A11102 4A741D

NBS Ambient Magnetic Field Meter for

Measurement and Analysis of Low-Level

Power Frequency Magnetic Fields in Air

P. M. Fulcomer

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Center for Electronics and Electrical Engineering

Electrosystems Division

Gaithersburg, MD 20899

December 1985

Prepared for: Department of Energy

Office of Electric Energy Systems

nr jnue, S. W.

100

• U56

86-3330

1985

NBS research information CENTER

NBSIR 86-3330

NBS AMBIENT MAGNETIC FIELD METER FOR

MEASUREMENT AND ANALYSIS OF LOW-LEVEL

POWER FREQUENCY MAGNETIC FIELDS IN AIR

P. M. Fulcomer

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Center for Electronics and Electrical Engineering

Electrosystems Division

Gaithersburg, MD 20899

December 1985

Prepared for: Department of Energy

Office of Electric Energy Systems

1000 Independence Avenue, S. W.

Washington, DC 20585

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Director

TABLE OF CONTENTS

Page

LIST OF FIGURES iv

Abstract 1

1 . INTRODUCTION 1

2. INSTRUMENTATION 2

2.1 General Specifications and Design Considerations 2

'2.2 The Probe 4 2.3 The Detector . 8

3. CALIBRATION. 15

3.1 General Considerations 15

3.2 Calibration Procedure for the Least Sensitive Ranges 16

3.3 Calibration Procedure for the Most Sensitive Ranges 18

3.4 Calibration Uncertainties 22

4. SAMPLE MEASUREMENTS. . 30

5. ACKNOWLEDGMENTS 46

6. REFERENCES 47

APPENDIX 48

iii
LIST OF FIGURES

Figure 1 .

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.

Figure 8.

Figure 9.

Figure 10

Page

AMFM-1 frequency response as function of signal amplitude.

Frequencies at which clipping occurs (see text) for

the various scales are indicated 5

Equivalent circuit of AMFM-1 magnetic field probe.

R^

n

is the approximate detector input impedance 7

Test set-up for determining the approximate value of the

resonant frequency, f , of the magnetic field probe 7

Calculated frequency response for the AMFM-1 magnetic

field probe (ratio of probe output voltage to the emf

induced by the field vs. frequency of the field) using

various values for the detector input K resistance, R 9 in

Oscilloscope display of the magnetic field waveform

superimposed on waveform of the output signal from AMFM-1

Amplitudes of the two waveforms have been made equal for

purposes of comparison 11

Spectrum analyzer display indicating frequency components

of the waveforms shown in figure 5. The traces for the two

waveforms are superimposed 11

AMFM-1 circuit diagram. Approximate amplifier gains

are shown beside the range switch positions. The gain

of amplifiers A1 , A2, A3, and A5 is determined by range

switch sections SI, S2, S3, and S4, respectively.

Buffers A4 and A6 have unity gain. Stage A7 is part of

the half-wave rectifier supplying output amplitude

information to the analog panel meter. This panel meter

is used to obtain a peak reading, and also to measure

battery voltage when the on, off switch is in the battery

check positions (V+ or V-)The digital panel meter

indicates magnetic field strength 13

Test set-up and basic procedure for AMFM-1 calibration

by voltage injection 21

Angles formed between the axis of a solenoid and

lines joining a point, P, along the axis to the outer

edges of the solenoid 25

Spectrum analyzer vertical scale correction 37

iv
LIST OF FIGURES (continued)

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Page

lla. Oscilloscope display of laboratory ambient magnetic field

waveform. Overhead fluorescent lights on. AMFM-1

indication = 42 nT rms. Vertical scale = 50 nT/div.

Horizontal scale = 5 ms/div 33

llb. Absolute scale spectrum analyzer display of figure 11a

waveform showing the significant harmonics to be the first,

third, and fifth. Vertical scale = 10 nT/div.

Horizontal scale = 50 Hz/div. ...... 33

llc. Normalized spectrum analyzer display for the waveform

of figure 11a (laboratory ambient field with overhead

fluorescent lights on). Percentage of harmonics relative

to the fundamental can be determined from this display after

applying correction factors from figure 10.

Horizontal scale = 50 Hz/div 35

12a. Oscilloscope display of laboratory ambient magnetic field

waveform. Overhead fluorescent lights off. AMFM-1

indication = 27 nT rms. Vertical scale = 50 nT/div.

Horizontal scale = 5 ms/div 34

12b. Absolute scale spectrum analyzer display of figure 12a

waveform showing the significant harmonics to be the first,

third, fifth, seventh, and ninth, Vertical scale = 10 nT/div.

Horizontal scale = 100 Hz/div 34

12c. Normalized spectrum analyzer display for the waveform of

figure 12a (laboratory ambient field with overhead fluorescent

lights off). Horizontal scale = 100 Hz/div 35

13a. Oscilloscope display of office ambient magnetic field

waveform. Computer terminal/disc drive on. AMFM-1

indication » 0.32 pT rms. Vertical scale = 0.2 pT/div.

Horizontal scale = 5 ms/div 36

13b. Absolute scale spectrum analyzer display of figure 13a

waveform showing the major harmonics to be the first, third

and fifth, with contributions from many others. Vertical

scale = 0.1 pT/div. Horizontal scale = 100 Hz/div 36

13c. Normalized spectrum analyzer display for the waveform

of figure 13a (office ambient field with computer

terminal/disc drive on). Percentage of harmonics relative

to the fundamental can be determined from this display after

applying correction factors from figure 10.

Horizontal scale = 100 Hz/div 38

v
LIST OF FIGURES (continued)

Page

Figure 14a. Oscilloscope display of office ambient magnetic field

waveform. Computer terminal/disc drive off. AMFM-1

indication = 0.32 pT rms. Vertical scale = 0.2 pT/div.

Horizontal scale = 5 ms/div 37

Figure 14b. Absolute scale spectrum analyzer display of figure 14a

waveform showing the significant harmonics to be the first,

third, fifth and seventh. Vertical scale = 0.1 pT/div.

Horizontal scale = 100 Hz/div 37

Figure 14c. Normalized spectrum analyzer display for the waveform of

figure 14a (office ambient field with computer terminal/disc

drive off). Horizontal scale = 100 Hz/div 38

Figure 15a. Oscilloscope display of ambient magnetic field waveform

obtained in a home, 30 cm from, and on same level with

a section of unloaded 120 V ac branch circuit wiring located

within the wall. AMFM-1 indication - 10 nT rms. Vertical

scale = 10 nT/div. Horizontal scale = 5 ms/div 39

Figure 15b. Absolute scale spectrum analyzer display of figure 15a waveform

showing the significant harmonics to the first, third, fifth,

and ninth. Since the amplitude of the first harmonic falls at

the top of the verticle scale, this figure can also be used

as the normalized spectrum analyzer display. Vertical

scale = 1.0 nT/div. Horizontal scale = 100 Hz/div 39

Figure 16a. Oscilloscope display of ambient magnetic field waveform

obtained in a home, 60 cm from the front center of an operating 26-inch screen television set. AMFM-1

indication = 0.17 pT rms. Vertical scale =* 0.2 pT/div.

Horizontal scale = 5 ms/div 40

Figure 1 6b . Absolute scale spectrum analyzer display of figure 1 6a waveform

showing a number of significant harmonics which decrease in

amplitude from the second through the nineteenth. Vertical

scale = 0.2 pT/div. Horizontal scale = 200 Hz/div 40

Figure 16c. Normalized spectrum analyzer display for the waveform of

figure 1 6a (home ambient field 60 cm from front of operating

26-inch TV). Percentage of harmonics relative to the

fundamental can be determined from this display after

applying correction factors from figure 10.

Horizontal scale = 200 Hz/div 41

vi
LIST OF FIGURES (continued)

Page

Figure 1 7a. Oscilloscope display of ambient magnetic field waveform

obtained in a home under the same conditions as figure 1 6a except that the TV is turned off. AMFM-1

indication = 8.5 nT rms. Vertical scale = 20 nT/div.

Horizontal scale = 5 ms/div 42

Figure 17b. Absolute scale spectrum analyzer display of figure 17a

waveform showing the significant harmonics to be the

first and third. Vertical scale = 2.0 nT/div.

Horizontal scale = 200 Hz/di v 42

Figure 18a. Oscilloscope display of ambient magnetic field waveform

obtained in a home 15 cm from the front of an operating

microwave oven. AMFM-1 indication = 4.7 pT rms. Vertical

scale - 5 pT/div. Horizontal scale = 5 ms/div 43

Figure 18b. Absolute scale spectrum analyzer display of figure 18a

waveform showing the significant harmonics to be the first,

third, fourth and fifth. Vertical scale =1.0 pT/div.

Horizontal scale - 50 Hz/div 43

Figure 18c. Normalized spectrum analyzer display for the waveform of

figure 18a (home ambient field in front of operating

microwave oven). Percentage of harmonics relative to the

fundamental can be determined from this display after

applying correction factors from figure 10.

Horizontal scale = 50 Hz/div 45

Figure 19a. Oscilloscope display of ambient magnetic field waveform

obtained in a home under the same conditions as figure 18a

except that the microwave oven is off. AMFM-1

indication = 52 nT rms. Vertical scale = 50 nT/div.

Horizontal scale = 5 ms/div 44

Figure 19b. Absolute scale spectrum analyzer display of figure 19a

waveform showing the significant harmonics to be the first,

second, third and fifth. Vertical scale = 10 nT/div.

Horizontal scale = 50 Hz/div 44

Figure 19c. Normalized spectrum analyzer display for the waveform of

figure 19a (home ambient field in front of non-operating

microwave oven). Horizontal scale = 50 Hz/div 45

Figure 20. Configuration of Helmholtz coil pair for generating a magnetic field in the Z direction, together with the

coordinate system used in the discussion of field variation

at points away from center 49

vii

NBS AMBIENT MAGNETIC FIELD METER FOR MEASUREMENT AND ANALYSIS OF

LOW-LEVEL POWER FREQUENCY MAGNETIC FIELDS IN AIR

P. M. Ful comer

Abstract

This report describes a portable, battery-powered magnetic

fieldmeter which has been developed to provide improved accuracy in the

measurement and analysis of low-level and ambient power-frequency

magnetic fields. Accurate measurement of such fields is becoming

increasingly important as public concern grows over the possibility that

exposure to such fields may produce effects on human health. Included in

the report are a description of the instrumentation, a circuit analysis,

a discussion of the calibration procedures together with an uncertainty

analysis, and some sample measurement results. The instrumentation

enables measurement of power-frequency magnetic field in air with an overall uncertainty of less than one percent over a range from

50 nanotesla (500 microgauss) to 200 microtesla (2 gauss) and an overall

uncertainty of less than two percent down to 2 nanotesla (20 microgauss).

It also enables the percentage of each harmonic present in the field to

be determined to an uncertainty of less than three percent.

Keywords: ambient magnetic field; calibration; calibration uncertainty; flux

density; low-level magnetic field; magnetic fieldmeter; magnetic

field strength; magnetic flux density; magnetic induction; measure;

meter; power frequency magnetic field.

1 . INTRODUCTION

The results of some recent epidemiological studies [1, 2, 3] have

generated public concern over the possibility that exposure to power frequency

(50-60 Hz) magnetic fields may produce effects on human health, even when the

field strength is relatively low, i.e., that which may be present in the home

due to nearby transmission lines and/or to electrical wiring and appliances

within the home. This has led to biological testing, designed to determine if

there is any relationship between magnetic fields and human health. Accurate

measurement of low level fields is, of course, necessary both in the

biological testing (to assure that the magnetic field level corresponding to

specific test results is correctly known), and in determining the field levels

to which humans are normally exposed in everyday life. This report describes

a portable, battery-powered magnetic fieldmeter which has been developed to

provide improved accuracy in the measurement and analysis of such low level

ambient magnetic fields.

The instrumentation is described in Part 2, the instrument calibration

procedures and an uncertainty analysis are discussed in Part 3, and some sample measurement results are shown in Part 4.
2. INSTRUMENTATION

2.1 General Specifications and Design Considerations

The portable, battery-powered instrument developed to measure low-level

ambient magnetic fields* has been designated "AMFM-1" for ambient magnetic

fieldmeter - version #1. It consists of two parts: (1) an electrically

shielded magnetic field probe consisting of 2000 turns of wire, wound on a donut-shaped non-inductive core approximately 10 cm in outside diameter, and

(2) a chassis box approximately 7 cm x 20 cm x 25 cm deep which contains the

detector consisting of amplifiers, an integrator, buffers, output indicator

and battery power supply. Development time for the present instrument was reduced by using a suitable commercial probe. The probe is connected to the

chassis box with a specified length of standard 50-Q coaxial cable.

The rms value of the output signal is, at present, read with a portable

4-1/2 digit rms multimeter but provision has been made for inclusion of an rms

to dc converter within the box and a 4-1/2 digit LCD readout on the front

panel. Also included on the front panel is a small analog output display for

determining the maximum field at a given location and for checking battery

voltage. Two nine-volt batteries power the unit and should enable continuous

operation for at least 36 hours.

A portable, low frequency (5 Hz to 50 kHz), commercial, spectrum analyzer

is included as part of the measurement system. Connection of the spectrum

analyzer to the AMFM-1 output permits determination of harmonic content in the

magnetic field. The percent of each harmonic present can be measured with an uncertainty of less than ±356 of reading. Harmonics below the 11th can be

measured to this uncertainty even when larger than the fundamental. Higher

order harmonics must be less than the fundamental.

Five measurement ranges, in multiples of 10, are provided by the AMFM-1

from 0.02 microtesla (0.2 milligauss) to 200 microtesla (2 gauss) full scale.

Uncertainty of measurements which are above one-tenth scale on the three

highest ranges and above one-quarter scale on the fourth highest range is less

than ±1$. This includes a measurement range from 50 nanotesla

(0.5 milligauss) to 200 microtesla (2 gauss). Measurements down to

2.0 nanotesla (20 microgauss) can be made with at least 4-digit resolution on the most sensitive range with an uncertainty of less than ±2%. Measurements

down to 0.2 nanotesla (2 microgauss) are possible with 3"digit resolution but

uncertainty is an order of magnitude greater.

*A magnetic field may be described and measured in terms of magnetic flux

density, represented by the symbol B, or in terms of magnetic field strength,

represented by the symbol H. The two are related by the magnetic

permeability, u, of the medium in which the measurement is made (B-uHK V r air, this permeability is a constant so that either quantity is applicable.

The instrument described herein is calibrated in units of magnetic flux

density (tesla).

2
Frequency response of the instrument is, at present, limited mainly by

the probe (pickup coil) and varies less than one db from approximately 20 Hz

to 3 kHz, thus allowing complex fields consisting of a 50- or 60-Hz

fundamental frequency and various percentages of harmonics and subharmonics to

be characterized. Between 30 Hz and 600 Hz the frequency response is flat to

within 0.4 dB or approximately 555. The frequency response of the detector

alone (not including probe) varies less than ±1 dB from 10 Hz to more than

20 kHz. The probe frequency response is down 3 dB at 6 kHz and 6 dB (50$) at

12 kHz.

Despite frequency limitations imposed by the present probe, an improvement in probe frequency response would not necessarily lead to an improvement in the overall frequency response of the present instrument. With

the exception of Hall effect probes, the signal from commercially available

magnetic field probes is proportional to the derivative of the magnetic field.

Consequently, the percentage of each harmonic present in the magnetic field is

weighted by its harmonic number. One advantage of this phenomenon is that an oscilloscope trace of the amplified signal clearly shows the presence of

harmonics. However, a meaningful measurement of magnetic field level cannot

be made until the harmonics are returned to their true proportion of the

fundamental. This is accomplished by means of an integrator included in the

detector. To avoid signal-to-noise and nonlinearity problems in the

integrator at very low level inputs, some stages of amplification must precede

the integrator. A potential difficulty arises when higher level signals with

high harmonic content are applied to this amplifier. The undue weighting and

subsequent amplification of the harmonic frequencies can overload a final

amplifier stage causing limiting or clipping to occur. Compromises in design

must be made to avoid this situation if a higher frequency response is

desired.

The use of a Hall-device probe to by-pass the problems described above

has, unfortunately, other disadvantages. At present, achieving high

sensitivity is a problem when using a probe based on the Hall effect. The use

of one was not attempted here because of the need to measure very low level

signals. This does not preclude the use of such a probe at a later date

however, if probe materials with higher Hall coefficients become available.

Use of a Hall probe would require that (1) the integrator stage be replaced by an amplifier, (2) suitable changes be made in the input network and possibly

in overall amplifier gain, and (3) the instrument be recalibrated.

When using a field-derivative-type probe (as used by the AMFM-1 ) a reduced overall output might solve the potential amplifier-overloading problem

but at the expense of good low noise performance on the most sensitive range.

Other solutions would be to reduce the dynamic range of the instrument or to

vary the position of the integrator within the amplifier stages depending on

the range selected. None of the above alternatives was used in the AMFM-1,

however, because each has an offsetting disadvantage and because even at full

scale output, where the clipping would first occur, the AMFM-1 responds to

signals up to 600 Hz without clipping on all but the highest or least

sensitive, 200 pT, range. This means that in most practical situations (where

ambient fields are less than 20 pT) the 10th harmonic of 60 Hz could be 100$

of the fundamental and still be measured correctly by the AMFM-1 . For output

signals which are a lower percentage of full scale or for harmonic frequencies

which are a lower percentage relative to the fundamental (or both), the

3
harmonic frequency that can be measured (no clipping) increases as shown in

figure 1. As an example, the harmonic content of a signal whose fundamental

amplitude is below 1555 of full scale can be measured to beyond 3 kHz, even if

the amplitudes of the harmonic components are equal to the fundamental. The

same approximate 3"kHz limit applies to harmonic components which are less

than approximately 1555 of a full scale fundamental. This performance permits

accurate measurement for nearly all practical situations and further

complication of the design was not warranted.

On the least sensitive range (200 pT), clipping of harmonic components

which are 1 0055 of a full scale fundamental will occur at frequencies above

120 Hz. The clipping initiation point improves to 240 Hz for signals which

are 5055 of a full scale fundamental and to 1.2 kHz for signals which are 1055 of a full scale fundamental. Figure 1 gives a summary of the above results.

A check to determine if clipping is occurring on a given range can be

made by switching the detector to the next higher (less sensitive) range. The

signal reaching the integrator will now be a smaller percentage of full scale,

and less or no clipping will occur. The two readings will be significantly

different if clipping is occurring on the more sensitive range. The readings

for the two ranges will be about the same if no clipping is occurring.

2.2 The Probe

The probe is an inductive type which is widely used in the measurement of

alternating current magnetic fields. It consists of 2000 electricallyshielded turns of wire, wound on a donut-shaped noninductive core. According

to Faraday's Law, the voltage (emf) induced in the wire loop by a time varying

field is

emf = -NA (dB/dt) , (1

)

where B is the component of the magnetic field parallel to the coil axis, N the number of turns in the coil, and A the area enclosed by the coil. The

magnetic field is assumed to be uniform over area A. Higher sensitivity can

be achieved by making the product NA large, but this must be balanced against

either or both (1) poorer frequency response, as a result of higher inductance

(more turns) in the coil, and (2) decreased ability to measure small areas of

concentrated magnetic field, since the field measured is the average of that over the area A. As previously noted, the AMFM-1 is intended to measure the

general level of ambient power frequency magnetic fields. In this particular

case, sensitivity has a higher priority than either high frequency response or the ability to resolve the field measurement over a small area. The mean diameter of the probe is approximately 8.75 cm, and its response is down

approximately 3dB at 6 kHz.

For sinusoidal magnetic fields, eq (1) may be expressed (neglecting the

negative sign) as

emf = 2irfNABcos<j> , where f is the frequency, B is the rms value of the magnetic field, and $ is

the angle between the field and the axis of the probe. The cosine term

4
*

o

*

CO

*

CO

*

o

o

CO

o

o

CO

o

o

o

CO

o

CO

N

I

>

o

z

IDD

o

LD

CC

LL

(gibos iin* p %) ganindwv ivnois i.-iAidwv

5

Figure

1.

AMFM-1

frequency

response

as

function

of

signal

amplitude.

Frequencies

at

which

clipping

occurs

(see

text)

for

the

various

scales

are

indicated.
becomes unity if the probe is slowly* rotated to achieve the maximum B value

as indicated by the instrument front panel analog meter.

Frequency response of the probe can be calculated from the equivalent

circuit shown in figure 2 [4]. The probe and the coaxial cable connecting it

to the detector are represented by an inductance L in series with a resistance

r plus a parallel distributed capacitance C. Emf is the voltage induced in

the probe and FL nis located at the detector input.

The probe output, v which is applied to the detector input, is related

to the emf induced in the probe by [4]

V

p (R. +r) _ 2

/ L \ 1

2

1 ° — .A ip

' ~ emf R. W LC

\R . + Cr

L in J i \ in / J

1/2

(3)

where to is equal to 2irf. To reduce the possibility of oscillation in the

detector amplifiers, the value of A should remain close to unity and not peak

before falling off with increasing frequency. Higher values for R in cause peaking and a sharp fall-off in A, a possible cause of oscillation. Lower

values for R. allow the value of A to roll off gently with increasing

frequency, i'oo low a value, however, causes unnecessary reduction in the

frequency response.

For values of R. such that 1/R. >> wC and R, m in in

A

’ (R in+r)2

/ U)L

OJ 1

1 R . 2

’

111 K

9

> <dL, eq (3) reduces to

(4)

because the terms containing the capacitance C can be dropped. It should be

noted that because the C of eq (3) includes the distributed capacity of the

cable connecting the probe and detector, cable lengths longer than 1 meter may

require more analysis. Longer cable lengths will require the use of a dedicated cable. Equation (4) describes the behavior of a low pass RL filter

with a cutoff frequency oo = R/L. For frequencies less than w

c

, A is

determined by

|A R. /(R . +r) in in(5)

For frequencies above m the attenuation is dominated by the second term of eq

(4) and

I A | ~ o> c /m ( 6 )

*Slow rotation is required to avoid a false indication that an ac magnetic

field is present, when in truth the indication may be caused by rotating the

coil through the earth’s dc magnetic field.

6
L r

Figure 2. Equivalent circuit of AMFM-1 magnetic field probe. FL is the

approximate detector input impedance.

out

o- Function

generator

o- gnd

* Vb

Dual beam

oscilloscope

-o Input #1

-o Input #2

-o gnd

Figure 3. Test set-up for determining the approximate value of the resonant

frequency, f , of the magnetic field probe.

7
Approximate values for L and r can be obtained with a good quality RLC

bridge. An approximate value for C can be calculated by first experimentally

determining the resonant frequency, f , of the probe, and then using the

relationship below, (frequency of resonance for a parallel LC circuit where

coL >> r)

f = — 0

2ir LC

1/2

(7)

to solve for C by substituting for the values of f and L. The approximate

value for f can be determined experimentally by means of the relatively

simple test set-up shown in figure 3. The function generator frequency should

be increased while keeping its output, V^, constant. The frequency at which

the voltage across the probe, V^, peaks is the approximate resonant frequency.

Input impedance of the vertical oscilloscope amplifier used to measure V

g should be at least 1 M£2. Probe coil resistance, r, reduces the peak value of

V but has little effect on f . The value of R in figure 3 may have to be

changed to achieve best sensitivity for observing the peak value of V . D Methods for rigorous determination of the probe coil parameters r, L, and

C [4] of figure 2 are not specified nor needed here. Approximate values

enable determination of a suitable value for R^

n to maximize the probe

frequency response. The approximate values for L, r, and C of the pickup coil

used for the AMFM-1 are shown in figure 4 along with curves showing the

variation in V /emf with frequency as calculated from eq (3), for various

P0 values of R . The best value for R is that which results in a probe

frequency response which is flat to roll-off, such as that which a value R.

n between 27 kft and 30 kQ provides* (see figure 4). Calibration of the field

meter at various frequencies then provides the complete instrument frequency

response (see figure 1).

2.3 The Detector

The detector portion of AMFM-1 amplifies and integrates the voltage

induced into the probe by the ambient magnetic field, resulting in an ac voltage whose waveshape and harmonic content (within the frequency range of

the AMFM-1) matches that of the ac currents which produced the ambient

magnetic field. This ac voltage is measured by a 4-1/2 digit true rms meter

to indicate the magnitude of the magnetic field present, and is also available

at two front and one rear panel output connectors for observation by an oscilloscope or for spectrum analysis to determine the number and percentage

of harmonics present.

termination of the probe with a relatively low value resistance results In a very small circulating current due to the back emf induced in the coil by the

magnetic field which is being measured. The field produced by this current

is, at the center of the coil, approximately 0.38$ of the field being measured

and very nearly in phase quadrature with it. The effect is taken into

account, however, when the probe and detector are calibrated as one unit. The

phase shift introduced is negligible, i.e., less than 0.22 degrees.

8
9

Figure

4.

Calculated

frequency

response

for

the

AMFM-1

magnetic

field

probe

(ratio

of

probe

output

voltage

to

the

emf

induced

by

the

field

vs.

frequency

of

the

field)

using

various

values

for

the

detector

input

resistance,

R

in

»
To confirm AMFM-1 operation, the probe was placed within a set of

Helmholtz coils and the current* to the coils was supplied by a programmable

waveform generator/ power amplifier combination. Figure 5 shows an oscilloscope display of the current waveform superimposed on the waveform of

the AMFM-1 output signal. The amplitudes of the two waveforms have been made

the same for purposes of comparison. The current waveform contains about 40$

3rd harmonic, 19$ 5th harmonic, 8.5$ 7th harmonic and 4$ 9th harmonic. The

phases of the 3rd and 5th harmonics have been shifted +90° relative to the 60

Hz fundamental. Figure 6 is the superimposed spectrum analyzer display for

the two waveforms shown in figure 5. No differences between the superimposed

displays of figures 5 and 6 are discernable, indicating that for the

frequencies shown, the probe and detector of the AMFM-1 adequately

characterized the spectral composition.

In addition to amplifiers and an integrator, the detector also includes

(1) the 4-1/2 digit LCD front panel readout and accompanying true-rrns-to-dc

converter necessary to drive it, (2) a small, front panel, dc current, analog

meter for use in determining maximum reading** and in checking battery

voltage, plus a simple half wave rectifier to drive the meter from the ac output when used for determining maximum reading, (3) an on-off battery check

switch, (4) a range switch, and (5) the battery power supply. At present,

item (1) above, has not yet been physically incorporated into the detector

box. The detector ac output is instead indicated on the 2.0 V rms scale of a separate portable, battery operated, 4-1/2 digit, true rms multimeter.

The output indication is calibrated in tesla for each of the instrument '

s

five ranges. For the two highest or least sensitive ranges (200 and

20 microtesla), calibration is accomplished by placing the probe in a known

magnetic field and recording the output meter Indication for various values of

this known field. Because of the presence of uncontrollable low level ambient

fields, the lowest or most sensitive ranges (2.0, 0.2 and 0.02 microtesla)

cannot be calibrated by this method. A "voltage Injection" technique is used

instead. Voltage injection is also used for portions of the 200 and 20

microtesla ranges for comparison with the direct method (where the probe is

inserted in a known magnetic field). Calibration procedures are explained

more fully in the next section.

The magnetic field probe described in section 2.2 is found experimentally

to produce an output voltage, v^ , of approximately 3.91 mV per microtesla at

60 Hz. This Vp is actually the°input voltage for the amplifier and can be

expressed as

= v in 3.91 - mv/yT , 60

( 8 )

*This current produces the magnetic field within the coils, and Its waveform

coincides with that of the magnetic field.

**Determination of maximum is difficult when using a digital meter.

10
Figure 5. Oscilloscope display of the magnetic field waveform superimposed on waveform of the output signal from AMFM-1 . Amplitudes of the two

waveforms have been made equal for purposes of comparison.

Figure 6. Spectrum analyzer display indicating frequency components of the

waveforms shown in figure 5. The traces for the two waveforms are superimposed

.

11
where f is the frequency of any harmonic contributing to the total magnetic

field, e.g., for the third harmonic f = 1 80 Hz and v. = 11.73 millivolts/

microtesla. Full scale indication on the digital rea8out requires 2.0 V rms

at the AMFM-1 output or

v

q

= 2.0 V rms, full scale . (9)

Since the most sensitive range (range E) for the AMFM-1 is 0.02 microtesla

full scale, v in for full scale output at 60 Hz would be, from eq (8),

v. = 3.91 — —— x 0.02 yT = 78 uV and

60 yT

the amplifier gain, G, required to produce the 2.0 V rms full scale output

meter indication is thus

G

2.0 V

78 yV

25,640 .

Amplification required for the four less sensitive ranges (ranges D to A) are progressive factors of ten less than the above.

At minimum battery voltage, overload or clipping of the amplifier output

signal occurs when the signal exceeds approximately 11.5 volts peak-to-peak or

4 V rms. This is no problem for low harmonic content 60-Hz signals, but as described in section 2.1, it does become a problem for signals with relatively

large amounts of higher order harmonics. Equation (8) indicates that the

input signal amplitude (and hence the output signal of a linear amplifier)

increases with frequency. Integration counteracts this effect. The

amplification or gain of an integrator stage is a function of 1/f.

The AMFM-1 detector consists of an amplifier section with maximum gain of

approximately 5128 followed by an operational amplifier integrator with a maximum gain of 5.* The two together produce the required 25,640 gain for

full scale indication on the most sensitive range. Maximum output from the

amplifier section is approximately 0.4 V rms at 60 Hz for ranges B through E,

and will not increase to the 4 V rms clipping limit until 100{ of the tenth or higher harmonics are present - an exceedingly unlikely occurrence. See

section 2.1 and figure 1 for further discussion of design considerations in

amplifier-integrator placement and of the limit to operation imposed by

possible clipping.

Three stages of amplification are used (see circuit diagram of figure

to provide the high total gain of 5128 needed for the most sensitive range.

The maximum gain of an individual stage is 25. Noninverting operational

amplifier stages are used for the high input, low output impedance th.it they

provide.

*The integrator gain is reduced to unity for range A.

12
13
A buffer to provide impedance matching separates the last amplifier from

the integrator, and a buffer is also placed between the integrator and the ac voltage output. All stages are ac coupled except for the input to the

integrator. The low frequency cut off of the interstage coupling is set high

enough to prevent random low frequency noise from causing a variation in the

output voltage on the most sensitive ranges. The ac coupling also prevents

effects from the input offset voltage and current and from the input bias

current of individual amplifier stages from accumulating and causing extreme

variations in the quiescent voltage of the output amplifier.

The integrator, A5, is basically an inverting operational amplifier stage

in which the feedback resistor has been replaced by a capacitor to produce a gain, A^ , of

A = . (10)

oo * R 1 6 *C5

This assumes that R17, which is in parallel with C5, is much greater than

1 / j ooC5 . For ranges B through E, R 1 6 is 5.3 kG and for range A (highest or least sensitive) another 21.2 kft is added for a total R 1 6 of 26.5 kfl. The

capacitor, C5, is a low leakage 0.1 yF. At 60 Hz the integrator gain is thus

unity on range A and 5.0 on ranges B through E.

The value chosen for C5 influences the maximum slew rate (SR) for the

integrator, i.e., the time rate of change for the output voltage.

( 11 )

where I is the maximum current available from the circuit to charge C5.

O Q13.X Higher voltage and/or higher frequency outputs require a faster slew rate. If

C5 is too large, the slew rate will be reduced below an acceptable value.

At dc and very low frequencies the integrator gain is

lL

R1

6

or simply the gain of an inverting operational amplifier. This occurs because

at dc and very low frequencies the term 1/ajC5 is much greater than R 1 7 and the

impedance of the parallel combination of C5 and R 1 7 is essentially the

resistance of R17. The frequency, f , occurs where the integrator gain equals

the dc gain, or from eqs (10) and (l£)

2trf *R1 6 *C5 R1 6 c Solving for f gives

f - C 2ir-R17-C5

For operation in the linear integration region, the lowest frequency of

interest, f should be much higher than f , i.e.,

Li C

14
( 15 )

(16)

Operational amplifier stage A7 is a half-wave rectifier with R24 selected

so that the analog meter reads 80$ of full scale for a full scale output on

the digital meter. This allows an analog indication of the amount of

overranging up to 125$.

Two alkaline 9-volt clip-in batteries furnish power for the unit, one for

the positive supply and one for the negative supply. The network R29,Z1 ,C9

(or R30,Z2,C10) limits the battery voltage applied to the circuits to

approximately 9.1 volts, thereby protecting against over-voltage from

installation of incorrect battery, reverse polarity, etc. The battery check

circuit is comprised of R25, R27, and D5 (or R26, R28, and D6) with R27

selected to approximate the current drain of the instrument and R25 selected

so that the analog meter indicates the approximate battery voltage, i.e.,

80 pA = 8.0 volts.

Operational amplifiers A1 , A4, A5, and A7 require approximately 1.2 mA

quiescent current each. Stages A2, A3, and A6 are able to use a low current

op-amp and thus require only 0.2 mA each. Total current drain is presently

less than 6 mA from each battery, permitting at least 48 hours of continuous

operation. Total operating time will be somewhat longer when operated

intermittently. Once the rms to dc converter and digital display are added,

the total current required from each battery will increase to about 8 mA.

Operating time should then be at least 36 hours continuously from a set of

fresh batteries.

f >> 1 L 2tt *R1 7*C5

and hence

R17 >>

2ir *f^C5

3. CALIBRATION

3.1 General Considerations

The instrumentation described in section 2 provides a suitable and stable

method for measuring low level ambient magnetic fields. Equally important is

the method by which the instrument is calibrated. Stability and a calibration

traceable to a known magnetic field provide the information necessary to

specify measurement uncertainty. Since stable measurement instruments are

not difficult to design, it is the calibration procedure and its traceability

to an absolute value that often determines how small the instrument

uncertainty specification can be.

The method for generating the basic reference magnetic field, and the

description of a transfer standard to establish a more easily accessable

secondary calibration field are described in the next section. A secondary

calibration field was necessary in this investigation because (1) generation

of the basic reference magnetic field requires the use of equipment that is

often in service for other purposes, (2) transit time to the site of the basic

reference field and set-up time for the equipment is considerable, and (3) the

basic reference field, though highly accurate, is not sufficiently uniform

over an area large enough to accept the AMFM-1 probe.

15
Briefly, the basic reference field is a dc magnetic field generated

within a well defined solenoid. A relatively portable, highly accurate and

stable magnetometer is used to measure this dc field, thereby providing

calibration of that instrument for use as a transfer standard. This same instrument is then used to measure and calibrate the dc field generated by dc

current flowing through a set of Helmholtz coils* which serve as the secondary

or local calibration setup. The ratio of the dc magnetic field to the

accurately measured dc current determines the Helmholtz coil factor.** As

will be shown in the next section, this coil factor is equally applicable when

the Helmholtz coils are supplied with power frequency alternating current.

Thus the local ac reference magnetic field can be determined as the product of

the coil factor and an accuately measured ac current through the coils.

Following its use in measuring the Helmholtz coil dc field, the transfer

standard is returned to the basic reference dc field and used to remeasure

that field, thereby closing the loop. Periodic comparisons, i.e., once every

two to three years can be made between the basic reference field and the local

calibration set up but no change should occur if the Helmholtz coil pair

retains its original physical dimensions.

3.2 Calibration Procedure for the Least Sensitive Ranges

The dc magnetic field generated within a solenoid constructed with a relatively large number of closely spaced turns and for which the dimensions

and number of turns are precisely known, can be calculated [6, 7]. At the

center of the solenoid,

B =

s

V NI

o s

(4a

2

+i

2

) 1/2 (17)

where y is the permeability of a vacuum, N is the number of turns through

which tRe current I passes, and a and l are the radius and length of the

solenoid, respectively. Since all factors on the right side of eq (17) are constant, except current, the equation can be rewritten as

B

s K I s s

( 18 )

2 2 1/2 where K = y N/(4a + £ ) .It is this constant which is precisely known [ 8 ].

The fiefd, B°, is the basic reference magnetic field, which can be varied by

changing the3 value of dc current through the solenoid.

*A pair of flat, circular coils having equal numbers of turns, equal

diameters, arranged with a common axis, spaced one radius apart and connected

in series. This design produces a relatively uniform magnetic field at the

center of the structure [5].

**The Helmholtz coil factor can be computed directly from dimensions of the

coil, number of turns, etc., but unless the coils are very large, the

dimensional uncertainties due to the finite size of the wire bundle cau3<" an overall uncertainty which is greater than that resulting when the coil factor

is determined as described above (see section 3.4).

16
The solenoid [8] is located in a building specifically constructed to

provide a nonmagnetic environment [9]. The solenoid is oriented in a horizontal East-West direction and centered within a system of three large

Helmholtz coil pairs, the individual axes of which are oriented East-West,

North-South and up-down, respectively. Selective energization of each

Helmholtz coil set serves to cancel the earth's magnetic field within the

solenoid.

A null-type magnetometer, in which the magnetic field measured at its

sensor is neutralized by a precisely calibrated current passed through a solenoid surrounding the sensor element, is used to measure the basic

reference field B at the center of the solenoid. The neutralizing field can

be set to five significant figures (±4 digits in the last figure) with full

scale sensitivity selectable between 100 and 0.025 microtesla. Measurements

are made for three or four different values of B . A sufficient number of

points are chosen so that the magnetometer can be calibrated, i.e., a specific

five significant figure reading on the magnetometer is equivalent to a specific known value of the basic reference magnetic field. Accuracy of the

magnetometer readout as compared to the actual field calculated from eq (18)

is not particularly important for our purpose here, but stability of the

magnetometer calibration i£ important.

The magnetometer is then moved to the local laboratory and used to

measure the dc field B^' generated within a set of Helmholtz coils. The

Helmholtz coil pair ispositioned so that the field generated will be

horizontal. With no current through the coils, the Helmholtz pair and the

magnetometer probe (aligned with the Helmholtz coil axis) are first rotated in

the horizontal plane to minimize any ambient reading due to the earth's dc

field. The coils are then energized briefly with ac current to produce a field of approximately 50 microtesla. This ac field should have essentially

no effect on whatever ambient dc field is present and serves to confirm that

surrounding ac distribution lines and equipment do not effect the dc

measurements. The next step is to move nearby equipment and again note the

effect on the ambient dc field. For minimum error due to iron core transformers, etc., nearby equipment is located so that a relatively large

displacement is necessary to produce a measureable change in the ambient dc

field.

Any dc field measured with no current in the coils, B„ , is likely due

H

either to the earth's magnetic field and/or nearby iron core transf ormers

.

This must be subtracted from the dc field measured with current in the coils,

B^ ' , to arrive at the magnetic field generated by the current through the

Helmholtz coils, i.e.,

DC current, I H

, through the Helmholtz coils produces a magnetic field

which can be accurately calculated [5, 10] as

b

h

- V - b

h

(19)

O

B, I (20)

H

1/2

H

5 [5] r

17
where p Q

is the permeability of a vacuum, N is the number of turns on each

coil, and r is both the radius and/or spacing of the coils. The factors

inside the brackets make up a constant called the coil factor, K . Measurement of the dc current through the coils, which generates^ , and

measurement of with the magnetometer allows an accurate computation of this

coil factor. Rearranging eq (20) and substituting for the factors inside

the brackets gives

K

h

= B

h

/Ih

. (21)

Since frequency is not a factor* in eq (20), the coil factor for ac rms currents, K^, is the same as that for dc currents, i.e., K

H

= K^. An accurate

determination of ac rms current through the Helmholtz coils thus allows an accurate determination of the ac rms magnetic field, B , generated within the

Helmholtz coil pair, or

B

h

= Vh * (22)

where = K^. It is this field, B , which is used to calibrate the AMFM-1 on

its least sensitive ranges (ranges A and B). The uncertainties involved in

this calibration are discussed in section 3.4 and a worst case uncertainty

specification is determined.

The calibration is accomplished in a normal laboratory, i.e., when

constructed there were no special provisions taken for reducing the ambient ac fields present. The Helmholtz coil pair is located and oriented so that the

effect of the ambient magnetic field measured at the center of the Helmholtz

coil pair is reduced to a minimum, but this ambient field cannot be reduced

much below 0.04 pT. This value has negligible effect when calibrating the

least sensitive range (A) and the upper portion of range B. It becomes

noticeable in the middle portion of range B and significantly raises the

uncertainty of calibration for range C (2 pT full scale). The three most

sensitive ranges (C, D, and E) are therefore calibrated using a voltage

injection technique. Both methods are used on portions of ranges A and B to

verify the correlation of the two methods.

3.3 Calibration Procedure for the Most Sensitive Ranges

Calibration of the most sensitive ranges (C, D, and E) is achieved by

using an accurate voltage divider to inject a voltage Vp

M

, directly into the

AMFM-1 input terminals, thereby bypassing the pickup coil

i and the uncertainty

caused by ambient magnetic fields in the laboratory. The voltage to be

injected is determined from the AMFM-1 probe factor k , and the probe factor

is obtained from information recorded during the caliBration procedure for the

least sensitive ranges, A and B.

*This is not true for magnetic field frequencies ra^ch tjigher than those of

interest here. A correction factor equal to [1-(f /f )], where f is the

magnetic field frequency and f is the resonant frequency of the Helmholtz

pair, would have to be applied [4].

18
( 23 )

The probe factor,

k

p

k is defined as

P

J

where v is the rms voltage generated at the output of the AMFM-1 probe for a

P

0

given, rms, 50-Hz, magnetic field, B^, which is perpendicular to the plane of

the probe. This voltage can be determined when the probe is positioned within

the Helmholtz coils for calibration of the least sensitive ranges, i.e.,

centered with the probe axis in line with the Helmholtz coil axis. The units

for k are volts per tesla. The probe output voltage will change slightly

when connected to the AMFM-1 because of loading provided by the AMFM-1 input.

The desired probe factor can thus be expressed as

k ' - —— , ( 24

)

? B

h

where v_u is the rms input voltage to the AMFM-1* and B. is defined above.

FM . n

l To calculate k ' , the value of v„„ and the B, which causes it should be

p FM . h

determined for three or four different points on each of ranges A and 3. The

lower end of range 3 may result in a less accurate determination because of

the increasing error caused by ambient fields. An average for k ' can be

calculated from the various values obtained. This average shoulH not differ

from the extremes by more than the ’incertainty of making the V and 3.

r . ri measurements , provided that the ac ambient fields are low relative to 3 V

. Uncertainties are discussed more fully in the next section. The closeness

(see section 3*4) of the various values for k^' indicates and confirms the

linearity of the AMFM-1 probe at the higher magnetic fields. There is no physical reason why this same probe should not be linear at the lower magnetic

fields which are measured on ranges C, D, and E.

Once the probe factor k ' has been determined, a calibration check of the

more sensitive ranges can be y achieved by applying a 60-Hz voltage, v_„ , r n

.

directly to the AMFM-1 input terminals and measuring the output. The voltage

can be calculated by rearranging eq (24) to give

*Note that connecting an ac voltmeter to the AMFM-1 input (in order to measure

Vp,,^ ) causes additional loading upon the probe output, thereby reducing both

v

1 and the AMFM-1 output meter indication from what they would be without

r M

.

the voltmeter connected. To obtain the correct value for v_u , the Helmholtz

r n

.

coil current and hence must first be increased ’until the A^FM-1 output

meter indication is the same as it was before the ac voltmeter was connected

to the AMFM-1 input.

19
Here, represents the desired AMFM-1 output meter calibration check point.

As an example, the probe factor for the present AMFM-1 probe is 3.91 mV/yT.

To check the full scale indication for range D (0.2 yT), a value for v of

FM

.

1 3.91 mV rms

UT

x 0.2 yT = 0.7820 mV rms

must be inserted into the AMFM-1 input terminals. To check the full scale

indication of range E, the input voltage, v , would be only 78.2 yV rms.

r M

.

1 The above examples show that the required input voltage may be too low

and hence too noisy to provide either (1) a relatively clean signal for

calibration purposes, or (2) a signal which can be accurately measured. For

this reason a shielded voltage divider is used. The divider is composed of

two accurate and stable resistors, a 10 k!l upper resistor, R^, in series with

a 10 ft lower resistor, R^ , both enclosed within a shielded box. The junction

of the two resistors is connected to the AMFM-1 input via a shielded

connector. The divider ratio is chosen so that the ac rms voltage at the top

of the divider, supplied by a sine-wave generator, is sufficiently large to be

measured accurately, and noise in the signal is attenuated along with the

signal. The shielded leads reduce pickup noise sufficiently to check

calibration down to midscale on the most sensitive range. A diagram of the

calibration setup is shown in figure 8.

The divider ratio can be calculated as (R +R

p )/Rp where R

p is the

parallel combination of R T and the AMFM-1 input impedance, R . This latter

impedance consists of R . (a 30.1 kfi resistor) in parallel with the

combination of Cl and Ri n in series with the parallel configuration of R3 and

the input impedance of A1 (see figure 7). The input impedance of A1 is at

least an order of magnitude larger than the 1-Mft value of R3 and can therefore

be neglected. The impedance of R4 and Cl at 60 Hz, which is at least two

orders of magnitude less than R3 and even less at higher frequencies, can also

be neglected. An accurate measurement of the AMFM-1 input impedance can,

therefore, be made between the input and ground after removing A1 and shorting

across Cl . This value is approximately 29 kfl. Since R FM.is at least 2800

times greater than R , its presence changes the divider ratio by less than

0.04$. The voltage V , obtained from a sine-wave generator, is that required

at the top of the divfder to produce V

pM

at the junction between R^ and R

( .

Distributed capacitance to ground is indicated at the AMFM-1 input by

C

pM

in figure 8. This capacitance should have little effect on the divider

ratio, however. A value of 15 pf would change the divider ratio by less than

0.1 ppm at 60 Hz. The capacitance across Rp is represented by Cp. A 10 pF

value for C would change the divider ratio by less than 0.004J at 60 Hz. An

experiment to determine whether distributed capacitance across Rp or Rj is

affecting the divider ratio is discussed later in this section.

Assuming the effects of distributed capacitance to be negligible,

20
H-I

O

>,o .

/—* c

.u 03

X

X S3 - 03 O' r—V

4-> 03 CQ X • • 03 <*H Q.

r— 03 0 1 CO • 4H 4-3 s 

03 CO Du os >—

S 03 03 i—1

/\ > rH

CO /\O 0 e 03 X3 S3 o 4-3 •rH 03 4-3 X \ s O

«>-. CO Du •a 0

4-> OS 03 TD

C rH 4-3 sz 0 o o 03 CQ X ——t > • rH i *rH

4-3 03 S3 /p-- 0

03 c rH

O <c 0 o •H CO i—1 a

•rH 03 03

a

•oX 4-3

O 0 j c o 4-3 CQ

•rH 4-3 c b0 0 o •pH > —- 4-> 03 • S3 <*-. c 03 X o

Q. o x: 03 0

•U3 03 •pH 4H 4-3

X

X> 4-3 03 •pH

O

O 03 03 E 0 X a •a 0

X3 Q. •pH •rH 4-3 •o

OQ o •a > D

vD

T c o a.

X

T3 S 1 •pH

x 4-3 CQ 0 Xh s a S3 X Cl-! TO O II ~H 1—1 2: 03 o

CO <— < X 4J 03

—

03 •pH sz 0

•o + 03 CO

X 4-3 x: 03 o Z

03 4-3 o 4-3 c 0

os 03 o

03 \ CO 03X 4-3

O

Q •pH sz 03 x: s

S3 OS 4-3C CQ 0

•o i i — 03

O o Q. CO bO i—1 - X —.

S* •pH 03 0

Q.

C x: 03 33 a.

0Q 03

m > 4-3

OX 03 o •

4-> ” a 03 •o 3 03 i x: c 1 s

b0 03 03 0 Du > c x S n •pH 4-3 <

03 CO

4-3 bO T3 0

03 > 03 03 4-3 H sz 0 0

S3 4-3X rH

C3 S3 r~H 4-3 T3 o

03 03C rH

O 00 c0 0O • • • <*: DQ O I

21

Figure

8.

Test

set-up

and

basic

procedure

for

AMFM-1

calibration

by

voltage

injection.
where f is the frequency of the input signal.* Combining equations (25) and

(26) yields

k 'B

P h

g L

+ R,

Solving for v yields

v

g

k ' B, P h

60

f

(27)

( 28 )

where v is the rms voltage which, when applied to the top of the divider,

should produce the magnetic field indication, B^, on the AMFM-1 output meter.

The presence of distributed capacitance in the voltage divider (C

D or

C

FM

in figure 8), which is sufficiently large to effect the calibration

results, can be determined in either of two ways. One involves raising the

sine-wave generator frequency to f and noting whether the output meter

reading obtained using f is exactly f^/f

^ less than the value obtained using

f^= If it is not, then distributed capacitance may be having an effect.

Another method involves calculating the value for the AMFM-1 input voltage

from eq (26) and then comparing the result with the value measured using an ac rms voltmeter. In doing this, the value chosen for v must be large enough to

enable a relatively noise free measurement of v_w an§ the effect of any ac voltmeter loading across the lower part of the divider must be taken into

account. Both checks were performed on the voltage divider used to calibrate

the AMFM-1 and no effects from distributed capacitance were noted.

3.4 Calibration Uncertainties

All of the uncertainties associated with the calibration procedures just

described are tabulated in this section and an overall uncertainty figure for

the AMFM-1 is derived. The root-sum-of-the-squares method is used to arrive

at total uncertainties except where the individual uncertainties may not be

totally independent of one another. For these cases, they are added directly.

The calibration of AMFM-1, as explained in section 3.1, is ultimately

referenced to the value of the dc field, B , generated within a solenoid, the

dimensions of which are accurately known. Equation (18) from section 3-2

gives the value of B as

s B = K I (29)

s s s

*The term (f/60) is necessary because, as explained in section 3.1, the AMR-' i probe provides a differentiated signal, thereby resulting in a larger prob^

output for magnetic field harmonic frequencies.
where I is the dc current through the solenoid and K

factor in tesla per ampere. From eqs (17) and (18) tfii U 0

N K =

s , , 2 . 2 . 1/2

(4a +1 )

is the solenoid coil

s factor is

(30)

Allowing for variation between determinations, the value of K for the

precision solenoid is known to an uncertainty of less than ±1

8

ppm or ±.001$.

The current, I , can be set to six decimal places by means of a precision

current source

S and remains stable to better than ± 1 digit in the last place.

This results in a current that is stable to better than ±.006$ of the set

value for the range of currents necessary to produce dc magnetic fields of

20 uT or greater within the solenoid. The absolute value of I is determined

by measuring the voltage it develops across a series precision resistor, or

I = V /R

s s s Substituting eq (31) into eq (29) gives

( 31 )

(32)

The uncertainty in the value of the precision resistor, allowing for

temperature variation due to environment and/or power dissipation, is less

than ±.01$. The voltage can be measured using a dc voltmeter with a one year

uncertainty over a temperature range of 15 to 25°C of <±.008$ of reading at

full scale and <±.01$ of reading at one tenth scale. Applying the boldfaced

uncertainties to eq (32) results in an uncertainty of <±.01 5$ for B at the

center of the solenoid.

Three or four different values of B are measured with an accurate and

stable magnetometer, thus calibrating the magnetometer as a transfer standard.

The transfer standard is used to measure the dc field, B , generated by a set

of Helmholtz coils which are located in a more readily accessable location for

calibrating the AMFM-1 (see section 3.2). The Hemholtz dc coil factor is

then calculated from eq (21), section 3.2 as

K

h

= B

h

/I h

. (33)

As discussed in section 3.2, the dc and ac coil factors for the Helmholtz coil are identical (K

H

=K

h

); hence once is known, the value of the ac rms magnetic field generated within the Helmholtz coils can be calculated from eq

( 22 )

B

h

k

h

r h

( 3*0

where 1^ is the rms current through the coils. This current is determined by

I h VR

h

(35)

where V is the rms voltage, developed across a precision resistor, R , in

series with I. . h

The uncertainties connected with the magnetometer measurement of B (not

the uncertainty of the actual field value present which was discussed earlier

23
in this section) are due to (1) error in centering the probe within the

solenoid, (2) averaging of B over the sensing area of the probe, and (3)

instability within the magnetometer itself.

The size of the sensing area for the magnetometer probe used is

approximately 6 cm long by 1.5 cm square. Combining placement error (1) with

finite sensor size (2) results in the center of the sensing area having a maximum displacement of perhaps ±3 cm away from the solenoid center along its

axis and perhaps ±2 cm away perpendicular to the solenoid axis. The field

within a solenoid at any point away from its center along the axis may be

computed as [7, 11]

where u , N, 1 and I have all been defined earlier and e is the angle formed

between the axis and a line connecting one edge of the coil to the point, P,

in question, and 6 is the angle formed between the axis and a line connecting

the other edge of the coil to the same point (see the diagram of fig. 9). At

3 cm from the center along the axis of a 1000 turn solenoid, one meter long

and 28 cm in diameter, the field calculated from eq (36) is approximately

0.04? smaller than the value at the center. Since the sensor averages over

its entire 6 cm sensing length, the latter figure is used as a worst case.

Calculation of the error due to probe displacement perpendicular to the

solenoid axis is more complicated. However, shifting of the probe within the

solenoid showed experimentally that (for the maximum displacements indicated

earlier) the error due to displacement along the axis is large compared to the error due to displacement perpendicular to the axis and the latter can be

neglected.

Stability of the magnetometer transfer standard has been shown to be of

the same order of magnitude as the uncertainty in the reference field itself

(0.015$), i.e., there was less than 0.02$ difference between readings taken

one month apart during which time the magnetometer was transferred to the

local calibration site and then returned to the reference field generated by

the solenoid.

I— [cose.! +cose

2

l , (36)

Total uncertainty in the magnetometer measurement of the known solenoid

generated field, B , (and hence the uncertainty in the calibration of the

magnetometer for ifs use as transfer standard) can be calculated in the worst

case, using the uncertainties in bold type above, as

[(0.015$)

2

+(0.02$)

2

] 1/2

+ 0.04$ = 0.065$ ,

i.e., the calibration factor for the magnetometer has an uncertainty of

±0.065$.

From eq (20), section 3.2, the dc field produced at the center of the

Helmholtz coil pair is

L 5 [5]

/ 2

(37)

24
Figure 9. Angles formed between the axis of a solenoid and lines joining a point, P, along the axis to the outer edges of the solenoid.

25
where the factor in the bracket is the Helmholtz coil factor K or K . Rearranging (37) allows Ku to be determined as

n h - b

h

7i

h

( 38 )

where is measured with the magnetometer, and dc current through the coils

is determined by measuring the dc voltage, V^, across a precision series

resistor, Ru . Then

H

b

h

rh

(39)

Four or five different I vs B„ measurements are made to arrive at an average

value for K . n The uncertainties involved in the determination of B^ are due to (1) the

uncertainty of the magnetometer calibration, previously determined as ±0.065?,

(2) the error in centering the probe within the Helmholtz coil pair, (3) the

averaging of B^ over the area of the probe, (4) ambient dc fields within the

area, and (5) reading error in the magnetometer.

The combined uncertainty due to possible misplacement of the magnetometer

probe in the Helmholtz coils, and to averaging over the area of the probe was found by experimentation, i.e., moving the probe by measured amounts, to be

approximately ±0.22%. The combined uncertainty was also calculated (see the

Appendix) and found to be ±0.24?. The latter figure is used. Either figure

is a significant portion of the total uncertainty and could be reduced by

construction of a larger set of Helmholtz coils. The uncertainty due to

ambient dc fields is of course largest at the lowest calibrating fields used

but does not exceed ±0.0556. Reading error in determining the magnetometer

null, i.e., the variation in the null point, is less than ±0.156. The root sum

of the above boldfaced uncertainties results in a ±0.26556 uncertainty in B^

.

The uncertainty in the measurement of using an accurate digital

voltmeter* is less than ±0.0156 provided R is selected to keep V within the

upper portion of the voltmeter range. A larger value for R^ is thus used when

I„ is reduced to produce lower values of B„.

n H

Standard resistors with uncertainties less than ±0.0156 were used for R^

with values of 1.0 ft, 10.0 0, and 100.0 0 and maximum currents of 0.3, 0.1,

and 0.03 mA respectively. A 0.1 0 fan-cooled resistor with ±0.03? uncertainty

and capable of passing 5 to 1 0 amperes was used when current in this range was necessary to produce Helmholtz coil fields in the 100 to 200 microtesla range.

Using the worst case resistor uncertainty and the uncertainties

previously determined for B^ and V^, the uncertainty in determination of the

dc Helmholtz coil factor, K , from eq (39) is thus

H

*Several different manufacturers produce instruments with a specified dr- voltage measurement uncertainty of less than ±0.01?.

26
or ± 0.27

$

[( 0.265$) . 2

+ (0.0U)

2

+(0.03^)

2

] 172

The coil factor, K , can also be calculated from

H

8UoN

5 [5]

1/2

r

> ( 40 )

where N is the number of turns wrapped on each coil and r is the radius (or

spacing) of the coils (see the discussion involving eq (20)). Because of the

difficulty in measuring either N or r exactly, however, eq (40) serves mainly

as an approximate check of the value for K . n Since the dc and ac coil factors are identical (K^ = K^), the ac field,

B^, produced by ac current, I , through the Helmholtz coil pair can now be

determined from eq (22). A specific calibration field for the AMFM-1 is set

by adjusting I . This current is determined by measuring the ac rms voltage,

it produces across an accurately known series resistor, R^. The equation

for determining B^ thus becomes

B

h

k

h \ (41)

As noted earlier, the uncertainty in k^ (same as K^) is less than

±0.27?. The uncertainty in the measurement of the ac rms voltage, V^, across

the series resistor is ordinarily somewhat larger than it is for the dc

measurement, V . The uncertainty in the ac measurement will also normally

depend more upon what portion of the range is used for the measurement. Worst

case total uncertainty for the ac rms instrument used was ±0.18$ (this

occurred at a voltage just above that which would give a full scale indication

on the more sensitive range immediately below).

The resistor used for R , whether 0.1 £2 or 1 .0 £2, has a temperature

coefficient less than 2 ppm/^C, a frequency response that goes well beyond the

20 kHz required in this application, unmeasureable self-generated noise and

excellent long term shelf and load life stability. The uncertainty in the

resistance value over the operating conditions can conservatively be put at

less than ±0.03$. The uncertainty in the value of B^ at the center of the

Helmholtz coil structure and parallel to the coils axis, as determined by eq

(41), is thus less than

[ (0. 27)

2

+ ( 0 . 1 8)

2

+ (0.03)

2

] 172 or < ± 0.33$ .

The AMFM-1 is calibrated by placing its donut-shaped probe at the center

of the Helmholtz coil pair with the plane of the probe perpendicular to the

coil axis. The sources of calibration uncertainty are due to (1) the

aforementioned uncertainty in the determination of B^ (±0.33$), (2) the

ambient ac magnetic field present, (3) the variation in B^ from its central

value over the area of the probe, (4) possible misalignment of the probe from

its intended central position within the coils, and (5) the AMFM-1 output

meter readout uncertainty.

As indicated in section 3.2, the Helmholtz coil is positioned for minimum

ambient ac magnetic field within the coil but some ambient will be present.

27
During the initial calibration of AMFM-1 , the ac rms ambient magnetic field

varied between approximately 20 and 60 nT. Using an average 40 nT figure, the

uncertainty in caused by the ac ambient field is ±0.04? at 100 yT (midscale

on range A) and ±0.4? at 10 yT (midscale in range B).

The effects of the uncertainty due to items (3) and (4) above, can be

combined and have been determined to be ±0.24? (see Appendix B). The

uncertainty in reading the AMFM-1 digital output is ±1 digit or 0.005? at full

scale, 0.01? at midscale, and 0.05? at 10? of full scale. Using the bold

faced uncertainty figures given above, the total uncertainty for the AMFM-1

calibration at midscale on the B range (10 yT) is thus

[(±0.33) 2+ (±0.4)

2

+(±0.24)

2

+(±0.01

)

2

] 1/2

= <±0.57?

of a midscale magnetic field reading.

The uncertainty due to the ambient magnetic field (±0.4?) is obviously

the largest contributor to the overall uncertainty of the AMFM-1 calibration.

With negligible ambient field, the uncertainty of calibration for all ranges

would simply be the uncertainty in the value of the calibrating field, B , plus the AMFM-1 probe position uncertainty and the meter readout uncertainty.

Using the worst_case foe meter readout uncertainty, this calculates as [(0.33) +(0.24) +(0.05) ] = 0.41?. Adding the percent uncertainty. caused

by a 0.04 yT ambient field, results in [(0.41 ) + [(0.04/100) x 100] ] or 0.412? uncertainty of calibration at 100 yT, i.e., the ambient effect is

negligible on the least sensitive range. Adding the percentage of uncertainty

in the ambient field to a 2 yT calibrating field results in [(0.41) + [(0.04/2) x 100] ] or 2.04? uncertainty of calibration at 2 yT (10? of full

scale on the B range or full scale on the C range) . Because of the growing

uncertainty in directly calibrating the more sensitive ranges, the AMFM-1 is

calibrated by voltage injection on these ranges, as explained in section 3.3.

The total uncertainty of the AMFM-1 calibration using voltage injection

includes uncertainties (1) in determining the AMFM-1 probe factor, k , (2) in

determining the voltage divider ratio, (3) in setting the generator Prequency,

(4) in measuring the generator output voltage, and (5) due to the noise

present at the AMFM-1 input.

The probe factor (the rms voltage output from the probe for a given 60 Hz ac magnetic field applied perpendicular to the plane of the probe), multiplied

by the resistive divider ratio, the desired magnetic field indication on the

AMFM-1 meter, and the ratio of 60 Hz to the calibrating signal frequency gives

the voltage required at the input to the divider to produce the correct

calibrating signal at the AMFM-1 input. See section 3-3 and eq (28) which,

for convenience, is reproduced below:

v = g

FM,

60

f

‘ (42)

The probe factor, k ' , is computed from information gathered during

calibration of the less Sensitive AMFM-1 ranges while using the Helmholtz x'

to produce the calibrating field. The uncertainties involved in determining

k

1 are (1) in the voltage measurement of the ac rms signal from the prot • ,

28
(2) in determination of the Helmholtz coil ac magnetic field which produces

this voltage, and (3) in positioning the probe correctly within the field so that it records the field determined in (2). Item (1) is simply the

previously determined worst case 'uncertainty of the ac rms voltmeter reading

(±0.18$). Item (2) uncertainty has already been calculated to be ±0.33$ with

an additional ±0.4$ due to possible presence of ac ambient fields. Item (3)

uncertainty was determined (see the Appendix) to be ±0.24$. This results in an uncertainty for k ’ of [(±0.l8$r + (±0.33$; + (±0.40$r + (±0.24$)

2

] 2

= ±0.60$ . As indicateH in section 3-3, the value for k ' to be used in eq (42)

is calculated from the average of four or five determinations at different

magnetic field values. This average should not differ from the extremes by

more than the ±0.60$ maximum uncertainty in the determination of each

individual value. If it does, the additional error should be added to obtain

the total uncertainty in the value of k^ f .

The uncertainty in the resistor divider ratio [R^/R^+1] is a function of

how accurately the absolute value of the resistances can be measured.

Accuracy is increased by using a highly stable ohmmeter for which a correction

factor has been computed. Ohmmeter stability is not always specified but can safely be assumed to be greater than the stated uncertainty of the instrument.

A 6-1/2 digit, 4-terminal meter which can integrate over 100 power line cycles

and which has- an uncertainty of less than ±0.006$ (for resistance values below

1.2 Mfl) was used. A correction factor for the meter was determined by using

the meter to measure a ±.002$ standard resistor of approximately the same

value as those used to make up the divider resistors and then dividing the

standard value by the measured value. This correction factor, which is as accurate as the standard resistor (assuming meter stability to be of the same

order of magnitude) is then applied to subsequent resistance measurements made

in that range during the same day. This enables absolute resistance values to

be obtained with an uncertainty of, at most, ±0.004$ of the corrected

value, and the divider ratio uncertainty to be calculated as [(±.004) +(±.004r] 2

= ±.0057$.

The generator frequency, f, can be measured with any reasonably good

counter to an uncertainty of less than ±0.02$. There is no uncertainty

connected with B since it is the selected value of the ac rms magnetic field

that the calculated value of v (from equation (42), and applied in the manner

of figure 8) is supposed to pr§duce on the AMFM-1 output meter.

Using the boldfaced uncertainties from above, the value for v can thus be calculated with an uncertainty of [(0.60; + (0.0057)

2

+ (§.02)

2

] ±0.60$ . The uncertainties in determining the divider ratio and frequency are

seen to be small compared to that in determining the probe factor, k^'

.

Once the appropriate value for v is determined (within the above

calculated uncertainty) it must still 8 be measured. The uncertainty of this

measurement, plus the effect of inherent noise at the divider output (input to

AMFM-1) must be added to obtain a total uncertainty of calibration using

voltage injection.

The k ’ for the current AMFM-1 probe is 3.91 millivolts per microtesla

and the voftage divider ratio (R^/R^ + 1 ) is 693-1 . Using eq (42) to

calculate v , for 60 Hz, a value of 2}.1 mV is required for a B, indication of

O 1

1

29
10 nT (midscale on the most sensitive range) and 5.4 mV for a B indication of

2 nT (10? of full scale on the most sensitive range).

An ac rms voltmeter with a 200-mV full-scale-range was used to measure v with an uncertainty less than ±0.2$ for v equal to or exceeding 20 mV. Belo§

this value, the uncertainty increases becluse of absolute uncertainty in the

last two digits of the display, i.e., a 5-1/2 digit meter with a lowest range

of 200 mV full scale providing an accuracy of 0.1$ of reading plus 20 digits

will result in an uncertainty of ±0.2$ at 20 mV, but 0.3$ at 10 mV and 0.5$ at

5 mV.

The percentage uncertainty due to inherent noise at the AMFM-1 input is

calculated by taking the ratio of the noise present at the AMFM-1 input to the

AMFM-1 input voltage required for calibration. (At 60 Hz, the AMFM-1 input

voltage required to produce B is simply k * B . ) A typical value for

inherent noise during the AMFM-1 calibration was 1.3 microvolts, resulting in

negligible uncertainty at midrange on range C (1.0 mG), but increasing to

0.33$ [1.3 x 10 jv(3.91 x 10 x 0.1)] at midrange on range D (0.1 pT) and

to 1.66$ [1 .3 x 10 4- (3.91 x 10 x 0.02)] at the upper end of range E (0.02 pT )

.

Total uncertainty of the voltage injection calibration for midrange on C

(1.0 pT), midrange on D (0.1 uT), and the upper end of E (0.02 pT) is

therefore [(0.60) + (0.2) ] = ±0.63$; . CIO. 60; + (0.2T + (0.33; ] ^ - ±0.71$; and [(0.60) + (0.2)^ + (1.66) j = ±1.78$, respectively.

Calibration uncertainties remain below ±1$ for measurements of magnetic field

down to 50 nT (ranges A through the upper 75$ of D) and below ±2$ for

measurements down to 15 nT (upper end of Range E)

.

Calibration uncertainties due to inherent noise from the voltage

injection divider increase to about ±15$ at the lower end of range E. Under

operating conditions, however, inherent noise is not a problem because of the

low source impedance of the AMFM-1 probe. Because of this and the fact that a check of range E made at higher voltage levels showed range E to be as linear

as the others, there appears to be no reason why measurements down to 2 nT

(lower end of Range E) cannot be made with an uncertainty of ±2$ of the

indicated value. Performance of the calibration in a shielded room might

reduce inherent noise sufficiently so that a calibration check could be

performed at the lower end of range E. This was not attempted.

4. SAMPLE MEASUREMENTS

This section provides a sample of some ambient magnetic field

measurements made with the AMFM-1 and its accompanying equipment.

Measurements were performed in three general locations; a laboratory, an office, and a home. The results consist of (1) the AMFM-1 4-1/2 digit rms indication of the maximum magnetic field in a given area, (2) an oscilloscope

time domain representation of the field, and (3) a spectrum analyzer frequency

domain representation of the field. Items (2) and (3) are reproduced in

figures 11 through 19 and item (1) is included in the figure captions for

item (2). Both oscilloscope and spectrum analyzer are connected to the output

of the AMFM-1. All of the above measurements are made after integration of

the signal within the AMFM-1 and as such are a true representation of the

ambient magnetic field present (see section 2.1).

30
A small, light-weight, battery-operated oscilloscope will normally be

used with the AMFM-1 to produce the time domain representation of the field.

For this report, however, a larger screen size and hence larger photographs

for easier viewing was achieved through use of an ac powered oscilloscope.

The oscilloscope was located at some distance from the measurement location so

as to not, of itself, affect the ambient field located there. The

approximately 6 meters of coaxial cable required to transfer signal between

the AMFM-1 and the oscilloscope produced a total capacitance to ground of

about 600 pf. Even at the highest frequency of interest, however (“3 kHz),

this added capacitance causes negligible loading on the output impedance of

the AMFM-1

.

The spectrum analyzer is a battery-operated device which did not

introduce measureable additional magnetic field even when located within

1.5 meters of the measurement site. Because of a temporary defect, the base

line or zero of the spectrum analyzer display was not adjustable to the bottom

line of the display graticule. A calibration curve, reproduced in figure 10, was therefore prepared and used to obtain correct amplitudes, e.g., an indication of 0.7 on the linear vertical scale is actually 0.715, and an indication of zero is actually 0.045.

Both absolute and relative indications produced by the spectrum analyzer

are shown in the figures. For the absolute indications, the rms value of each

harmonic can be determined from the vertical scale, after applying the

correction indicated in figure 10. For the relative indications, the 60 Hz

fundamental signal is adjusted to 1.0, thus allowing the percentage of other

harmonics to be determined from the vertical scale.

The laboratory ambient measurements were taken at the center of the

Helmholtz coil pair used for AMFM-1 calibration (coil not activated) with the

fluorescent lights immediately overhead both on (fig. 11a through 11c) and off

(fig. 12a through 12c). The office ambient measurement were taken in a room with metal walls at a position approximately 140 cm from the nearest wall and

80 cm from the front of a computer terminal/disk drive combination.

Measurements were made with the terminal/disk drive both on (fig. 13a through

13c) and off (fig. 14a through 14c).

The ambient measurements in a house were taken: (1) in a bedroom at a location 30 cm from, and on the same level with, a section of unloaded 120 V ac branch circuit wiring located within the wall (fig. 15a through 15c); (2)

in front of and 60 cm from a family room 26-inch television set, both with the

TV on (fig. 1 6a through 16c), and off (fig. 17a and 17b); and (3) 15 cm from

the right front of a kitchen microwave oven, both with the microwave on (fig.

18a through 18c) and off (fig. 19a through 19c).

It should be emphasized that the above test situations were selected to

evaluate the performance of the measurement system under typical applications.

No effort was made to determine whether or not specific nearby field

generating equipment or systems were typical of a class of devices; this

means, for example, that no effort was made to assure that the television set

used in this study was ’’typical.”

31
SPECTRUM

ANALYZER

LINEAR

SCALE

INDICATION

Examples: An indication of 0.7 on the linear vertical scale is actually 0.715.

An indication of zero on the vertical scale is actually 0.0^5.

Figure 10. Spectrum analyzer vertical scale correction.

32
Figure 11a. Oscilloscope display of laboratory ambient magnetic field waveform.

Overhead fluorescent lights on. AMFM-1 indication » 42 nT rms. Vertical scale = 50 nT/div. Horizontal scale = 5 ms/div.

Figure 11b. Absolute scale spectrum analyzer display of figure 11a waveform

showing the significant harmonics to be the first, third, and

fifth. Vertical scale » 10 nT/div. Horizontal scale = 50 Hz/div.

33
Figure 12a. Oscilloscope display of laboratory ambient magnetic field waveform.

Overhead fluorescent lights off. AMFM-1 indication - 27 nT rms. Vertical scale = 50 nT/div. Horizontal scale - 5 ms/div.

Figure 12b. Absolute scale spectrum analyzer display of figure 12a waveform

showing the significant harmonics to be the first, third, fifth,

seventh, and ninth, Vertical scale = 10 nT/div. Horizontal

scale = 100 Hz/div.

34
Figure 11c. Normalized spectrum analyzer display for the waveform of

figure 11a (laboratory ambient field with overhead fluorescent

lights on). Percentage of harmonics relative to the fundamental

can be determined from this display after applying correction

factors from figure 10. Horizontal scale = 50 Hz/div.

Figure 12c. Normalized spectrum analyzer display for the waveform of figure 12a

(laboratory ambient field with overhead flourescent lights off).

Horizontal scale = 100 Hz/div.

35
Figure 13a„ Oscilloscope display of office ambient magnetic field waveform.

Computer terminal/disc drive on. AMFM-1 indication - 0.32 yT rms. Vertical scale =0.2 yT/div. Horizontal scale = 5 ms/div.

Figure 13b. Absolute scale spectrum analyzer display of figure 13a waveform

showing the major harmonics to be the first, third and fifth, witn

contributions from many others. Vertical scale - 0.1 yT/div.

Horizontal scale = 100 Hz/div.

36
Figure 14a. Oscilloscope display of office ambient magnetic field waveform.

Computer terminal/disc drive off. AMFM-1 indication = 0.32 pT rms. Vertical scale = 0.2 pT/div. Horizontal scale = 5 ms/div.

Figure 1 4b . Absolute scale spectrum analyzer display of figure 14a waveform

showing the significant harmonics to be the first, third, fifth

and seventh. Vertical scale = 0.1 pT/div. Horizontal

scale = 100 Hz/div.

37
Figure 13 c„ Normalized spectrum analyzer display for the waveform of

figure 13a (office ambient field with computer terminal/ disc drive

on). Percentage of harmonics relative to the fundamental can be

determined from this display after applying correction factors

from figure 10. Horizontal scale = 100 Hz/di v.

Figure 14c. Normalized spectrum analyzer display for the waveform of figure

14a (office ambient field with computer terminal/disc drive off . Horizontal scale = 100 Hz/di v.

38
Figure 15a. Oscilloscope display of ambient magnetic field waveform obtained in

a home, 30 cm from, and on same level with a section of unloaded

120 V ac branch circuit wiring located within the wall. AMFM-1

indication - 10 nT rms. Vertical scale = 10 nT/div. Horizontal

scale => 5 ms/div.

Figure 15b. Absolute scale spectrum analyzer display of figure 15a waveform

showing the significant harmonics to be the first, third, fifth

and ninth. Since the amplitude of the first harmonic falls at

the top of the vertical scale, this figure can also be used as the normalized spectrum analyzer display. Vertical

scale =* 1.0 nT/div. Horizontal scale = 100 Hz/div.

39
Figure I6a„ Oscilloscope display of ambient magnetic field waveform obtained in a home, 60 cm from the front center of an operating 26-inch screen television set. AMFM-1 indication = 0.17 yT rms. Vertical

scale =0.2 pT/div. Horizontal scale = 5 ms/div.

Figure 16b. Absolute scale spectrum analyzer display of figure 1 6a waveform

showing a number of significant harmonics which decrease in

amplitude from the second through the nineteenth. Vertical

scale = 0.2 pT/div. Horizontal scale = 200 Hz/div.

40
Figure 16c. Normalized spectrum analyzer display for the waveform of figure 1 6a

(home ambient field 60 cm from front of operating 26-inch TV).

Percentage of harmonics relative to the fundamental can be

determined from this display after applying correction factors from

figure 10. Horizontal scale = 200 Hz/div.

41
Figure 17a. Oscilloscope display of ambient magnetic field waveform obtained in a home under the same conditions as figure 1 6a except that the TV

is turned off. AMFM-1 indication - 8.5 nT rms. Vertical

scale = 20 nT/div. Horizontal scale = 5 ms/div.

Figure 17b. Absolute scale spectrum analyzer display of figure 17a waveform

showing the significant harmonics to be the first and third.

Vertical scale = 2.0 nT/div. Horizontal scale - 200 Hz/div.

42
Figure 18a. Oscilloscope display of ambient magnetic field waveform obtained in

a home 15 cm from the front of an operating microwave oven. AMFM-1

indication » 4.7 uT nns. Vertical scale = 5 yT/div. Horizontal

scale = 5 ms/div.

Figure 1 8 b . Absolute scale spectrum analyzer display of figure 18a waveform

showing the significant harmonics to be the first, third, fourth

and fifth. Vertical scale = 1.0 yT/div. Horizontal

scale = 50 Hz/div.

43
Figure 19a. Oscilloscope display of ambient magnetic field waveform obtained in a home under the same conditions as figure 18a except that the

microwave oven is off. AMFM-1 indication - 52 nT rms. Vertical

scale = 50 nT/div. Horizontal scale => 5 ms/div.

Figure 19b. Absolute scale spectrum analyzer display of figure 19a waveform

showing the significant harmonics to be the first, second, third

and fifth. Vertical scale = 10 nT/div. Horizontal

scale = 50 Hz/div.

44
Figure 18c. Normalized spectrum analyzer display for the waveform of figure 18a

(home ambient field in front of operating microwave oven).

Percentage of harmonics relative to the fundamental can be

determined from this display after applying correction factors from

figure 10. Horizontal scale = 50 Hz/div.

Figure 19c. Normalized spectrum analyzer display for the waveform of figure 19a

(home ambient field in front of non-operating microwave oven).

Horizontal scale = 50 Hz/div.

45
5. ACKNOWLEDGMENTS

The author is pleased to acknowledge the assistance of Arnold Perrey in

the layout and construction of the fieldmeter, the assistance of Barbara Frey

and Roberta Cummings during preparation of this manuscript, and the useful

conversations with Martin Misakian, Owen Laug, Robert Hebner and

Oskars Petersons. The support of the Department of Energy is also gratefully

acknowledged.

46
6. REFERENCES

[1] N. Wertheimer and E. Leeper, "Electrical Wiring Configurations and

Childhood Cancer," American Journal of Epidemiology, Vol. 109, No. 3,

(1979), pp. 273-284.

[2] "Extremely Weak Magnetic Fields Affect Behavior," Microwave News,

Vol. 4, No. 9, (1984), pp. 1-2.

[3] G. Theriault, "Critical Review of Epidemiological Studies on the

Relationship Between Various Electromagnetic Parameters and the

Incidence of Cancer," School of Occupational Health, McGill University,

Montreal, Quebec, Canada, May 10, 1984, 27 pages.

[4] P. Beiersdorfer and E. J. Clothiaux, "High-Frequency Magnetic

Measurement Using Small Inductive Probes," American Journal of Physics,

Vol. 51, No. 11 (1983), PP- 1031-1036.

[5] J. R. Reitz and F. J. Milford, "Foundations of Electromagnetic Theory,"

Reading MA: Addison-Wesley; I960, p. 156.

[6] M. A. Plonus, "Applied Electro-Magnetics," New York: McGraw-Hill; 1978,

p. 225.

[7] J. A. Stratton, "Electromagnetic Theory," New York: McGraw-Hill, 1941.

P. 233.

[8] E. R. Williams and P. T. Olsen, "New Measurement of The Proton

Gyromagnetic Ratio and A Derived Value of the Fine Structure Constant

Accurate to A Part in 10 ," Physical Review Letters, vol. 42, No. 24,

(1979), pp. 1575-1579.

[9] Forest K. Harris, "A Nonmagnetic laboratory for the National Bureau of

Standards," IEEE Spectrum, Nov. 1966, p. 85.

[10] S. Ramo and J. R. Whinnery, "Fields and Waves in Modern Radio," New

York; John Wiley and Sons; 1944, p. 1 4 1 f f

.

[11] E. R. Peck, "Electricity and Magnetism," New York; McGraw-Hill; 1953,

p. 209.

47
APPENDIX

CALCULATION OF COMBINED UNCERTAINTY DUE TO POSSIBLE PROBE MISALIGNMENT

WITHIN HELMHOLTZ COILS AND TO FIELD VARIATION OVER AREA OF PROBE

The uncertainties due to the possible misalignment of the AMFM-1 magnetic

field probe from its intended central position within the Helmholtz coil pair

and to the variation in magnetic field, B^, from its central value over the area of the probe can be combined and calculated. For simplicity, this is

done in two steps, first determining the variation in B that occurs within

the Helmholtz coils over an area somewhat larger than the probe to allow for

probe misalignment from its intended center position while its plane remains

perpendicular to that of the coil axis, and then adding to this the error which can occur if the plane of the probe is not perpendicular to the coil

axis. The same procedure also applies to possible misalignment of the

magnetometer probe which is used in determining the dc Helmholtz coil factor,

Referring to the diagram of figure 20, the field parallel to the

Helmholtz coil axis, B , at any point p whose location is defined by spherical

coordinates r and e [l5] is

B (r , 0) = u

y NTb‘

o h

2 4 [2+A o [P„(cos0) ]r + A^CP^CcoseDr +.

2 ( b

2

+ d

2 )’- 5

2 2

.]

where A^ = 2 2 2

15d -3(b +d ) ,.2 . 2.2

(b +d )

A

4 -

2 2 2 2 2 2 4 15(b +d ) - 21 0d (b +d ) + 315d

4(b

2

+d

2

) 4

(B-1

)

and b is the coil radius, d is one-half the coil spacing, is the

permeability of air (vacuum), N the number of turns on each coil, 1^ the ac current through the coils and P (cose) are Legendre polynomials of order m. For Helmholtz coils where, 2d=b, the term involving A vanishes, the value

of A. becomes approximately 1/7(d) and the field is fairly uniform over a volume surrounding the center. The dimensional uncertainty of b and d due to

the finite size of the wire bundle comprising N on each coil was accounted for

during the determination of the Helmholtz coil factor, K^, and does not add

further uncertainty.

Equation (B-1) was evaluated by computer over a volume defined by a cylinder with axial symmetry, centered within the coils, 6 cm thick along the

z axis and 16 cm in diameter in the x,y plane. Since the AMFM-1 probe outer

dimensions are approximately 2 cm thick by 10 cm in outside diameter, the

probe could be positioned off center by 3 cm in any direction and still remain

within the above defined cylinder. The values of (1) 6-90° with r - 0.08

meter and (2) 9 = cot (z/x) with x equal to plus or mltjus 0.08 m^t^i^and z equal to plus or minus 0.03 meter (and hence r = [(0.08) (0.03) ] define

the edges of said cylinder. Computer evaluation provided a maximum deviation

in B (equivalent to B. ) of ±0.15$ from nominal at the outer edge of the

defined cylinder. The worst case occurs when the probe is shifted only in the

x,y plane away from center, i.e., 0 = 90° and r - 0.08 meter. However, If the

48
z

a

d

y

Figure 20. Configuration of Helmholtz coil pair for generating a magnetic

field in the Z direction, together with the coordinate system used

in the discussion of field variation at points away from center.

/ 49
outer edge of the probe were 8 cm from the Helmholtz coil central axis, the

center of the probe would be approximately 3 cm from the axis and the error at

this point (0=90° and r=0.03 meter) is only 0.003$. Since the probe averages

the magnetic field over its area, an uncertainty specification of ±0.1$ is

more than adequate for this portion of the position error.

In addition to being centered along the Helmholtz coil axis, the plane of

the probe should also be perpendicular to the axis. Variation of the probe

plane from perpendicular to the axis produces a percentage error which can be

determined by (1-cos <j>) x 100 where <J> is the angle between the plane of the

probe and a plane perpendicular to the coil axis. Assuming a maximum possible

misadjustment of 3 degrees, the uncertainty resulting is (1-cos 3°) x 100 or

0 . 14$. Adding this to the uncertainties due to possible position error

(0.1$ + 0.14$) results in a total possible uncertainty due to AMFM-1 probe

misalignment of < ±0 . 24$ .

The magnetometer probe sensing area is approximately 6 cm long and 2 cm square, hence the outer limits of its reasonable misplacement should also fit

within the cylinder defined above. In fact, because of its smaller area normal to the Helmholtz coil axis, displacements greater than 3 cm from the

axis should easily be noticed. Angular misadjustment would also be more

noticeable because of its shape, hence the three degree maximum assumed for

the AMFM-1 probe is applicable.

50
jlftS.IMA (REV. 2»H0>

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

4. TITLE AND SUBTITLE

1. PUBLICATION OR 2 REPORT NO.

NBSIR 86-3330

. Perform

722

ing Organ. Report NoJ 3. Publication Date March 1986

NBS Ambient Magnetic Field Meter for Measurement and Analysis of

Low-Level Power Frequency Magnetic Fields in Air

5. AUTHOR(S)

P. M. Fulcomer

S. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions) 7 . Contract/Grant No. NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE g. Type of Report & Period Covered

WASHINGTON, D.C. 20234

!. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

Department of Energy

Division of Electric Energy Systems

1000 Independence Avenue, S. W.

Washington. DC 20585

II. SUPPLEMENTARY NOTES

J Document describes a computer program; SF-185, FIPS Software Summary, is attached.

II. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

This report describes a portable, battery-powered magnetic

fieldmeter which has been developed to provide improved accuracy in the

measurement and analysis of low-level and ambient power-frequency

magnetic fields. Accurate measurement of such fields is becoming

increasingly important as public concern grows over the possibility that

exposure to such fields may produce effects on human health. Included in

the report are a description of the instrumentation, a circuit analysis,

a discussion of the calibration procedures together with an uncertainty

analysis, and some sample measurement results. The instrumentation

enables measurement of power-frequency magnetic field in air with an overall uncertainty of less than one percent over a range from

50 nanotesla (500 microgauss) to 200 microtesla (2 gauss) and an overall

uncertainty of less than two percent down to 2 nanotesla (20 microgauss).

It also enables the percentage of each harmonic present in the field to

be determined to an uncertainty of less than three percent.

I

I

'2. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) qmbient magnetic field;. calibration; calibration. uncertainty; flux density;

Lowrlev^l magnetic "field ; magnetic • fieldmeter ; magnetic field strength; magnetic flux

density; magnetic induction; measure; meter; power frequency magnetic field

l1, AVAILABILITY

14. NO. OF

0 Unlimited PRINTED PAGES

For Official Distribution. Do Not Release to NTIS 58

O 20402 ^ r°m Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

15. Price

0Order From National Technical Information Service (NTIS), Springfield, VA. 22161

- $11.95

u SCOMM-DC 6043-P80
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