NBS

Reference publ1cat10ns

NATL INST. OF STAND .& TECH

A111Q5 1bfib^3 ^

•"•CAU O* % NBS TECHNICAL NOTE 1076

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

inn

.15753

No. 1076

1934
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards' was established by an act of Congress on 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's technical work is per- formed by the National Measurement Laboratory, the National Engineering Laboratory, and

the Institute for Computer Sciences and Technology.

THE NATIONAL MEASUREMENT LABORATORY provides the national system of

physical and chemical and materials measurement; coordinates the system with measurement

systems of other nations and furnishes essential services leading to accurate and uniform

physical and chemical measurement throughout the Nation's scientific community, industry,

and commerce; conducts materials research leading to improved methods of measurement,

standards, and data on the properties of materials needed by industry, commerce, educational

institutions, and Government; provides advisory and research services to other Government

agencies; develops, produces, and distributes Standard Reference Materials; and provides

calibration services. The Laboratory consists of the following centers:

Absolute Physical Quantities2 — Radiation Research — Chemical Physics —

Analytical Chemistry — Materials Science

THE NATIONAL ENGINEERING LABORATORY provides technology and technical ser- vices to the public and private sectors to address national needs and to solve national problems; conducts research in engineering and applied science in support of these efforts; builds and maintains competence in the necessary disciplines required to carry out this research and technical service; develops engineering data and measurement capabilities;

provides engineering measurement traceability services; develops test methods and proposes

engineering standards and code changes; develops and proposes new engineering practices;

and develops and improves mechanisms to transfer results of its research to the ultimate user. The Laboratory consists of the following centers:

Applied Mathematics — Electronics and Electrical Engineering2 — Manufacturing

Engineering — Building Technology — Fire Research — Chemical Engineering2

THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts

research and provides scientific and technical services to aid Federal agencies in the selection, acquisition, application, and use of computer technology to improve effectiveness and

economy in Government operations in accordance with Public Law 89-306 (40 U.S.C. 759), relevant Executive Orders, and other directives; carries out this mission by managing the Federal Information Processing Standards Program, developing Federal ADP standards

guidelines, and managing Federal participation in ADP voluntary standardization activities; provides scientific and technological advisory services and assistance to Federal agencies; and

provides the technical foundation for computer-related policies of the Federal Government.

The Institute consists of the following centers:

Programming Science and Technology — Computer Systems Engineering.

'Headquarters and Laboratories at Gaithersburg, MD, unless otherwise noted; mailing address Washington, DC 20234. 'Some divisions within the center are located at Boulder, CO 80303.
HA7IONAL BUREAU OF STANDARDS

LIBRARY a

Small Aperture Analysis of the Dual TEM

Cell and an Investigation of Test Object ) Scattering in a Single TEM Cell

P. F. Wilson

M. T. Ma

Electromagnetic Fields Division

National Engineering Laboratory

National Bureau of Standards

U.S. Department of Commerce

Boulder, Colorado 80303

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued October 1984
National Bureau of Standards Technical Note 1076

Natl. Bur. Siand. (U.S.), Tech Note 1076, 60 pages (Oct. 1984)

CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1984

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

Page

1 . Introduction 1 2. Small Aperture (Obstacle) Theory 3 3. Polarizabilities 6 4. The Dual TEMCell 12

5. Small Object Scattering in a TEM Cell 19

6 . Conclusions 23

7 . References 24 Appendi x A 48

ill

Small Aperture Analysis of the Dual TEM Cell

and an Investigation of Test Object Scattering

in a Single TEM Cell

P. F. Wilson and M. T. Ma

Electromagnetic Fields Division

National Bureau of Standards

Boulder, Colorado 80303

Small aperture theory is used to investigate the dual TEM cell. Analyzing coupling

through an empty versus a loaded aperture leads to a model of dual TEM cell shielding

effectiveness measurements. Small obstacle scattering yields results for both the field

perturbation and the change in a cell's transmission line characteristics due to the

presence of a test object in a TEM cell. In each case, theoretical values are compared

to experimental data.

Key words: dual TEM cell; perturbation; shielding effectiveness; small

aperture/obstacle theory; test object loading.

1. Introduction

The transverse electromagnetic (TEM) cell is well established as a device for creating a known,

broadband, isolated test field [1]. TEM cell applications include the emissions and susceptibility

testing of electronic equipment for electromagnetic compatibility (EMC) purposes [2-8], the

calibration of antennas and probes [9,10], as well as the study of biological effects of radiofrequency (rf) radiation [11-13]. The basic TEM cell design, as shown in figure 1, consists of a section of rectangular coaxial transmission line (RCTL) coupled via tapered sections to ordinary

50 Q coaxial cable. Excluding the gap regions, the central RCTL test section supports a linearly

polarized TEM mode which is similar to a free space plane wave. Both the TEM cell's waveguide

properties [14-20], especially the appearance of the higher-order modes, and the manner in which TEM

cell results may be related to the free space environment [3-5, 21-24] have been carefully studied.

As the usage of TEM cells has become increasingly refined, interest has grown in applying its

well defined characteristics to additional metrology areas. One such example is the dual TEM cell

concept which is being proposed as a method to measure the shielding effectiveness of materials

subjected to rf radiation [25-29], As the name suggests, the dual TEM cell consists of a pair of

cells coupled via an aperture in the common wall. A comparison of the power coupled through an empty aperture to that transferred through the aperture when covered with the test material provides

a relative measure of the material's shielding effectiveness. In general such a waveguide coupling

problem is quite difficult to analyze. Fortunately, the TEM cell is basically a low frequency

device. Therefore dual TEM cell coupling is well suited to an investigation based on the small

aperture theory pioneered by Bethe [30]. Although the dual TEM cell is the primary motivation for

the present study, the basic results may be formulated in a fairly general fashion and thus are
applicable to other TEM cell associated problems such as the loading effect on a single TEM cell by

a small object.

Section 2 summarizes the basics of small aperture theory, as well as the dual small obstacle

formulation. If the aperture or obstacle is electrically small, then the scattering effect is essentially equivalent to that produced by an appropriate set of dipole moments. These dipole

moments may be used to predict the scattered fields, which in the case of the dual TEM cell give a description of the expected aperture coupling. The dipole moments depend on both the incident

(exciting) fields and the shape, size, and orientation of the aperture or obstacle. These latter

effects are summarized in a quantity termed the aperture (obstacle) polari zabi 1 ity . As discussed in section 3, few polari zabi

1

ities may be derived directly. Therefore, various approximations such as numerical approaches or empirical values are inevitable. Nonetheless, in practice Bethe's basic

technique has been shown to yield excellent results [31].

In section 4, small aperture theory is applied specifically to the dual TEM cell and the

shielding effectiveness procedure. First, coupling via an empty aperture is considered, including

the case of an appreciably thick aperture. The agreement between theoretical results and measured

data is found to be quite good and serves to establish the usefulness of the present approach.

Coupling through a material -covered aperture (loaded) is less straightforward to analyze due to the more complicated geometry and the difficulty in specifying certain material parameters. The

particular loaded aperture model chosen here does yield curves which qualitatively agree with

measured shielding effectiveness data. More importantly, our analysis provides insight into the

basic coupling mechanism. In doing so, it points out which parameters are the most critical to dual TEM cell measurements and thus which factors need to be controlled most carefully in order to obtain

meaningful shielding effectiveness data.

Normal TEM cell applications involve introducing a test object into the cell. To some extent

the test object will perturb the TEM cell environment from its well studied empty state. The TEM

mode will be scattered and higher-order modes excited, although the latter will usually be quickly

attenuated. If the TEM cell is viewed as a transmission line circuit, then the test object

represents a load which will alter the cell's overall impedance characteristics. Typically, the

test object size is restricted to some fraction of the pertinent cell dimensions and any loading

effects are ignored. Based on small obstacle theory, we are able to derive an equivalent circuit

representation for the test object loading. The resulting loaded cell transmission line circuit

yields the expected impedance change. In particular, impedance curves are generated for a sequence

of centrally located spherical conductors of increasing diameter. Results suggest that the change

in impedance is not likely to be severe enough to cause problems in a normal cell application. In addition to the above transmission line circuit, section 5 presents results for the scattering of

the first four RCTL modes. The modes themselves are discussed in Appendix A. It appears that the

field variation from the empty cell case can be significant, especially the backscattered TEM

mode. Together, the loaded transmission line circuit model and the field perturbation results,

enable one to better judge whether a particular measurement procedure needs to account for the

effects of test object presence.
A short conclusion, summarizing results, and suggesting further TEM cell problems of interest,

is given in the final section.

2. Small Aperture (Obstacle) Theory

In free space a source distribution (currents, charges, etc.) may be represented by an equivalent multipole expansion which generates the same fields outside of some minimal volume

containing the sources [32], If the sources are small compared to the free-space wavelength, then

the initial multipole expansion terms are sufficient to predict the far fields. For example, this

is the justification for replacing small current loops with magnetic dipoles. The same basic

argument holds in a confined region, such as a waveguide, although with some modification [33], The sources now excite waveguide modes or cavity resonances. If only the initial multipole terms are retained, then the number of modes whose excitation may be accurately described is limited.

Typically though, the higher-order modes are not of any great interest because they are rapidly

evanescent away from the scattering region. Thus, equivalent to the far field restriction in the

free space case, results should be valid except in the immediate vicinity of the source region where

the higher-order modes may still contribute substantially.

Small aperture theory, as well as its small obstacle dual, is based on generating the leading

terms in such a multipole expansion. Most details may be found elsewhere [31,34,35] and need be

only briefly summarized here as applicable to the TEM cell. The notation is essentially that of

Collin [34], Given a discontinuity in a waveguide excited by some incident field

- - - + - + distribution E.. H. , the scattered fields E ", H may be expanded in terms of the normalized 11 s s - + - + waveguide modes E , H according to

n n

E

~ = V a E ,H = I a H

s L nns L nn n n (1)

E

" = I b E"

H

" = Y b H"

s nn n nn n n

where + indicates propagation away from the discontinuity in either the forward (+) or backward (-)

direction. If we let the z-axis lie along the direction of modal propagation and reference the zero plane to the discontinuity center (arbitrarily defined), then the normalized waveguide modes may be

written as follows:

- + ,- - , +18 z

E = (E + a E 1 e

P

n

n nt z nz

H ±

= f± H + a H ) e +1p

n Z

n nt z nz
where (3 is the propagation constant of the n-th mode, a time convention exp (ioit) has been

suppressed, and the transverse field components E and H are related via the admittance

nt nt dyadic Y

n

H . = Y • E . (3) nt n nt

Implicit in (2) is that the field components inside the parentheses, E , H etc., depend only on the transverse position (x, y). The orthonormal

i

zation condition takes the form

J (E x H • a ds = 6 4 1 y mt nt ' z inn CS

where CS is the waveguide cross section (assumed independent of z) and 6 is the Kronecker delta

mn function .

The leading multipole expansion terms in k Q

, the free space wave number, are the

electric (P) and magnetic (M) dipole moments. Given this equivalent source representation of the

discontinuity, the expansion coefficients a

n and b

p are found to be [34]

a = ^ ( u H

"

• M - £

"

• P)

n 2

* o n n

;

i uj , - + - - + - s b = =-" t\x H • M - E • P)

n 2 ^o n n

;

(5)

where u is the free space permeability. The dipoles are located at the defined center of the

discontinuity region. The incident field, which excites the sources, is assumed to be essentially

uniform over the electrically small scattering discontinuity. Therefore it is reasonable to decompose the dipole moments into the incident field at the dipole location E , H times a term

which characterizes the scatterers geometric and material properties. These latter quantities are

the electric (a ) and magnetic (a ) polarizabi 1 ities and are in general dyadics. In terms

of a emand a the expansion coefficients become

a = — ( u. H

n 2 AHb n

n 2 VH

o n

a • H. m i

- e E o n• a • E . e i

a • H. m l

- +

- e E o n

• a • E . e i

(6)

where the free space permittivity e has been introduced for symmetry.
This is the basic equation describing waveguide scattering. In order to apply (6) to a particular problem, three quantities need to be specified; (1) the normalized waveguide

- + + modes E n

H 2 the polarizabilities a and a , and (3) the incident field

e m distribution E., H. . The normalized waveguide modes in a TEM cell can be found using either a conformal mapping solution [21] or a singular integral equation approach [16,23]. Polarizabilities

constitute a problem of longstanding interest with solutions ranging from the relatively simple

static solution of Bethe [30] to more recent computer based numerical techniques [36], Finally, the

incident fields must be detailed. In the case of a dual TEM cell (see fig. 2), the incident field

is the TEM mode in the driving cell while the scattered fields may be analyzed in either the sensing

cell or the driving cell itself. In discussing test object loading, the TEM mode will again excite

the scattering obstacle and the scattered fields are confined to that cell.

Before proceeding we may take advantage of relationships between the modal

components E

" and H" to expand (6) somewhat. The admittance dyadic Y is given by

n n . n

fa a y xa a ) x y

J

where Zn is the wave impedance of the n-th mode. Substituting (7) into (6) and assuming that the

polarization dyadics are diagonal yields

2

Lf o

* n nt

a • H. + e E m it o nt

a • E.. e it

- u H a H. o nz mz iz

e E a E. o nz ez iz

b =ir •[- H * E J • a • hV + e E M

n 2

L o

^ n nt * m it o nt

a • E.. e it

- u H a H. + e E a E. o nz mz tz o nz ez iz

This may not appear to be a useful expansion of (6). However, consider the following; if the

incident field is a forward traveling TEM mode (n=0), as will be the case for the two present

applications, then

H. - Y • E. it o it

H. = E. = o IZ 1Z
Substituting these restrictions into (8) yields

-ik n r\

a = T— {(a + —- a ) E E. +(a + ^ a )E E.

n 2tionex Z my nx ix ey Z mx ny ly

n

(10)

- i k r) ti b = —- {(a -_° a ) E E. + (a - -% ) E E. } n 2rionex Z my nx ix ey Z mx ny iy

n

where n is the free space wave impedance. In terms of the fields, we need specify only in (10) the

electric field components of the n-th mode and the incident TEM mode, at the dipole location. This

simpler form (10) will be the basic equation needed for the present investigation. We next consider

the polarizabil ities needed to apply the above result.

3. Polarizabil ities

The electric and magnetic dipole moments may be defined in terms of the currents and charges

induced on the scattering object by the incident field distribution. If the scatterer is a perfect

conductor (e > ») or a perfect magnetic conductor (u. *<=), then P and M may be defined as follows [34]

(electric conductor) (magnetic conductor)

~ £o

P

= / r p ds or —^— f r x J ds

s e 2S

:n:

M = Tr/rxJds or — frpds 2

}c e u. i Km

S ^o S

where p^ and p are the electric and magnetic surface charges, J and J are the electric and

e

p m

3 3 e m magnetic surface current densities, r = xa + ya + za is a position vector, and S denotes the

x y z scattering surface. For nonperfect materials, that is e and u finite, an additional volume

integral is required [33].

Notice that for a perfectly conducting obstacle, (11) implies that the electric dipole moment

is due to surface charge while the magnetic dipole moment is due to circulating currents. Thus

locally over a small surface element ds the electric dipole moment is tangential to the surface

while the magnetic dipole is in the direction of the surface normal. For a perfect magnetic

conductor, duality suggests that these roles are reversed. In fact, if we consider the fields

(E , H ) for the electric source fp , J ) case versus the magnetic source case

e e

v e e

(E H , P , J ,) then duality principles [37] (E - H , H - -E , p - p , J - J , and

m m m m

J K *• e m e m ^e m e m

^o

** e o^

^ mp ^ the following relationships
P (electric conductor) = e a (electric conductor) • E o e e

=

J

r Pe ds - J r Pm

ds (12)

= \x a (magnetic conductor) • H = u. M (magnetic conductor)

o m mo

and

M (electric conductor) = a (electric conductor) • H m e -\ J"rx5

e ds .1 /r x 5m

ds (13)

(13)

= a (magnetic conductor) • -E = — P (magnetic conductor)

e meo

Together with the comments above, equations (12) and (13) yield

a (electric conductor) - a (magnetic conductor]

e m

3

a (electric conductor) - a (magnetic conductor)

'141

In summary, the polarizabil ities are not independent. Rather, only certain canonical problems need

be solved.

It remains to relate the above results to a small aperture which is neither a perfect electric

or magnetic conductor. We find that the polarizabi lity for the above idealized aperture is related

to that of a magnetic conducting disk of the same shape. In fact, the relationship is [34],

a (aperture) = — a (magnetic disk)

e 4 e

3

(15)

a (aperture) = — a (magnetic disk) m 4 m

A factor of 1/2 is introduced because the disk has currents on two sides while the aperture is one- sided and, because the aperture dipole moments radiate into two half-spaces, the effective dipole

moments are reduced by an additional 1/2 multiplier.
The various integrals needed to evaluate pol arizabil ities are difficult to analyze directly.

Thus, a number of approximations are employed. As mentioned, the simplest approach is the static

model detailed by Bethe [30] which has antecedents in certain acoustical and electrical problems

treated by Lord Rayleigh [38,39] and fluid dynamics considerations given by Lamb [40]. In practice,

the infinite plane screen idealization requires that the aperture not be located too close to the

waveguide walls. Fortunately, if the aperture or obstacle is roughly a principal dimension away

from additional conducting walls, then the image terms do not significantly affect the

polarizabi 1 ity [41].

Conn [42-43] has measured values for a number of interesting shapes including rectangular

apertures, rosettes, and dumbells, using the electrolytic-tank method. More recently, the advent of

high-speed computers has led to numerical solutions based on static assumptions [44,36], Rayleigh

series (k

n

) corrections to the static solutions [33,36,45-47], and time domain considerations

[48,49], The latter paper by Butler et al . contains a very useful survey of aperture related

problems

.

An alternate approach to computing the polarizabil ity directly is to place bounds on its

possible values [50,51]. Jaggard and Papas [51] note that a circle contains the maximum area for a given perimeter length. Thus, the polarizabi 1 ity of an arbitrary convex aperture is bounded below

by the value for a circle with the same area (minimum perimeter) and above by the value for a circle

with the same perimeter length (maximum area). These bounds would be especially useful for shapes

of an essentially circular nature such as an octagon.

TEM cell applications will most likely involve spherical, or box-shaped scattering objects.

Apertures will also probably be circular, or rectangular. Therefore only a few of the above results

need to be explicitly detailed here. The polarizabi 1 ity of an arbitrary box (rectangular

paral lelopiped) is not readily available. However, the above logic suggests that bounds based on spheres of equal surface area (above) and volume (below) should give an indication of the proper

result. For the types of scatterers considered here only the diagonal elements of the

polarizabi 1 ity dyadics are nonzero. Letting the three orthogonal axes have unit vectors x., we

need only specify a ejjej . = x. • a • x. and amjjmj . = x. • a • x..

For ellipsoidal conducting obstacles we find that the static approximation gives [34]

a . = V/L.

ej J (ellipsoid) (16)

a . = V/(L. - 1) mj J

4 where V = T 7tr i r o

r 3123o is the volume, r-, , r , and r-j are the semi-axes, a . and a . are associated ' 1 ' c ' 3 ej mj

with the respective semi-axes, and the integral L- (j = 1, 2, 3) is defined by

J 2 j „ 1/2 {U)

(s + r/)[(s + r^)(s + 0(s + r/) ]
The L- integrals may be evaluated in terms of elliptic integrals. In the case of a sphere (r-, = r-o

= r^ = r) L- = 1/3, and the pol ari zabi 1 i ties reduce to

A 3 a . = 4-nr ej (sphere) . (18)

a . o 3 mj = -2itr

If we let rj = r^ and r^ = 0, then the result is a circular disk of radius r. Equations (16) and

(17) then yield a , = a o = a o J = 0, and

ml m2 e3

16 3 ael= aeZ=T r

_o 3 (circular disk) .

v ' a -. = —~ r m3 3

In the case of a square conducting disk of side length d, the polarizabil ities are approximately

given by [52]

3 a , = a = 1 .032 d el e2

a - = -0.455 d m3

i ,-n ( 20 ) o (square disk)

The polarizabil ities a , , and a

? are associated with axis aligned with the sides of the square

while a - is associated with the surface normal direction. As with the circular disk,

eo

ml m2 e3

Using duality (15), equations (19) and (20) immediately give the pol arizabi 1 ity for a circular

and square aperture. Specifically we find that a , = a „ = a ~ = 0,

2 3 a = —o r e3 3

a , = a o = sr r ml m2 3 and

a - = -0.114d

3 e3

. _ (circular aperture)

^ (square aperture) . (22) a , = a = 0.258d

ml mi

In the future, we will simply speak of the aperture polarizabilities a and a . Their

orientations (normal and tangential) will be understood.

The validity of (21) and (22) is based on the assumption of an infinitely thin conducting

plane. In fact, the aperture could have an appreciable thickness. Cohn [53] and others have

suggested that a thick aperture be modeled as a section of waveguide operating below cutoff. The

equivalent dipole moments effectively excite the evanescent modes in the aperture waveguide. These

modes then generate a new set of dipole moments at the aperture's other end. A very simple

thickness correction follows from only considering the lowest-order mode excited individually

by P and M . For example, given a square aperture, the electric dipole moment P is normal to the

aperture and thus longitudinal to the aperture waveguide. Therefore, P will excite TM modes with

9
the TM-jj being the first mode for a square cross section. Thus a should be replaced by

TM

a e" P ll T (23)

e

TM where 3

' is the propagation constant of the TM-q mode and T is the aperture thickness,

Likewise, M will excite both TE and TM modes, thus the TE

1(j mode effect will be included,

Therefore a is replaced by m

K J

-pJo

t (24)

where p in is the TEiq propagation constant. Alternate thickness corrections are provided by

McDonald [54] who uses the reaction concept to generate an equivalent circuit for the thick aperture

and by Akhiezer [55] who generalizes Bethe's approach.

Shielding effectiveness measurements involve loading the aperture with the material under

test. If the aperture is actually fitted with the test material, then the above waveguide model can

be applied. One simply modifies the propagation constants to reflect the new waveguide medium.

Realistically, it will be more convenient to cover, rather than plug the aperture [25-26]. Thus, an alternate approach to determine the loaded polarizabi 1 ities , designated a and a , is needed.

Some authors have generalized the basic aperture problem to allow for different media on each

side of the conducting plane [56-58], The static approximation yields [56].

2e, a /a

e e e, + e 9

a /a =

(different media) (25)

mm u, + \u

where j = 1, 2 determines from which side the incident field originated and the direction of the

electric dipole moment is into the material on each side of the aperture. These values might be

useful if the sample covering was very thick. However, in practice, thin samples are more likely.

Therefore the problem of a thin sheet, possibly lossy, is of interest. Marin [59] gives some

static approximations for the polarizabi 1 ity of a circular aperture when a dielectric

sheet (a = 0) of thickness h is present. He derives closed-form expressions for very thick and very

thin sheets. In the latter case for example, he finds that

~

/ i

, 3 ^ E r2

" X

)

r 2hx „ r 2h> . r 2h

»

, 9 ,* a

e /ae

= 1 +

2 TO9 (—) *"(—) + °(—

)

(26)

r2 (dielectric sheet-circular aperture radius r)

10
where e „ is the dielectric constant of the material and 2h/r is the quantity assumed small in the

thin sheet case. An air backing is assumed on each side of the sheet. As may be seen, the

normalized pol arizabil ity (26) goes to unity as the thickness h vanishes. The magnetic

pol arizabi 1 ity will be unaffected by the dielectric sheet and therefore is still given by the second

expression in (21)

Actual shielding materials will be conductive (a » 1) since it is desirable that a shield

material both reflect and absorb fields as well as provide a continuous path for induced surface

currents [60]. A lossy sheet presents a further complication in determining the pol arizabi 1 ities

In the static limit, the sheet will appear as a perfect conductor to the electric fields and

transparent to the magnetic fields [61], that is a * o while a remains unchanged. These zero-th

order terms provide some insight into the expected behavior of a loaded aperture; however, the

dependence on the material properties is still hidden.

Casey [60] has developed an integral equation solution for the case of wire mesh loading. By

modeling the mesh in terms of an equivalent resistive sheet, he is able to generate a first order

correction to the static limit values. As with Marin's effort [59], Casey's results are for a circular aperture. He finds the following

-a /a = [1 +-—] e e 3u

r-, In a /a = [1 + , .. ~ m m 3it(l + z v c

'wire mesh - circular aperture radius r) [21]

,-1

where

=

1 um r • ^0 m 21

s

C r

s e 2e a o s

z

c = 2*yZs (28)

Z

s =

Z wa

s + iwLs

-2ur /a -1

in (1 - e u s

) C

s 2«e (erl + e r2 ) a

$

n a -2-nr /a -1 Ls'-^O-e "

S

)

11
a c denotes the mesh size, r is the mesh wire radius, R r is the contact resistance,

S CO c

* and e , and e are the dielectric constants of the material (if any) on each side of the mesh. The

internal impedance per unit length Z' is given by

A I (A)

co oo 2 I, (A)

where R

1 is the dc resistance per unit length of the mesh wire, A = Moo x J , x = u. o r is the

to ^uroocoojoj

diffusion time constant of the wire, \x and a are the wire's permeability and conductivity, and

co to r J

I (y = 0,1) denotes a modified Bessel function of the first kind. These expressions are somewhat

formidable but are included because many shield materials are indeed such wire mesh loaded sheets.

The polarizabil ities in (27) also apply to a simple lossy sheet if we properly modify the

equivalent sheet impedance Z,. in (28). If we let r /a. +0 (zero wire thickness)

^ CO S then C<- -* °° and L<- -* implying that Z

s has only a resistive term and that p

-> =°, which means the

normalized electric polarizabi 1 ity in (27), is again zero as in the static case. In addition, one

may show that for an electrically thin resistive sheet [34]

z =4t (3o;

s oh v

where a is the conductivity and h the sheet's thickness. Thus we have

i 4u) li r a h am /a

m

" t 1 + 3n (1 + 2u R ah)^

c

(lossy sheet - circular aperture radius r) (31'

a /a =0 . e e

If the contact resistance R , and the material properties a and h are known, then these expressions

may be readily applied, as will be seen in the case of the dual TEM cell.

4. The Dual TEM Cell

The basic goal of EMC/EMI engineering is to insure that electronic equipment will function

properly in a specified electromagnetic environment. This requires both that a system not be overly

susceptible to the expected ambient fields and that the system itself does not contribute undue

amounts of spurious radiation. Satisfying these requirements has led to the general concept of

shielding, as well as numerous interference control guidelines, test facilities, and test procedures

[62-65].

12
Roughly speaking, EMC test objects may be separated into three levels; (1) materials, (2)

components, devices, etc., and (3) systems. The desire at each level may be to study shielding

effectiveness (SE), however, each grouping presents a quite different test problem. For example,

the SE of a plain sheet of material may be quite different from the SE of a container, or box formed

from the same material [66,67]. Similarly, a complex system may fail to satisfy a set of EMC

requirements, even though each component individually meets those same requirements [68]. Thus

although a knowledge of a material's SE is of great value in predicting its behavior in a larger

system, SE figures should not be used in an absolute sense. In addition, there is great variance

among test results just at the materials level [29].

For materials, a SE test procedure based on the dual TEM cell has certain advantages over the

widely used shielded room technique based on MIL STD-285 [25,26]. Dual TEM cell measurements

require less time, offer excellent repeatability, are readily standardized, and require only

moderate sample sizes. Perhaps more importantly, given the wide variation in test results mentioned

above, the dual TEM cell is more readily analyzed theoretically than most techniques. This greatly

enhances the interpretation of SE test results since it is clearer what is being measured and what

values should be expected for a given material sample. Dual TEM cell disadvantages are primarily

the limited frequency range (low) inherent to TEM cells in general and the difficulty in controlling

the aperture environment and the mounting of the test material. This latter difficulty is shared by

most methods using limited sample sizes [29], including the new ASTM proposed transmission line and

dual-chamber standards [69].

As shown in figure 2, a dual TEM cell consists of a pair of TEM cells coupled via an aperture. The aperture serves to transfer power from the driving cell, shown here as the upper cell

with the signal source located at port 1, to the receiving or sensing cell, here the lower cell with

the output measured at either port 2 or port 3. The insertion loss (IL) provided by the shielding

material is defined as the ratio of the received power (P) for an empty aperture to that (P), for

the loaded aperture case, or

IL = 10 log |4| (dB) . (32)

P

In each case the input power should be held constant. Received power may be measured either at port

2 (backward port) or port 3 (forward port) with the other terminated in a 50 Q load, as shown in figure 2 for a forward port measurement.

Dual TEM cell coupling may be described via the small aperture theory developed in the previous

two sections. Because a TEM mode is used as the incident field, equation (10) applies, with (E QX ,

E ) being the TEM mode electric field components in the driving cell and (E nx , E ) denoting the

n-th mode electric field components in either the driving or receiving cell. Although the cells may

be kept general, we will consider the simpler case of identical cells. In addition, if the aperture

is longitudinally centered, then the evanescent modes should not couple appreciable power to the

output ports. Thus only the TEM mode expansion coefficients a Q

and b Q are of interest. For identical cells, equation (10) yields

13
'33)

-i k

a = - ° {(a + a ) E E. + (a + a ) E E. } o 2rj ex my ox ix ey mx oy iy

-i k b = -=—- {(a - a ) E E. + (a - a ) E E. } o 2ti ex my' ox ly ey mx oy ly

The normalized field components in (4) for the TEM mode are found in Appendix A (A-10).

Referring to figure 3, which defines the relevant RCTL dimensions (a, b-, g) as well as the x-y axes orientation, we find that for symmetrical cells (b^ = b£ = b)

r 2 ,1/2 r smh M (b - py) . M . ., , , M , E = — Z ) —u—~-r—iLLJ- sin Mx sin Ma J ( Mg

,

xac L , smhMb o va ' mo=l

!34)

P 2 ,1/2 r cosh M (b - py) ., M . , /,. » E = p — Z )

• u m k "^ - cos Mx sin Ma J (Mg)

y

K ac L

. sinn M b o

3

J mo=l

where the characteristic impedance 1

Q is given by

-1

Z = t, | [in (--) - X - (1 " "th Mb)] . (35)

c o 8 iig , m mo=l

mo refers to the summation over odd m only (m=l,3,5 . . .), M = mu/2a, and p is a sign function,

with p=l above the septum and p=-l below the septum. In the driving cell E^

x

= E

x and E^ = E while in the receiving cell E QX

= E x and E = -E . Notice also that (x, y) need to be properly

defined in each cell. For example, the aperture is located at y=-b in the upper cell but at y=b in

the lower eel 1 .

Insertion loss measurements are based on the power coupled to the receiving cell. Thus, we

will concentrate on the expansion coefficients a and b in the lower cell. If the aperture is centered transversely, (x=0) . then E = E. = and equations (33) and (34) combine to give

o / \ r 2

a = -s— (a + a ) E o 2ti ey mx' oy

i k „

b = y—2. (a - o )• E

• (36)

o 2n

Q ey mx' oy

r 2 ,1/2 v sin Ma , ,., .. E = — Z

' ) . , '

J (Mg) oy a c

L

, sinh Mb o

3

J mo=l

14
This is the basic equation describing dual TEM cell coupling. As may be seen, the result is quite

simple. Notice that the normalization relationship in (4) implies that the power carried by the

,2 ,? scattered TEM mode is given by a \'/ n and b / in the forward and backward directions,

o ' 2 ' o ' 2 respectively. Finally, the differing signs in the equations for a and b imply that power is

coupled asymmetrically to the sensing cell. Because a and a are of opposite sign for an aperture,

b Q will be greater in magnitude than a Q and thus the dual TEM cell acts more as a backward than

forward coupler.

The dual TEM cell used for measurements at NBS featured a square aperture, thus the

polari zabi 1ties for the unloaded case are given by (22). Substituting these into (36) yields

i k a„ = -5-2- (0.144) d

3

E rt 2

2r| oy

'37'

b = -T—2- (0.372) d

3

E 2 o 2-n

v

' oy

The relevant cell dimensions are: a = 9 cm, b/a = 2/3, g/a = 0.24, and d/a = 0.56 which gives each

cell a characteristic impedance Z c of approximately 50.6 Q. Equation (37) implies that the

asymmetry in coupling should be about 8.3 dB . We will first employ (37) to predict dual TEM cell

coupling for the unloaded case in order to establish the usefulness of the small aperture

equations. Next, the loaded polari zabi

ities developed in section 3 will be used to analyze actual

IL measurements made on a particular sample material. Finally, dual TEM cell results will be

related to those of a shielded room when coplanar loop antennas are used, as was done by the Tecknit

group [25,26].

For an unloaded aperture, the power coupled to the receiving cell normalized by the input power

is given by

P = 20 log3

-77 la I (forward - port 3)

2 ' o

or (381

P = 20 loga 4 lb | (backward - port 2)

2 ' o

K

Figure 4 shows the theoretical values for both ports versus the measured values for port 3. Data

for port 2 were not available for this particular measurement run. The cells were screwed tightly

together assuring good contact and a thin aperture. As may be seen, theoretical and measured data

agree to within a decibel over the usable frequency range of these cells, which is up to about 833

MHz, where the first significant higher-order mode (TE-^g) appears. At 800 MHz, k Qd = .84, therefore

the aperture is no longer electrically very small. However, results remain surprisingly good

largely because the TEM mode remains uniform over the aperture.

15
A second set of measurements is shown in figure 5 against the same theoretical curves. In this case power was measured at both sensing cell ports, again for an unloaded aperture, but the cells were no longer screwed together. Instead, conductive gasketing was placed around the aperture and a 50-pound weight was used to create electrical contact. This configuration has the advantage of

quick access to the aperture if materials are to be tested, but does not provide quite as clean an aperture environment as when the cells are screwed together. Figure 5 indicates that agreement is reasonable, to within a few decibels, but not as good as with the tightly joined cells. Because the

gasketing significantly thickened the aperture to about 6mm, (23) and (24) may be used to modify the

polarizabi 1 i ties . The results are shown in figure 6. Agreement has been improved, especially for

the port 3 measurements. Taken together, these curves indicate the importance of carefully joining

the cells and point toward the aperture environment and sample mounting as potential problems that

must be carefully addressed.

Insertion loss measurements involve a loaded aperture. The appropriate polarizabi 1 ities for a resistive sheet of conductivity a, thickness h, and contact resistance R

c are given by (31) for a circular aperture. Unfortunately, the equivalent result for a square aperture is not available.

However, we may generate an approximate loaded square aperture pol ari zabi 1 ity by defining a radius r which yields the same magnetic polari zabi 1 i ty a for the unloaded case, that is

3 4 ~3 a = 0.258 d = = r (equivalent circular aperture]

m 3 M r :391

Solving, we find that r ~ .579 d. Because this equivalent radius reproduces the unloaded square

aperture polarizabi 1 ity , it should yield reasonable results for the loaded polarizabil i ty

.

Recalling the definition of insertion loss (32), we find the following

IL (P3) = 20 log

IL (P2) = 20 log -

:40!

where, as in section 3, a tilde is used to designate loaded quantities. If we insert the unloaded

aperture polari zabi

1

ities (22), and the loaded values based on (31) with the equivalent radius

defined above (39), then the IL equations become

IL (P3) - -5.1 + 20 log 1 +

i 4io li r oh _q

3 n (Tv + 2 n R IF c

(cm;

IL (P2) - 3.2 + 20 log 1 +

i 4u> li r oh M3 3n (T+ 2it R oh)

c

(41)

:<jb)

16
Note that (41) implies that as the frequency decreases (to > o) the insertion loss seen by the

forward port (P3) may be negative, or more power is coupled into the sensing cell when the material

is present than for the unloaded aperture. The cause may be seen in the basic coupling equation

(36). In the forward direction the electric and magnetic fields interfere destructively

(a + a ) . If a lossy test material is introduced, the electric field is screened out,

„ ey mx „ a * o. Thus although a is also reduced, the lack of interference may more than compensate for

reduced magnetic coupling, and thus the apparent gain due to the material loading. This same effect

has been observed in shielded room IL measurements as well [70].

Tests were performed on a piece of sample material which consisted of three layers; polyester,

aluminum, and vinyl. The layers were of thickness 0.01, 0.01, and 300 micrometers respectively.

The gasketed aperture of figures 4 and 5 was used to seat the material. In order to apply (41), we need to specify o, h, and R . The dielectric layers, polyester and vinyl, will not provide

-8 7 significant shielding, thus only the aluminum layer (h * 10" m, o « 3.7 x 10 S/m) will be

considered. The contact resistance R

c for our test runs is unknown. Thus curves for representative

values (R = 0, 1, 2 Q) will be presented. Figures 7 and 8 show the measured IL at the forward and

backward ports respectively. At the forward port, the R = 1Q curve well fits the data while at the backward port, the measured data falls between the R = 1Q and R = 2Q curves. The important

point is not to try and match one of these curves, since R is unknown and the contact impedance may

in fact be capacitive rather than resistive; rather, that the curves qualitatively show the proper

behavior. If indeed the contact resistance is known (measured), then (41) should yield accurate IL predictions. Also note in figure 7 that as the frequency approaches a few megahertz, the forward

port IL does indeed go negative as predicted. In fact, in both cases, the measured data tend toward

the proper static limit (41), that is IL(P3) +-5.1 dB and IL(P2) ->3.2 dB . Because a thick

aperture was used we may again introduce the waveguide corrections (23) and (24). The thickness

corrected results are shown in figures 9 and 10. The correction to the previous figures is only

slight, since the IL ratios (41) tend to divide out the thickness modifications. Thus IL measurements should be fairly insensitive to aperture thickness (a definite advantage), and this

effect may be ignored.

Finally, we may make some comments about the comparison between SE measurements made in a shielded room versus a dual TEM cell. If a shielded room test procedure uses coplanar loops to transmit and receive via the coupling aperture [25,26], then we expect a low-impedance field at the

aperture for low frequencies, that is a largely magnetic field. The loops act essentially as magnetic dipoles. Thus, coupling is essentially through the magnetic pol arizabi 1 ity alone. As in

(40), the geometry and antenna considerations basically divide out when determining IL, therefore we should approximately have

IL (shielded room) ~ 20 log (42:

for the case of coplanar loops. For other types of antennas, the fields exciting the aperture will

be different and consequently so will the polarizabil ity combination. If the shielded room IL (42)

is compared to the forward port dual TEM cell IL (40), we find that

17
IL (shielded room) - IL (P3) - 5.1 dB '43:

The Tecknit group performed precisely this comparison [25,26], and, in general, the shielded room

gives a greater IL as predicted by (43).

Ondrejka and Adams [29] present IL measurements on the above described sample for five types of

SE test procedures; (1) time domain above a ground screen, (2) time domain through a loaded aperture

in a screen room, (3) cw through a loaded aperture in a screen room, (4) dual TEM cell, and (5)

coaxial transmission line with flange holder. The results are shown in figure 11, with the curves labeled according to the above numerical listing and IL is defined as in the dual TEM cell case

(32). Clearly, there is significant variation among test results and a number of contributing

factors are discussed in their paper. However, the dual TEM cell curve (#4) gives significantly

less IL than the other procedures which are roughly grouped into a 15 dB band. Curve #4 was generated with the thick aperture configuration, consisting of the same data as presented in figure

10 (backward port). What figure 11 demonstrates is the importance of controlling the contact

resistance. If we place the theoretical zero contact resistance curve from figure 10 onto figure

11, as shown by curve #6, then the predicted dual TEM cell IL is more in agreement with the results

from other techniques, especially at the higher frequencies. The contact resistance is very

important in dual TEM cell measurements since there are direct current paths between the input

(transmitter) and output (receiver) ports. In the other techniques, except for the coax line, the

receiver and transmitter are electrically isolated, therefore the material mounting may not be as critical. For the coax line, the large flanges which hold the material create capacitive coupling

which may be sufficient to essentially short across the material thereby effectively giving a zero contact resistance. Clearly, the aperture environment is a critical factor which deserves continued

attention .

The small aperture analysis of dual TEM cell coupling presented in this section appears to be a useful technique for analyzing SE and IL measurements. As the dual TEM cell concept is refined, the

above analysis may well allow one to accurately predict the expected IL given the material

parameters a, h, and R . This may well aid in theoretically designing shield materials, wire meshes

etc., for specific shielding problems. Alternately, if a given material's electrical properties are unknown, then dual TEM cell measurements could be used to generate an equivalent sheet impedance

which would help in predicting the material's expected behavior in other EMI environments.

One final comment: insertion loss measurements made at both ports may be used in (40) to solve

for a and a . This allows us to consider the "magnetic field" insertion loss (ILm ) mx ey 3 m

IL = 20 log

m

3 mx

mx

and the "electric field" insertion loss (IL

e

)

18
IL = 20 log

e

3 ey

ey

separately. This should aid in relating the dual TEM cell SE measurements to results obtained via

other methods [71]. We have already mentioned that small loops (magnetic dipoles) should

essentially give Il_ m

(42) in the near field. For conductive shield materials, we should have

IL me< IL , that is, less shielding of the magnetic fields. The various SE test procedures K should

give insertion loss values somewhere between these two limits. Thus dual TEM cell measurements can

be used to determine a shielding range expected for a material.

5. Small Object Scattering in a TEM Cell

As indicated in the introduction, most TEM cell measurements involve placing some test object

inside the cell and then exciting the TEM mode. If the test object is kept small compared to the

test chamber height and its dimensions are much less than the operating wavelength, then it is reasonable to assume that the cell environment is not significantly perturbed from its empty

state. The small aperture theory developed in section 2 may be used to investigate the effects of test objects from two viewpoints. First, when only the scattered TEM mode is considered, the TEM

cell may be viewed as a transmission line circuit with the test object introducing some type of load. Analyzing the reflected and transmitted TEM mode enables us to represent the test object

loading in terms of an equivalent circuit. Thus the change in the overall TEM cell transmission

characteristics due to the test object presence can be studied. Second, the excitation of the

initial higher-order modes may be modeled. This enables us to theoretically assess the expected

field perturbation due to test object scattering. In each case, the indication is that, indeed, the TEM cell environment is not greatly disturbed for the simple types of scattering objects considered

here. If the sensitivity of the desired measurement is such that even small deviations in cell

characteristics are important, then the present theory should be useful for predicting what limits

should be placed on the test object size and the measurement frequencies.

As in the previous section, we will again assume that the scattering obstacle is excited by an incident TEM mode. Therefore, the basic equation is (10). The scattered TEM mode (n=0) will be

considered first.

(34), we find that

Noting that E = E. = E and E ox lx x oy

E.iyE , where E and E are given by

y y

-i k

( 2tl

{(a + a ) E 2 + v ex my x a + a

ey mx ^

1441

i k

i 2tu

{(a - a ) E + (a

ex my x ey

a ) E

2

} mx y

The expansion coefficient b represents the reflected TEM mode while a Q gives the scattered TEM mode

in the forward direction. Thus, the reflection (R) and transmission (T) coefficients are given by

19
R = bo

T = a o

'

(45;

Including the incident TEM mode as well, the dipole model of the scattering obstacle implicitly

yields a symmetric scattering matrix S given by

(,: T t) 146!

The scattering matrix S may be related to a normalized impedance matrix via

Z = (I + S) (I - S)~ where I is the identity matrix. The equivalent T-network circuit, shown in

figure 12a, follows [34] from the impedance matrix Z. The impedances Za and Z^ are related to R and

T, and thus a Q

and b Q

, according to

7=7 , ( R - T )

, = 7 r

a °

" °

1 a c (2 - R + T) c

l 2 + a - b>

(47)

1\ 1 , -, , 1_ . 1^ 1

i + b

o o

7 = 7 f — -) - — 7 = -Z ( = + -1 - - 2

"b c

l R + T 2> 2

l

a c

l a + b 2> 2 a

where Z c is the characteristic impedance of the section containing the scattering obstacle (in this

case the RCTL impedance)

.

If a Qand b Q are small, which is typically the case, then Za and Z^ are approximately given by

(a - b ) Z --Z ° °

a c 2

(48)

L - -2 ' 1 ^ b c

v a + b• o o

As the obstacle size vanishes, both a and b tend toward zero. Therefore

Z -> o (short circuit) and Z, > = (open circuit) and the equivalent circuit reduces to a simple

transmission line as expected.

As an example, consider a spherical conducting obstacle; in this case a and a are given by

(18) and a substitution into (44) along with the field components (34) yields

20
Z 2

a = -i 4u— k rf-1 F L o n

o

o

y aJ xy

Z 2 b = -i 12k — k r (-) F ^

[49!

2 where the dimension! ess quantity F defined by

F

2

= I i

S1

' n

; yS - Py ) sin Mx sin Ma J (Mg)

xy L, sinh M b o

3

J

|_ mo=l

[Y cosh_

* , sin

mo=l

hM 6"^ cos Mx sin Ma J ^ Mg ^

(50:

2

contains the field dependence due to the obstacle location. If the sphere is both electrically

small (k r < 1) and small compared to the primary cell dimension "a" (r/a < 1), then (48) and (49)

give:

Z 2

Z « -i Z 4n — k r (-) F

~ a c ti o

v a ' xy

Z 2 „

Zk » -i Z {I6it — k r (-1 F ] b c

l ti o

l a

J xy

1

(51)

1

Thus we see that the loading due to a spherical conductor consists essentially of a small series

capacitance (

a term) and a large shunt capacitance (Z^ term). In general, conducting objects

placed in a TEM cell should behave in this fashion.

The equivalent T-network representing the obstacle loading may be included in the overall TEM

cell transmission line circuit as shown in figure 12(b). The loading is assumed to be centered in

the RCTL section of length 2L^ CTL . Ideally, the tapered sections of length LTA p ER should have the same impedance as the RCTL, i.e. Z^p^ = Z

c

; however, since in practice this is generally not the

case, the taper sections are shown explicitly.

Tests were performed in a typical NBS cell to assess the validity of the above equivalent

circuit representation. The cell has dimensions a = 15 cm, b/a = 1, g/a = .17 which yields a theoretical RCTL impedance of 51.6 Q (Z

c ). The taper and RCTL impedances were also measured using a time domain ref lectometer (TDR). This technique yielded 1 « 51 Q and Z « 49.5 Q. Agreement

between the theoretical impedance computations, measured impedances, and the desired 50 Q value is

usually considered acceptable if within an agreement of 2 Q. In evaluating the TEM cell circuit

21
model, the measured impedances will be used. The RCTL section has a length 2L., rT|

= 30 cm; however,

the taper length is somewhat ambiguous since it may be measured along the center of the inner

conductor (L-t^per

= 15 cm), along the outside taper edge (Ly^pf_R

= 25 cm), or in between. Because

this cell has a narrow gap, the fields should be strongest near the gap, therefore we will take the

outside dimension as the proper choice, i.e., Ly^pjrp = 25 cm.

The cell was terminated with a 50 Q load and a spectrum analyzer was used to measure the input

impedance. Three spherical conductors were used to load the cell. Thus equation (51) will be used

to determine the loaded cell equivalent T-network. We begin first with an empty cell. Figure 13 shows the magnitude of the input impedance for both measured data and theoretical values based on the circuit of figure 12(b) with one end terminated with a 50 Q load. At very low frequencies

(< 100 MHz), the well defined load impedance dominates. As the frequency is increased, the taper

impedance (51 Q) and the RCTL impedance (49.5 Q) become important. The theoretical curve appears to

be first dominated by the taper (around 250 MHz) and then by the RCTL (around 450 MHz). The

measured data shows a similar behavior up to 400 MHz whereupon the results start to deviate

significantly. A limiting factor on the circuit model is the stability of the various impedances

with frequency. Although measured impedance values were used, TDR results represent time averaged

values, in this case over a spectrum reaching into the 12 GHz range. In fact, at specific

frequencies the actual RCTL and taper impedances may deviate up to 1 Q or so from these average

values. In practice this means a VSWR of less than 1.05, which is acceptable from the cell usage

point of view, but it is not reasonable to expect the circuit model to give better than the

qualitative agreement found in figure 13. What our analysis does give is the basic variation in impedance magnitude with frequency.

Figure 14 shows the magnitude of the input impedance for the same parameters as in the previous

unloaded cell case, except that a conducting sphere of 4.35 cm in diameter has been introduced. The

sphere is centered in the test chamber, i.e. x = and y/b = .5 and this particular sphere occupies

slightly less than a third (29%) of the chamber height. The curves show little variation from the

unloaded cell case, except above 400 MHz where the measured data show a decrease in the input

impedance. Next a 6.5 cm sphere (approximately 43% of the chamber height) was tested and the

results are shown in figure 15. Again the theoretical curve is little perturbed from that of the

empty cell while the measured data show a further decrease in input impedance for the upper

frequency range (> 400 MHz). Finally, we introduced a sphere occupying two-thirds the chamber

height (diameter = 10 cm or 67% of the chamber height). The cell is significantly perturbed as shown by the results in figure 16. In this case the actual perturbation (measured) is greater than

theoretically predicted, most likely because of significant coupling between the sphere and the cell

walls. In addition, this sphere excites the cavity resonance associated with the TEq^ mode at around 400 MHz, and the transmission line model is no longer a reasonable description of the cell

behavi or.

Together these curves demonstrate that the small obstacle theory gives a good initial model of the loaded TEM cell test circuit. Up to the first cell resonance, the theory reasonably well

predicts both the frequency dependence and the variations in the input impedance. Thus the model

should be useful in estimating the VSWR change expected when loading a cell. More importantly, as the loading does not cause significant variation for the initial two spheres (< 43% of the test

22
chamber height), the present analysis supports the common practice of ignoring the loading effect

when the size of the test object is no greater than one third of the chamber height.

A second concern is the change in the field distribution due to a test object's scattering of

the TEM mode and its excitation of higher-order (evanescent) modes. Only the RCTL section will be

considered and again, for simplicity, a centrally located (x = 0, y/b = .5), spherical conducting

object, of diameter .4b will be used. The modes will be scattered according to equation (1) with

the expansion coefficients given by (10). The incident mode is assumed to be a forward travelling

TEM mode, thus the TEM mode expansion coefficients are given by (49) while those for the TE-^q and

TE-q modes are determined by (10) with the proper field expressions, (A-18) and (A-28) respectively,

inserted. The TEg-^ mode should not be excited if the diameter of the sphere is less than half the test chamber height. Modes beyond these first three are not expected to contribute at normal TEM

cell frequencies.

Rather than consider the field distribution at any specific point, we will investigate the

perturbation to the TEM mode field components (E , H

x

) at the test chamber center line (x = 0, y = l/2b) as a function of z, the longitudinal distance from the scattering sphere. These two components are of primary interest since they form the basic test field. The wave impedance E /H

x will also be considered. Each parameter will be normalized by its empty cell value at that point,

thus a result of unity represents a zero perturbation due to the scattering sphere. Figure 17 shows

the numerical results of the above analysis with the frequency chosen to give an electrical cell

width of k a = 1. As may be seen, there is no perturbation in the forward direction, however, the

greater scattering of the TEM mode in the backward direction fib I > la I) combined with the phase

beating between the incident and reflected modes yields a noticeable change for z < 0. The electric

field is reduced while the magnetic field is enchanced, thus, the wave impedance shows the greatest

deviation. If the contributions from the individual modes are examined, it is found that the

scattered TEM mode essentially accounts for all of the perturbation shown in figure 17. If the

frequency is increased, so that k a = 1.4 which nears the TE-^q cutoff value of n/2, then as expected the perturbation is increased as shown in figure 18. The reflected fields are greatly

altered, resulting in a wave impedance change of greater than 10%. In addition, we now see some variation in the forward fields, although the beating effect is significantly less. Again, the

variation is largely due to the scattered TEM mode. These figures indicate that it may not be safe

to assume that the fields are unchanged in the presence of a test object. Noting that the 6.5 cm scattering sphere in figure 15 is nearly of the same diameter (normalized to b) as in figures 17 and

18, it appears that the input impedance is much less sensitive to loading than is the field

perturbation, especially for z < 0.

Taken together, the above results indicate that it is reasonable to assume that the cell's

impedance characteristics are unchanged by a small test object. However, more care must be taken if

the same assumption is to be applied to the field distribution.

6. Conclusions

This report has dealt with the question of how an electrically small discontinuity changes the

characteristics of a TEM cell. This quite simple formulation was then applied to two specific

examples; (1) the dual TEM cell and its coupling characteristics, and (2) the loading effect of a

23
test object in a TEM cell. In each case, experimental data were compared to theoretical results in order to verify the usefulness of this particular analytical model. It was found that the dual TEM

cell behaves as predicted if the aperture is empty; while for a loaded aperture, results indicate

qualitative agreement as well as which coupling parameters (primarily the contact resistance) need

to be controlled if better correlation is to be achieved. The analysis of TEM cell loading suggests

that the fields inside the cell are more sensitive to the scattering effect of the test object than

is the cell's transmission line behavior, such as its characteristic impedance. Roth, however,

should not be significantly perturbed in the course of normal TEM cell usage.

In addition to these two present applications of small aperture (obstacle) theory to the TEM

cell, others may arise in the future. For example, it has been suggested [72] that a small TEM

cell, with an aperture in one of the walls parallel to the septum, could be used as a low frequency

field probe. If the incident field could be specified, the above theory would again predict how the

TEM mode would be excited in the cell, and consequently, how much power the cell would receive. The

advantage of such a TEM cell probe is that the fields couple directly into a known, shielded

transmission line thus circumventing the problem matching the probe antenna and the inevitable

coaxial feed cable. Also, because aperture coupling is a very common EMC concern, a standard

aperture coupling probe could be used to predict the impact the same aperture would have if present

on a piece of electronic equipment. Thus, TEM cell probe results could be used as a building block

toward developing more complicated EMC/EMI models for electronic systems.

7. References

[1] Crawford, M. L. Generation of standard EM fields using TEM transmission cells, IEEE Trans, on Electromagn. Compat . EMC-16: 189-195; November 1974.

[2] Crawford, M. L.; Workman, J. L. Using a TEM cell for EMC measurements of electronic equipment.

Nat. Bur. Stand. (U.S.) Tech. Note 1013; April 1979.

[3] Sreeni vasiah, I.; Chang, D. C; Ma, M. T. Characterization of electrically small radiating

sources by tests inside a transmission line cell. Nat. Bur. Stand. (U.S.) Tech. Note 1017;

February 1980.

[4] Sreeni vasiah, I.; Chang, D. C; Ma, M. T. A method of determining the emission and

susceptibility levels of electrically small objects using a TEM cell. Nat. Bur. Stand. (U.S.)

Tech. Note 1040; April 1981.

[5] Ma, M. T.; Koepke, G. H. A method to quantify the radiation characteristics of an unknown

interference source. Nat. Bur. Stand. (U.S.) Tech. Note 1059; October 1982.

[6] Hoeft, L. 0.; Karaski ewi cz , R. J.; Hofstra, J. S.; Andrews, T. J. Measurement of the magnetic

field reduction provided by generic equipment cases and enclosures. Symposium record of the

IEEE 1982 Int. Symp . on EMC; 49-52; Santa Clara, CA; September 1982.

24
[7] Hermeling, G. C. Method for immunity measurements on home entertainment products using the 2 meter TEM cell. Symposium record of the IEEE 1982 Int. Symp . on EMC; 574-580; Santa Clara,

CA; September 1982.

[8] Koepke, G. H.; Ma, M. T.; A new method for determining the emission characteristics of an unknown interference source. Symposium record of the IEEE 1982 Int. Symp. on EMC; 1151-156;

Santa Clara, CA; September 1982.

[9] Crawford, M. L. Generation of standard EM fields for calibration of power density meters, 20

kHz - 1000 MHz. Nat. Bur. Stand. (U.S.) NBSIR 75-804; January 1975.

[10] Baird, R. C. Methods of calibrating microwave hazard meters, Biological Effects and Health

Hazards of Microwave Radiation; 228-236; Warsaw: Polish Medical Publishers; 1974.

[11] Blackman, C. F.; Elder, J. A.; Weil, C. M.; Benane, J. G.; Eichinger, D. C; House, D. E. Induction of calcium-ion efflux from brain tissue by radio-frequency radiation: effects of

modulation frequency and field strength. Radio Science. Vol. 14, no. 6s. 93-98; NovemberDecember 1979.

[12] Joines, W. T.; Blackman, C. F.; Hollis, M. A. Broadening of the RF power-density window for

calcium-ion efflux from brain tissue. IEEE Trans, on Biomedical Engineering. BME-28: no. 8. 568-573; August 1981.

[13] Hill, D. A. Human whole-body radio frequency absorption studies using a TEM-cell exposure

system. IEEE Trans, on Microwave Theory Tech. MTT-30: no. 11. 1847-1854; November 1982.

[14] Tippet, J. C; Chang, D. C. Characteristic impedance of a rectangular coaxial line with offset

inner conductor. IEEE Trans, on Microwave Theory Tech. MTT-26: 876-883; November 1978.

[15] Tippet, J. C; Chang, D. C; Crawford, M. L. An analytical and experimental determination of the cutoff frequencies of higher-order TE modes in a TEM cell. Nat. Bur. Stand. (U.S.) NBSIR

76-841; June 1976.

[16] Tippet, J. C; Chang, D. C. Higher-order modes in rectangular coaxial line with infinitely

thin inner conductor. Nat. Bur. Stand. (U.S.) NBSIR 78-873; March 1978.

[17] Mittra, R.; Itoh, T. A new technique for the analysis of the dispersion characteristics of

microstrip lines. IEEE Trans, on Microwave Theory Tech. MTT-19: 47-56; January 1971.

[18] Crawford, M. L.; Workman, J. L.; Thomas, C. L. Expanding the bandwidth of TEM cells for EMC

measurement. IEEE Trans, on Electromagn. Compat . EMC-20: 368-375; August 1978.

[19] Tippet, J. C; Chang, D. C. Dispersion and attenuation characteristics of modes in a TEM cell

with a lossy dielectric slab. Nat. Bur. Stand. (U.S.) NBSIR 79-1615; August 1979.

25
[20] Sreeni vasiah, I.; Chang, D. C. A variational expression for the scattering matrix of a coaxial

line step discontinuity and its application to an over moded TEM cell. Nat. Bur. Stand.

(U.S.) NBSIR 79-1606; May 1979.

[21] Tippet, J. C; Chang, D. C. Radiation characteristics of dipole sources located inside a rectangular coaxial transmission line. Nat. Bur. Stand. (U.S.) NBSIR 76-329; January 1976.

[22] Crawford, M. L. Experimental evaluation of the radiation characteristics of dipole sources enclosed in a TEM cell. Conference Proceedings; IEEE Conference on Precision Electromagnetic

Measurements; 57-59; 1976 June; Boulder, CO. 1976.

[23] Wilson, P. F.; Chang, D. C; Ma, M. T. Excitation of a TEM cell by a vertical electric

hertzian dipole. Nat. Bur. Stand. (U.S.) Tech. Note 1037; March 1981.

[24] Ma, M. T.; Koepke, G. H. Uncertainties in extracting radiation parameters for an unknown

interference source based on power and phase measurement. Nat. Bur. Stand. (U.S.) Tech. Note

1064; June 1983.

[25] Scheps, R. D. Shielding effectiveness measurements using a dual TEM cell fixture. EMC

Technology. Vol. 2: 61-65; July-September 1983.

[26] Faught, A. N.; Dowell, J. T.; Scheps, R. D. Shielding material insertion loss measurement

using a dual TEM cell system. Symposium record of the IEEE 1983 Int. Symp . on EMC; 286-290;

Washington, B.C., August 1983.

[27] Wilson, P. F.; Chang, D. C; Ma, M. T.; Crawford, M. L. Theoretical and experimental analysis

of coupling characteristics of dual TEM cells. Symposium record of the IEEE 1983 Int. Symp.

on EMC; 513-517; Washington, D. C. August 1983.

[28] Wilson, P. F.; Ma, M. T. Small aperture analysis of the dual TEM cell. Proceedings of the

1984 Natl. Symp. on EMC; San Antonio, TX . April 1984.

[29] Ondrejka, A. R.; Adams, J. W. Shielding effectiveness (SE) measurement techniques.

Proceedings of the 1984 Natl. Symp. on EMC; San Antonio, TX . April 1984.

[30] Bethe, H. A. Theory of diffraction by small holes. Phys . Rev., Vol. 66: 163-182; October 1944.

[31] Levy, R. Directional couplers, Advance in Microwaves, Vol. 1, New York, NY: Academic Press;

1966.

[32] Jackson, J. D. Classical Electrodynamics, chapter 4, New York, NY: Wiley and Sons; 1962.

[33] Van Bladel, J. The multipole expansion revisited, Archiv Elek. ULertrag (AEl'i). Vol. 31, 407-

411; October 1977.

26
[34] Collin, R. E. Field theory of guided waves, New York, NY: McGraw-Hill; 1960.

[35] Oliner, A. A. Equivalent circuits for small symmetrical longitudinal apertures and obstacles.

IEEE Trans, on Microwave Theory Tech. MTT-8: 72-80; January 1960.

[36] Okon, E. E.; Harrington, R. F. The pol ari zabi 1ties of electrically small apertures of

arbitrary shape. IEEE Trans, on Electromagn. Compat. EMC-23: 359-366; November 1981.

[37] Johnk, C. T. A. Engineering electromagnetic fields and waves. New York, NY: Wiley and Sons,

1975.

[38] Rayleigh, Lord On the incidence of aerial and electrical waves upon small obstacles in the

form of ellipsoids or elliptic cylinders, and on the passage of electric waves through a circular aperture in a conducting screen. Scientific papers, Vol. IV: 306-326; Cambridge, UK: Cambridge University Press; 1903.

[39] Rayleigh, Lord On the passage of waves through apertures in plane screens, and allied

problems. Scientific papers, Vol. IV: 283-296; Cambridge, UK: Cambridge University Press; 1903.

[40] Lamb, H. Hydrodynamics, 6th ed .

, 492-520; New York, NY: Dover Press; 1945. 492-520.

[41] Hill, D. A.; Wait, J. R. Electromagnetic scattering of a small spherical obstacle near the

ground. Can. J. of Phys . Vol. 50: 237-243; 1972.

[42] Cohn, S. 8. Determination of aperture parameters by electrolytic-tank measurements. Proc. IRE,

Vol. 39: 1416-1421; November 1951.

[43] Cohn, S. B. The electric polarizabi 1 ity of apertures of arbitrary shape. Proc. IRE, Vol. 40: 1069-1071; September 1952.

[44] De Meulenaire, F.; Van Blade!, J. Pol arizabi 1 ity of some small apertures, IEEE Trans, on Antennas Propagat. AP-25: 198-205; March 1977.

[45] Rahmat-Samii , Y.; Mittra, R. Electromagnetic coupling through small apertures in a conducting

screen. IEEE Trans, on Antennas Propagat. AP-25: 180-187; March 1977.

[46] Bouwkamp, C. J. Diffraction theory, Repts. Prog, in Phys., Vol. 17: 75-100; 1954.

[47] Van Bladel, J. Field penetration through small apertures: the first-order correction. Radio

Science. Vol. 14: 319-331; March-April 1979.

[48] Groves, B. D.; Crow, T. T.; Taylor, C. D. On the electromagnetic field penetration through

apertures. IEEE Trans, on Electromagn. Compat. EMC-18: 154-162; November 1976.

27
[49] Butler, C. M.; Rahmat-Sami i

, Y.; Mittra, R. Electromagnetic penetration through apertures in conducting surfaces. IEEE Trans, on Antennas Propagat. AP-26: 82-93; January 1978.

[50] Fikhmanas, R. F.; Fridberg, P. Sh . Theory of diffraction of small apertures. Computations of

upper and lower boundaries of the pol ari zabi lty coefficients. Radio Eng. Electron: Phys . (USSR). Vol . 18: 824-829; 1973.

[51] Jaggard, D. L.; Papas, C. H. On the application of symmetrization to the transmission of

electromagnetic waves through small convex apertures of arbitrary shape. Appl . Phys. Vol. 15: 21-25; January 1978.

[52] Susskind, C. Obstacle-type artificial dielectrics for microwaves. Jr. Brit. IRE. Vol. 12: 49-

62; January 1952.

[53] Cohn, S. B. Microwave coupling by large apertures. Proc. IRE. Vol. 40: 696-699; June 1950.

[54] McDonald, N. A. Electric and magnetic coupling through small apertures in shield walls of any

thickness. IEEE Trans. Microwave Theory Tech. MTT-20: 689-695; October 1972.

[55] Akhiezer, A. N. On the inclusion of the effect of the thickness of the screen in certain

diffraction problems. Soviet Phys. Tech. Phys. (in English). Vol. 2: 1190-1196; 1958.

[56] Van Bladel, J. Low frequency asymptotic techniques, Modern Topics in Electromagnetic

Techniques. London: Peter Peregrinus Ltd.; 1977.

[57] Thomas, D. P. Electromagnetic diffraction by a circular aperture in a plane screen between

different media. Can. J. Phys., Vol. 47 2: 921-930; 1969.

[58] Butler, C. M.; Umashankar, K. R. Electromagnetic penetration through an aperture in an infinite, planar screen separating two half spaces of different electromagnetic properties.

Radio Sci. Vol. 11: 611-619; July 1976.

[59] Marin, L. Dielectric effects on the electric polarizabi 1 ity of an aperture. Archiv Elek.

Ubertrag. (AEU). Vol. 30: 8-12; 1976.

[60] Casey, K. F. Low-frequency electromagnetic penetration of loaded apertures, IEEE Trans, on Electromagn. Compat . EMC-23: 367-377; November 1981.

[61] Kleinman, R. E.; Senior, T. B. A. Low-frequency scattering by space objects. IEEE Trans. Aerospace Elec. Syst . AES-11: 672-675; July 1975.

[62] Pearlston, C. B. Case and cable shielding, bonding, and grounding considerations in electromagnetic interference. IEEE Trans, on Electromagn. Compat. EMC-4: 1-16; October 1963.

28
[63] O'Young, S. L.; Goldman, R.; Jorgenson, L. Survey of techniques for measuring RF shielding

enclosures. IEEE Trans, on Electromagn. Compat . EMC-10: 72-81; March 1968.

[64] Schulz, R. B. A rational basis for determining the EMC capability of a system. IEEE Trans, on Electromagn. Compat. EMC-16: 109-114; May 1974.

[65] Osburn, J. D. M.; Lassise, R. M.; Anderson, M. K. A program for experimental verification of

electromagnetic compatibility analysis models. Symposium record of the IEEE 1983 Int. Symp . on EMC; 15-20; Washington, D.C.; August 1980.

[66] Bridges, J. E. Comparison of shielding calculations. IEEE Trans, on Electromagn. Compat. EMC10: 175-177; March 1968.

[67] Schlicke, H. M. The challenge of industrial EMC. IEEE Trans, on Electromagn. Compat. EMC-22:

6-15; February 1980.

[68] Staggs, D. Single design approach to commercial EMC step-1. Symposium record of the IEEE 1983

Int. Symp. on EMC; 570-573; Washington, D.C.; August 1983.

[69] Oberholtzer, L. C; Mauriello, A. J.; Stutz, D. E. A treatise on the new ASTM EMI shielding

standard. ITEM 1984, 174-178; 1984.

[70] Adams, J. W., private communication.

[71] Wilson, P. F.; Ma, M. T. Some problems associated with interpreting shielding effectiveness

measurements. Proceedings of the 1984 SPE Regional Technical Conference, Chicago, IL; June

1984.

[72] Crawford, M. L., private communication.

[73] Weil, C. M.; Joines, W. T. and Kinn, J. B. Frequency range of large-scale TEM mode rectangular

strip lines. Microwave J. Vol. 24: 93-100; November 1981.

[74] Hill, D. A. Bandwidth limitations of TEM cells due to resonances. J. Microwave Power. Vol. 18: 181-195; 1983.

29
I/O

CD

en

Q_ U_

30
TOP VIEW

PORT 1

SIGNAL

SOUF.CE

50 OHM

LOAD

PORT 2 SIDE VIEW

PORT 4

CENTER

PLATE

50 OHM

LOAD

APERTURE

SIGNAL

DETECTOR

CENTER

PLATE

PORT 3

Figure 2. Dual TEM cells with common aperture,

31
t

I

2b

©

i

2w

2a

t

i

g

Figure 3. The cross section of an RCTL

32
ED

T3

0-3

O

u

D.3

t-EL

Ld

ELECu

CLECZ)o

Ln

Ld

ECO

-20

-26

z -36

-A A

-52

-B0

-68

-76

-92 h

-]00

THEORETICAL VS. MER5URED DRTR ( 5MRLL RPERTURE THEORY ""—I—'—

-> r l

r

THEORETICAL VALUES

*** MERBURED VALUES

J_ I J_ 6 100 286 300 460 500 BB0

TREQUENCY ( MHz

700 800 906 1666

Figure 4. Received power in the sensing cell for

the case of well joined cells about a square aperture

33
w

B

M

a,ou

a.cu

a

c

=)

ina

u

co

-20

-2fl

-36

-A A

-5S -

-60 -

-68 -

-76 -

-34 -

-92

THEORETICRL VS. MER5URED DRTR (5MRLL RPERTURE THEORY")

-100

-

'

1 1 —i1 —

I

1

' 1 ' 1

' 1 ' 1

'

1 —

i

-

+ -

P2 .J—* *r~*r~*'

* * *

*

'

-

* *

* *

X * *

* * * *

-

. / * . _ </*

* THEORETICRL VRLUE5 _

. + +4+ MERBURED DRTR P2 . * *** MER5URED DRTR P3

-

-

i 1 1 _i 1 __i 1 i i.i.i.i, 1

, 6 100 260 300 406 506 600 766 600 S66 1660

FREQUENCY ( MHz

)

Figure 5. Received power in the sensing cell utilizing

a square, gasketed aperture.

34
-20

r*. CDD

-26

"-'

13z -36

_J

CL3

O -44 U

u

a

Zl -52

tCtu

a

CE -SB

U

a

CE=3 -68

O

Ula

u

-76 a

cco

THEORETICRL VS , MER5URED DRTR ( SMRLL RPERTURE THEORY)

-J 00

-84 -

-92 -

T T T

MERSURED DRTR P2 *** MEASURED DRTR P3

x

100 206 380 408 560 BBS

FREQUENCY ( MHz

700 800 386 1866

Figure 6. Received power, thickness corrected, in the

sensing cell utilizing a square, gasketed aperture.

35
58 MESH FRTTEPN IL - FORWHRD FORT

1

> 1

,

1 i 1 i 1 i 1

i 1i 1>

1

i

44 -

aa -

32 - -

25 - _____________

______-——~""_ 20 —

.—-~_~~_ .^- * *__:

H -

.--•-""" RC_1 I—-* ^~

____—*?- ~* * ———

a

_,-•'" _____--*~~

" __——

_—

S -*•-*" * —

'

"" / ...---*""" _-—--"

/ Jf*?* _---~~~~~ RC " 2 T -

/ .*'" ..'-"""

. >

•-'"' --' '

-4 - V.--"""" **** MERBURED DRTR

. i n 1,1,1,1,1,1,1,1,1,

1_Q 20Q 3QQ 400 506 EE3 700 800 900 1000

FREQUENCY ( MHz

)

Figure 7. Insertion losses measured at the forward port (P3) for a layered polyester-aluminum-vinyl

sample versus frequency, compared with contact resistance (R

c )-dependent theoretical curves.

36
LJ

50 MESH FRTTERN IL - BRCKWRRD FORT

44 -

3a -

32 -

26 -

50

s

2

-4 -

-10

•£__--

RC = B .

RC=1 __——

1~~~

_^.— * * * * * * _ , -

RC-2

**** MERBURED DRTR

* * --*

e lea ;00 see 4QB 506 E00

FREQUENCY ( MHz

70© S00 90S 10Q0

Figure 8. Insertion losses measured at the backward port (P2) for a layered polyester-aluminumvinyl sample versus frequency, compared with contact resistance (R

c )-dependent theoretical

curves

37
Ln

nu

LTI

50 MESH PRTTERN IL - FORWRRD PORT - THICKNE55 CORRECTED

,

, | , |, | i |i |i | i | i |i

44 -

33 -

32 -

26 RC = B ___——-~~--~

- ___-—

" J 20 - ..--— _

- M - ^^

RC-1 -

Jt—*r~

" ——*—

y J£_ *~~ * * _—

~

3

..„- ^ ^ _.-——""~""~~~^

" / ^^^ "^

_

2 / ,*r -—"" pr-2

' *sC**^

~

* '"1--"""^ -4 **** MEREURED VRLUE5

. l n 1,1,1,1,1,1,1,1,1,

iaa 26Q 3QQ 400 500 EDO 700 893 300 1000

FREQUENCY ( MHz

)

Figure 9. Insertion losses measured at the forward port (P3) for a layered polyester-aluminum-vinyl

sample (after thickness correction) versus frequency, compared with contact resistance (Independent theoretical curves.

38
Hi

5Q

44

33

32

25

20

H

3

2

-4 h

ME5H PRTTERN IL - BRCKWRRD PORT - THICKNESS CORRECTED

-10

T T T T T

X

.*- *:--*

RC = D

RC-1

RC-Z

**** MEREURED VRLUEB

8 100 2@Q 300 408 500 E0D 780 80S 3 80 1088

FREQUENCY ( MHz

Figure 10. Insertion losses measured at the backward port (P2) for a layered polyester-alumi numvinyl sample (after thickness correction) versus frequency, compared with contact resistance

(R

c )-dependent theoretical curves.

39
1-TD ON GROUND SCREEN

2-TD THRU SCREEN ROOM APERTURE

3-SCREEN ROOM, CW AVERAGED

4-DUAL TEM CELL 5-COAX WITH FLANGE HOLDER

6-DUAL TEM CELL RC-0

Frequency (MHz)

Figure 11. Insertion losses due to a layered polyester-aluminum-vinyl sample measured with various

test procedures.

40
(a) The equivalent T-network circuit for a small scattering obstacle.

"a "a -—i—oZ TAPER

Z RCTL

Z RCTL

Z TAPER

L H

TAPER RCTL

LRCTL

LTAPER

(b) The TEM cell transmission-line circuit,

including the small obstacle loading.

Figure 12. TEM cell equivalent circuit representations

41
IXn

u

CL

GQ

56

u 56 -

54

50

ia

46

44 -

40

EMPTY CELL

1

1

'

1

' 1 1

'

1

'

1

'

I

' i

,

1

i

- / * *\ *

*

*

•Hi * *

' * \

r.,-- ----

J

- -

- **** MEASURED DRTR-

- THEORETICAL VALUES -

1 1 , 1

1 1 1,1,1, 1 i 1 1 1 59 1 0@ 15Q 2 00 250 3 G FREQUENCY ( MHz

)

350 4Qfl 450 500

Figure 13. Input impedance versus frequency for the empty TEM cell

42
uj 56

54 -

52 -

50

48

46

44

40

" 1 r " 1 r LORDED CELL - -1.35 (CM' D1RMETER CONDUCTING SPHERE

SB i

1

1

1

1

1

1

1

56

\

/

/ *

/ * *\

\

'

' *

V\

**** MEASURED DRTR

THEORETICRL VALUES

I Q 58 100 150 2 8Q 258 300

FREQUENCY ( MHz

_L 358 400 458 588

Figure 14. Input impedance versus frequency for the TEM cell with a 4.35 cm diameter conducting

sphere present.

43
u

n:

GQ LORDED CELL - 5.5 (CM) DIAMETER CONDUCTING SPHERE

5S -

U 56 -

54 -

52 -

50

48 -

46

44

40

X ~r i

**** MEASURED DRTR

THEORETICAL VALUES

188 158 288 £58 3E3G 358 403 458

FREQUENCY' ( MHz )

Figure 15. Input impedance versus frequency for the TEM cell with a 6.50 cm diameter conducting

sphere present.

44
u

I

u

n

ibU

58

56

LORDED CELL - 10 (CM; DIRMETEP CONDUCTING 5FHEPE

! 1 ' 1 ' 1 ' 1 ' 1

1

1

1

1

' I

i

1

i

- +-

- + - -

_...---"•... % -

- /* ^

•

- /

/ \

*

- - ''' * -

,/ * -

\ _.-•'"

--"-— —

* * \ y

-

- *

-

. - *+*+ MEASURED DRTfl £ _

- THE .-iRETIi :RL VRLUE3 i - " .1.1.1. i

, I

i 1 1 . 1 1

-

5-1 -

55 -

50 *—

y

ia -

4B -

44

40

150 2 S3 250 300

FREQUENCY' ( MHz ) :50 400 450

Figure 16. Input impedance versus frequency for the TEM cell with a 10.00 cm diameter conducting

sphere present.

45
1 . 12

J .03 -

rr 1 .86 m

CLP

rr

] .03 u

D.n 1 u

M

i—

i CL .97

\ro

.94

,31

,33

,35

FIELD PERTURERTION - SPHERICAL OBSTACLE - KEF- 1 . Fl 1

' 1

' 1

'

1

' 1

1 ' I ' I

'

1 '

****• EY

+ + + + H X 0000 EY/HX CWRVE IMPEDANCE)

-> S

'-ft^—*..__ ^*~<

\ *"* * * *—*^ Q

V|Sk. .&

;;S-*9—*—*—*—i—*—*-

-1.6 -1.2 -o.: -0.4

z/a

0.4 0. 1.2 1.6

Figure 17. Field perturbation due to a conducting sphere of diameter 6.0 cm with k Q

a = 1.0,

46
FIELD PERTURBRTION - 5PHERICRL OBSTRCLE - K0R- L .

u

D.n

LiM

1.12 -

1 .09 -

i . es -

] .03

,9? -

.94 -

.91 -

,aa -

.35

i 'i

'

i 'i

'

i **** EY ++++ HX 0000 EY/HX CWRVE IMPEDRNCE)

-* * *_

^fc

\ \

\ -* *-" \

V. f!> 1 1 ^--J"""* *--

""""y'fr

-'" o—&

Q—o ^4—ft ^"i*...—*.^

/

V

J_ _i_ _L J_

-2 -1.6 -1.2 -0.8 -0.4 0.4 0.8 1.2 1.6 2

z/a

Figure 18. Field perturbation due to a conducting sphere of diameter 6.0 cm with k Q

a - 1.4,

47
APPENDIX A

The Normalized Modes In a TEM Cell

The higher-order modes in a TEM cell are difficult to analyze and are largely ignored.

Primarily, interest is in the dominant TEM mode and the associated RCTL impedance characteristics.

The higher-order modes are considered only to the extent that their appearance limits the TEM cell's

usable bandwidth. Thus, given the current TEM cell applications, a complete modal description is both unavailable and unnecessary. The present investigation will only look at the first four

hi gher-order modes

.

Several solutions for the TEM mode fields have appeared. For the case of a centrally located

inner conductor, a conformal mapping approach [21] accurately describes the fields in terms of

elliptic functions. Alternately, the singular integral equation method [23], along with the

condition that the gaps (see fig. 3) be small, results in field expressions involving infinite sums

of simple functions. The latter solution allows for a vertically offset inner conductor and also

covers the higher-order modes of interest here. Therefore, the singular integral equation results

will be used here, although strictly speaking, this solution is not accurate for points very near the gaps. Accurate results are obtained in the central test area, however.

The first four RCTL modes are the TEM, TEqj, TE-^q, and TE-jj modes respectively [73] for typical

cell dimensions (small gap). However, the TEq^ mode does not interact with a test object centrally

located in the test zone (x = 0) as this mode largely confined to the gaps [74]. Therefore the

TEqj mode may be ignored. The other three modes need to be orthonormal ized according to equation

(4). For m * n, (4) is satisfied via modal orthogonality (34); while for m = n, (4) reduces to

/ (E

2 + E 2

) ds = Z (A-l)

r

j. * nx ny J n

v

where Z

n is the wave impedance of the n-th mode.

The desired TE-modes may be found from a knowledge of each mode's longitudinal magnetic

field. The singular integral equation approach mentioned above solves for the TE-fields excited by

an elementary vertical electric dipole. In the transform domain (z-di rected) , we find that

cos K (b . - py

)

m

v j VJ J

K s i n K b . mo m m j

H U) =p^-a (p) I ^ — sin Mx sin Ma J (Mg)

z K a o

H L KsinKb. o

9

Id! G.{x, y, 0, y

Q

) , (A-2;

where the RCTL dimensions are defined in figure 3, p is the transform variable corresponding to propagation in the z-direction, j = 1,2 refers to the upper and lower chambers

7 7 7 respectively, Km

= (M - k~j + p j , Id! is the dipole moment, (0, y ) is the dipole location, and

48
t^o o, -1 M cos K (b, - y ) 33 mo m m 1 .2 cot K b . ,

j=l mo m

, M cos K (b . - py)

G

j (X

' y ' °» V = HT Z K sin K

J b. Sin Mx cos Km

y

o mo m m j

The remaining notation is defined in conjunction with (34). Note that the dipole excitation nature

of these equations is extraneous here, however, for simplicity the results of [23] will be applied

di rectly

The TE modes may now be found by evaluating the appropriate pole. We may first

evaluate H

l which will determine the remaining TE field components, or we may use the following

relationships

~ (j) =

ionx ~ (j)

H~(JL^±or a H

~ (J)

k 2 _ a

2 y z x 2 2 x z O (A-4)

E (j) =

9

i("% 5 H (j)

H = : ia

9 5 H (j) y

k 2

- a

2 X Z y k 2

- a

2 y Z

and again evaluate the proper residue. One final comment about H

J is in order before proceeding

to specific modes. The first term in (A-2) contains the gap perturbation information and therefore

is associated with gap dependent modes such as the TEM mode. If there is no gap, the TEM mode

cannot exist. The second term is an unperturbed term associated with the modes which would exist in

the dipole chamber if the gap were closed. Thus this term will not contribute to the TEM or TEii

modes .

(1 ) TEM mode : the TEM mode is due to poles at p = ± k .As mentioned, the second term in (A-2)

° (i) does not contribute (further details may be found in [23], Appendix C). The H

J term will be zero

for the TEM mode, thus the field components need to be found directly from (A-4). Because we are after the field distribution, we need only evaluate one pole, say the forward propagating

mode (p = -k ), and consider the electric field components since the magnetic field components are related via the intrinsic wave impedance ti . A residue calculation yields

t) ng sinh M(b . - py)

E = ~ a (-k ) I r-u-Eik r sin Mx sin Ma J (Mg)

x 2a o

K o

L sinh Mb. o

3 mo

p ri -ng cosh M(b . - py)

E = -~ a (-k ) I

. . I. cos Mx sin Ma J (Mg! y 2a o

v <r

L sinh Mb. o

3 ' mo j

49

:a-5:
From [23, eq . 58] we find that

a „(- k J = 4^— (A-6)

where V is the TEM mode voltage. Thus (A-5) may be written

sinh M(b - py)

E = t± )'

. J M, sin Mx sin Ma J (Mg)

x a

L sinh Mb. o

3 mo j

2y

cosh M(b. - py)

E = p

)

. r

J

... cos Mx sin Ma J (Mg) y 'a L sinh Mb. o

a

J mo j

:a-7)

To normalize we note that the power (P) carried by the TEM mode is given by

2

/ (E ± x H **) • a" = + 2P = + ¥=- . (A-8)

CS ° °

z Z

c

If we expand the integral via (2) we find that (A-8) is equivalent to

/ TE ot x"H

ot ) .a

z -£ . (A-9)

CS c

1/2 Therefore, we need only normalize by Z /V to satisfy (4) or alternately (A-l). Thus we arrive at

y 1/9 sinh M(b. - py)

E = - I L,c

I

r

J sin Mx sin Ma J (Mg)

"x a c

i sinh Mb . ..- , mo

(A-10)

? 1/? cosh M(b, - py)

E = p^ Z

' ] . . J cos Mx sin Ma J (Mg) y

K

a c ^ sinh Mb

.

o

v 3

J mo j

The magnetic components are determined by (9).

(2) TE^q mode: the TE-^g mode is due to poles at p = + p lf) in both the perturbed and

unperturbed terms of (A-2), where p, n is the unperturbed rectangular waveguide TE^q mode propagation

constant, i.e. p 1Q= (k

Q

2

- (rc/2a)

2

) 1/2

. Note that for p = + p1Q , Kj = 0. For K

1 small, (A-2)

yields

50
p? a o<fW

si n

7IX 2a

b. K,

J 1

2 o va ; ij

KX

Id A n Sin

2a

a 2a

b

x K

}

2

(A-ll)

a

o

{ ho'

Id A 2 , > iig > g 4ab o

l 2a j

where we have let the dipole location (y ) be in the upper chamber (j=l). The proper residue for

the forward TE-^q mode follows readily from (A-ll) and we find

yj) _ -.-Ida it drl nx ,6ij P

] 2 , 2 ,jg_ n 7T 6^ sin 2? {"¥T- 2FT7 J o

( 2T)} * 4a 1 J 2 P 10 [A-12]

Notice that for j = l,2 we find that the term in parenthesis gives l/2b if terms on the order

of (iig/2a) . are neglected. Thus

u (J) - j IdJL ti . itx _ . , nx

H - i

y- -— sin t- - A sin jz 8a

2

b ho 2a 2a

[A-13]

As expected, (A-13) simply describes a rectangular waveguide TE-^q mode with the magnitude A determined by the dipole strength and guide dimensions. The electric field components follow from

(A-13), i.e.

"X

:(Ji ., 2a . tix ik -n — A cos 7j- o'o 1 2a

:a-h)

We now apply the normalization condition (A-l) which requires that

( 1 2a^2 .2 t „ 2 nx . h k ti — A J cos -7T- ds = Z

1 'o it J r

^ 2a 10

(A-15)

where the TE-^q wave impedance is given by,

Z 10

= k oV p 10

* :a-i6]

Combining (A-15) and (A-16), integrating over the cross section (x e [-a, a], y e [-b~, b,]), we

find that

z in 1/2

2ab ;

i k ti 2a [A-17)

51
Thus the proper normalized components are

E VJ/ =

x

E (j) = ( *°) cos^

y vab ; 2a

/ > • Z 1n 1/2

(J) -^-(oS sinIA-18]

H 2a k n ^2ab

o 'o 2a

The remaining magnetic components follow from (9). The final result (A-18) could have been written

directly, since for the TE^q mode, the RCTL is nothing but a rectangular waveguide of cross section

2a by 2b. However, developing (A-18) via the full residue calculation serves as a useful guide when

evaluating the more complicated TEii mode. In the case of a zero gap, the TE^ mode should reduce

to the TE 1Q result (A-18) .

(3) TE-q mode: the TE^ mode arises from poles in a ( p) when p = + p., , , where p, , -> p, „ as

g + o. The unperturbed term will not contribute. Again evaluating the forward mode (p = -Pii) we

find

, . > cos K (b . - py)

H U; = pM Residue ( a (p )) I m

.—I—r sin Mx sin Ma J (Mg) . z

K a oH ll L K sin Kb. o

3 mo m m j

(A-19)

Because we expect the TE-q mode to propagate nearly the same as the TE^q mode, we may write p, , as

fol lows

2 2 2

3 11

=

P 10 " 611 'A-20)

where 6,, should be small

2 2 6,, > as g -> 0). Indeed, if 6;, << 1, then

6nm=l

iM m>3

:A-21)

Substituting (A-21) into (A-19) yields

i(j) - ~^

cos 6 n

(bj - py! Hl Jj

- p2l Residue(a ( p"

.

)

) ,,,, ,. „ , , o

K

* i i I 6,, sin 6,, b. 2a o

v 2a

tcx , / irg \ sin —J (of)

=° cosh M (b . - py)

y 53

L

, M, sin Mx sin Ma J (Mg'

-, M sinh Mb . o

v b ' mo=3 j

(A-22)

52
To normalize the TE^ mode we may ignore the terms outside the brackets as was done with the

TE 1Q mode in (A-13). However, to insure that hT J ' tends toward the proper limit as g * an additional term of

J Ug/2a) /(6n

sin &u

b . )

will be factored out. Thus the relevant components are given by

,(j) _

H' p A {cos 6, , (b . - py) si n

T[X 2a

sin 6,, b. cd cosh M(b . - py)

-6., -=—i

I .JM

, sin Mx sin Ma J (Mg) } 11 , /itgi L - sinhMb. o

a J {£) mo=3 j

E x

j)

=

" ik o% & 6

11 A tsin 6 n ( bj -py) sin-g

si n 6, , b . <*> sinh M(b . - py)

+ ±i_J. y __J sin

/ng-> ^ _' sinh Mb

J o (2?) mo=3 J

2a

2

1 k % ( ~} 6 n p A { 2f\[ cos 6 n

(b

j - py) cos

Mx sin Ma J (Mg)

}

nx2a

:A-23)

si n 6,

1 b . co cosh M(b . - py) —~ I c mk cos Mx sin Ma J (Mg)}

, r iig a L

o sinh Mb

a J (2?) mo=3 j

Note that as 6,, * (no gap), the field components reduce to the TEjq [expressions (A-13) and (A14)] with only an additional p factor which accounts for the even (TE^q) or odd (TE-q) polarity of

the TE-^q modes in the individual chambers.

These expressions may be substituted into (A-l). Noting the orthogonality between cos Mx and

sin Mx over the interval (-a, a), one finds the following

4 1 *2 ,2a^ c 2 „2

(

1 k o%" O 6 py; ii A a _/ fe2^ cos an<

b

j

- ^ + sin 6 n

(b

j

sin 6,, b

co j (Mg)

-

2 " J I -2-2 cosh 2M(b - py) dy = Z iT f-29-) mo=3 sirrtr Mb. J

v 2a ;

.-1

where Z-q is defined as in (A-16) . Evaluating the remaining integral yields

'A-24;

53
:' koV

2 'f'

4

6 n

A? a I

( <?ri^»

2 d^ (6

11

b

j + 1

s1 " 6

11

b

;

jj- (6 U

bj -j sin 2 6 nbj)

2 2 sin 6, , b. =o J (Mg)

11 J y o

v a

i 2 , -rig ^ ^ _ M

JQ (-£) mo=3

coth Mb. } = Z,.

IA-25!

4 2

If we now neglect terms like 6,,, and (-n:g/2a)", then (A-25) reduces to

!1 k .

o

) 2 (f-f A

2 2ab = Z n

. (A-26!

Thus we find that

1/2

11

l 2ab J

i k n 2a

o o (A-27)

which is equivalent, as might have been expected, to (A-17).

normalized components:

Combining results, we find the

(j) . (Hi r 11 _, baB*

{_T— sin 5 ll

(b

j - py) sin TIX 2a

2a 6,,

+ — sin 6,, b. I

tc 11 J ^

» sinh M(b . - py)

. , .,1 sin Mx sin Ma J (Mg)}

sinh Mb . o

v 3 mo=3

Z 1/2

Ey

j) -^

{C0S 6 ll(b

j "P^ C0S f :a-28]

2a 6 11 sin 6, , b . V

71 11 J _£

cosh M(b . - py]- cos Mx sin Ma J Mg)

}

; u sinh Mb

.

v 3/

' mo=3 j

^J) - P z i k n ^2a

o 'o

Z ^2

) ^2ab^

{cos 6

ll

(b

i " py ^ sin I

cosh M(b . - py'

I mo=3 j

>, , sin 6,, b. V —u— . \,. -sin Mx sin Ma J (Mg)}

11 11 J _o M sinh Mb, o

v

where the small gap approximation has been retained. Again, note that as 6,, * (no gap) these

reduce to the proper TE^y forms modulo polarity.

Finally, for the small gap case considered here, it is found [16], [23] that 6,, is approximately given by

54
6, , = it b, b„ /ab Zn[—

11 12 v -nn

; :A-291

Tnis result may be used to determine p, , and Z^j via (A-20) and (A-16) respectively. Actually,

(A-29) is not a particularly accurate expression since the assumption of a small gap implies

that In [8a/ng) >> 1, which is not the case even for g/a = .1. A better approximation follows from

solving the TE-,i small gap modal equation [16, 23]

o—j—- (cot 6, , b, + cot 6,, b„) = Jin f —1 -2

2a 6, , 111 112 '"nq ; 11 ;a-3o)

from which (A-29) was found assuming both that 6,, b. << 1 and Jin (8a/itg) >> 1

55
NBS-1 "i4A irev. 2-8C) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBS TN-1076

2. Performing Organ. Report No 3. Publ ication Date

October 1984

4. TITLE AND SUBTITLE

Small Aperture Analysis of the Dual TEM Cell and an Investigation of

Test Object Scattering in a Single TEM Cell

5. AUTHOR(S)

P. F. Wilson and M.T. Ma

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions]

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City, State, ZIP)

10. SUPPLEMENTARY NOTES

|] Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

Small aperture theory is used to investigate the dual TEM cell. Analyzing

coupling through an empty versus a loaded aperture leads to a model of

dual TEM cell shielding effectiveness measurements. Small obstacle

scattering yields results for both the field perturbation and the change

in a cell's transmission line characteristics due to the presence of a test

object in a TEM cell. In each case, theoretical values are compared to

experimental data.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

dual TEM cell; perturbation; shielding effectiveness; small aperture/obstacle

theory; test object loading.

13. AVAILABILITY

r%| Unlimited

| | For Official Distribution. Do Not Release to NTIS

[J] Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402. J Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

60

15. Price

USCOMM-DC 6043-P80
NBS TECHNICAL PUBLICATIONS

PERIODICALS

JOURNAL OF RESEARCH—The Journal of Research of the National Bureau of Standards reports NBS research and develop- ment in those disciplines of the physical and engineering sciences in which the Bureau is active. These include physics, chemistry,

engineering, mathematics, and computer sciences. Papers cover a broad range of subjects, with major emphasis on measurement

methodology and the basic technology underlying standardization. Also included from time to time are survey articles on topics

closely related to the Bureau's technical and scientific programs. As a special service to subscribers each issue contains complete

citations to all recent Bureau publications in both NBS and non- NBS media. Issued six times a year. Annual subscription: domestic

$18; foreign $22.50. Single copy, $5.50 domestic; $6.90 foreign.

NONPERIODICALS

Monographs—Major contributions to the technical literature on

various subjects related to the Bureau's scientific and technical activities. Handbooks—Recommended codes of engineering and industrial

practice (including safety codes) developed in cooperation with in- terested industries, professional organizations, and regulatory

bodies. Special Publications—Include proceedings of conferences sponsored by NBS, NBS annual reports, and other special publications

appropriate to this grouping such as wall charts, pocket cards, and

bibliographies. Applied Mathematics Series—Mathematical tables, manuals, and

studies of special interest to physicists, engineers, chemists,

biologists, mathematicians, computer programmers, and others engaged in scientific and technical work.

National Standard Reference Data Series—Provides quantitative data on the physical and chemical properties of materials, compiled from the world's literature and critically evaluated. Developed under a worldwide program coordinated by NBS under

the authority of the National Standard Data Act (Public Law

90-396).

NOTE: The principal publication outlet for the foregoing data is the Journal of Physical and Chemical Reference Data (JPCRD)

published quarterly for NBS by the American Chemical Society

(ACS) and the American Institute of Physics (AIP). Subscriptions,

reprints, and supplements available from ACS, 1 155 Sixteenth St., NW, Washington, DC 20056.

Building Science Series—Disseminates technical information developed at the Bureau on building materials, components,

systems, and whole structures. The series presents research results,

test methods, and performance criteria related to the structural and

environmental functions and the durability and safety characteristics of building elements and systems.

Technical Notes—Studies or reports which are complete in themselves but restrictive in their treatment of a subject. Analogous to monographs but not so comprehensive in scope or definitive in treatment of the subject area. Often serve as a vehicle for final reports of work performed at NBS under the sponsorship of other government agencies.

Voluntary Product Standards—Developed under procedures

published by the Department of Commerce in Part 10, Title 15, of

the Code of Federal Regulations. The standards establish nationally recognized requirements for products, and provide all concerned interests with a basis for common understanding of the

characteristics of the products. NBS administers this program as a supplement to the activities of the private sector standardizing

organizations. Consumer Information Series—Practical information, based on N BS research and experience, covering areas of interest to the con- sumer. Easily understandable language and illustrations provide

useful background knowledge for shopping in today's technological marketplace. Order the above NBS publications from: Superintendent of Documents, Government Printing Office. Washington. DC 20402. Order the following NBS publications—FIPS and NBSlRs—from

the National Technical Information Service, Springfield, VA 22161.

Federal Information Processing Standards Publications (FIPS

PUB)—Publications in this series collectively constitute the Federal Information Processing Standards Register. The Register

serves as the official source of information in the Federal Govern- ment regarding standards issued by NBS pursuant to the Federal Property and Administrative Services Act of 1949 as amended.

Public Law 89-306 (79 Slat. 1127), and as implemented by Executive Order 1 1 7 1 7 (38 FR 1 23 1 5, dated May 1 1 , 1 973) and Part 6 of Title 15 CFR (Code of Federal Regulations).

NBS Interagency Reports (NBSIR)—A special series of interim or

final reports on work performed by NBS for outside sponsors

(both government and non-government). In general, initial dis- tribution is handled by the sponsor; public distribution is by the National Technical Information Service , Springfield, VA 22161,

in paper copy or microfiche form.
U.S. Department of Commerce

National Bureau of Standards

Washington, DC. 20234

Official Business

Penalty for Private Use $300

POSTAGE AND FEES PA

U S DEPARTMENT OF COMN

COM-215

SPECIAL FOURTH-CLASS BOOK