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\ NBS TECHNICAL NOTE 687

*<"*AU 0* h

U.S. DEPARTMENT OF COMMERCE / National Bureau of Standards

Measurement of

RF Power-Absorption in

Biological Specimens

(10 to 100 MHz)
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards' was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology

and facilitate their effective application for public benefit. To this end, the Bureau conducts

research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau consists of the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology,

the Institute for Computer Sciences and Technology, and the Office for Information Programs.

THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United

States of a complete and consistent system of physical measurement; coordinates that system

with measurement systems of other nations; and furnishes essential services leading to accurate and uniform physical measurements throughout the Nation's scientific community, industry,

and commerce. The Institute consists of the Office of Measurement Services, the Office of Radiation Measurement and the following Center and divisions:

Applied Mathematics — Electricity — Mechanics — Heat — Optical Physics — Center

for Radiation Research: Nuclear Sciences; Applied Radiation — Laboratory Astrophysics 2 — Cryogenics ~ — Electromagnetics " — Time and Frequency 2

, THE INSTITUTE FOR MATERIALS RESEARCH conducts materials research leading to improved methods of measurement, standards, and data on the properties of well-characterized

materials needed by industry, commerce, educational institutions, and Government; provides

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THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts research and provides technical services designed to aid Government agencies in improving cost effec- tiveness in the conduct of their programs through the selection, acquisition, and effective utilization of automatic data processing equipment; and serves as the principal focus within

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divisions: Computer Services — Systems and Software — Computer Systems Engineering — Information Technology.

THE OFFICE FOR INFORMATION PROGRAMS promotes optimum dissemination and

accessibility of scientific information generated within NBS and other agencies of the Federal Government; promotes the development of the National Standard Reference Data System and

a system of information analysis centers dealing with the broader aspects of the National Measurement System; provides appropriate services to ensure that the NBS staff has optimum

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1 Headquarters and Laboratories at Gaithersburg, Maryland, unless otherwise noted; mailing address Washington, DC. 20234.

- Located at Boulder, Colorado 80302.
9

Measurement of RF Power -Absorption

in Biological Specimens (10 to 100 MHz)

Frank M. Greene

Electromagnetics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

***T

\

£&3

V»u of *

U.S. DEPARTMENT OF COMMERCE, Elliot L. Richardson, Secretary

Edward O. Vetter, Under Secretary

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

U.^ NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

Issued November 1976
NATIONAL BUREAU OF STANDARDS TECHNICAL NOTE 687

Nat. Bur. Stand. (U.S.), Tech Note 687, 29 pages (November 1976)

CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1976

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

(Order by SD Catalog No. C13. 46:687) Price 75 cents. (Add 25 percent additional for other than U.S. mailing)
CONTENTS

Page

1. INTRODUCTION 2

2. THEORY 3 2.1 Introduction 3

2.2 Forward and Reflected Power 4 2.3 Analysis of the Field Generator 5

3. MEASUREMENT APPLICATIONS 10

3.1 Key Equations and Curves 10

3.2 Measurement Example 10

4. OPERATING PROCEDURE 14

5. MEASUREMENT SENSITIVITY 15

5.1 Basic Sensitivity 15

5.2 Increasing the Sensitivity 15

6. MAGNETIC-INDUCTION HEATING IN A LOSSY DIELECTRIC 19

6.1 Introduction-' 19

6.2 Theoretical Background 19

6.3 RF Heating Density 21

6.4 Total RF Heating 21

7. THE CALORIMETER METHOD 23

8. CONCLUSIONS 24

9. REFERENCES 25

1X1

MEASUREMENT OF RF POWER-ABSORPTION IN BIOLOGICAL SPECIMENS

(10 to 100 MHz)

Frank M. Greene

Electromagnetics Division

National Bureau of Standards

Boulder, Colorado 80302

ABSTRACT

A method is described for accurately determining the rf

power being absorbed by a biological specimen during non-ionizing

radiation-exposure testing using the NBS RF Near-Field Synthesizer

in the frequency range 10 to 100 MHz. This method is based

solely on measuring the forward and reflected power on the

transmission line feeding the synthesizer. Commercially available rf wattmeters can be used, and an automatic data-acquisition

system employed, if desired, to "read" the meters and rapidly

calculate, display, and record the rf power flow.

The method has the advantage that the exact measuring point

on the feed line is not critical, as it is with methods employing

direct impedance measurements, and that the required measurements

can be made without interfering with the exposure tests.

Key words: Electromagnetic field hazards; electromagnetic field

synthesizer; electromagnetic radiation-exposure testing (nonionizing) ; near-fields; rf biological hazards.
1. INTRODUCTION

A method will be described for determining the total amount

of rf power being absorbed by a biological specimen during nonionizing radiation-exposure testing using the NBS RF Near-Field

Synthesizer in the frequency range 10 to 100 MHz [1] . This method

is based solely on measuring the forward and reflected power on

the transmission line feeding the field synthesizer. Commercially

available rf wattmeters and an automatic data-acquisition system

can be employed to further simplify the procedure.*

The near-field synthesizer is installed and operated in a doubly-shielded copper room having a shielding efficiency of

60 dB or more. Any electromagnetic radiation from the synthesizer or test specimen is reduced by a factor of at least 10

by the shielding. Radiation losses are therefore considered

to be completely negligible. Coupling between the synthesizer

and the interior copper walls of the shielded room has been

found to be essentially reactive. Very little resistance is

coupled back into the synthesizer from the walls of the room. The rationalized mks International System of Units (SI) is

used throughout this report.

*This report is the outgrowth of work originally sponsored by the

USAF School of Aerospace Medicine at Brooks AF Base, and the National

Institute for Occupational Safety and Health of the Department of HEW.
2. THEORY

2.1 Introduction . The NBS RF Near-Field Synthesizer consists of both an electric-field, and a magnetic-field generator.

These two field generators consist of a balanced parallel-plate

stripline and a balanced four-gap single-turn loop inductor for

generating the "wanted" electric and magnetic fields, respectively [1] . Multiple feeds and balanced symmetry are used to

minimize the "unwanted" magnetic and electric field components and

to permit superposing the "wanted" fields without significant cross

coupling. For the sake of producing hazard-level fields with a minimum of driving power, these field generators are resonated. > The two generators can be operated simultaneously to produce a large range of values of E/H, or individually [1]

Each field generator has its own driving transmitter (source)

and rf feed system, and the two generators can be considered to

be operating essentially independently. The analysis that follows applies to each field generator individually. If both field

generators are operating simultaneously, the total power absorbed

by the biological specimen may be obtained by adding the power

absorbed from each field generator. It has been found at NBS and

elsewhere [2] that the magnetic field may represent a greater

biological hazard than the electric field in the frequency range

under consideration here. Therefore, this analysis will probably

be used for the most part with the magnetic-field-generator

portion of the near-field synthesizer.

The use of steady-state, sinusoidally time-varying rf driving

sources is assumed throughout this report. It is not necessary

that these sources be matched to their respective feed lines with

this method since only the ratio of the reflected power to the

forward power is involved. The sources comprise tuned Class-C rf

power amplifiers which must be operated with as much as a 5:1

impedance mismatch in order to obtain the required rf power

output with a plate efficiency of 75 to 80 percent [3]
2.2 Forward and Reflected Power . Either field generator is

fed rf power by means of a reasonably low-loss 50-ohm transmission line. Either field generator can be tuned and adjusted

independently to present a 50-ohm load to its feed line at the

operating frequency before the biological specimen is put in

place. After the specimen is inserted, the rf power that it

absorbs can be determined directly in terms of the reflection

that it produces.

The quantities to be discussed now are to be measured on the

transmission line feeding either field generator. Since only

measurements of the component forward and reflected waves are

involved, the exact point at which they are measured is not

critical on a low-loss line. This is one of the advantages of

this method over methods based on direct impedance measurement.

The complex reflection coefficient, T, at the receiving end

of a uniform lossless transmission line is given by [4,5]

Z T - Z Zl - 1

r = ^ *--£ , (D

z l

+ z o

Z L

+ x

where Z' = Z T /Z . Z T is the load impedance presented by either

J_i J_j O J-j field generator 3 to its feed line, and Z is the characteristic

o impedance of the line. For this analysis Z_ and Z are both

considered to be resistive as will be discussed later, making r real in the limit.

The forward power , P_ , flowing toward the load is given by

P

f = — , (2)

Z o where Vf is the rms value of the magnitude of the forward-traveling

voltage wave.

The reflected power , P , flowing back to the source is given

by

V

2 P

r = — , (3)

Z o
where V is the rms value of the magnitude of the backwardtraveling (reflected) voltage wave. Also

V

r

= r V (4)

Therefore, the reflected power is also given by

p = -

z o

(5)

The ratio of the reflected power to the forward power is

therefore given by

p o -^=r2

. (6)

p

f The load power , P , actually absorbed by the load, Z , is the

arithmetic difference between the forward power , P

f

, and the

reflected power , P , if Z is resistive, i.e.,

P

L

= P

f - Pr

. (7)

The ratio of the load power to the forward power is given by

P—L 2 = i - r 2

, (8)

p

f

as obtained from eqs . (6) and (7)

2.3 Analysis of the Field Generator . Each field generator

can be represented by an equivalent, tapped, parallel-resonant

tank circuit, as shown in figure 1. It should be pointed out,

however, that the basic results obtained from this model are also

valid near resonance when used with transmission-line types, as well as waveguide types of resonators [6], as will be discussed

in connection with eq. (11)
From Ohm's law it can be shown, with the aid of figure 1,

that the power absorbed by the biological specimen, P , and the

load power , PT

, are in the same ratio as the internal rf loss

resistances involved. That is,

P R„ a 2 P

L

R

x + R

2

(9)

where R, represents the loss resistance of the field generator

itself prior to inserting the biological specimen, and R? is the

loss resistance coupled into the generator from the biological

specimen after retuning.

It is assumed that the presence of the specimen and the

subsequent retuning do not cause a sufficient change in the

field distribution within the field generator to change its

internal metallic losses. This is believed to be a reasonable

assumption. The metallic conductivities involved are so high

that the form of the fields is unchanged by the losses that

result. The total loss can therefore be computed by adding

directly the values of the metallic losses and the dielectric

losses [7]

The internal resistance of the field generator is transformed at its input terminals at resonance in accordance with the

following relationship, valid provided Q >^ 10 [8]

X

2

~ 1

z

T = — , (10) L R

where, from figure 1, X-, is the inductive reactance of the shunt

matching inductor, and R is the total series rf resistance of the

tank circuit. When eq . (10) is substituted into eq. (9) we obtain,

after rearranging,

P R-, Z — = 1 =1 - = 1 - Z'

,

(11)

PTR-, + R Z L 12 o
->A/sA \AAAFigure 1 . The equivalent lumped-constant circuit diagram of

either the electric-field or the magnetic-field generator.

Figure 2 . Vector diagram representing the numerator, Z L

- Z

( and the denominator, z"L

+ Z , of eq. (la), where Z q

is considered to be resistive.
2 2 since Z = X

1 /(R

1

+R

2 ), and Z q

= X

1 /RL = 50 ohms, from eq. (10),

with Z' limited to the range < Z' < 1. Equation (11) shows the

L — -Li —

basic relationship between the power absorbed by the biological

specimen, P , and the input impedance of the field generator at

a resonance, Z T

, and can be used with any type of two-terminal

resonator or cavity, as previously mentioned.

In practice, the field generator is first tuned and adjusted

for zero reflected power (by adjusting both X-, and X, of figure 1)

to give an input impedance of Z = 50 ohms before the biological

specimen is put in place. Afterwards, the field generator is

retuned for minimum reflected power (by adjusting X-. only) . This

cancels any reactance coupled in from the specimen, making Z resistive in both cases as shown in the following paragraph.

The complex receiving-end reflection coefficient is given by

eq. (1) , rewritten as

Z T - Z z" r - =^^ - =* • (la)

Z T + Z Z_, L o B

The numerator is the vector difference and the denominator the

vector sum of Z T and Z , as shown in figure 2, where Z is con- L o

3 o sidered to be resistive. The numerator of eq . (la) will be a minimum and the denominator a maximum simultaneously when Z becomes resistive, thus minimizing r as can be readily seen from

figure 2

Solving eq. (1) for Z' gives

i + r z; =

x

. (12) L

l - r Substituting eq. (12) into (11) gives

p 2|r| — = , (13)

p. i + I r I
with r limited to the range -1 <_ T <_ . Using eq. (6) , eq . (13) can also be written

P 2/P/pT

a r' f

P T l + /p~7pT L r f

(14)

To obtain the ratio of the power absorbed by the specimen,

P , to the forward power , P

f

, eq. (13) must be multiplied by

eq. (8) , giving — = 2|r| [i-|r|l . (15)

Pf L J

Using eq. (6) again, eq . (15) can also be written

P

a

P = 2/v^[i - /v^]-

f

Finally, eq. (8) can be included in the form

(16)

P P — = 1 . (17)

P P *f f
3. MEASUREMENT APPLICATIONS

3.1 Key Equations and Curves . Equations (14), (16), and

(17) are the key equations to be used in this technique. As can

be seen, the power absorbed by the biological specimen, P , can

be obtained relative to either the load power , P , or the forward

power , P

f

, knowing only the ratio of the reflected power to the

forward power , P /P f

, as summarized in table I.

Equations (14) and (17) are shown plotted in figure 3 as curves (a) and (b) , respectively. Equations (16) and (17) are

shown plotted in figure 4 as curves (a) and (b) , respectively.

It is interesting to note from curve (a) of figure 4 that the

power absorbed by the specimen, P , can never exceed half of the

a forward power , P f

. This maximum occurs when the reflected power

is 25 percent of the forward power .

3.2 Measurement Example . An example will be given to

illustrate the use of the equations and curves. It is assumed

that the field generator is first tuned and adjusted for zero

reflected power to give an input impedance of 50 ohms before the

biological specimen is put in place. Afterwards, the generator

is retuned for minimum reflected power to cancel any reactance

coupled in from the specimen, as previously discussed.

Example

Assume that the forward power , P

f = 100 watts, and the

reflected power , P =11.1 watts. Then P /P_ = 0.111. The

load power , P

T

, can be obtained from eq. (17) or curve (b) of

figure 3, if desired, as P = 100-11.1 = 88.9 watts. From eq.

(14), or curve (a) of figure 3 (corresponding to P /P f = 0.111)

the ratio P /PT = 0.500. That is, half of the l oad power, or

a j_i 44.4 watts, is absorbed by the biological specimen, and the other

half goes into heating the field generator. This same value of

absorbed power , P , can also be obtained directly from eq. (16)

,

or curve (a) of figure 4, giving P /P^ = 0.444, or P =44.4 watts

a r a as before.

10
Table I

RF Power Absorbed by a Biological Specimen

Power Ab- Power AbReflected Load sorbed by sorbed by

Power Power

Eq. (8)

Specimen

Eq. (14)

Specimen

Eq. (6) Eq. (16)

P

p^ x 100

f

p^ x 100

P

p^- x 100

L

P

H^ x 100

f

(%) (%) (%) (%)

0.00

0.10

0.20

0.50

1.00

2.00

4.00

6.00

8.00

10.00

11.11

15.00

20.00

25.00

30.00

40.00

50.00

60.00

70.00

80.00

90.00

100.00

Theoretical limiting value

100.00 0.00 0.00

99.90 6.13 6.12

99.80 8.56 8.54

99.50 13.21 13.14

99.00 18.18 18.00

98.00 24.78 24.28

96.00 33.33 32.00

94.00 39.35 36.99

92.00 44.10 40.57

90.00 48.05 43.25

88.89 50.00 44.44

85.00 55.83 47.46

80.00 61.80 49.44

75.00 66.67 50.00

70.00 70.78 49.54

60.00 77.49 46.49

50.00 82.84 41.42

40.00 87.30 34.92

30.00 91.11 27.33

20?.00 94.43 18.89

10.00 97 - 37 (a)

9.74

0.00 100.00 v ' 0.00

11
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:::::::

_l - - — • V»+- ;i3f *

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| ; | V; ; ; ; ; v

1 Q. Li ' ^

ut ' / \ ];-;! ; ; 1\ '

! V _i ! . ! . ! ; !

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.

' . ( 01 ' II

"O~ /

«—1 /

<D vj / • ... .-^ .............. . (_J «*,'„,, v . ...;..,.,.; rt- T^ " ± 1 -------- ± Oil 1 O ! I !/

'

i

i

!

I ^ III/] 1 i II T T

>ionu- <—> 41 J:

*->

*v r i 1 , V f\J «-» rv| i ::::: r^ o I - i 1

1 1! r i \

f

(

1 ± __ _ . _ ___

o'lllilllilllllllllllllilllllllllllllilillHi.lnlllli 1 1 1 1 1 1 1 1 1 M 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 ,1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ITsI O

o

o

a.

a>$o

0_"Oo

O

20 40 60

Reflected Power, (P

r /Pf )xi00, %

80 100

Figure 3 . (a) RF power absorbed by the biological specimen,

and (b) load power, (Pr/P f

(P ) x 100, % ; both

a/P

L

) x 100, %; vs the reflected power, (P /Pf

) x 100, %; where P

f is the

forward power in watts

12
o O

1

1 i i 1. 1 1

1

1 1 1

1

i ii 11 11 1 1

1 M i ii 1 1 1, 11 n 1, o

N

>S ifc

s 5±E

::::::::::::::;:::::::::::::;::::::: :::::;;:;:

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*- / ? /' —*""

| T

o / 1 T T o^ ri / - j:i ">X /-> "- tJ J^ ii i i rw r '-'

(\| I .. .... ! 4 "S4! . . . ._,_-,- oj O 1

v

^1 t^H -,- ,

<^> 1 I i M J ;

: 1 : :: l 1 1: , ; 1 : : ; ; i : : : : 1 : ; : ; i ; ; : , i , , , 1 1 1 1 M t f 1 1 1 1 1 1 1 1 1 1 M M 1 1 1 1 1 1

! : 1 : :: : t : : : 1 1 ; : i : 1 : ! ; : 1 ; ! ?TsJ o

20 40 60

Reflected Power, (P

r /Pf )xl00, %

80 100

Figure 4 . (a) RF power absorbed by the biological specimen,

(P /P

f

) x 100, %; and (b) load power, (P L/P

f

) x 100 > % ? both

vs. the reflected power, (P /P

f

) x 100, %; where P

f

is the

forward power in watts.

13
4. OPERATING PROCEDURE

(a) The rf directional couplers of the wattmeters being used

should be inserted in the feed-line to each field generator,

usually within one or two meters of the generator input

terminals. The exact location is, however, not critical

with this method, as discussed in section 2.2.

(b) The input channels of the automatic data-acquisition system

can be connected directly to the respective dc terminals of

the microammeters used to indicate forward and reflected

power. Store the calibration data of these wattmeters in

the associated computer as part of the data acquisition

program (i.e., rf watts input to the coupler vs. dc millivolts

output)

.

(c) The field generator should be adjusted at the desired operating frequency (in the absence of the biological specimen)

in accordance with the usual procedure [1]

.

(d) Adjust the generator matching networks for zero reflected

power , so that the generator presents a load impedance

Z T = 50 ohms to its feed line.

(e) The rf power input to the field generator should then be

reduced and the biological specimen placed at its center.

(f) The rf power should then be gradually increased and the

tuning capacitors of the generator matching units carefully

readjusted for minimum reflected power. This cancels the

reactance coupled into the field generator from the specimen

as discussed in section 2.3

(g) Read the forward power , P

f

, and the reflected power , P

r Calculate the ratio, P /P £ , and the load power, PT = P_ - P . ' r' f ' *- L f r The remainder of the calculations should be made as outlined

in section 3.2.

14
5. MEASUREMENT SENSITIVITY

5.1 Basic Sensitivity . The basic measurement sensitivity

[9] or resolution, 6, of the method being described is given by

the ratio of the reflected power , P /Pf

, to the power absorbed

by the biological specimen , P_/P

f

/ at the final operating point

on the characteristic curve (eq. (16)), i.e.,

P /P

f Measurement sensitivity = 6 = — . (18)

P /P*

a' f

From eq. (16) or curve (a) of figure 4, it can be seen that

the measurement sensitivity is zero when P /P f = 0, and increases

with increasing values of P^/P-r to a sensitivity of 0.500 when

P /P, = 0.500, probably the upper limit of the useful measurement

a r range. While the sensitivity is deemed to be adequate over most

of the measuring range, it can be increased for low values of

P /P^ by: (a) using a more sensitive wattmeter element for

a t measuring the reflected power (readily available) ; (b) reducing

the power and increasing the coupling between the specimen and

the field generator to increase P /P f

; or (c) choosing the

initial operating point higher on the characteristic curve.

5.2 Increasing the Sensitivity . The latter method of

increasing the measurement sensitivity involves adjusting the

input impedance of the field generator, Z , to an initial value

greater than 50 ohms prior to placing the biological specimen in

the generator. The resulting relationship between pr/P

f

and

P /P_ can be determined by rewriting eq. (11) as

P Z' SL = 1 - J± , (19)

PT N

J-J where N = Z T /50. Z' is limited to real values in the range

La J-i < Z* < N. Equation (12) is then substituted into eq. (19) and — Ls —

15
the result multiplied by eq . (8) , giving

Pa . (N-l) - 2T - (N+1)T

(20)

P

f

N

N-l where T is limited to real values in the range -1 £ T <_ ^rrUsing eq. (6), eq. (20) can be written

D (Pr/Pf

) (21)

P

a (N-l) ± 2/P

r/Pf

- (N+l) (P r/P

f

)

P

f

N

where the (+) sign is used when r is negative (Z < 50 ft) , and

the (-) sign when r is positive (Z > 50 ft) . The rf power meters used in this technique, of course,

cannot distinguish between positive and negative values of r, so that some other means must be employed. One such simple technique would be to slowly increase the value of Z . If this

Li causes P to increase, then Z T > 50 ft. If an increase in Z x r L L

causes a decrease in P , then Z T < 50 ft. r ' L

Equation (21) is shown plotted in figure 5 for values of

N = 1, 2, 3, 5, 10, and °°, for the permissible range of values

of r given for eq. (20) . The upper part of each curve results

from negative values of T , and the lower part from positive

values. As can be seen, the measurement sensitivity (when

Pa/Pf = 0) has a value of 6 = when N = 1, increasing to a limiting value of 6 = 1 as N is increased. This represents an improvement in sensitivity for values of P /Pf

< 0.5.

As can be seen from figure 5, the reflected power (caused

by the initial mismatch) is given by the intercept of each

curve with the P /P^ = axis. These values of P /P^ can

a i r i

be determined from the expression,

P.. r .

p

-iT ( 22)

[

N-l

N+l J

' f

and are 0.000, 0.111, 0.250, 0.444, 0.669, and 1.000, respectively,

for the values of N = 1 , 2, 3, 5, 10, and °°. The measurement

16
sensitivity can be determined approximately from the inverse

slope of each curve at its intercept point. As the biological

specimen is introduced into the field generator, Z will

decrease in value, improving the match. This technique should

probably be investigated further and may require modification

of the present tuning procedure used with the near-field

synthesizer.

17
20 40 60 80

Reflected Power, (P

r /P

f )xiOO, %

100

Figure 5 . RF power absorbed by the biological specimen,

(P /P

f

) x 100, %, vs. the reflected power, (P r/P

f

) x 100, %,

for values of N = 1,2,3,5,10, and °°, where N = Z /50 from

eq. (19).

18
6. MAGNETIC-INDUCTION HEATING IN A LOSSY DIELECTRIC

6.1 Introduction . The quasi-static "magnetic-induction"

heating caused by an essentially uniform rf magnetic field, H, in

a homogeneous, lossy dielectric of permittivity, e, and conductivity, a, will be determined in this section. The dielectric

specimen is in the form of a right circular cylinder of radius,

r, and height, h, as shown in figure 6, with H parallel to the

axis of the cylinder. The dimensions involved in the dielectric

are assumed to be small compared with the operating wavelength.

As pointed out previously, the heating caused by the magnetic

component of the field may often be greater than that caused by

the electric component in the frequency range under consideration

here [2]

6.2 Theoretical Background . The electric field, E, and the

magnetic field, H, within the dielectric are related at any point

by Maxwell's equation

V x e = - || . (23)

Integrating eq. (23) over the cross-sectional area of the cylinder,

A = ur , and applying

sinusoidally in time,

2 A = -ur , and applying Stokes's theorem gives, if H is varying

2irr

cb E-cU = -jwyHA, (24) o or

2fTrE = -j(joyH

zA. (25)

It should be noted that eq. (24) and eq . (25) are independent of

the dielectric properties of the cylinder.

Solving eq. (25) for the magnitude of the electric field

gives

|E| = ^l£ . (26)

19
z = h —

y

Figure 6 . The geometry of the lossy dielectric specimen is

in the form of a right circular cylinder of radius, r, and

height, h, with H parallel to the axis of the cylinder.

-- 1.0

Wh-0.5

1.0 0.5 0.5 1.0

Figure 7 . Normalized radial variation of the density of the

rf heating, W ,

, in a cylindrical lossy dielectric specimen

from eq. (28) , with H parallel to the axis of the cylinder.

20
The electric-field lines are in the form of closed circles concentric

witn the axis of the cylinder and lie in planes normal to H. As can be seen, the magnitude of E is proportional to the radius of

the circular E-line in question.

6.3 RF-Heating Density . The density of the rf heating

in the dielectric cylinder is given by

W

d

= E

2 a, W/m3

. (27)

The component of the rf heating due to the magnetic field within

the cylinder can be determined by substituting eq. (26) in eq. (27),

giving '4 2 2 2 2 W

d

= ^ , W/m . (28)

Note that the resulting density of the rf heating, and hence

2 2 the hazard, is proportional to lo , and H , and is independent of

the dielectric constant, e, of the specimen. As can be seen, this

heating is not uniformly distributed within the cylindrical

specimen, but is zero along the axis and increases as the square

of the radius, r, as indicated by eq. (28) and shown in figure 7.

There is no variation in. W. in either the <b or z directions.

Equation (28) neglects internal thermal-conduction processes

within the specimen, including blood flow in the case of living

tissue, which tend to equalize differences in the heat distribution. Thermal radiation must also be taken into account as indicated later in eq. (33) of section 7. In a practical sense, the

total rf heating within the specimen may be more meaningful than

the rf heating density , since the former averages the rf heating

density and may correlate better with the actual temperature

rise within the specimen.

6.4 Total RF Heating . The total rf heating in the dielectric cylinder will now be determined. The heating, dW, in a differential volume, dV, is given by

dW = E a dV = E

2 a r dr deb dz. (29)

21
Substituting eq . (26) in eq . (29) gives

dW =

gaj %

H r dr dcj) dz. ( 30)

Integrating eq. (30) over the volume of the dielectric cylinder,

gives for the total rf heating,

2 2 2 4 n au u H ir h , . W

fc = ti—

g

, watts. (31)

4 Note that the total heating is proportional to r , whereas the

2 heating density given by eq. (28) is proportional to r .

Example

Assume the following values for the various parameters in

eq. (31):

a =1 mho/m (1% saline solution)

;

e =80;

f = 26 X 10 , Hz;

u = 4tt x 10~ 7

, H/m;

H = 50 A/m (rms)

;

r = 0.1m; and

h = 0.1 m. The total heating, W . , generated in the dielectric cylinder

due to the value of magnetic field assumed above is 414 watts.

It is interesting to note that over 90 percent of this total

heat is developed in the outer half of the cylinder radius, as determined from eq. (31), or that half of the heat is developed

in the outer 16 percent of the radius.

22
7. THE CALORIMETER METHOD

The value of the rf power absorbed by a specimen can be

verified using a calorimeter technique if a one-percent saline

(Ringer's) solution [10] is used as the specimen. This test

solution (made up with distilled water) should be used at room

temperature in a low-dielectric-constant polyfoam-insulated

container. The walls should have a thickness of 2.5 cm or more to minimize heat loss due to thermal convection. The rf

power being absorbed by the solution (in the absence of thermal

radiation and convection) is given by

W = 69.77 w(T

2

-T

1 )/(t2

-t1

)

(32)

where W = net power absorbed by the water, watts, w = weight of the water, kg.

(T

2 ~T,) = temperature increase of the water, °C.

(t,,-t,) = elapsed time of the experiment, minutes.

If the weight of the water is 3.14 kg, from the example in

section 6 ; W = 414 watts; and t- - t, =1 min; the resulting

temperature rise will be 1.89°C. Due to the small temperature

rise involved, the effect of thermal radiation can be shown to

be negligible from the Stef an-Boltzmann equation for black-body

radiation [11]

W

bb

= ° t4 ' W/m2 ' (33 > _ o where a = 5.672 x 10 , and T = absolute temperature, K.

This will provide a worst-case test since a black-body

radiates more than any other at or near room temperature. The body

is in thermal equilibrium when its surroundings are at room

temperature, T, . The net radiation will therefore be proportional

to the difference of the fourth powers of the two absolute

temperatures involved, T, and T 2# where T

2 = T, + 1.89°, from

the above example. This gives a value of W,, = 1.11 watts (for

a surface area of 0.126 m ) which is negligible compared to the

414 watts used in the above example.

23
8. CONCLUSIONS

A relatively simple method is described in this report for

accurately determining the rf power being absorbed by a biological

specimen during radiation exposure testing in the frequency range

10 to 100 MHz. The method will permit researchers to monitor rf

power flow into the specimen measuring solely forward and reflected

power on the feed line to the field generator with conventional

rf wattmeters. The measurement accuracy is limited only by the

quality of the directional couplers used. A commercially available

automatic data-acquisition system can be used to "read" the

meters and rapidly calculate, display, and record the rf power

flow.

The method has the advantage that the exact measuring point

on the feed line is not critical, at it is with methods employing

direct impedance measurements. The required forward-and reflectedpower measurements can be made at a full operating rf power level

of several hundred watts without interfering with the exposure

tests. Additional measurements to determine the effect of changes

in the field distribution within the field generator, caused by

the presence of the biological specimen, would be helpful.

24
9. REFERENCES

[1] Greene, F.M. , Development and Construction of an Electromagnetic Near-Field Synthesizer, NBS Technical Note 652

(May 1974). For sale by the Superintendent of Documents,

U.S. Government Printing Office, Washington, D.C. 20402

(Order by SD Catalog No. C13. 46:652) $0.50.

[2] Guy, A.W. , Electromagnetic Power Deposition in Man Exposed

to High-Frequency Fields and the Associated Thermal and

Physiologic Consequences (University of Washington, Seattle,

Washington 98105). Report SAM-TR-73-13 to USAF School of

Aerospace Medicine, Brooks Air Force Base, Texas 78235

(December 1973)

[3] Terman, F.E. , Electronic and Radio Engineering, pp. 466-473

(McGraw-Hill Book Co., Inc., New York, N.Y. , 1955).

[4] Guillemin, E.A., Communication Networks, Vol. II, pp.

33-79 (John Wiley & Sons, Inc., New York, N.Y. , 1935).

[5] Ramo, S., Whinnery, J.R., and VanDuzer, T., Fields and

Waves in Communication Electronics, pp. 23-53 (John Wiley

& Sons, Inc., New York, N.Y., 1965).

[6] Ibid. , pp. 565-568.

[7] Montgomery, C.G., Dicke, R.H., and Purcell, E.M., Principles

of Microwave Circuits, M.I.T. Radiation Laboratory Series,

Vol. 8, p. 367 (McGraw-Hill Book Co., Inc., New York, N.Y.

1948) .

[8] Terman, F.E., op. cit., pp. 44-57.

[9] IEEE Standard Dictionary of Electrical and Electronics

Terms, p. 520. The Institute of Electrical and Electronics

Engineers, Inc. (John Wiley & Sons, Inc., New York, N.Y.,

1972) .

[10] Kail, A.R. , Radiation Hazards Caused by High-Power, HighFrequency Fields, p. 111-27 (Ark Electronics Corporation,

Willow Grove, Pennsylvania) report to United States

Information Agency, Washington, D.C. (June 1968)

[11] Machol, R.E., System Engineering Handbook, p. 16-3 (McGrawHill Book Co., Inc., New York, N.Y., 1965).

25
NBS-114A (RE\ 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR RKFORT NO. NBS TN-687

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE Measurement of RF Power-Absorption in Biological Specimens

(10 to 100 MHz)

5. Publication Date November 1976

6. Performing Organization Code 276.03

7. AUTHOR(S)

Frank M. Greene

8. Performing Organ. Report No. NBS TN-687

9. PERFORMING ORGANIZATION NAME AND ADDRESS NATIONAL BUREAU OF STANDARDS DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No 2763281

11. Contract/Grant No.

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

Same as item 9

13. Type of Report & Period Covered pinal 1/1/76 to 10/1/76

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES This report is the outgrowth of work originally sponsored by the USAF School of Aerospace Medicine at Brooks Air Force Base, and the National Institute for

Occupational Safety and Health of the Department of HEW.

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant bibliography or literature survey, mention it here.) A method is described for accurately determining the rf power being

absorbed by a biological specimen during non-ionizing radiation-exposure

testing using the NBS RF Near-Field Synthesizer in the frequency range 10

to 100 MHz . This method is based solely on measuring the forward and

reflected power on the transmission line feeding the synthesizer. Commercially

available rf wattmeters can be used, and an automatic data-acquisition

system employed, if desired, to "read" the meters and rapidly calculate,

display, and record the rf power flow.

The method has the advantage that the exact measuring point on the feed line is not critical, as it is with methods employing direct impedance

measurements, and that the required measurements can be made without

interfering with the exposure tests.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons

)

Electromagnetic field hazards; electromagnetic field synthesizer; electromagnetic

radiation-exposure testing (non-ionizing); near-fields; rf biological hazards.

18. AVAILABILITY (j£ Unlimited

For Official Distribution. Do Not Release to NTIS

| X ' Order From Sup. of Doc, U.S. Government Printing Office Washington, D.C. 20402, SD Cat. No. C13 .46:687

I Order From National Technical Information Service (NTIS)

Springfield, Virginia 22151

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

29

22. Price

$0.75

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