NTIA Report 80-49

Field Maxirna

Inside Habitable Structures

Exposed to 2.45 GHz

Plane Wave Radiation

H. J. Liebe

u.s. DEPARTMENT OF COMMERCE

Philip M. Klutznick, Secretary

Henry Geller, Assistant Secretary

for Communications and Information

October 1980

TABLE .OF CONTENTS

LIST OF FIGURES

LIST OF TABLES

EXECUTIVE SUMMARY

ABSTRACT

1. INTRODUCTION

1.1. The Incident Microwave Radiation Field

1.2. Formulation of the Hot Spot Problem

2. MICROWAVE COUPLING INTO AN ENCLOSURE

2.1. Direct Coupling

2.2. Aperture Coupling

2.3. Diffuse Coupling

3. INTERNAL REFLECTIONS

3.1. Reflective Losses from Metals

3.2. Absorption and Reflection by Dielectric Materials

3.3. Dielectric Properties of Typical Materials

4. POSSIBLE RESONANCE CHARACTERISTICS OF HABITABLE SPACE

4.1. Cavity Resonator

4.2. Open Resonator

4.3. Modeling of Resonance Fields

5. MEASUREMENTS

5.1. Strength of 2.6 GHz Satellite Signal Inside Houses

5.2. Fields in Anechoic Chambers

5.3. Fields in Mine Tunnel (Dielectric Waveguide)

; ; i

Page

v

vi

vii

2

3

6

7

7

9

9

10

13

15

20

20

21

22

24

25

26

27
TABLE OF CONTENTS (cont.)

6. MITIGATIVE MEASURES FOR MICROWAVE HOT SPOTS

6.1. Outside Reflectors and Absorbers

6.2. Inside Absorbers

6.3. Mode Scrambler

7. CONCLUSIONS

8. ACKNOWLEDGMENTS

9. REFERENCES

Page

27

28

28

29

29

31

33

APPENDIX A. SPS POWER DENSITY PATTERN AT RECTENNA SITE 35

APPENDIX B. FORMULAS F-OR THREE SIt·1PLE TYPES OF CAVITY RESONATORS 38

iv
Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.

Figure 8.

Figure 9.

Figure A-1.

Figure A-2.

LIST OF FIGURES

The coupling coefficient qi of·a circular aperture

as a function of the diameter d/A. Shown are the

results of two different theoretical treatments.

E

i

-f ie1d distribution in circular and square

apertures (d 0.1 A).

Spatial interference pattern due to a reflected

wave.

Two examples of field patterns between two opposing plate reflectors for the case that two space harmonics

superimpose.

Two-dimensional metal reflector arrangements with the

potential of supporting multiple reflections.

Attenuation rate a of various building materials at

f = 3 GHz as a function of the water content.

Examples of open resonator geometries~

Examples of measured free space SWR (interference

patterns).

Probability distribution of hot spot occurrence inside

si ng1 e story wood frame house wi th meta1 s idings exposed to a 2.57 GHz satellite signal.

Proposed SPS transmitted power density pattern.

Microwave power distribution on rectenna at equator.

v

Page

8

8

11

11

16

19

23

25

26

37

37
LIST OF TABLES

Page

Table 1. Measured Insertion Loss of Building Materials 9

Table 2. Reflective Properties of Metals (~ GHz) 12

Table 3. Electromagnetic Enclosure Properties 12

Table 4. Power Attenuation Rate in Dielectric Material at 2.5 GHz 14

Table 5. Conversion Table for Return Loss, Reflection Coefficient,

Standing Wave Ratio, and Peak-to-Peak Field Strength Variations Relative to Unity Reference 16

Table 6. Low Loss Dielectrics (D < 0.01 at 3 GHz) 17

Table 7. Lossy Dielectrics (0 > 0.01 at 3GHz) 18

Table 8. Dielectric Properties of Water at 3 GHz 18

Table 9. Dielectric Properties of Various Building Materials

Reported at 3 GHz 19~

vi
EXECUTIVE SUMMARY

It is necessary for the EMC analysis of the SPS to know microwave field

strengths that would be expected inside various structures, particularly buildings and vehicles. Theoretically, such structures could concentrate incident

microwave energy to produce fields more intense than would otherwise be expected.

Very little work has been done explicitly on this problem, but a substantial body

of theoretical and experimental information is available on the coupling of

microwaves into enclosures and their behavior therein. An exact, detailed

analysis of the microwave properties of habitable structures is not practical due

to the tremendous variety of materials and complex geometries involved.

The problem of estimating the fields inside habitable structures exposed to

microwaves near an SPS rectenna is analyzed in this report, with particular

attention to the possibility of increases in field strength. This study describes

and discusses relevant physical processes, lists measured values for many of the

quantities involved, and cites actual microwave field strengths measured inside

houses exposed to 2.6 GHz radiation from a satellite. Key results are summarized

below.

To determine microwave field strengths inside a structure, the coupling of

energy into the structure and its behavior inside, including reflections (possibly

resonant), must be understood. Coupling to the interior could occur via relatively

microwave-transparent openings (windows, for example) or through wall materials,

wh ich in general do not transmit mtcrowaves as we ll, The following approximate

microwave transmissions for representative structural elements have been measured:

%Trans'm;ssion

Structure

Wooden Wall

Frame Wall

Window (wood sash)

Dry

15

40

70

Wet

6

15

40

Metal walls or screening, or even foil, transmits very' little 2.45-GHz microwave

energy (less than 1%) if openings or joints are substantially less than an inch

long.

vii
Average field strengths inside structures are expected to be less than those

outside, due to coupling losses. The structure could, however, alter the spatial

distribution of energy to produce localized areas of increased field intensity.

Reflections within structures are the most likely causes of locally-increased field

strength. Metallic surfaces are the most common elements of habitable structures

likely to produce significant field tncreases , In the absence of any absorbing

material, a single "metallic reflection could increase power density at some

locations by as much as a factor of four above that incident on the surface. ~1ore

complex geometries involving multiple reflections could~ in principle, produce

larger field increases. However, such large increases require special geometries

and very little microwave absorption in the system. Neither of these criteria is

likely to be satisfied by real habitable structures. In particular it should be

noted that the presence of people, who are significant microwave absorbers and

reflectors, modifies reflection patterns in a time-varying way as the people

move and absorb energy, reducing the field increases possible due to reflections.

Measurements have been reported giving the ratio of microwave field strength

inside to that outside single family houses illuminated by 2.6 GHz microwaves from

a satel"ite (Wells, 1977). Average fields inside were found to be about 25% of

those outside, although interior fields varied substantially from point to point.

For the case of highest ratio of average inside fields to outside fields, the

probability of encountering a microwave field inside that was larger than that

Qutside was only 15%. If, in specific cases, interior microwave field strengths

w'ere found to be a problem, they could easily be reduced by methods described in

the present report.

viii
FIELD ~~XIMA INSIDE HABITABLE STRUCTURES EXPOSED

TO 2.45 GHz PLANE WAVE RADIATION

Hans J. Liebe*

This report discusses microwave engineering data

relevant to assess the potential of the Satellite Power

System (SPS) to cause microwave field enhancements (socalled IIhotspotsll

) inside habitable structures (house,

trailer, car, etc.) located in the fringe area of the"

receiving rectenna. Mitigative measures are included in

the discussion.

1. INTRODUCTION

In feasibility studies of the SPS microwave energy beaming concept, the

question was raised whether local free space field strength maxima (hot spots)

inside habitable structures located in the fringe area of the receiving rectenna

can exceed the uniform power density of the incident free space plane wave

radiation. The answer lies in the quantitative assessment of penetration,

storage, and dissipation of field energy into and within the space surrounded by

a lossy dielectric (e.g., house), metallic (e.g., vehicle, atrplane}, or composite dielectric-metallic (e.g., trailer) shell.

The many parameters of the problem (electromagnetic properties of building

material, furnishings, biota; geometric shapes, openings, and dimensions; outside

and inside obstructions; etc.) make it virtually impossible to predict the

internal field distribution with certainty by analytical means. As in many

complicated problems, attempts are made to simplify the analysis by considering

subproblems which can be treated independently. The final answer is then looked

upon as a combination of such solutions. The following sub-areas (including some

key words for variables and/or effects) are considered:

1. Incident Radiation (power dens;tydistribution, obstruction

loss, polarization, and elevation angle dependences).

2. Interaction with the Exterior (reflection, diffraction, scattering,

and absorption effects by the outer shell of the structure).

3. Penetration of SPS Field Energy into the Interior (three coupling

mech~n;sms: direct, aperture, diffuse).

*The author is with the U.S. Department of Commerce, National Telecommunications

and Information Administration, Institute for Telecommunication Sciences,

Boulder, Colorado 80303.
4. Possible Field Maxima (multiple refl ections ; excitation of resonances;

dissipation of resonant energy; the empty, furnished, occupied chamber) ..

1.1. The. Incident Mtcrowave Radiation Ffel d

The SPS field incident upon a habitable structure is qssumed to be a

coherent plane wave with linear verti.cal polarization. The proposed frequency

is in.the UHF range at

f o = 2.4~ 6Hz or ~o =12.2 cm (1 )

for the wav~length in free space. The direction of propagation is to the south

(geostati onary orbit; i. e -, equator plane) with e1 evation angles

~. = 30° to 60° (2)

for the continental United States. The. proposed maximum power density So at the

beam center is

(3)

and it is the valid index of a.plane-wave field apart from phase, polarization,

and direction {Wacke'r and Bowman, 1971). The energy density (3) compares with

ether known ones as follows (in units of mw/cm2) :

2 x 10-4 moon light

10~6 to 10-3 UHF radio radiation in an urban area

<0.1 fringe area of SPS rectenna

10 current u.s. standard for maximum continuous microwave

exposure level (acceptable thermal burden for humans)

23 SPS maximum power density (3)

120 sunlight on a clear day (50% IR, 40% visible, 10% UV)

103 localized microwave therapy

2 x 105 microwave cooking

1.2 x 1010 breakdown of sea level atmosphere (tontzetton).

2
The power density incide.ntin the fri..nges of th.e receiving site (see

Appendix Afar comp l ete power denstty patte.rn) t.s given by

(4)

(E is the peak electric field amplitude, Zo =3770 is the characteristic free

space impedance), where L (dB) is the average power reduction factor as a

function of the radial distance from.the beam axis (Appendix A):

r (km)

L (dB)

o

o

5

15

10

24

20

33

50

43.

The incident field might be further reduced by obstructions causing

diffraction loss (e.g., trees located close to a housing structure). The

diffraction edge for trees in full leaf was measured at 2.95 GHz to coincide

with the physical height (LaGrone, 1977). In this case, the knife edge diffraction approximation can be used yielding additional 3to 30 dB reductions

in the effective power density s.

1.2. Formulation of the Hot Spot Problem*

The electromagnetic field within a habitable structure is expressed via

its electric field components interacting with dielectric and metallic material.

The free space field distribution in chambers, such as rooms in a house, cockpit

of a vehicle, cabln of an aircraft, etc., is to be investigated for local field

energy maxima (hot spots) E~. For a point with the internal space coordinates

x, y, Z, one can define

(5 )

and write a maximum power transmission coefficient to be (see equation 4)

2 2

q. = E./E

1 1 (6)

The objective of this study is to identify and, if possible, to quantify

situations that might exhibit a fie.ld Hot Spot Problem (HSP) defined by

q. > 1

1 (7)

*The term "hot spotll is used for a local electric field maximum; for the resulting thermal effect see equation (26).

3
Such a condition can exist within a volume element as small as (0.5 1 )3 assuming o

the maximum spatial periodicity between field maxima and minima to be It /4. Even

o

before discussing the various electromagnetic effects that might lead to q. > 1, 1

one has to take note of the complexity of the problem by pointing to the fact

that an average habitable space has a large number of potential hot spots (e.g.,

the room size 4 x 5 x 2.5 m ha~ about 2xl05 possibilities).

Reflections of the incident radiation from intercepting surfaces are the key

to assessing the likelihood of a HSP. Single reflections from curves surfaces

can focus plane wave fields into spots, and multiple reflections can lead to

resonant standing wave patterns with locally well defined field concentrations.

The total power P available to cause effects is that "seenll by the shadow

cross section X cast by a structure exposed to SPS radiation and is given simply

by

P = SX w (8)

The shadow area X is typically between 5 and 500 m2; the power density S in the

fringe area of the rectenna is not expected to exceed 0.1 mW/cm2 (see Appendix A),

hence the total maximum exposure power falls in the range

p0 5 to 500 W (9)

IIWorstll cases would exist when (a) all of the power Po is focussed into lionel!

spot such as is the case for a parabolic or spherical reflector with an onaxis or offset ~ca1 potnt or when (bl the power Po is used to sustain a low loss

resonance field. Neither condition~ however, will occur inside a habitable

structure since both have to be very' carefully engineered for such purposes to

ensure "perfectll reflections and lIperfectll geometries.

The following discussion will concentrate on the field energy that is

consumed in the interior space of a structure, which is only a part of the

total P (8). One can divide the cross section X into three components,

p S(X + Xt + X.) s 1 (J 0)

where the contribution denoted SXs is lost by reflection qnd qbsorption on the

outside of the structure, the componentSXtdescribes the loss via transmission

through the structure tnto the ground, and only Pi SX1 is the power dissipated

in the interior space.

4
Enhanced field strength is best understood by considering the simple case

of a direct and a reflected plane-wave signal interfering with each other.

Enhancement occurs at all points in space where direct and reflected wave fronts

differ in phase by multiples of 2TI. A HSP exists when an arrangement of

reflecting surfaces supports multiple reflections allowing a standing wave

(resonance) field to build up. The phase relationship between direct and

reflected monochromatic (fo) signals will be influenced by the size and shape

of the enclosure, by the presence and location of objects and persons, and by

the position of the test point.

A practical resonator stores electromagnetic energy at the resonance·

frequency fr and, simultaneously, suffers a power loss Pr from conduction,

dielectric, and diffraction effects. Two dimensionless factors can be defined

to describe the resonance case. They are the quality- or Q-factor,

Q = 2n(energy stored)/Pr

and the coupling coefficient,

= energy available to sustain a resonance field

q - total energy available (SX i )

One speaks of a resonance when

Q > 1

With respect to a field strength maximum Eo of a resonance within

habitable space, we assume the following:

1) Only part of the penetrated energy SX i is coupled to support'a

resonance field which yields for (12) that

q < 1

2) Any local maximum E of the resonance field is enhanced by the

0 2 2 quality factor Q over the field energy qE i = qi qE , which excites

the resonance.

3) The field strength is distributed around the resonance frequency

f r accordi ng to

(11 )

(12 )

(13)

(14 )

Vim (15 )

where the frequency is normalized to a = 2Q(fo - f )/f in multiples of rr

the resonance halfwidth f

r

/ 2Q with reference to the SPS frequency fo'

5
AHSP condition T > 1 exists when the reductions by coupling (qi' q) and

detuning (fo - fr) are overcome by the field enhancement QE i. The resonance case

leads for (7) to the reformulation

(16 )

At this point~ let's briefly reiterate the train of thought that led to the

array of variables introduced in equations (1) through (16). The first step is to

find the incident power density S~ which determines with (4) the exposure field

strength E. Next~ the coupling q~ <1 {6) into a chamber is specified and 1 -

followed by an identification of inner surfaces that might support multiple

reflections at or close to foe Then~ the effective Q-factor of the resonance

and the coupling q to the internal field strength Ei are estimated. For example,

r =10km, L = 24 + 6 (tree shading) dB, S = 0.23 W/m2, E = 13 VIm; direct

coupling (window), qi 0.9; resonance between two metal partitions with

Q 4at fr = fo and a coupling factor of q =0.05. It follows from (16) that

there would be no HSP (T D.7).

To obtain a more reliable assessment of a HSP, one needs to conduct a

careful appraisal of field characteristics pertinent to specific reflector

configurations in terms of their electromagne~c properties (reflection

coefficient~resonancecondition, dielectric constant, loss tangent, etc.).

The identification of all arrangements which support enhanced or resonant fields

based on available theoretical and experimental knowledge for the innumerable

configurations is an impossible task. Real hot spot conditions can only

be verified by "in situ" measurements in suspected areas.

The following sections are intended as a fact-finding exercise to sketch

properties of a 2.45 GHz field within habitable space in simplistic terms to

bring out basic principles, while more detailed discussions of the points

raised can be found in the references.

2. MICROWAVE COUPLING INTO AN ENCLOSURE

The coupling (6) of microwave radiation involves factors that scale with

wavelength. There are basically two ways to enter an enclosure. The first is

to radiate through natural openings (e.g., windows, open access holes, cracks,

etc.); the other is to penetrate through the surrounding walls. The interior

energy SXi depends in a complicated manner on aperture size, polarization and

anqle-of-arr-tvatTor the incident wave, and on the electromagnetic properties

6
of the walls. A great deal of work ha~ been done on the,coupl~ng problem in

context with EMP (electromagnetic pulse,due to a nuclear explosion} effects

(Butler etal ; 1978, and 166 references .. there'[n}. The tr-eatment of aperture

coupling distinguishes two cases depending upon the relation of the largest

aperture dimension d with respect to the wavelength ~o:

(1) d > ~o ' direct coupling, and

(2) d A

o/ 2 , aperture coupling

2.1. Direct Coupling

A sufficient approximation for apertures with dimensions larger than the

wavelength Xo is to equate the coupled energy Pi with the incident field energy

SX and assume for the cross-section X the surface area Aof the opening. This

yields simply that

qi = 1 and Pi = SA w (17)

Theoretical calculations of the coupling through circular, elliptical, and

rectangular cross sections confirmed (17) (e.g., Koch and Kolbig, 1968)-. An

example of qi for a circular aperture is given in Figure 1 as a function of

(2d/A) > 2 (d is the diameter).

2.2. Aperture Coupling

When the largest dimension d of an aperture falls below A

o

/ 2 = 6 cm, the

analysis of the coupled field energy is more complicated (Butler et al., 1978;

Jaggard, 1977). The coefficient qi can vary between zero and 1.7 (Figure 1);

however, the total energy transmitted will be small (e.g., S =0.23 w/m2,

A = A~/4 = 3.6.10-3 m2, q < 2, P < 2 mW). Several noteworthy points are:

1. The electric field strength Increases by as much as a factor of 5 at

the edge of the aperture (Butler et al.,1978). An example is given

in Figure 2.

2. The coupling reaches a maximum when d 0.4 X

o. The increase to

qi 1.7 (Figure 1) is expla ined by the fact that energy is collected

from all angles over a hemisphere,surrounding.the ~perture.

3. Maximum transmission through a circular aperture 6ccurs for graz\ng

incidence of a.polarized plane wave; i.e., the'magnetic field vector

is al igned wt th the center axts (J.·a.ggard, 1977·).

7
2 3 4

2d/X

o ~____""' ~_-...I

o

1.8 ..-----.---,..----..-----.

_A

.,II · c- • \

s -I \. :~ 1.0 I--.....+--~F_~~

'+-

"toQ)

o

U

0'

.s

Q.

::;,

o

U

Figure 1. The coupling coefficient q. of a circular aperture as a

function of the diameter d!A. Shown are the results of

two different theoretical treatments (Koch and Kolbig,

1968)

o d/2

y

x=o

( b)

-d/2

0.5

0.5 0.3 d/A=O.1

-q. - - - -/~-........ 1 /

I

I

d/2

x

o

(0)

-d/2

0.3

0.1

0.5

Figure 2. Ei-field distribution in circular and square apertures

(a < 0.1 A) excited by an E -field - x

(a) Ei field sampled along x-axis

(b) Ei field sampled along y-axis

(Butler et al., 1978)

~8
4. In an array of apertures (e.g., windows along the fuselage of an

aircraft), the coupling increases when the line of apertures is

parallel to the incident magnetic field vector (Jaggard, 1977).

2.3. Diffuse Coupling

Microwave energy can penetrate into a cavity by means of; IIdiffusion ll through

the walls when the wall conductivity is finite (Lee and Bedrosian, 1979). A wall

is considered electrically IIthinll when the skin depth 0 is larger than the wall

thickness d (see equation 21). A few measurements have been reported on the

insertion loss Li of typical composite building materials and are listed in Table 1.

Table 1. Measured Insertion Loss of Building Materials (Wells et al.,

1975; private communication)*

Loss Li, dB

dry wet

Wooden wall 8 12

Frame wall 4 (5.3) 8

911 Brick wall + insulation +

plaster 1.5 4

Window, wooden sash 1.5 3

Window, leaded panes 13

Frequency, GHz

3.3

3.3 (4.7)

1•1

3.3

3.3

Diffuse coupling plays a major role with nonmetallic structures. The total

exposure power SX (8) will be attenuated; however, the amount reaching the

inner space could still be substantial and contribute to a hot spot problem

should field concentrating devices exist internally.

3. INTERNAL REFLECTIONS

Reflections from the enclosure walls significantly affect the 'field distribution inside. The local energy density will be greater than obtained in

free space when, at a test point, the majority of reflected energy is of proper

phase to add to the energy arriving directly. The phase of a reflected signal

and hence the local power density both are extremely sensitive to:

size and shape ~f the enclosure,

location of the test point,

presence and location of objects (e.g., furniture,

etc.) and persons.

*Wells, P. I., D. A. Hill, A. G. Longley, R. G. FitzGerrell, L. L. Haidle, and

D. V. Glen (1975), An experiment design for the measurement of building

attenuation, OT Technical Memorandum 75-199.

9
A substantial amount of reflected energy will radiate out through the same

aperture (e.g .• window, door~ etc.) through which the incident energy came.

Determination of the reflectivity level in an enclosure is understood by

conSidering the Simple case of a direct-path plane-wave signal EO (constant

magnitude and phase) combining with an interfering plane-wave signal E

Rarriving

at the test point under an angle <p (see Figure 3). Amaximum is produced by two

wave fronts whose phases differ by 2TI. The maximum amplitude is

and the angle <p is given by

ep = sin-1 (Alp)

Vim (18)

(19 )

The spatial periodicity lip" depends upon the angle between the interfering wave

fronts. The resulting field will form a standing-wave pattern with field maxima

twice the value of the incident wave if a once-reflected signal does not suffer

losses, that is

E = 2E.

max 1 Vim (20)

The field strength E

max

and the periodicity pare altered when several wave

fronts with different reflection angles <p interfere. Two ex~mples of superimposing space harmonics are depicted in Figure 4.

3.1. Reflective Losses from Metals

A surface with high reflectivity for the SPS microwave radiation consists

typically of metal, of wire mesh (mesh size <1.5 cm), or of a multilayer

arrangement of low-loss dielectric plates (Harvey, 1970), whereby the dielectric

multilayer reflector ;s unlikely to occur in habitable structures.

~~etals refl ect imi crowaves and conduct field-induced currents. A very

small fraction of the incident energy is absorbed by the metal surface. The

loss in one reflection is (f in GHz)

a

r = 4.19 x 10-3 f 0 % (21 )

where the skin depth 0 in llm is the distance the field strength has fallen to

lie 0.368 of its surface value. In nonmagnetic metals,

(22)

10
ED Wavefront

ER Wavefronts /

t

p

•

Emax (HSP)

Figure 3. Spatial interference pattern due to a reflected wave

ED - direct ray

ER - field,from specular reflection

p - spatial periodicity

(Crawford, 1974)

Field Strength E,

HSP

Detected Voltage E~ HSP

Figure 4. Two examples of field patterns between two opposing plate

reflectors for the case that two space harmonics superimpose

11
Table 2. Reflective Properties of ~1eta 1s (2 GHz)

Metal ConductivitY6 Skin Depth Reflective Loss

Ow (mho/mjl O 8, 11m a

r, %

Aluminum 38.2 1.82 0.0152

Brass (66-34) 25.6 2.2 0.0185

Chromium 38.5 1.8 0.0151

Copper 58. 1 1.48 0.0124

Gold 41.0 1.76 0.0148

Platinum 9.52 3.65 0.0307

Silver 61.7 1.43 0.0120

Steel 22.7 2.5 0.0210

Tin 8.8 3.80 0.0319

with oM being the conductivity in Siemens (mho) per meter (see Table 2). The

calculated values of ar in Table 2 are greater than measured values by a

typical factor of two; however, all metal surfaces are excellent reflectors

for SPS radiation.

Bare metal surfaces of significant area will be rare within the confinement of habitable boundaries. The chamber material, instead, which reflects,

absorbs, and transmits the field can be anisotropic and, in addition, it can be

non-stationary varying the field in space or time or both. Such media are

difficult to deal with from the standpoint of solving the reflection problem.

Already the general I case of oblique incidence on a lossy homogeneous material is

quite complicated. To gain some handle on the rather loosely defined term

lIhabitable structure", we categorize it in Table 3 by means of the enclosure

material, and look first at the microwave properties of lossy dielectric material.

Table 3. Electromagnetic Enclosure Properties

Case Enclosure Properties Coupling Real Structure Equivalent

diffuse, aperture

aperture, diffuse

1

2

3

lossy dielectric

composite of lossy

dielectric and metal

metal plus dielectric aperture

coating

12

brick, frame, stone house

trailer, house with metal

sidings, industrial building

vehicle interior, aircraft

cabin
3.2. Absorption and Reflection by Dielectric Material

Habitable space may be made from metals ~nd other materials such as

complex arrangements: of natural and art tfic lal dielectric materials. Dielectrics are a storage medium for f ie ld ene:rgy and dissipate such energy by conduction and other irreversible processes [e.g., volume inhomogeneity scatter

(Roth and Clachi, 1975)J. Two frequency-dependent, dimensionless quantities,

the relative dielectric constant K

and the loss tangent D

(1 to 80)

(0 to 10)

(23)

are needed to calculate conductivity, heat loss, and attenuation rate. An

appreciable interaction effect occurs when the thickness of the material is

larger than Ao/ 4 3 em. The wavelength in the medium is shortened by

(24)

The dielectric quantities K and D of materials related to habitable structures

are given in the following Section 3.3.

The dielectric conductivity is obtained from

cr = 0.0556 f KD o mho/m (25)

Values of 10-4 are typical for insulators, while semiconductors fall in the

range of 102 mho/m.

In dielectric heating, the power absorbed per unit volume of material

follows from

(26)

being a function of position. The power attenuation rate is expressed by

(VonHippel,1954)

0.= 1.29 f { K[~1 + D

2 - 1] f/2 dB/cm (27)

and covers at f

o the ranges given in Table 4.

13
Table 4. Power Attenuation Rate in Dielectric Material at 2.5 GHz

Relative Dielectric Constant K

1 2 5 10 20

a. in dB/em

0 10-3 0.002 0.003 0.005 0.008 0.010 ..f-,) 10-2 c 0.024 0.034 0.052 0.075 0.10 OJ

t::7> 10-1 C 0.24 0.34 0.52 0.75 1.0 lCS

I- 1 2.2 3.0 4.7 6.8 9. 1 Vl

Vl

0 10 10 14 21 31 43 --I

Reflections - Upon striking the surface of a dielectric material, the

incident field is split into two components of which one is reflected and the

other passes through the medium. Specular reflections from a smooth surface

cause the angle e of the reflected wave front to be equal to angle of incidence

(Snellls law). For the HSP of interest, the amount of reflected energy is

expressed by

(28)

where p is the reflection coefficient. We learned that for metals p = 1, for

practical purposes (Table 2). In case of dielectric material , p becomes a

function of wave polarization, angle of incidence e, and the properties Kand D.

Relatively simple expressions exist for the special case D 0 (loss-free

dielectric), where two different situations occur depending upon the orientation

of the Ii-vector with respect to the plane of incidence:

(i )

( i i )

E; is in the plane of incidence,

E. is perpendicular to the plane of incidence.

1

For reflection on a horizontal surface, this mean~ that for (i) the wave is

horizontally and for (ii) vertically polarized. The respective reflection

coefficients are (VonHippel, 1954)

14
( i)

• l-~ cose

Ph 1';; cose

and

(t t)

cose-i-sin2e p :: --------...........---~ 'v .......-~

cose+VK-stn 2e

(29)

For normal and zero incidence, Ph = P

v; in all other cases, Ph > pv.At

the special angle (Brewster) e

S = tan~l..JK, all reflections are avoided for

case (i), i.e., Ph = O. In practice one can expect partial reflections

(p < 1).

Returning to the picture of reflecting and interfering rays and disregarding the shape of the boundary, tt follows that th-e resulting field

amplitude enhancement (free space SWR, to be measured alon~ three orthogonal

axes of the interior space) can be ~ignificant only when repeated reflections

with little loss occur. Figure 5 gives three examples of geometries that ~re

in principle capable of sustaining multiple reflections. The point-to-point

free space SWR of two interfering wave fronts can be made plausible with the

simple phasor diagram depicted and evaluated in Table 5. The actual ratio

within a chamber will be extremely dependent on position due to the complex

variation of the reflected signals. Experimental results have shown spatial

variations of electric field strength as great as 40 dB ;n a room with

bare metal surfaces (Donaldson et al., 1978).

Depolarization is another effect which is counter to a HSP. The extent

of depolarization of incident radiation in habitable space is a function of

the complexity of the confinement, Obstacles will scatter omnidirectionally,

thus mixing vertical and horizontal field components to become equal. Even

oblique reflections from dielectric-coated metal surfaces can depolarize a

wave train. For example, a lacquer paint (K 10) with a thickness of 0.04 mm

causes a decrease in the cross polarization isolation (19 GHz, e 45°)

between'vertical and horizontal from 40 to 36 dB (Chu and Semplak, 1976).

3.3. Dielectric Properties of Typ ica l Materials

This section 1tsts diele-ctric data of material .that mi.gh_t be assoc iated

with habitable structures. The data sunmarized tn Tabl es 6 to 9 were obtained

from a survey of the sources referenced CVonHi ppel , 1954;. Well s et a1., 1975;

15
(0)

2~

(b)

Ray

Paths

(c)

Figure 5. Two-dimensional metal reflector arrangements with the

potential of supporting multiple reflections

(a) Hot spots near 90° corner reflector

(b) Opposing folded metal surfaces

(c) Closed multi-angled box with aperture (Harvey, 1970)

,~~(1+x)

Table 5. Conversion Table for Return Loss a , Reflection xl" "\~

\ / Coefficient p, Standing Wave RadiorSWR, and ........'

Peak-to-Peak Field Stength Variations (1 ±x) 1 (1-x)

Relative to Unity Reference.

Clr p SWR l+x 1-x Remark

dB dB dB

1 0.891 17 . 391 5.535 -19.27

3 0.708 5.848 4.650 -10.69 HSP

6 0.501 3.010 3.529 -6.041 Possible

10 0.316 1.925 2.387 -3.302

12 0.251 1.671 1.947 -2.513

15 0.178 1.433 1.422 -1. 701

20 0.100 1.222 0.828 -0.915

25 0.056 1. 119 0.475 -0.503

30 0.032 1.065 0.270 -0.279

40 0.010 1.020 0.086 -0.087 IAnechoic

50 0.003 1.006 0.027 -0.028 Chamber

60 0.001 1.002 0.009 -0.009

16
Emerson, 1973; Donaldson et al., 1978; Emslie et al., 1975), most notable from the

comprehensive treatment by VonHippel. For a HSP, we look after material that is a

good reflector K > 3) and has a small loss tangent (D < 0.01). Low loss dielectrics

(Table 6) are artificial materials normally not common in habitable structures but

especially developed for microwave applications. The materials commonly used to

construct habitable space are more or less lossy (see examples listed in Table 7).

Table 6. Low Loss Dielectrics (D < 0.01, f = 3 GHz)

K D K D

Fused Quartz 3.78 0.00006 Phosphate 4.9 to 0.0018 to

Glass 5.2 0.0046

Styrofoam 1.03 0.00010 Borosilicate 4 to 0.0012 to

Glass 8 0.0058

Teflon 2. 1 0.00015 Corning 7070

Glass 3.9 0.0031

Polystyrene 2.55 0.00033 Lucite 2.58 0.0035

Butyl Rubber 2.35 0.0009 Plexiglas 2.60 0.0057

Porcelain 8.9 0.0011 Phenolic Board 1. 19 0.0058

Polyglass 0 3.23 0.0012

Water is a very lossy dielectric, and the water content of materials

determines to a large extent their dielectric behavior such as attenuation

a (27) and reflectivity p (29). Water plays a role on the outside of habitable

structures where it acts as a weather-variable shield. Also, the high water

content of biota turns them into significant absorbers and reflectors. Their

dielectric effects are simulated by a 4 percent aqueous salt (NaCl) solution.

Reported dielectric properties of water are in Table 8; water content-dependent

properties of various building materials are given in Table 9 and Figure 6.

Wooden structures will allow a certain amount of diffuse coupling (see 2.3),

while window areas are good direct-coupling apertures (2.1) with partial

reflections on both sides.

17
Tab1e. 7. Lossy Dtelectrics (D > 0.01 , f ;:; 3 6Hz)

K D

Alkali Glass 4.8 to 6.0 0.00.5 to 0.012

Balsa 1.22 0.010

Soda Glass 5 to 7.5 0.01 to 0.02

Nylon 66 3.03 0.013

Granite 4.8 to 6.3 0.014 to 0.03

Poplar 1.50 0.015

Plywood 1. 5 0.022

Silicone Rubber 5.7 0.025

Shellac 2.86 0.025

Mahogany 1.88 0.025

Araldite 3.0.9 0.027

Fir 1.82 0.027

Fiberglass 4.4 0.029

Birch 2. 13 0.033

Polyglass 4.86 0.034

Nylon 610 2.94 0.036

Bakelite 3.7 0.044

Buna Rubber 2.45 0.044

Neoprene 2.84 0.048

Paper 2.70 0.056

Formica 3.57 0.060

Artifical Absorber I\~a teri a1 5 to 25 0.1 to 10

Table 8. Dielectric Properties of Water at 3 GHz

Pure Water

Salt Solution

20° C

Solid State

18
Table 9. Dielectric Properties of Various Building

Materials Repo~ted at 3 GHz

Dry vJet

Sand, loam K_ 2.5 20 ( 15% water) D 0.001-0.006 0.13

Clay K 2.3 11 3 ( 20% water) D 0.015 0.25

Magnetite K 1.0 30 ( 11% water) D 0.10 0.32

Brick wall ex 0.5 0.7 dB/em

Wooden panel a 0.5-1 1-2 dB/em

Roofing shingles ex 1.1~2.7 3.3-3.6 dB/em

E

o

<,

CD

-c

e

c

o

+=o

:J

C

Q)

... ...

<t

2

3 GHz

2 4 6 8 10

O-L------I------I-----+--------t-----t---

o

Percent Water Content

Figure 6. Attenuation rate a of various materials at 3 GHz as

a function of the water content.

19
4. POSSIBLE RESONANCE CHARACTERISTICS OF HABITABLE SPACE

The term resonance implies the existence of reflective boundaries and the

build-up of high field amplitudes (equation 15) by multiple reflections. A

standing-wave field alternates between electric and magnetic energy storage and is

sustained by the energy coupled into the resonator. The·Q-factor (11) can be

calculated for simple cases (Appendix B) or determined, for example, by exciting

a resonant structure with pulsed microwaves and measuring the ringing time T

yielding

(30)

(31)

After the time T, the energy content of the resonance has dropped to lie of its

starting value.

4.1. Cavity Resonator

In general, any closed and somewhat reflecting cavity will support resonances

regardless of its shape if only its dimensions are fixed and large compared to

the wavelength A

o. In most cases such conditions are met by habitable space.

The spectrum of possible resonances for a given A

o becomes increasingly

dense with growing cavity dimensions. The number of allowed resonance modes for

a given geometry (see examples in Appendix B), the so-called "mode densityll, is

approximately given by (Wilson et al., 1946, Kinzer and Wilson, 1947)

N

v 8V/A~ for a cavity of volume V

For example, a room of the size 4 x 5 x 2.5 = 50 m3 can exhibit, in principle, on

the order of Nv~ 2.3 x 105 resonance (AO = 12 cm) modes. These modes are

expected to exhibit low Q-factors (Q < 10) in houses owing to the fact that walls

usually are made from dielectric materials and reflect only part of the incident

wave. Metal walls on the other hand are subject to ohmic (field-induced currents)

and dielectric losses (wall coatings). In addition, the presence of lossy interior

objects will dampen the resonance field.

20
The field distributions of the following cavity shapes have been calculated

rigorously (Harvey, 1970):

(a) rectangular box, which most closely resembles a typical room,

(b) circular cylinder,

(c) spheres,

(d) elliptical cylinders,

(e) conical, toroidal, and cigar shapes,

(f) confocal spheroids and paraboloids.

The field equations for the geometries (a) to (c) are given in Appendix B.

Case 3 (Table 3) might resemble to some degree one of these geometries.

Theoretically, the peak value of the stored field energy density in an apertureexcited cavity can be up to two orders of magnitude above the incident value

(e.g., Safari-Naini et al., 1977). Losses in a practical configuration, however,

make a HSP very unlikely. The effective Q-value is calculated from

(32)

where the ratio between time-averaged field energy and (a) power dissipated in

the walls by conduction loss (Qw)' and (b) power radiated out through the

aperture (QA)' and (c) dielectric heating loss by material in the cavity (QM)

defines the individual quality factors. Large apertures cause a low value for

QA (roughly the ratio between enclosure and aperture area). The ratio is close

to one for vehicles. In aircrafts, the enclosure-to-aperture ratio 1son the

order of 10 to 100.

4.2. Open Resonator

For Case 2 (Table 3), a resonant wave field can be sustained by caustic

shapes of two bounding, reflective surfaces, while free space provides the

missing confining boundary. The mode density for an open resonator is

(Weinstein, 1969)

(33)"

where Xl is the effective area. A pair of opposing metal surfaces having an

area of 1 m2 can support up to 800 modes at f

o.

21
Practical configurati.ons of open resonator's are innumer-abl e (e ,g., Wei nstein ,

1969; Schulten, 1976; Auchterlon'leand Ahmed, 1977)~ Some. of the simpler cases

are depicted tn Fi.gure 7. Jhese conflqurations suppor-t the. more intere.sting

modes with small radlation 1ossea.vThetr mode patterns can be represented by

two beams of rays propaqatlnq in oppos i te dtrections wt.thout losing energy

through transverse radiatton. .The Q~fa,ctor of q resonance 1'5 determined by

radiati.on loss due to diffractton out of the. bounding surt'acesand by conduction

loss w·i.thinthem.Open resonator q",·vql~e.s are. very susceptible to misalignments.

of the ideal geometry~ High Q-va1ues afford little tolerance. to dimenstonal

changes. For example, in the case of a,plane pargllel mtrror p~ir, a deviation

by as small as Ao/lOO from betng equidlstant drops .the Q-value to below 10

from the value on the order of 10,000: for a "perf'ect" geometry'. Ihe stringent

accuracy requirements make a HSP due to open resonators unl ik_ely. Some geometri es are 1ess sensitive (sel f'-focuslnq) than others to misa1ignments. For

example, two square (~lOA x lOA) .aluminum sheets slightly but arbitrarily

bent in a crossed cylinder arrangement had fairly high (> 102) Q-factors

(Schif fman , 1970; see Figure 7g).

4.3. Modeling of Resonance Fields

The limited time available for this study did not permit giving the

modeling aspect of HSP more than a cursory glance. To remedy some of these

shortcomings, the references covering relevant topics might be consulted.

Modeling the field distribution of resonances in habitable space has its

place to identify "worst" case situations , Since the peak value of the stored

energy varies rapidly with position, calculations at a very large number of

locations will be required (Safari-Naini et al., 1977). While the model should

accurately describe the resonant field distribution leading to a HSP, it will

also contain a lot of conjecture and simplification about the real situation.

It is logical to proceed as follows:

1. Examine the possibility of resonant modes ina given structure

assuming perfectly reflecting walls.

2. Consider the excitation chances for these modes via coupling

to the incident field energy.

3. Introduce losses resulting (a) from imperfect specular or diffuse

reflections, (b) from metallic or dielectrit conductton, (c') from

22
(b) ( c)

Field Envelope

-L~._. c __• .--.....

(0)

(d)

--. b

(e)

--...........-.. - ------ .. I

( f)

rl,2 - radii of

curved mirrors

b - radius defined

by case (b)

(g)

Figure 7. Examples of open resonator geometries (Harvey, 1970; Schiffman,

1970; Weinstein, 1969)

(a) Plane parallel

(b) Symmetrical confocal

(c) General·spherical

(d) Asymmetric confocal

(e) Concentric

(f) Semi-confocal

(g) Crossed cylinders

23
diffraction and aperture radiation, and Cd) from the presence of

furnisnings and biota.

4. Superimpose all possible resonant modes to the composite field

pattern.

To complicate matters further, a possibility exist$ for latent resonances; i.e.,

resonances that are tuned in by a diel ectr-ic object moving within the enclosure.

A person inside a resonant cavity wtll cause a perturbation of the resonance

properties roughly proportional to the filling factor kl~ which is defined

one-half the ratio between body and cavity volumes. The effective Q-factor (32)

and shift in resonance frequency are approximately

(34)

The combination of loss and high dielectric constant (0 0.5, K 60) makes the

chances of sustaining a resonance in a small room very remote. For one person,

the ratio k

l will vary typically between 10-1 (e.g.~ cabin of a vehicle) and <10-4

(e.g., large hall).

5. MEASUREMENTS

No systematic measurements of a HSP in habitable structures have been reported, and only a few data on internal signal strength have been gathered at

microwave frequencies. In some cases, these results were compared with values

taken simultaneously on the outside to define a building penetration loss Lr for

the purpose of assessing signal coverage inside buildings. In those instances,

the mean value for Lr was always positive (see equation 4). The general consensus

from these efforts was that such measurements are complicated by reflection,

diffraction, and scattering both inside and outside the enclosure; that multipath

effects cause signal level variations of about 20 dB (see Figure 8) when scanning

across an arbitrary room axis; that these results are extremely sensitive to size

and shape of the enclosure and the presence and location of furnishings and people;

that normal incidence of incoming radiation produced the lowest penetration loss

L

r; and that metals and glass with wire mesh effectively.shielded the field.

Th~ internal field E~ (5) is best mapped with a miniature (dimensions 0.1A)

isotropic probe and a scanning mechanism. By coupling the linear motion of the

probe and themeasufed signal strength to a recorder, ~n interference pattern

similar to SWR curves is obtatned (Crawford, 1974). Amplitudes and periods of

the recorded oscillations can be analyzed to locate the source of the interfering

signal for mitigative measures.

24
Room Axis

CD

"'C~~~-==-_-+-_-I--~~~~~=:J

..

)(

Wcut-----+----,r---f=3lr---+-----+--.....

"'C

:;,

+- r----+-----I------+--+Y~---I+.\---l-----1

c..

2.6 GHz ---+--_+-+.-_--1-+-__--1

Y

x ~} Room --t-----+--4f.--+-'-f--J-------I size z =7 m

t

3dB

+

3 GHz

x =4 m----t----~___H~--4+-----J

y=4m

z=2m

Probe x Travel

Figure 8. Examples of measured free space SWR (interference- patterns)

(a) Empty anechoic chamber

(b) Anechoic chamber with structure in middle axis

(Crawford, 1974)

(c) Anechoic chamber with some absorbers removed

(Appel-Hansen, 1973)

5.1. Strength of 2.6 GHz Satellite Signal Inside Houses

A recent extensive measurement series by Wells and Tryon (1976), and Wells

(1977) of the 2.6 GHz signal strength (from the geostationary ATS-6 satellite

beacon) inside 27 single-family houses across the continental United States comes

the closest to assessing a HSP that we could find in an experimental study. The

penetration loss L

r

was determined by making spot measurements of the field

strength in two rooms at two probe heights and eight randomly chosen locations

both inside and outside a house. The details of the experiment design are reported

by Wells et al., (1975) in a report of limited distribution (see footnote on page

9). The loss L

r

was investigated as a function of construction type, climate,

elevation angle, and room position with respect to the incoming radiation.

A statistical treatment of the data base revealed the following. The penetration loss for all cases was L = 6.3 + 1.2 dB. The average loss from case-to- r -

case varied due to the position of the room in the house by 0.6 dB, due to the

exterior construction material (e.g., wood, brick) by 1.2 dB, and due to the

insulation in ceilings and walls by 1.6 dB. The polarization dependence was

significant in that the relative horizontal component was about 1.8 dB greater

than vertical. There was little change (+ 1 dB) in L with elevation angle - r

25
"

ATS6

42.30

1630

,..---, Room

I Outside I "

; Reference•

I Area I "'- .J......-__

8 randomly located

test points each on

inside and outside

L (Median) Room 1 : 5.19 dB

1 Room 2 : 6.25 dB

House:

single story wood frame

with aluminium siding

• Room2

..

..........- :

........-- f

--_......- .....-.'

Room 1 - -- ....... -1- ~-+-.

- .........--- O ~-

• - - - - - - - - - ...:;:1-: - .. -- I·. - HSP Vertical polarization component I·.. - 1 -_- of circularly polarized ATS 6 1

signal at 2569 MHz I

I

I

I

I

I

to

"to

o

c

0::: -10

.. (\I .....

(\J

w

o 50 100

Probability that Ordinate is Exceeded, 0/0

Fiqure 9. Probability distribution of hot spot occurrence inside sinqle story

wood frame house with metal sidings (worst case) exposed to a 2.57

GHz satellite siqnal (Hells and Tryon, 1976)

The variability of the inside signal level (e.g., + 9 dB) was in all cases

about twice as high as the outside reference level (e.g., t 4 dB). Figure 9

gives the probability distribution of the individual L

r values for two rooms

in a house (metal sidings, signalcQupled through the roof) which had the lowest

median for L

r (5.1 dB) of all houses measured. The 10 percent probability of a

HSP occurring is insignificant in view of the large scatter of the data points.

5.2. Fields in Anechoic Chambers

The reflectivity level in anechoic chambers has been studied extensively for

obvious reasons (Appel-Hansen, 1973; Crawfo~d, 1974; Donaldson et al., 1978). A

statistical sampling of data points (Wells and Tryon, 1976; Donaldson et al., 1978)

is not sufficient to capture the complicated three-dimensional interference pattern. A free-space SWR probe has to be scanned along several orthogonal axes

because a high degree of uncertainty exists about Ei (x, y, z). The examples in

Figure 8 show that reflecting objects in the quiet zone or missiD9 absorber

material quickly deteriorate any low reflectivity level. The local maxima are

26
indicative of hot spots; however, in this case, the reference to an outer incident

field (see equation, 7) is missing. In principle~ it is possible'to locate the

source of reflections from a completely known spati~l interference pattern, but

findi:ng that pattern at every point from a theoretica l evaluation Is prevented by

the compl Icated prcbl em of defininq the refl e..cttng boundaries.

5.3. Fields,in Mine Tunnel fO'telectri.c Waveguide)

Cavity boundaries made. of diel ectrtc CK.. ;> 3), low-loss (D < 0.02) materia l

can guide SPS mtcrowave rad iatlon tn any number of modes when the inner dimensions

are larger than A

o. All of these modes are lossy (typically betwe.en 0.02 and

0.5 dB/m at 2.5 GHz) since diele.ctric wall: is not a perfect reflector. Detailed

electric field distributions have been measured, for example, in mine tunnels

(e.g., Emslie et al., 1975). The lowest attenuation r~tes are those when, in

geometric optics terms, the wavefront impinges upon a reflect~ng boundary with

small grazing angles. Even modes in this category display low Q-factors in

closed tunnel chambers. A dielectric waveguide might guide SPS radiation to a

resonance structure that otherwise is not coupled to the outside.

In summary of Sections 2 to 5, we can say that the analysis has fallen short

of its purpose. Other than an awareness of the significance of certain interaction processes (coupling, reflection, loss) which are essential to a HSP, no

firm estimates of upper bounds and variabilities in the quantities entering

equation (16) were obtained. This is mainly due to the almost infinite number

of possible geometric space configurations for empty habitable space.

6. MITIGATIVE MEASURES FOR MICROWAVE HOT SPOTS

Two principal means exist to achieve certainty that there is no hot spot

problem; namely, to avoid penetration into the interior and/or to secure a

uniform internal field distribution. In other words, apertures of sizes in

the range::;:;: (0.3 to 3)1.0 and low-loss~ permeable building material are to be

avoided at the exposure site to minimize the cross section Xi (J01~ and little

stored field energy isaccomp1ished by SUppres,sing internal reflections [low

Q-factors (ll)]. To circumvent~n overapplication of absorber material, ·one

should perform tn suspected spaces a. three-d lmensiona1 f iel d scan and make sure

that the' free field SWR is within 1tmits (say about!. 6 dB', s.ee Tabl e 5) by

judici.ously placing absorbers 'and rearrangi,ng specular /re.flectors.

27
6.1. Outside Reflectbrs and Absorbers

Shielding is an effective way to reduce the cross section Xi (lO) which

defines the power dissipated in the interior space. Measures to ~ccomplish

this are as follows.

Uti lize natural obstructions Ce~g., tree qrove}.

Use high-reflectance surfaces for the outer shell (met~l stdings)

especially towards the south.

Shade.apertures with metal awnings or cover them with wire mes~.

The insertion loss of wi~re mesh In copper or ste.el at 2.45 GHz

is:

Li , dB

Size, meshes/em

44

7x7

51_

9x9

58

nxn .

Cover apertures with resistive sheet material or embed absorbing

cord around the edges where the highest electric coupling field

strength occurs (see Figure 2).

Keep unnecessary openings (slots, cracks, etc.) away from the

exposed side or keep them below 2 cm in size (then qi 0.1).

6.2. Inside Absorbers

Field uniformity is the desi.red objective for anechoic chambers and has

been studied extensively (Appel-Hansen, 1973; Crawford, 1974; Emerson, 1973;

Donaldson et al., 1978). In these applications, it is attempted to keep the

free-field SWR below 0.5 dB (see Table 5). In the case of habitable space,

one could lessen the SWR tolerance. The application of nonreflecting absorbers

to exposed metal surfaces should be an effective measure to mitigate potential

hot spots.

Absorbers provide nearly reflection-free surfaces by matching their impedance

Z to the free-space value Zo (4). They come in three basic types:

1. Broad band absorbers are typtcql tn anechoic cha,rnbers. To be

effecti.ve under al Lanql es of incidence, they have to be shaped

(e.g., cones) and mounted In thick layers Cd' ?lOA1 .. D'if'ferent

absorber materials can be stagge-reu to reduce the thickness and

improve matching.

28
2. Resonance absorbers..are much. thinner. than the broad-band type by takt ng

advantage of the coherency tn radi:ati·on.They are well suited for SPS

applteations. Refl ections at the surface. are suppressed by canceling

them with refl ect ions from the conductinq base when the..thtckness

= Ao/ 4. Under this type fall the Sel isbury Screen absorbers (used

tn radar appl Ications rwhet-e the remaining front-face reflections are

reduced by a resistive layer. Covering metallic.surfaces results in

a typ ica reductionfn ref'lectivtty by 25 dB (Emerson, 1973).

3. S~rface absorbers are destgned to attenuate field-induced surface

currents. They are not as effective as the other two types since

«A, but they are easy to apply'as spray or paint.

6.3. Mode Scrambler

Uniformity can be achieved by perturbing the f ie l d both. in time and space

with a moving reflector (rotating vane, oscillating metal sheet, etc.) within

the chamber. Such a mode stirrer tunes the enclosure through.all possible

resonant modes at the frequency fa. The electric field will pass through the

possible maxima Eo for each sequent.tal ly excited mode, thus essentially "smoothing"

any spatial field distribution.

If feasible, another suggestion for mitigative measures of field hot spots

deals with the possibility of randomly frequency-modulating the SPS microwave

carrier being the electronic equivalent to a mode scrambler.

7. CONCLUSIONS

Incide~t SPS microwave energy which falls outside the rectenna area upon

habitable structures will penetrate their chambers via aperture and IIdiffusion"

coupling. The concentration into field "hot spotsll (i.e., exceeding the incident

level) by focusing, caustic surfaces or by multiple reflection mechanisms is, in

principle, possible; however, dielectric losses and scattering from odd-shaped

obstacles, normally part of habitable space, should clutter any spatial field

pattern.

The foregoing treatment dealt in an elementary way with coupling of field

energy into an enclosure.and its possible spatial redistribution in standing

wave or resonance f iel ds . It should be emphasized that habttabl e space presents

a poorly'defined EM problem and that the whole subject has not received much

attention. We attribute the lack of theoretical field ~nalyses to the overwhelming complexity of the enclosure-cOntents cORfigurattons. The presence of

29
dielectric loads in the enclosure creates situation$ with the potential of being

a complicated resonant system with several coupled oscillations which can only

be clarified by measurements.

Modeling of.the internal field structure based on given geometric and

structural situations seems to be useful for related one- and two-dimensional

cases to gain general insights into the true nature of a three-dimensional

problem. In first approximation, the methods of geometric optics are to be

applied. The exact distribution of internal radiation requires the application

of field theory ((\1axwell's equations) for a .meaningful interpretation of interference patterns, standing wave f;elds,hotand dead spots, reactive zones, etc.

r~easurements of reflectivity levels in certain chambers will be required

employing an isotropic field probe and a scanning mechanism. Such a probe

responds equally to signals of any direction and polarization, but can also

be switched to select orthogonal field components for the location of reflection

sources which might cause a particular "hot spot" problem.

Simple mitigative measures can effectively suppress the onset of hot spots.

If reflections of the 2.45 GHz radiation at the outside are enhanced by metal

sidings, awnings, and screening of apertures and dampened on the inside by

lossy walls of low reflectivity, lossy furniture, avoidance of bare, opposing

metal surfaces, etc., one can expect with some certainty that there is no HSP

at all points of the inner space. If one has to be absolutely sure, then field

uniformity can be attained by perturbing the field with a mode stirrer (e.g.,

rotating vane, pulsating reflector, moving body) or by random FM modulation of

the SPSmicrowave power, which requires a certain bandwidth for the energy beam.

In summary, in any type of habitable enclosure there will be a nonuniform

field strength distribution due to reflected and scattered field components

interfering with each other. Essential to field enhancements are multiple

reflections in a resonance mode, which are then proportional to the product

of a quality factor Qand a coupling coefficient~. For almost all practical

purposes it was concluded that this product Eq. (16) will not exceed unity.

30
8. ACKNOWLEDGMENTS

Pacific Northwest Laboratory, u.S. Department of Enerqy , gratefully

acknowledges the following people'for their reviews and comments of the first

draft of this report.

James H. Atkinson

Scientific Advisor

Electromaqnetlc Compatibi l ity Analysis Center North Severn ' Annapolis, MD 21402

Bernard F. Burke

Massachusetts Institute of Technology

Department of Physics Cambridge, MA 02139

Julian T. Dixon

Chief, Research and Standards Division

Federal Communications Commission

Washington, D.C. 20554

Sidney ~1etzger

Assistant Vice President and Chief Scientist

Communications Satellite Corporation 950 L'Enfant Plaza~ SW

Washington, D.C. 20024

R. M. Showers

Professor of Electrical Engineering Moore School of Electrical Engineering University of Pennsylvania Philadelphia, PA 19174

Albert Y. Yeh

Bell Telephone Laboratories

Holmdel, NJ 07733

31
9. REFERENCES

Appel-Hansen, J. (1973), Reflectivity level of radio anechoic chambers, IEEE

Trans. AP-21 (4), 490-498.

Auchterlonie, L. J., and I. Y. Ahmed (1977), Microwave wideband open resonator

of large aperture, J. Physics E-10, 691-694.

Butler, C. M., Y. R. Samii, and R. Mittra (1978), Electromagnetic penetration

through apertures in conducting surfaces, IEEE Trans. EMC-20 (1), 82-93.

Chu, T. S., and R. A. Semplak (1976), A note on painted reflecting surfaces,

IEEE Trans. AP-24 (1), 99-101.

Jaggard, D. L. (1977), Transmission through one or more small apertures of

arbitrary shape, AFC-GL Interaction Notes, Note 323, September.

Kinzer, J. P., and I. G. Wilson (1947), Some results on cylindrical cavity

resonators, Bell Syst. Techn. J. 26, 410-445.

Koch, G. F., and K. S. Kolbig (1968), The transmission coefficient of elliptical and rectangular apertures for electromagnetic waves, IEEE Trans. AP-16 (1),.

78-83.

LaGrone, A. H. (1977), Propagation of UHF electromagnetic waves over a grove of

trees in full leaf, IEEE Trans. AP-25 (6), 866-869.

Lee, K. S., and G. Bedrosian (1979), Diffuse EM penetrat~on into metallic

enclosures, IEEE Trans. AP~27 (2), 194-198.

Roth, L. E., and G. Clachi (1975), Coherent electromagnetic losses by scattering from volume inhomogeneities, IEEE Trans. AP-23 (5), 674-675.

Safari-Naini, S., S. W. Lee, and R. Mittra (1977), Transmission of an EM wave

through the aperture of a cylindrical cavity, IEEE Trans. Et1C-19 (2),

74-81.

32
Schiffman, B. M. (.1970), Crossed cylinder microwave resonator, IEEE Trans.

MTT-18 (8), 509-510.

Schulten, G. (1976), Mircrowave optical ring resonators, IEEE Trans. MTT-15 (1),

54-55.

VonHippel, A. R. (1954)~ Dielectric materials and applications, published by J. Wiley &Sons, New York, NY. .

Wacker, P. F., and R. R. Bowman (1971), Quantifying hazardous electromagnetic fields: scientific basis and practical considerations, IEEE Trans.MTT-19

(2), 178-187.

Weinstein, L. A. (1969), Open resonators and open waveguides, published by The G~lem Press, Boulder, CO.

Wells, P. I., and P. V. Tryon (1976), The attenuation of UHF radio signals by

houses, Office of Telecom. Report 76-98, August (NTIS Access No. PB-258447).

Wells, P. I. (1977), The attenuation of UHF radio signals by houses, IEEE Trans.

VT-26 (4), 358-362.

Wilson, I. G., and C. W. Schramm, and J. P. Kinzer (1946), High Q resonant

cavities for microwave testing, Bell Syst. Techn. J. 25, 408-434.

33

APPENDIX A. SPS POWER DENSITY PATTERN AT RECTENNA SITE

RADIUS AT EQUATOR, km

5 10 100 1000

- - - --- 10 mW/cm2

--- -----1 mW/cm2

- --- 0.1 mW/cm2

-. 0.01 mW/cm2

±1 min ARC

ATTITUDE CONTROL] GRATING LOBES

10 m SUBARRAY

10deg rms ±ldB

2% RANDOM

• SUBARRAY

I I. FA ILURES

\.

o

10 :E

c(

20

30

c(

40

o 50 ....

LU

> 60 ....

c(

....J

70

80 "0

90

100

0.001 0.01 0.1 1 10 100

ANGLE FROM BORES IGHT. deg

Figure A-1. Proposed SPS transmitted power

density pattern (Dickinson, 1970).

CODE: dB mW/cm 2

A 0 20

B - 3 10

C -10 2

D -16 0.5

E -25 0.063

F -30 0.02

G -35 0.0063

H -40 0.002

CIRCULAR ARRAY 1 krn DIA.

6.5 GW AT 2450 MHz

10.0dB GAUSS IAN TAPER

UNIFORM SQUARE ELEMENTS, 10 m

H

H

H

5 km 10 km

H

o

G

~~~~ ~~~~PII----+---.---,-.....=-t---~~Ill'It--...,.,~~ H

G

H

H

10 km H

G

5 krn G

H

·0

Figure A-2. Microwave ~bwer distribution on

rectenna at equator (Dickinson, 1978).

35
l~PPENDIX B. FORMULAs~FeR THREE SIMPLE TYPES OF

CAVITY RESONATORS

(K1nzer and' ~lilson, 1947)

Field Components

TYPE OJ-: CAVITY 8.

CO-ORDINATE ~YSTLM

w

o

o

:! rlELD EQUATIONS * DEF,t-,JITIONS RESTRICTIONS

oNq,m,n

RECTANGULAR PRISM

TM

TE

EX =* k~~3 cos kl'X. SIN k 2 y SIN K3Z

Ey=* k~3 SIN k.x cosk2y SIN k3z

,nI k2 +k2

Ez =-v~ --T SIN klx SIN k 2 y COS k 3z

H x '= - kk2 SIN k.x cosk2 y COS k 3z

k l Hy = k COS klx SIN k2y COS k3z

HZ = 0

EZ = 0

Hx = K~3 SIN k,'X cos k2 y COS k3 z

H Y= k~~3 cos kl'X. SIN k2 y cos k 3z

k~+k~ Hz=-~COSk,x cos k 2 y SINK3Z

.Q,m,n - INT EGRAL INDICES

IDENTIFYING THE MODES. MAY

ASSUME THE VALUE ZERO, SUBJECT TO RESTRICTIONS GIVEN

IN ADJOINING COLUMN

2 > 0

m>O

Q+ rn>o

n>O

Ep=-# k: Ji(K1P)COS16 SIN k 3Z

CIRCULAR CYLINDER Ee - ~t k 3 Jf(k,P) SIN i6 SIN k 3z - € k kiP

Ez = V¥ JQ(kIP) COS~6 cos k 3Z

TM

Z _ Jr (k l p) SIN Qe Hp = COS k 3z (kiP)

He = - J Q(k I p) COS Qe cos k3z

~l Hz = 0

L

----~j E P = - V¥R Ji(k,p) sIN2e SINk3z € kIP " e",

E e = - '!¥ J6 (kiP) cos se t:a::J SIN k 3 z

E z = 0

Q,m,n = DEFINED AS FOR

RECTANGULAR PRI5M

rQm = mt h ZEFlO OF J Q(x)

FOR TM MODES

n >0

m>o

m>o

rgm = mt h ZEF:O OF Ji (x)

FOR TE MODES

2rfm k l = --aH P = kk3 Ji(K,p) cos t e COS k3Z

He = -.t Ja(kIP) slNDe COs k3 Z k KIP

k l Hz = k J~(kIP) cos ee SIN k 3Z

TE

SAM E AS FOR CIRCULAR

CYLINDER, BUT SUBSTITUTE:

ZQ (k, p) =JQ (k, p) - AY9. (K1p)

Z'f (k l p) =JQ (KI p) - AYa (k l P)

FULL COAXIAL

Z TM

TE

WHERE

FOR

FOR J'Q (k l p)

SAME AS

CIRCULAR CYLINDER, EXCEPT:

r~ m = mt h ZERO OF

[Ji(T)'X) YQ(X) '-JQ(x) YtdT)'X)]

JQ(rg m)

A =YQ(r2m)

FOR TM MODES

r'm = mt h ZERO OF

[J2(T)X) Ye (x) ,-Ja (x) Y~ (11X)]

Ji(rtm)

A = Y2(r2m.l

FOR TE MODES

m>o

SPECIAL CASE OF

TM 0,0, n MODE,

WITH rRm = 0

m>o

n>o

SOURCES: HANSEN t JNL.APP. PHYS., 9,P.654 BORGNIS, HOCHF:TECH u..ELEK:AKUS.,56,P.47

BORGNIS t ANN.d.PHYS., 35,P.359 BARROW & MIEHER,PROC.I.R.E., 28.P.184 * n-E TIME FACTOR HAS BEEN OMITTED;

THE E· FIELD IS IN TIME QUADRATURE

WITt-II HE H-FIELD, WITH w= ck

36
Resonances

Nor~MAL WAVELENGTHS

A- .2

SAME AS TM MODES

~1ode

Density

APPROXIMATION FOR

TOTAL NUMBER OF

MODES (TE & TM)

HAVING A> AO

v p. N =8.38 -----

~5 >'0

v =abL

p =a-b-t,

Q-factor Calculat'on

FORMULAS FOR Q t

I

.3bL. (p2+q2)(p2+q2+r2)2

4 p2b(a+L) +q2a(b+L)

abL

3

abL . (p2+q2)(p2+q2 t r 2)2

4 aL [p£:r2 +(P2tq2)2]t bL [q2 r 2 + (p2+q2)2] tab r 2(p2+q2)

3

a bL • (q2 t r 2)2

2 q2 L (b s aa) t r 2b (Lt2a)

3

abL • (p2 t r 2)2

2 p2 L (at2 b) t r 2a (Lsab)

I

--..!.!!L r [ I t p2 R2 2. ]- __I

2Tr I+R

DEFINITIONS

n >0

n = 0

p = f

q = .m,

b

~m>O r = n

T

Q= 0

m=O

n>o

C =Vi:I€ =VELOCITY OF

ELECTROMAGNETIC WAVES

IN DIELECTRIC

f = FREQUENCY

SAME FORM AS FOR

CYLINDER

rQ m HAS DIFFERENT

VALUES

v S N =4.38 A5 +O.09~

v = ll'a2 L 4

S =11'aL

N ~4.4 A.o

WITH SOME DOUBT

AS TO VALUE OF THE

COEFFICIENT

rfm I

-'-1l'-2+R

ram (I -T)2H')

---;r = 2 (I tT')H')+ R(I-T)2H')

THESE EXPRESSIONS ARE NOT VALID FOR SMALL '1 WHEN R=0

WHERE

37

n=o

n>o

n=o

R = ..!.-

L

n1T

p = 2rRm

n'Tr

p = 2r2m

FORM NTIA-29

(4-80)

u.s. DEPARTMENT OF COMMERCE NAT'L. TELECOMMUNICATIONS AND INFORMATION ADMINISTRATION

BIBLIOGRAPHIC DATA SHEET

1. PUBLICATION NO.

NTIA Report 80-49

2. Gov't Accession No. 3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Field Maxima Inside Habitable Structures Exposed to

2.45 GHz Plane Wave Radiation

7. AUTHOR(S)

Hans J. Liebe

8. PERFORMING ORGANIZATION NAME AND ADDRESS

National Telecommunications & Information Administration

Institute for Telecommunication Sciences

1-3449 325 Broadway

Boulder, CO 80303

11. Sponsoring Organization Name and Address

Department of Energy

Washington, D.C. 20545

14. SUPPLEMENTARY NOTES

5. Publication Date

October 1980

6. Performing Organization Code

9. Project/Task/Work Unit No.

910 4422

10. Contract/Grant No.

12. Type of Report and Period Covered

13.

15. 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 discusses microwave engineering data relevant to assess the potential

of the Satellite Power System (SPS) to cause microwave field enhancements (socalled "hot spots") inside habitable structures (house, trailer, car, etc.)

located in the fringe area of the receiving rectenna. Mitigative measures are

included in the discussion.

16. Key Words (Alphabetical order, separated by semicolons)

17. AVAILABILITY STATEMENT

£;J UNLIMITED.

D FOR OFFICIAL D!STRIBUTION.

"* U.S. G·OVERNMENT PRINTING OFFICE: 1980-0-777-602/111

18. Security Class. (This report)

UNCLASSIFIED

19. Security Class. (This page)

UNCLASSIFIED

20. Number of pages

37

21. Price: