NISTIR 3988

APERTURE COUPLING TO

SHIELDED TRANSMISSION LINES:

THEORY AND EXPERIMENT

D. A. Hill

M. L Crawford

M. Kanda

U.S. DEPARTMENT OF COMMERCE

Technology Administration

National Institute of Standards

and Technology

Electromagnetic Reids Division

Electronics and Electrical Engineering Laboratory

Boulder, Colorado 80303

D. I. Wu

Department of Electrical and

Computer Engineering

University of Colorado

Boulder, Colorado 80309

NIST

NISTIR 3988

APERTURE COUPLING TO

SHIELDED TRANSMISSION LINES:

THEORY AND EXPERIMENT

D. A. Hill

M. L Crawford

M. Kanda

U.S. DEPARTMENT OF COMMERCE

Technology Administration

National Institute of Standards

and Technology

Electromagnetic Reids Division

Electronics and Electrical Engineering Laboratory

Boulder, Colorado 80303

Department of Electrical and

Computer Engineering

University of Colorado

Boulder, Colorado 80309

April 1992

U.S. DEPARTMENT OF COMMERCE

Barbara Hackman Franklin, Secretary

TECHNOLOGY ADMINISTRATION

Robert M. White, Under Secretary for Technology

NATIONAL INSTITUTE OF STANDARDS

AND TECHNOLOGY

John W. Lyons, Director

D. I. Wu
KlMMII
CONTENTS

Page

1. INTRODUCTION 1

2. COAXIAL AIR LINE 3

2 . 1 External Current and Charge 3

2.2 Received Power 4

2.3 Measurements in a Reverberation Chamber 6

2.4 Corrections for Shield Thickness and Chamber Geometry 7

3. TEM CELL 9

3.1 Theory 9

3.2 Measurements in a Reverberation Chamber 10

4. CONCLUSIONS AND RECOMMENDATIONS 11

5 . ACKNOWLEDGMENTS 12

6. REFERENCES 13

APPENDIX. RANDOM FIELD EXCITATION 14

iii

APERTURE COUPLING TO SHIELDED TRANSMISSION LINES:

THEORY AND EXPERIMENT

D.A. Hill, M.L. Crawford, and M. Kanda

Electromagnetic Fields Division

National Institute of Standards and Technology

Boulder, CO 80303

D.I. Wu

Department of Electrical and Computer Engineering

University of Colorado

Boulder, CO 80309

Coupling through circular apertures in the shields of a coaxial

air line and a TEM cell is studied theoretically and

experimentally. Polarizability theory is used to compute the

effective dipole moments that excite the transmission lines in

the internal region. Measurements of shielding effectiveness of

both structures were made in a reverberation chamber over wide

frequency ranges. Agreement between theory and measurements is

generally within ±10 dB. Recommendations for improvements in

the measurements and theory are made for achieving closer

agreement that would be desirable for an artifact standard for

shielding effectiveness measurements.

Key words: aperture; coaxial air line; dipole moment; effective

area; polarizability; reverberation chamber; shielding

effectiveness; TEM cell.

1 . INTRODUCTION

The shielding performance of cable shields [1] and connectors [2] is

difficult to characterize and to measure. For frequencies below

approximately 100 MHz, the surface transfer impedance provides a useful

characterization of cable shields and can be measured using a quadraxial

test fixture [3]

.

For radiated- field excitation at higher frequencies, an alternative

approach is to regard the entire cable assembly as a receiving antenna. In

this case the relevant quantity is the effective area A^ which is the ratio

of the received power P to the incident power density P^:

1
A - P /P.. (1)

e r d

Since P has units of W and P, has units of W/m““ , A has units of m^ . If we

r d e

normalize A to the effective area A of a reference antenna, we can also

e r define shielding effectiveness (SE) as

SE = -10 log

10

(A

e /A

r

), dB. (2)

In this report we present theoretical and experimental results for

coupling through small circular apertures in the shields of a coaxial air

line and a transverse electromagnetic (TEM) cell [4]. Hoeft and Hofstra [3]

have made surface transfer impedance measurements on a coaxial line at

frequencies below 100 MHz. In our theory and measurements we are

considering higher frequencies (above 100 MHz) , and we include the effects

of the external geometry and the terminating impedances on A^

.

The organization of this report is as follows. In Section 2 . 1 we give

the expressions for the current and charge on a thin circular cylinder in

the absence of the aperture for plane -wave excitation. The thin cylinder

can be either semi- infinite or of finite length [5]. In Section 2.2 we use

polarizability theory for a small circular aperture to compute the power

coupled to the air line with a matched load [6]. In Section 2 . 3 we compare

theoretical results with measurements made in a reverberation chamber. To

make this comparison we have to average the theoretical results over all

incidence angles and polarizations, as shown in the Appendix. In Section

2.4 we calculate the effect of shield thickness. In Section 3 we present a comparison of theory and measurements for a TEM cell with a circular

aperture in the shield. Conclusions are given in Section 4.

2
2. COAXIAL AIR LINE

2 . 1 External Current and Charge

In this section we consider plane -wave excitation of a thin cylinder of

radius b. The cylinder can be semi- infinite as shown in figure 1 or of

finite length as shown in figure 2. The incident field E

1

(r) is polarized

in the xz plane and is incident in the xz plane:

.a a ik

i

»r

E

1

(r) v - E^ (x cos 0, - z sin 0.) e , 0 i l

(3)

A A

where k. -= k(x sin 0. + z cos 6.), k - 2n/\,

l l l

and A is the free-space wavelength. The time dependence is exp(-icot).

For the semi- infinite cylinder, we follow the notation and the results

of Chang et al . [5]. The induced current 1(0^, z) can be written as

I(«.,z) - E* [V(tf z) - V(0 0) R(0 . ,z) U(z) ]

,

z > 0, (4)

1 C7 X IX

where the functions V, R, and U are defined in [5]

The first term in the

square brackets is the current that would exist on an infinitely long

cylinder, and the second term is a good approximation to the current

reflected from the end. The charge density p per unit length can be written

1 51(0 z)

P(*. .z) “ 7“ Ti 1 ICO 0 z (5)

The z derivative of I in (5) can be easily evaluated analytically.

We can use a similar theory to analyze a cylinder of finite length 2h

as shown in figure 2. By summing the multiply reflected currents from the

3
ends, Chang et al. [5] have derived the following expression for the induced

current I (9 , z)

K^.z) - Ej (V(0 .,z) + [A(*-0

i

,h-z)V(0.,h)

+ u(h - z) (6)

+ [A(tf . ,h+z)V(*-0.,h) + jg-ff cC,)] U(h+z)), | z | < h,

where the functions V, A, R, and C are defined in [5]. The charge per unit

length can again be obtained by differentiation as indicated in eq (5)

.

2.2 Received Power

In this section we consider coupling from the external region to an

internal coaxial air line through a small circular aperture. We specialize

the theory of Taylor and Harrison [6] to the case of matched terminations to

correspond to our experimental configuration. The geometry for a circular

aperture of radius a in a semi- infinite cylinder is shown in figure 3.

a sufficiently small radius a, the excitation of the coaxial line

of a radial electric dipole p and an x-directed magnetic dipole

ey

a p(9

.

,z_) a 1(9 . ,z n ) e l 0 , m l 0

27rb

an ^mx 2?rb

’

(7)

3 3 where a - 2a /3 and a — 4a /3

.

e m

The results in eq (7) can also be used for the finite-length cylinder by

using the appropriate expressions for p and I. The dipole moments in (7)

For

is that

P [6] : mx

4
produce an equivalent voltage source e and an equivalent current source i

g

[6,7]

e g

-ikr?p

47rb

mx and i

g

ikp

ex. 47T€bZ ( 8 )

1/2 where ry - (/i/e) , /i is the permeability of free space, e is the

permittivity of free space, and is the characteristic impedance of the

coaxial air line.

Since the air line is terminated in its characteristic impedance at z =

0 and z - s, there are no reflections. The current in the load at z = s simplifies to [6]

I(s)

exp [ ik(s-z~)

]

[e + Z i

Q-__ ... g c -gi

2Z

c

(9)

The power received in the load at z - s is

P - |I(s)| 2Z where |I(s)| 2 - |e + Z i | 2 /(4Z2

). (10)

L C g C g C

Since the line is assumed lossless and the load is matched, P is

r independent of s

The incident power density P^ is

P

d - |eJ|

2

/„. (11)

We write the effective area as A

g

(^.) to indicate that it depends on ^

A

e (0.) - b|I(s)| 2

]/[Z

c

|Ej| 2

]. ( 12 )

5
As indicated in the Appendix, the effective area should be averaged over all

incidence angles and polarizations to obtain the response in a reverberation

chamber. Since A^ is independent of the azimuthal angle <f>^, the <f>

averaging has no effect. Since A

g

is approximately zero for a ^-polarized

incident wave, the polarization averaging introduces a factor of 1/2 which

is consistent with the result of Tai [ 8 ]. Consequently the average value

<A > is

e

<A > = 7 j A (0.) sin 0. dO .

.

(13)

e 4 J

e l l l

The integration in eq (13) can be carried out numerically. For the semiinfinite cylinder there is a singularity at 6 ^ - n because I(?r,z) is

singular [5]. However, it is an integrable singularity and causes no

problem in the evaluation of eq (13). For the finite-length cylinder there

is no singularity [5].

The average effective area <A^> of the reference antenna in a

2 reverberation chamber is A /( 8 ?r) as shown in eq (A15) in the Appendix.

Therefore we can write SE for the apertured coaxial air line as

SE - - 10 log

10 [<Ae>/(A2

/8>r)], (14)

where <A

g

> is given by (13).

2 . 3 Measurements in a Reverberation Chamber

Measurements of SE for an apertured air line were performed in a

reverberation chamber at NIST [9] over the frequency range from 1 to 18 GHz.

The parameters for the apertured coaxial air line are: line radius

b = 3.5 mm, aperture location Zq — 10.7 cm, aperture radius a - 1 mm, and

6
characteristic impedance = 50 fi. A second air line was also constructed

with a larger aperture a - 1.5 mm.

Comparisons of measured SE and theoretical SE calculated from eq (14)

are shown in figure 4 for both aperture radii. The theory for the semiinfinite line is used in the comparison because a semi-rigid coaxial line

carries the signal from the apertured section to the chamber wall and

through the wall to the receiver. The section of semi-rigid line has about

the same radius as the apertured section and is long compared to the

distance Zq of the aperture from the end of the line. In using the semiinfinite model, we are neglecting any reflection of the external current

that occurs at the wall boundary.

The theoretical curves are fairly smooth, and this is a result of

averaging over incidence angle. The measured data show rapid frequency

oscillations that are characteristic of reverberation chamber data [9] and

have nothing to do with the apertured coaxial air line. The most disturbing

aspect of the comparison is that the theoretical curve lies well below

(about 7 dB) the measured curve for the smaller aperture (a - 1 mm) . We

would actually expect the theory to be more accurate for the smaller

aperture because one of the assumptions is that a « b. From the

polarizability theory in eq (7) , we would expect the curves for the two

aperture sizes to be separated by (1.5) or 10.6 dB. The separation between

the two measured curves is clearly greater than 10.6 dB. A possible

explanation in terms of the shield thickness is given in the following

section.

2.4 Corrections for Shield Thickness and Chamber Geometry

The polarizability theory given in eq (7) is valid for a circular

aperture in a planar sheet of zero thickness. Clearly the shield of the air

line is not planar and has some nonzero thickness t. We have no simple way

of correcting for the curvature of the shield (radius b) , but there is an

approximate correction for the shield thickness that is based on the theory

of a circular waveguide below cutoff.

7
For a wall (shield) thickness t and aperture radius a, McDonald [10]

has calculated correction factors for the electric and magnetic

polarizabilities as a function of t/a. The expressions for the modified

electric and magnetic polarizabilities a

^ and are

a' = a C and a

' “ a C , e e e m mm (15)

where C and C are correction factors and a and a are given in (7). For

e m e m

t/a TM 0 , C

0 - Cm * 1 . For general values of t/a, McDonald has published

curves for and C . For t/a > 0.4, the following approximate expressions

can by used:

C

e 0.825

-2.405

e t/a and C

m

0.84 e'

1 - 841 t/a

(16)

The shield thickness is approximately 0.65 mm for both apertured air lines.

Because the ratio t/a is greater for the smaller aperture, the correction is

also greater for that case. The corrected theoretical curves are compared

with the same measured curves in figure 5.

Another effect which we can compute approximately is the effect of

reflection of the external current from the chamber wall where the semirigid coaxial line passes through the wall. The geometry is shown in figure

6. If we use image theory to account for the wall reflection, then the

effective length of the air line is 2h as shown in figure 6. This geometry

matches the finite-length line shown in figure 2, and the appropriate

expression for the current I is eq (6)

.

The rest of the analysis is the

same as that for the semi- infinite model. The actual value for h in the

experiment is h - 1.3 m, and the theoretical curves for the image theory are

shown in figure 5

.

The curves for image theory and the semi- infinite model differ by less

than 3 dB at most frequencies. The agreement with the measured curve is

better for the smaller .aperture. This is to be expected since the theory

assumes that aperture radius a is small compared to b and A.

8
3 . TEM CELL

3 . 1 Theory

A cross section of a TEM cell is shown in figure 7. A circular

aperture is centered in the upper wall, and the cell is tapered down to a coaxial line at each end. Again the line is terminated in a matched load at

one end, and the power is received in a matched load at the other end. The

apertured TEM cell does not permit a rigorous analysis because the external

geometry is too complicated to compute the current density (tangential

magnetic field) and charge density (normal electric field) incident on the

aperture

An approximate analysis [4] has been performed assuming that the fields

incident on the aperture are equal to the free-space incident fields. The

same polarizability theory as used in eq (7) was used, and a similar theory

was used for excitation of the internal TEM mode by the aperture dipole

moments. No averaging over incidence angles was done, but an expression for

the maximum received power was derived. The maximum occurs when the

incident field is propagating along the z axis with the electric field

polarized in the y direction. In the case the maximum effective area A

max

is [4]

A

max - (Z

0/u) ( 16 a

3

Ac sinh(?rd/2c)

2

(17)

where the dimensions c and d are shown in figure 7. The septum width w does

not appear explicitly in eq (17), but the characteristic impedance

depends on w [4]

Since this theory deals only with the polarization2 matched case, we normalize by A /(4?r) to get shielding effectiveness:

SE = -10 log {(7TZ /n) l— 32 a

] 2

}, dB.

A c sinh(7rd/2c)

(18)

9
3.2 Measurements in a Reverberation Chamber

Measurements of SE for two apertured TEM cells were performed in the

same reverberation chamber at NIST. The parameters for the smaller TEM cell

are: a * 7 . 5 mm, c - 2.75 cm, d - 1.35 cm, and Zq = 50 Q. A comparison of

theory and measurements for frequencies from 100 MHz to 4 GHz is shown in

figure 8. The theory in eq (18) predicts a straight line when SE is plotted

as a function of log frequency. The measured curve shows fine structure

which is characteristic of most measurements made in reverberation chambers.

We do not expect close agreement because the theory represents maximum

coupling (minimum SE) and does not include the effects of the external

geometry on the fields exciting the aperture. It is fortunate that these

two effects partially cancel each other. The use of the maximum coupling

lowers the SE curve, and the omission of the external geometry effects

raises the SE curve. We do not include the effect of wall thickness in the

theory because the ratio of wall thickness to aperture radius is small.

The parameters for the larger TEM cell are: a - 1.55 cm, c = d = 6 cm|

and Zq - 50 Q. A comparison of theoretical and measured SE for frequencies

from 100 MHz to 2 GHz is shown in figure 9. The theory again predicts a

straight line, and the measured curve shows fine structure typical of

measurements in a reverberation chamber.

The measured curves in figures 8 and 9 show some spikes at high

frequencies (above about 1 GHz) ; these are due to higher-order mode

resonances within the TEM cell [11] . Normally TEM cells are operated at

frequencies below these resonances, but TEM cells are still useful at

frequencies between these narrow resonances. At low frequencies (below 200

MHz) , the measured curves show greater variability with frequency and drop

below the theoretical curve. These low-frequency effects could be caused by

lack of a sufficient number of modes in the reverberation chamber [9].

10
4. CONCLUSIONS AND RECOMMENDATIONS

Shielding effectiveness has been measured for apertured coaxial air

lines and TEM cells in a reverberation chamber. Polarizability theory for

circular apertures has been used to calculate coupling into both types of

shielded transmission lines. The theory of the coaxial air line is more

rigorous because it includes the effects of the external geometry on the

excitation of the circular aperture. The theory also uses averaging over

incidence angle and polarization for comparison with measurements made in a reverberation chamber. The theory for the TEM cell does not include these

features because the external geometry is too complicated for analysis.

Comparisons of theoretical and measured shielding effectiveness for

both transmission line geometries show qualitative agreement for the

frequency dependence. However, the theoretical curves are smooth, and the

measured curves show rapid frequency oscillations of about ±6 dB; these are

representative of the reverberation chamber. There are also some systematic

differences. The theory for the coaxial line shows a slightly higher

average value of shielding effectiveness than the measured data, and the

theory for the TEM cell shows a greater frequency slope than the measured

data. In general the theory and measurements agree within about ±10 dB, but

this agreement is not achieved at all frequencies.

If an apertured shielded transmission line is to be used as an artifact

standard for shielding effectiveness measurements, it would be desirable to

improve the agreement between theory and measurements. The potential for

improvement is greater for the coaxial air line because a more rigorous

theory is available. For this geometry it is important to have an aperture

radius that is small compared to the radius of the line and the wavelength.

In figure 5 the agreement is better for the smaller aperture radius. It

would also be desirable to have the thickness of the shield small compared

to the aperture radius so that the approximate wall thickness correction

[10] would be negligible in the theory. Also, the polarizability theory

might be improved by using Collin's correction [12] to achieve power

conservation in the coupling calculation.

The most important improvement of all would be to eliminate the section

of semi-rigid coaxial cable that carries the air line signal to and through

11
the chamber wall to the receiver. The theory for the finite-length air line

is available in eq (6), and the measurement variability should be reduced by

eliminating the section of semi-rigid line that passes through the chamber

wall. This would be particularly important in reducing variability from one

facility to another. A method to accomplish this is to detect the signal

within the section of air line and to run a fiber optic line [13] through

the chamber wall.

Additional SE measurements on the apertured air line should be made for

plane -wave illumination in an anechoic chamber. Such measurements would

allow comparison of theory and measurements as a function of incidence angle

and polarization in a less complex environment. The expected angular

dependence is given in eq (12). Such comparisons would allow a better

understanding of the coaxial air line and might point the way to

improvements in the theory.

Further improvements in measurements made in reverberation chambers

would be desirable both for this SE application and other applications. The

theory uses a ratio of the average powers received by the reference antenna

and the apertured air line to compute SE. The measurement actually uses the

peak powers (as a function of mode stirrer position) received by the

reference antenna and the apertured air line to compute SE. Experimental

data indicate that the offset between peak and average values is on the

order of 7 to 8 dB [9] independent of the test object. This offset should

cancel when ratios are taken for SE measurements. However, further study of

this issue would be desirable since recent experimental data show greater

offset and variability in peak values [14] and no rigorous theory is

available for the relationship between peak and average values measured in

reverberation chambers

.

5 . ACKNOWLEDGMENTS

This work was partially supported by Rome Air Development Center

(RADC) , Griffiss Air Force Base, Rome, New York.

12
6 . REFERENCES

[1] Vance, E.R. Coupling to Shielded Cables. New York: Wiley, 1978.

[2] Jesch, R.L. Measurement of shielding effectiveness of cables and

shielding configurations by mode-stirred techniques. IEEE Trans.

Electromag. Compat. , EMC-30: 222-228; 1988.

[3] Hoeft, L.O.; Hofstra, J.S. Measured electromagnetic shielding

performance of commonly used cables and connectors. IEEE Trans.

Electromag. Compat., EMC-30: 260-275; 1988.

[4] Wilson, P.F.; Ma, M.T. A study of techniques for measuring the

electromagnetic shielding effectiveness of materials. Nat. Bur. Stand.

(U.S.) Tech. Note 1095; 1986.

[5] Chang, D.C.; Lee, S.W.; Rispin, L. Simple formula for current on a

cylindrical receiving antenna. IEEE Trans. Ant. Propagat. , AP-26: 683-

690, 1978.

[6] Taylor, C.D.

Harrison, C.W. Jr. On the excitation of a coaxial line by

an incident field propagating through a small aperture in the sheath.

IEEE Trans. Electromag. Compat., EMC-15: 127-131; 1973.

[7] Chang, D.C.; Harrison, C.W. Jr.; Taylor, C.D. Note regarding the

propagation of electromagnetic fields through slots in cylinders. IEEE

Trans. Electromag. Compat., EMC-15: 152-154; 1973.

[8] Tai, C.T. On the definition of effective aperture of antennas. IEEE

Trans. Ant. Propagat., AP-9: 224-225; 1961.

[9] Crawford, M.L.

Koepke, G.H. Design, evaluation, and use of a

reverberation chamber for performing electromagnetic

susceptibility/vulnerability measurements. Nat. Bur. Stand. (U.S.)

Tech. Note 1092; 1986.

[10] 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; 1972.

[11] Crawford, M.L. Generation of EM fields using TEM transmission cells.

IEEE Trans. Electromag. Compat., EMC-16: 189-195; 1974.

[12] Collin, R.E. Small aperture coupling between dissimilar regions.

Electromagnetics, 2: 1-24; 1982.

[13] Kanda, M. ; Masterson, K.D. Optically sensed EM field probes for pulsed

fields. Proc. IEEE, 80: 209-215; 1992.

[14] Kostas, J.G.; Boverie, B. Statistical model for a mode-stirred chamber.

IEEE Trans. Electromag. Compat., EMC-33: 366-370; 1991.

13
[15] Kerns, D.M. Plane -wave, scattering-matrix theory of antennas and

antenna -antenna interactions. Washington, D.C.: Nat. Bur. Stand.

(U.S.) Monograph 162; 1981.

[16] Corona, P. ; Latmiral, G. ; Paolini, E. Performance and analysis of a reverberating enclosure with variable geometry. IEEE Trans. Electromag.

Compat., EMC-22 : 2-5; 1980.

APPENDIX. RANDOM FIELD EXCITATION

In this appendix we consider excitation of an arbitrary antenna by a

random field with application to a mode-stirred chamber. A physical

interpretation of the random field is that each member of the ensemble

corresponds to a different tuner position. Thus ensemble averages

correspond to averages over all tuner positions.

The geometry for an arbitrary antenna in an arbitrary field is shown in

Fig. 10. We represent the incident field E(r) as an integral of plane waves

over all real angles

E (?) - f F(0) e

ik ’ r

dfl, (Al)

47T

where the solid angle Q is shorthand for the elevation and azimuth angles, a

and and dfi - sina da dp. The wavenumber k is

k - -k (x

AAA

sina cosp + y sina sin/? + z cosa) . (A2)

The spectrum F(0) can be written

A A

F(C1) - a F (0) + 0 F.(Q), (A3)

a p

A A

where a and p are unit vectors that are orthogonal to each other and to k.

The square of the absolute value of E can be written

|ECr) | 2 - JJ [«

1

F

a

(Q

1

) + ^F (Q

1

)].[<»

2

F*(n

2

) + ^F*^) ] /• iHP '

14
(A4)

• e i(k

1

-k

2

)-r

dfi 2>

where * indicates complex conjugate. We now introduce the following randomfield assumptions

<F

a

(0

l

)F«

(n

2 )> -

|E

o'

8jt

{ < n

1

- n

2

) ’

(A5)

<F

«

(Q

1

)I

J

(Q

2 )> - <F^

n

i )Fa

(Q

2

)> " °*

where < > indicates ensemble average, is a constant, and 8 is the Dirac

2 delta function. We can evaluate <|E(r)| > by substituting (A5) into (A4)

and using the property of the delta function to evaluate one integration.

The second integration is easily evaluated as follows

<| E(r)

|

2

> S

4?r

ifoi

4?r

da E

ol (A6)

Thus the mean- square value of the electric field is | Eq

|

and is independent

of position. The average power density <P^> is also independent of position

<V - |E0

I h (A7)

The received signal b^ of an arbritrary receiving antenna can be

written in a form which is analogous to Kerns' plane-wave, scattering-matrix

notation [15]

b

Q - f SCO)

47T

F(Q) dfl, (A8)
where the spectrum F(fi) is given by (A3) and the receiving function S(fi) can

be written in component form

A A

S(O) - a S (fi) + 0 S (0).

a p

(A9)

The received power is proportional to jb^j which can be written

|b 0

l 2 - JJ [s

o

(Q

1

)F

a

(Q

1

) + s ( 0l

)F (opi [s*(q

2

)f*(o ) +

47T

(A10) * * + s^(Q

2

)F^(n

2

)] dn

x dn2

If we substitute (A5) into (AlO) and carry out the Q

2 integration, we obtain

the following average value

<|b

0

| 2

> - i

I

e

q

| 2 ^ J" [|Sa

(fi

1

)|

2

+ |S <n

x

)|

2

] dn

1

. (All)

4tt p

On the right side of (All), 1/2 results from polarization mismatch [8],

2

| Eq

|

is the mean square value of the incident electric field, and the

_ 2 integral is the average value of |S| over all incidence angles. Thus the

directional characteristics of 8(0!) are averaged out.

The result in (All) can be used to obtain two results of practical

interest. For the case of aperture coupling to a coaxial line considered in

this paper, the component is zero, and the component is independent of

azimuthal angle p. Thus the p integration yields a factor of 2n

,

and only

the integration over elevation angle remains. In the notation of Section

2.2, the average value of effective area is then given by (13).

For a more general receiving antenna, we can use the result in (All) - to

determine the average value of received power ^or a lossless,

16
impedance -matched antenna with radiation resistance R , we can use (All) to

write

<iV >

<P >

r R 2

<Pd>

-1 r 4* J 47T

R

[|sa(n

1

)|

2

+ |s^(ti1

) | 2] anr

(A12)

where we have used (A7) to introduce the average power density <P^>. We can

relate the integrand of (A12) to the effective area of an isotropic antenna

2

A /47t and the gain G(Q^) by

[|Sa

(0

1

)|

2

+ |S (opi

2

] - ^ G(np. (A13)

r p

If we substitute (A13) into (A12) , we obtain

<P

r> " 2

<Pd> t t JG < n

i> dQl-

(A14)

4?r

The integration in (A14) is easily evaluated because the average value of

G is one. Thus the desired result for <P > is

r

<P

r> “ 2

<Pd

> t- (A15)

The physical interpretation of this remarkably simple result is that the

average received power is equal to average power density times the effective

2

area A /4?r of an isotropic antenna times a factor of 1/2 to account for

polarization mismatch [8]

This result is independent of the gain and

polarization characteristics of the receiving antenna and is consistent with

the reverberation chamber analysis [16] of Corona et al . The result in

(A15) does not apply to the apertured coaxial air line because the line has

loss and is not impedance matched.

17
z

Figure 1. Plane wave incident on a semi- infini te cylinder.

18
z

M

Figure 2. Plane wave incident on a cylinder of length 2h.

19
Figure 3

Z

y

Electric and magnetic dipole moments induced in a circular

aperture. The internal air line is terminated in its

characteristic impedance.

20
Shielding

Effectiveness

(dB)

90

a = 1 mm

Measurements

50-

Theory ' = 1.5 mml , 'l

30

10

Frequency (GHz)

Figure 4. Theoretical and measured shielding effectiveness for a coaxial

air line with a circular aperture. Parameters: b - 3.5 mm,

Z n = 10.7 cm, Z “ 50 fl. U c

21
Shielding

Effectiveness

(dB)

Frequency (GHz)

Figure 5. Semi -infinite theory, image theory, and measurements

shielding effectiveness of a coaxial air line. Both theories

modified to include wall thickness.

for

are

22
chamber

wall

coaxial

air line ^

image

O

^ II ^„ hm

Figure 6. Geometry for an apertured coaxial air line passing through the

wall in a reverberation chamber. The image accounts for

reflection of external currents at the wall boundary.

23
Figure 7. Geometry for an apertured TEM cell.

24
Frequency (GHz)

Figure 8. Theoretical and measured shielding effectiveness for a TEM cell

with a circular aperture. Parameters: a = 7.5 mm, c = 2.75 cm,

d - 1.35 cm, Zq = 50 fl.

25
Frequency (GHz)

Figure 9. Theoretical and measured shielding effectiveness for a TEM cell

with a circular aperture. Parameters: a - 1.55 cm, c - d = 6 cm,

26
X

Figure 10. Plane -wave component of the electric field incident on an

arbitrary receiving antenna.

27
I

.
BL-H4A U.S. DEPARTMENT OF COMMERCE

(5-90) NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

AOMAN 15.01

BIBLIOGRAPHIC DATA SHEET

1. PUBLICATION OR REPORT NUMBER

NISTIR 3988

2. PERFORMING ORCtANIZATION REPORT NUMBER

B92-0123

3. PUBLICATION DATE

April 1992

4. TITLE AND SUBTITLE

Aperture Coupling to Shielded Transmission Lines: Theory and Experiment

5. AUTHOR(S)

D.A. Hill, M.L. Crawford, M. Kanda, and D.I. Wu

6. PERFORMING ORGANIZATION (IF JOINT OR OTHER THAN NIST, SEE INSTRUCTIONS)

U.S. DEPARTMENT OF COMMERCE

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

BOULDER, COLORADO 80303-3328

7. CONTRACT/GRANT NUMBER

8. TYPE OF REPORT AND PERIOD COVERED

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (STREET, CITY, STATE, ZIP)

10. SUPPLEMENTARY NOTES

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.)

Coupling through circular apertures in the shields of a coaxial air line and a

TEM cell is studied theoretically and experimentally. Polarizability theory is used

to compute the effective dipole moments that excite the transmission lines in the

internal region. Measurements of shielding effectiveness of both structures were

made in a reverberation chamber over wide frequency ranges. Agreement between

theory and measurements is generally within + 10 dB. Recommendations for improvements in the measurements and theory are made for achieving closer agreement

that would be desirable for an artifact standard for shielding effectiveness

measurements.

12. KEY WORDS (6 TO 12 ENTRIES; ALPHABETICAL ORDER; CAPITALIZE ONLY PROPER NAMES; AND SEPARATE KEY WORDS BY SEMICOLONS)

aperture; coaxial air line; dipole moment; effective area; polarizability;

reverberation chamber; shielding effectiveness; TEM cell

13. AVAILABILITY UNLIMITED

FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE TO NATIONAL TECHNICAL INFORMATION SERVICE (NT1S).

ORDER FROM SUPERINTENDENT OF DOCUMENTS, U.S. GOVERNMENT PRINTING OFFICE,

WASHINGTON, DC 20402. ORDER FROM NATIONAL TECHNICAL INFORMATION SERVICE (NTIS), SPRINGFIELD, VA 22161.

14. NUMBER OF PRINTED PAGES

30

15. PRICE

A02

ELECTRONICFORM
,

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