically and

experimentally. The effectiveness of guard rings in reducing the influence of

fringing fields and of nearby ground planes is also explored experimentally (iii)

and theoretically (iv).

( i

)

Perturbation of Surface Charge Density By Field Meter

Theory . Ideally the parallel plates should generate a uniform field of

sufficient extent in space that introduction of the field meter introduces negligible

perturbation of the field or charge distribution at the plates. Estimation of

surface charge density perturbations has been made in the following way. First a

conducting sphere or ellipsoid of appropriate dimensions is chosen to represent

the field meter (animals in biological experiments have similarly been represented).

It is next considered to be introduced into a uniform field, and perturbations of

the uniform field in a plane, where one of the metal electrodes for producing the

field will eventually be placed, are calculated from known solutions to the problem

(see, for example, Battelle Northwest Interim Progress Report to ERDA, "Biological

Effects of High Strength Electric Fields on Small Laboratory Animals," September 1976.

A draft dated April 1976 on E-field measurements prepared by CIGRE Working Group 36-01
-50-

also considers the problem in a similar way). It is then assumed that the

perturbation of the surface charge density, a, on a conducting surface located

in the plane will be nearly the same percentage as that of the field perturbation

because of the direct proportionality between the surface charge density and the

electric field at the surface.

The perturbed electric field E for the case of a sphere is given in spherical

coordinates by [16]

3

2

^V) cos

2

e + 0 - TT>

r sin e]

1/2

(Bl)

where a is the radius of the metal sphere, r is the radial distance from the

sphere's center and 0 is the angle the position vector r makes with E . Equation Bl

indicates that for a sphere of radius 10 cm, E/

E

q has come within 1% of the uniform

value when r = 60 cm and 50 cm for e = 0 and 90 degrees respectively.

Experiment . To test this approximate theory experimentally, a parallel plate

apparatus was constructed which permitted measurement of the surface charge density

on one of the plates. A schematic view is shown in Figure Bl . Two metal sheets

122 cm x 92 cm are separated by a distance of 38 cm. The top plate is connected

to a 60 Hz high voltage source and the bottom plate, with the exception of ten

isolated segments, is connected to ground. The E-field induced current, I, in

the isolated segments is measured with an operational amplifier and rms reading

digital voltmeter. A switching system grounds all the segments except one which is

being monitored. After the current has been measured, the rms value of the electric

field averaged over the area, A, of the segment is determined from the relation

E

=

I

1 20tT£ A

• o

(B2)
-51-

Figure B1 . Schematic view of apparatus for perturbation measurements.

Here e Q

is the permittivity of free space. Equation B2 is obtained by applying

Gauss' Law to the isolated segment and differentiating with respect to time.

Figure B2 shows measured values of the electric field as a function of distance

from the edge of the bottom plate with no objects placed between the plates. Each

value has been normalized by the "uniform field," E , measured at the center of the

plate. The experimental value, E q

, is within ±0.4% of the theoretical value V/t,

where V is the applied rms voltage and t is the plate spacing. The observed

discrepancy is comparable to the largest experimental uncertainty which is the

value of the center segment area A.

Also shown in Figure B2 is the theoretical normalized field dependence as a

function of position [11]. Good agreement is seen between experiment and theory for

distances up to about 25 cm from the plate center. For positions closer to the
-52-

edge, the experimental data are consistently lower in value. Qualitatively, much

of this is explained by the absence of any surrounding ground planes in the

theoretical treatment of the problem (see Appendix B.ii, below).

Measurements of surface charge densities on the bottom plate of a parallel

plate system before and after the introduction of isolated conducting spheres were

E/Ec

Figure B2. Experimental and theoretical field distribution along bottom plate.

subsequently made. The perturbation of the surface charge density directly below

the sphere was compared with the predictions of Equation B1 for 6=0

+ 2 4> r

{ B3)
-53-

The results “are tabulated below.

I

sphere radius (a)

( i ) 3 . 83 cm

| (ii) 2.37

(iii) 2.37

distance r

3

(°/%) = 1 +2 ( 7) (a/a ) 0

est.

r meas.

19.3 cm 1 .0156 1.030

18.5 1.0042 1.010

20.0 1.0033 1.006

The measured a/a

Q

values are believed to be accurate to within ±0.1%. It can be

seen that for the chosen a/r values, the estimated perturbations are in error by

a factor of about two. The error can be expected to increase for larger a/r ratios

|

,

because introduction of a conducting surface in the E-field will enhance the field

at an increasing rate as qualitatively shown in Figure B3.

I'

I

1

Figure B3

Using scaled-down versions of the two types of electric field meters, the

field perturbation at the center of the bottom plate was measured as a function of
-54-

height, H, above the plate. The results for metallic boxes approximately 1/2 and

1/3 the size of the Type B meter and approximately 1/3 the size of the Type A meter

are shown in Figure B4. The perturbed field, E , has been divided by the

experimental value of E . The height H is measured from the box center to the

plate surface. It can be seen that in all cases, the field perturbation at the

center of the bottom plate exceeds +1% when the metallic boxes are midway (19 cm)

between the plates. The same effect occurs at the top plate.

Perturbation measurements were also made at other points along the bottom

plate as the height of the simulated meters was varied. A metallic box approximate!

1/2 the size of the Type B meter was used to obtain the data presented in Figure B5.

The data show that the influence of the box becomes negligible as positions closer

to the plate edge are monitored.

Figure B4. Field perturbations at center of bottom plate produced by modeled

field meters.
-55-

Discussion

Concern regarding the magnitude and distribution of the field perturbation

at the plate surface arises because of the "feedback" effect on the E-field at

the location of the field meter which is to be calibrated. A perturbed field at

the plate surface means that the surface charge distribution a (= E p

/

E

q

) has been

changed. If this modified a is hypothetical ly "frozen" in place, the E-field

at the position of the field meter, r, (with the meter removed) can be calculated

using the expression [17]

E(r

)

-V -> a da (r-r*

)

r-r

1 3

(B4

)

The quantities da, r', and r are shown in Figure B6. Calibration of a field

meter at position r to an accuracy of N% requires that the calculated value of E

at r and the surrounding volume to be occupied by the meter not differ from E q

by more than N% in magnitude (it is assumed here that the field direction has

not significantly changed).

It is noted that an increase in o of N% at the center of the bottom plate

results in less than a N% "feedback" effect midway between the plates. That this

is the case can be seen by an examination of Figures B5 and B6 and Equation B4.

The field midway between the plates is a superposition (Equation B4) of fields

originating from "charges," a da. Because the perturbation of a becomes

i, negligible near the plate edges where much of the charge is located, the summation

given by Equation B4 will differ from the unperturbed case by less than N%. This

analysis was confirmed with a numerical calculation of E (Equation B4) at the

center of a 3 m x 3 m x 1 m spacing parallel plate system with a 2% charge density

perturbation at the plate surfaces directly above and below the meter. The

"feedback" effect was found to be only a few tenths of a percent.

ji
Figure B5. Distribution of perturbation at bottom plate.

(contributions from top plate omitted for clarity)

Figure B6
-57-

( i i ) Perturbation of Surface Charge Density By Nearby Ground Planes

As noted in Figure B2, the field intensity near the bottom (grounded) plate

edge was less than predicted by theory. This was attributed to the presence of

nearby ground planes. To systematically study this source of perturbation, a

much smaller parallel plate system, similar in design to the one described above,

was constructed. Details of the smaller parallel plate structure are shown in

Figure B7. Layers of aluminum foil (% 0.0025 cm thick) sandwich an insulating

sheet of paper 0.005 cm thick) and are glued to a flat supporting plexiglass

plate (22.9 cm x 30.5 cm x 0.6 cm) to form the bottom plate. The (rms) current, I,

induced in the isolated segments of the top sheet of aluminum is measured and

the E-field averaged over the segment area A (nominally 1 x 8 cm ) is calculated

using Equation B2. The bottom grounded aluminum sheet must be employed to

eliminate fringing E-field lines terminating on the underside of the isolated

segments. Similar shielding was used on the larger parallel plate structure.

The supporting plexiglass plate does cause some field enhancement at the

edge of the plate (^ 10%). This perturbation, however, is essentially independent

of the nearby ground planes and thus does not affect measurements of relative

field changes as the parallel plate structure is moved closer to the ground planes.

Dielectric rods 10.2 cm x 0.6 cm diameter were used to separate the plates.

A difficulty encountered while using this parallel plate structure was the

E-field perturbation produced by the energizing high voltage lead. This was not

a significant problem with the larger parallel plates because of some self-shielding.

The following measurement procedure was adopted to eliminate the problem. For a

fixed distance between the ground plate (wall or floor) and parallel plates, the

field distribution along the bottom plate is measured at average distances of

0.5, 2.0, 4.0, 8.0, and 11.4 cm away from the edge. Keeping the geometry fixed,

a second high voltage lead is connected to the top plate and the field distribution
-58-

BOTTOM PLATE

Figure B7. Construction details of smaller parallel plate system.

measurement is repeated. Because the perturbations of the two leads are additive

(superposition principle), the difference between the two sets of measurements

represents the perturbations introduced by the second high voltage lead. Finally,

the field distribution is measured again with only the second high voltage lead

connected. The perturbations introduced by the second lead are then simply

subtracted from this last set of measurements. The distance between the parallel

plates and ground plane is changed and the procedure is repeated.
HEIGHT ABOVE FLOOR (cm)

Figure B8. Perturbation of electric field (surface charge density) at plate

surfaces because of floor proximity.
-FIELD

PERTURBATION

(%)

-60-

WALL DISTANCE TO PARALLEL PLATE EDGE (cm)

Figure B9. Perturbation of electric field (surface charge density) at plate

surfaces because of wall proximity.
-61-

Figure B8 shows how the E-field along the bottom plate (B) is disturbed as a

i function of height above the floor. The distance between the plate edge and nearest

wall is about 150 cm for all heights.

Figure B9 shows similar results as the distance between the parallel plate

edge and wall is varied. It is noted that for the outermost element (0.5 cm),

the field is normalized to zero perturbation at 170 cm. Field perturbations due

to the wall actually continued to greater distances for this element, but the limited

room size prevented gathering of additional data (the influence of the opposite wall

became apparent). The height above the floor was fixed near 150 cm.

Because the E-field at the surface of the energized plate could not be directly

monitored (with current measuring electronics), the perturbations at the energized

plate were determined indirectly by raising the potential of the ground planes to

the value of the energized plate and measuring the perturbation of the grounded

plate as shown schematically in Figure BIO.

V (60 Hz)<

"FLOOR"

V (60 Hz)

- 1

'

" WALL" AV

it Figure BIO

With this configuration, the distance between an energized "wall" 2.5 m x 2.3 m

and a "floor" 1 m x 1 m was varied and the perturbation of the E-field at the

grounded plate was measured. The results (T) are shown in Figures B8 and B9.

The data show that under normal conditions (i.e., wails and floor at zero
w

-62-

potential) a much greater perturbation occurs at the energized plate. Because

the "floor" in Figure BIO was represented by a 1 m x 1 m screen, the accuracy of the

floor perturbation data in Figure B8 is not well known. The accuracy improved as

the distance was decreased.

( i i i ) Effectiveness of Guard Rings For Reducing External Perturbations

Guard rings have commonly been used to isolate the E-field between the plates

from external perturbations as well as to establish a larger region of field

uniformity by reducing the effect of fringing fields. Theoretical treatments

of the problem for the case of cylindrical symmetry are described below.

From visits and discussions with workers concerned with field meter

calibrations, it has been learned that the number of guard rings employed has

varied from three or four to much larger numbers for plate spacings of comparable

size. This prompted a systematic study of the effectiveness of guard rings using

the smaller parallel plate structure.

Initially, thirty-one equally spaced guard rings (0.3 mm diameter copper wire)

were used to grade the electric field at the perimeter of the parallel plates as

shown in Figure Bll. The potentials applied to the guard rings were graded with a

resistor divider linearly from top to bottom within a few tenths of a percent.

o (The resistor values chosen were all within ±0.1% of 6.203 x 10 ohms, a value

which is sufficiently small to shunt stray capacitance). The distance between

the floor and the parallel plate structure was changed and the electric field

was monitored at selected points along the bottom plate. Similarly, the distance

between the wall and the parallel plate structure was varied and the E-field

distribution was again monitored. This procedure was repeated with the number

of guard rings successively reduced to 15, 7, 3, and 1.

Figure B12 shows how the E-field along the bottom plate is perturbed as a

function of height above the floor and for different numbers of guard rings.
-63-

Similar data are shown in Figure B13 as the distance between a nearby wall and the

RESISTOR

DIVIDER

Figure Bll . Parallel plates with 31 guard rings.

I parallel plate edge is varied. Although error bars are not indicated, the

perturbation values are estimated to be accurate within ±0.5%.

Discussion: The data in Figures B8 and B9 indicate that a parallel plate

system with one plate grounded is very susceptible to perturbations from ground

planes, even when they are quite distant. While the results show the perturbed

field only on the inner plate surfaces, the qualitative conclusion can be made

that the E-field will be enhanced at and near the energized plate (T) and will

decrease as the grounded plate (B) is approached. Even at the center of the

plates, a measurable change can be expected when the walls are within a distance

of two plate spacings away. This was confirmed experimentally with the

3 m x 3 m x 1 m structure described in Section II. C. 3 using the commercial field

meters to measure E.
-64-

o

H

<

m

crD

l—

cnUJ

OlQ

_lUJ

U_

i UJ

Figure B12. E-field perturbation as a function of height above the floor and

number of guard rings (31, 15, 7, 3, 0).

The data in Figures B12 and B13 show that a few guard rings are relatively

inefficient for isolating and creating a greater region of uniform field

between the plates with one plate grounded. They do improve conditions, however,

and considerable advantage was gained in their use with one of the smaller

calibration facilities described in Section II. C. 4.

ii

ki
-FIELD

PERTURBATION

(%)

-65-

WALL DISTANCE TO ti-PLATE EDGE

0

-10

-—•* W ••• *—*-

1 1

1 1.4cm (MIDPOINT)

i

i i i 1— 1

i

Figure B13. E-field perturbation as a function of distance from wall and

number of guard rings (31, 15, 7, 3, 1, 0).

(iv) Parallel Plates With Guard Rings

The region of near-uniform field between two finite parallel plates may be

increased by the use of guard rings to properly grade the potential in the space

between the outside edges of the plates. A detailed discussion of this technique

is presented in the article, "An Absolute Electrometer for the Measurement of
- 66 -

High Alternating Voltages," by H. B. Brooks, et. al [18]. Because the theoretical

development is relatively straightforward, only an outline is presented here.

Further details as well as a description of a parallel plate apparatus employing

guard rings can be found in Ref. 18.

The geometry of the problem is shown in Figure B14. Two circular plates of

radius R are separated by a distance b. A voltage divider, made up of capacitors

of value C provides for a nearly linear potential change of the guard rings along

the bounding cylindrical surface. A limit bn the degree of linearity of the change

in guard ring potential is set principally by capacitive coupling to surrounding

objects.

The problem is attacked by first determining the electric potential, V(r,z),

in the cylindrical volume by solving Laplace's equation

9 2 V 1 3V

3r

2

9 2V

3Z

2

2

3 V

3(f) 2

= 0 ( B5

)

The electric field is then found by calculating the gradient of V(r,z).

Because of the symmetry with respect to <t> , the last term in Equation B5

vanishes. The boundary conditions for V(r,z) are

z = 0, V = 0 for all r values

z

= b, V=V for all r values (B6)

a

r = R, V = V

R (z)

where V

R (z) describes the potential distribution at the cylindrical boundary.

It is assumed to have the form

v R(z) = v

a

* §

+ v

a

1 \

sin ( kTrZ / b ) (B7)

k=l
-67-

c

c

c

Figure B14

where the first term describes the ideal linear change in potential and the second

term is a Fourier sine series giving the departures from linearity.

The procedure for solving Laplace's equation is the well known separation

of variables method [19]. A solution of the form

V = V

a z/b + F-j ( z ) F

2 (r) ( B8)

is assumed. Carrying out the differentiation indicated by Equation B5, leads to two

differential equations. One is Bessel's equation of zeroeth order

2

8 Fp , 3F — 9 9

f- + -— - y F 9 = 0

„ 2 r ar 2 ar

(B9

)
- 68 -

with the solution

F

2 = J o (iyr) .

The second equation

(BIO)

with the solution

3F3Z

+ y F- = 0

F, ( z ) = V (A cos yz + B sin yz) . a

(BID

(B12)

Because the separation constant y is arbitrary, the general solution to Laplace's

equation is found by summing over all possible solutions (i.e., with all possible

y's) and hence

V = V z/b

a + V Z [A. COS y. a k=1k z + B

k

sin

'k z] (B13)

Applying the boundary conditions, B6 and B7 yields

00 J (ikirr/b)

V = V

a 2/b + V

a ^

G

k sin (k«/b) • jo(ikT, R/b) • (B14)

The Bessel functions with imaginary arguments can be replaced by modified

Bessel functions [20] I with real arguments. We have then
-69-

I Ckirr/b)

o V V

a z/b + Va

* G

k

si " < k " z/b > ' T^Wbl (B15)

The Fourier coefficients, G^, are given by the approximation [18]

o n V , G

k = TiTT

E

,

( r - W\ ] Sln W k = ’• 2 --- n m= I a (B16)

Here n is the number of guard rings and Vm

is the measured potential of the mth

guard ring. As n is increased, the accuracy of the approximation. Equation B16,

improves, but the interested reader is encouraged to consult the relevant portions

of Ref. [18] to understand some of the subtleties of this approximation. With

increasing numbers of guard rings, n, the values of decrease so that all values

of G^ need not be used in the summation. Equation B15.

The two components of electric field are given by

E =-^ z az

E = - — r 9r

(B17)

Performing the differentiation on Equation 15, we have

- I (kirr/b)

E z

= ' E o ^ + k7rG

k cos ( k7TZ/b ^ * l°(kTrR/b)

= E oM (B18)

and
-70-

00 k.r7 Mk7Tr / b ) E = -E r Z kTTG. sin

^~n D/ . J = E N

r o

L

, _ n k b I (kfTR/b) J o (B19)

k=l

where E q

= V

g /b. The magnitude of the electric field relative to the uniform

value in the interior, if the plates were sufficiently large, is given by

^ = [M2 + N

2

] V2

0

(B20)

An alternative approach to the use of guard rings is to replace the rings with

bands of metal separated by narrow air gaps [13]. Far greater isolation from nearby

ground planes is attainable.

F
-71-

Appendix C

Ground Referenced Electric Field Meters

As noted earlier, ground referenced E-field meters have been used to measure

transmission line fields. Perhaps the most well known are the Miller meter [1] and

the "one square meter panel" [2] which has been used for calibration purposes. The

principle of operation of these two instruments is the same and an analysis is

now presented which indicates under what conditions the devices yield correct

results.

Schematic views of the Miller meter and the "one square meter panel" in the

presence of a quasistatic-uniform transmission line E-field, E q sin wt, are shown

in Figure Cl

.

CENTRAL

ELECTRODE

GUARD H

HOUSING

E 0 sin cut CENTRAL

SHIELDING ELECTRODE

|E 0 sin cut GUARD

t/TT////K/rrrmt

EARTH Cl) ^Itf-—SHIELDING AC^ 4r

AMMETER

AC

AMMETER

Figure Cl

Application of Gauss' Law to the central electrodes permits the derivation of the

relation

I = a) e A E sin wt

o (Cl)
- 72 -

where I is the induced current, e q

is the electric permittivity of space, E is

the electric field at the metal surface and A is the area of the central electrode.

Measurement of the current permits the determination of the E-field at the metal

surface. While Equation Cl is a valid expression for determining E at the surface

of the metal, it can be used to determine the uniform field, E , only under certain
-73-

where K is the space potential at z=0 prior to the introduction of the sphere.

The explicit sinusoidal time dependence of K is suppressed. At the surface of

the sphere (r=a), the magnitude of E is

r K-V , .3 r

E = —— + 3 E„ sin wt cos e a o

(C3

)

and the surface charge density is given by

O = E E = e + 3 E n sin wt cos e]

o" a (C4)

The total induced charge Q on the central electrode is found from the surface

integral

0 2 7T o

2

Q = / / a a sin e d<j> de

o o

= C-j (K-V) + C

2

E q

sin u)t (C5

)

Here C-j and C

2 are constants. The induced current for two cases is now considered,

(a) K = V. If the potential of the sphere is the same as the space potential K,

I - -r?- - u) C<5 E COS cot dt Z 0

(C6)

and the uniform field may be determined by measuring the current. Examples of this

case are the Miller meter and the one square meter panel operating at ground level,

i.e., V = K = 0. Allowing the sphere to electrically "float" in space is yet

another example where K = V and Equation C6 is valid. The commercial ac E-field

meters currently available in the U.S. operate under this condition.
-74-

(b) K + V. If the sphere's potential is maintained at some constant value, the

induced current becomes

1 =

eft = w C1 K + c

2 w E 0

sin wt • (C7)

Thus, the induced current will depend on the space potential K as well as the

uniform field magnitude. Moving the sphere to higher elevations above ground, where

the space potential is larger, will result in greater induced current. For

example, choosing V = 0 and K + 0 corresponds to the case of the Miller meter or

the "one square meter panel" being raised above the ground level (with the ammeter

still connected to true ground). This condition can develop for both devices even

when they are resting on the earth's surface. If the ground is sufficiently dry,

the true ground could be well below the surface and the induced current would then

be proportional to something other than just the uniform field value E q

.
- 75 -

Appendix D

Miniature Electric Field Probe

The theoretical discussion in Appendix C notes that a spherical E-field

probe, if it is to work properly, must be at the same electric potential as the

unperturbed space potential at the location of the sphere's center prior to

introduction of the probe. This condition is achieved for large E-field meters

by electrically isolating or "floating" the probe (sensing plates) from ground

with an insulating rod which is used to support the meter in the field; the

battery operated electronics are incorporated between the sensing plates.

A miniature E-field probe which is well removed from its battery operated

electronics has been developed and is shown schematically in Figure D1 . Shielded

wires rather than glass fiber optics [6,21] are used to couple the probe to the

electronics. The induced charge on the hemispherical sensing plates is measured

(similar to Type A meter) with a differential amplifier that is contained in an

electrically biased chassis box. This bias is adjusted to be the space potential

in the equatorial plane close to the equator of the spherical probe and is set

using the potentiometer— space potential probe-high impedance voltmeter combination.

A voltage null indicates when the bias is appropriately set. The space potential

probe consists of the open end of an otherwise 100% shielded miniature coaxial

cable and is brought near the field probe in the equatorial plane (see Figure D1

inset). Because one input of the differential amplifier is effectively connected

to the chassis, the potential of both hemispherical sensing plates and the shielding

will be "floating" at the appropriate potential when a null is achieved [22].

The space potential probe is removed during field measurements.
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Calibration of the E-field probe and electronics is readily performed with a

small parallel plate structure. Because of its size (1.2 cm diameter), the probe

will not significantly perturb the parallel plate surface charge densities

(Appendix B.i) when the plate spacing is as small as 20 cm.

Figure D1 . Simplified schematic view of miniature E-field probe, space potential

probe, and associated electronics. The inset shows the E-field probe

sensing surfaces. Two orthogonal field components can be measured

without changing the probe orientation.
- 77 -

The miniature E-field probe has proven to be useful in obtaining E-field

"maps" for parallel plate structures used for calibrating E-field meters

(Section II. B. 4). It has also been used in a similar fashion to characterize

E-fields in small parallel plate structures used for biological experiments.

Probes consisting of miniature parallel plates have also been fabricated and

used with success in the above measurements. The spherical probe shown in the

inset of Figure D1 , with sensing elements consisting of quarter spheres, is

designed to measure two perpendicular components of the E-field.

Acknowledgment

The authors are pleased to acknowledge the careful editorial and typographical

assistance of J. C. Pal la during the preparation of the manuscript.
-78-

Notes and References

1. C. J. Miller, "The Measurements of Electric Fields in Live Line Working,"

IEEE Trans. Power App. Syst. , vol . PAS-86, pp. 493-498, April 1967.

2. Transmission Line Reference Book - 345 kV and Above , Electric Power Research

Institute, Palo Alto, California, 1975, p. 274.

3. The surface charge density is given by 3 e Q

E cos e [J. R. Reitz and F. J. Milfc

Foundations of Electromagnetic Theory . (Aadison-Wesley, Reading, Mass., 1960)

p. 52]. Integration over the hemisphere gives Eq. 2.

4. The percent error is calculated by first determining the analog reading when

a given harmonic is present (see, e.g., E. Frank, Electrical Measurement Analysi

McGraw-Hill, 1959, pp. 303-309) and comparing it with the true rms value for the same waveform. That is

% Error = [^-eX?.ged mS" Reading - True RMS ReadM] 10Q True RMS Reading

See also

M. R. Negrete, "The Effects of Distortion on AC Voltmeters," Wescon Technical

Papers, Vol. 9, Part 6 (1965) and

W. G. Smith, "...What's Wrong With DVM AC Measurements," EEE: The Magazine of

Circuit Design Engineering, March 1971, pp. 52-56.

5.

Private communication from T. D. Bracken, Bonneville Power Administration,

Portland, Oregon.

! 0 .

6.

L. Wilhelmy, "Potential freie Feldstarkemessung im raumladungsfreien

periodisch zei tabhangigen und transienten elektrischen Feld," Thesis, University

of Stuttgart, 1972. (An English translation is available from Xerox University

Microfilms, Ann Arbor, Michigan. >11

7.

See IEEE Power Engineering Society Special Publication Number 10 (1975) for

translation of Russian article "Rules and Regulations on Labor Protection

at 400, 500, and 750 kV AC Substations and Overhead Lines of Industrial

Frequency (In the U.S.S.R.)."

8.

V. P. Korobkova, Yu. A. Morozov, M. D. Stolarov, and Yu. A. Yakub, "Influence

of the Electric Field in 500 and 750 kV Switchyards on Maintenance Staff and

Means For Its Protection," 1972 CIGRE Paper 23.06.

9.

Yu. A. Morozov and 0. M. Gromov, "Device For The Measurement of Industrial

Frequency Electric Field Intensity," Ref. 7 Translation.

0 . L. B. Young, Report to the U.S. Environmental Protection Agency on Effects of

Extremely High Voltage Transmission, July 1, 1975.
-79-

1. P. D. Thacher, "Fringing Fields in Kerr Cells," Sandia Report SLA-74-0302 (1974).

See also IEEE Trans. Elect. Insul

.

, vol. EI-11, pp. 40-50, June 1976.

|2. A clear introduction is provided in S. Ramo and J. R. Whinnery, Fields and

Waves in Modern Radio (John Wiley & Sons, 1953), pp. 127ff. See also Ref. 14.

3. B. Barber, "The Basic Design Data of a Guarded-Field Thimble Ionization Chamber:

A Theoretical Investigation," Phys. Med. and Biol., vol. 4, 1-9, 1959;

i| L.A.W. Kemp and B. Barber, "The Basic Design Data of a Guarded-Field Thimble

Ionization Chamber: A Precision Ionometric Investigation," Phys. Med. and

Biol. , vol. 3, 123-137, 1958.

4. See E. Weber, Electromagnetic Theory . (Dover, New York, 1965), p. 131 f f for

outline of derivation.

|

15. See Ref. 3, p. 59ff.

16. P. Moon and D. E. Spencer, Field Theory For Engineers (D. Van Nostrand, 1961),

p. 225ff

.

17. See Ref. 3, pp. 25-26.

18. H. B. Brooks, F. D. Defandorf, and F. B. Silsbee, J. Research NBS 20^, 253

(1938). See also Ref. 12, p. 156 for details of a related problem.

19. R. V. Churchill, "Fourier Series and Boundary Value Problems," (McGraw-Hill,

1941), p. 24ff

.

I20. M. Abramowitz and I. A. Stegun, ed. Handbook of Mathematical Functions , NBS

Applied Mathematics Series 55 (1964), p. 374ff.

21. A. R. Valentino, Proc. IEEE International Symposium on Electromagnetic

Compatibility, p. 265 (July 1972) (unpublished); available as IITRI Report

No. AD 742128 from NTIS, Springfield, Virginia 22161.

(22. In a uniform E-field, the unperturbed space potential, <f>p, at Z = 0 (Figure C2)

will be equal to the potential value in the equatorial plane after an electrically isolated sphere is introduced into the field. In the present

case, the sphere is initially at some arbitrary potential <|> =j= <j> 0

, and the

equatorial plane near the sphere will not be at the appropriate potential <|> 0

. As the voltage difference between the sphere and space potential probe is

reduced, however, the potential surfaces near the sphere approach the geometry

which is characteristic for an electrically isolated sphere.