.4pp/;d S~cpmwducriuiry Vol. 2, No. I, pp. l-5, 1994 Printed in Great Britain. All rights reserved

0964-l 807/94 $6.00 + 0.00 Copyright 0 1993 Pergamon Press Ltd

ELECTROMAGNETIC SHIELDING USING SUPERCONDUCTORS

ALOK TRIPATHI and T. S. VEDAVATHY

Department of Electrical Communication Engineering, Indian Institute of Science, Bangalore 560 012, India

(Received 9 June 1993)

Abstract-Expressions for the shielding effectiveness of thin superconducting film for near and far field interfering sources have been derived by modelling the superconductor as a dielectric material of negative dielectric constant. Computation of shielding effectiveness of thin film superconductor as a function of frequency is carried out. Results are compared with those of copper. It is observed that superconductors are better shields at lower ranges of millimeter wave frequencies and copper has a better shielding effectiveness at frequencies beyond 100 GHz.

1. INTRODUCTION

The Electromagnetic Interference (EMI) is a serious problem in extremely sensitive electronic equipment such as missile guidance, radar tracking systems, and equipment for biomedical applications. Ideally designed equipment should neither radiate electromagnetic energy nor be susceptible to receiving any unwanted radiation from an external source. The solution to this problem is to provide metallic enclosures to the devices and subsystems which provide an electromagnetic shield, so that the required performance in their operational environment is possible without suffering from or causing unacceptable degradation (EMC). The degree of isolation between the interior and the exterior being dependant on the material properties and the frequency of the radiation, it is felt that the use of superconductor sheets as shields would considerably improve the isolation.

The shielding effectiveness can be defined as the total loss of the electromagnetic energy as it tries to pass through the shielding material. This comprises of the loss due to attenuation in the material and reflections at the boundaries. So far, the analysis of such shields has been carried out following the conventional way of solving Maxwell’s equations in free space and London equation for superconductors. In this analysis a new concept has been made use of in modelling the superconductor as a dielectric material having negative dielectric constant [l]. Following this, the conventional methods for analysis can be suitably modified to the case of superconductors. This concept will also help in taking into account the anisotropic behavior of the superconductors by expressing the permittivity as a tensor having elements with negative real part.

In this paper expressions for the shielding effectiveness of a superconducting material for intersystem and intrasystem interference due to high impedance and low impedance sources are derived. Computations of the losses and the shielding effectiveness as function of frequency are carried out. The results are compared with those of copper.

2. ANALYSIS

Transmission line method is used for the analysis considering the shield as lossy transmission line [2]. Figure 1 shows a uniform plane wave incident normally upon boundary (1) of the shield and emerging out of the boundary (2). The wave is attenuated by a factor of e-@’ from boundary (1) to (2), where y = a + j/3 is the propagation constant in the material.

The overall electric and magnetic field transmission coefficients are given by

(1)

ALOK TRIPATHI and T. S, VEDA~A~Y

air 30

L Shield q air I) %

E x3,Hy3

Fig, 1. Wave propagation in a shield.

where

The shielding effectiveness

SE = - 2O*log(T)

= 20 log leYfl - 20 log 171 + 20 log/ 1 - pe-2y”l

=A+B+C (2)

where A is the loss due to attenuation in the material, R is the loss due to reflection and C is the loss due to multiple internal reflections when A is small.

3. SUPERCONDUCTOR AS NEGATIVE DIELECTRIC

Su~rconductor need not be assumed to be a conductor with infinite conductivity. Approximate models have been proposed to explain the electromagnetics of su~rconductors [l]. The working model for engineering applications is the two-fluid model for which the London equations are valid. The model proposed aims at describing the electromagnetic properties of a superconductor in terms of a temperature dependent complex conductivity or a dielectric with a negative c,,[l].

According to the two-fluid model the current in a superconductor can be written as

J = J, + J,, (3)

where J, = -n,,e<Y,) and J,, = -nsce(~,) with n = n, + n,,, f, is the current due to normal electrons and J,, is due to pairs of superconducting electrons. n,, and n,, are number densities of electron pairs and normal particle respectively. The hydrodynamic equations are, assuming superconducting electrons have also loss associated with them

W,) + m<v,> m dt

-= -eE %I

(4)

(5)

where (v,) and (Y,) are average velocities of superconducting and normal electrons. TV, t, are the

electromagnetic shieldjng using su~rconductors 3

average momentum relaxation time of the superconducting and normal electrons. m and e are mass and charge of electrons respectively, ~~ can be taken to be infinity.

The temperature dependence of n, and n, can be approximated by the Gorter-Casimir expressions Cl]. With help of Maxwell’s equation

V x H =jmOE + J (6)

and from equations (4), (5) and (5) and by considering supe~uid to be the limiting case of a lossy medium we obtain the dielectric constant as

2

W2=es e% s

?n&g ’ o,2=:--it (8)

m&o

where o, and w, are plasma frequencies of super and normal particle. Combining London equation (4) and equation (9) an expression for dielectric constant for

superconductor is obtained

C” & - sc jW&*

-L-+1 02j.f, AZ&,

= lim 1 dt,Z Q&3,” . &f (9) x,-m [( 02T2 n n a2r2 + 1 s wZz2+1 -J ” > ( 0(&,2 + 1) + 6&0%,2 + 1) )I

where A(T) is the penetration depth of superconductor. Since o, is of the order of l-10 tera Hertz for most of the superconductors, E,, will have a

negative real part and hence it can be assumed to be a material of negative dielectric constant. The shielding effectiveness formulas for superconductor shield are derived by replacing E by E,,. This analysis is valid for fields below the critical fields for superconductor and also T < T,.

4. RESULTS

The shields are considered to be 1.0 x 10e3mm thick and 1 = 1.8 x 10m4mm. Computation of the losses and the shielding effectiveness are carried out for both superconductor and copper for near and far field (r Q l//I and r $ l/p) interfering sources, of high and low impedance (q > q0 and q < q,) [3], as a function of frequency. Results for near field are shown in Figs 2-5. Results for far field are similar in nature and hence are not presented.

m, c .-

M

4

150+

loo-

- Su ottenuatbn loss f Cu ollenuaticn loss . Su reflection loss h Cu rellection loss 0 5.1 correction term x Cu correctton lerm

2 4 6 a 10 x

Frequency, IO’ Hz

Fig. 2. Low impedance near field losses vs frequency.

ALOK TRIPATHI and T. S. VEDAVATHY

- Superconductor -+ Copper

150

t,

2 4 6 6 10 x Frequency ,lOXHz

Fig. 3. Shielding effectiveness vs frequency for low impedance near field.

5. CONCLUSION

It can be observed that the shielding effectiveness of copper for low impedance near fields is very poor. Thin film superconductor has better shielding effectiveness in this case as shown in Figs 2 and 3. This can be explained by the diama~eti~ nature of superconductor. For high impedance

0 - Su attenuation loss

+ Cu attenuation loss _ l l Su reflection loss

0 * Cu reflection loss 0 0 Su correction loss

A 0 A X Cu correction loss

A l

-5 0 5 10 Frequency,lOXHz

Fig. 4. High impedance near field losses vs frequency.

Electromagnetic shielding using superconductors

a ‘0 .r 400-

- Superconductor

-0- Copper

-5 0 5 10 x

Frequency, 10’ Hz

Fig. 5. Shielding effectiveness vs frequency for high impedance near field.

near fields, both copper and superconductor provide good shielding. However, superconductor is better than copper at lower range of millimeter wave frequencies and copper is better than superconductor beyond 100 GHz range.

REFERENCES

1. K. K. Mei and Guo-chun Liang, IEEE Trans. Microwaoe Theory Tech. 39, 1545 (1991). 2. R. B. Shulz, V. C. Plantz and D. R. Brush, IEEE Trans. Electronzag. Compat. 30, 187 (1988). 3. S. A. Schelkunoff, Electromagnetic Waves, pp. 304310. Van Nostrand, Princeton, N.J. (1957).

Acknowledgemenrs-The authors are indebted to Professor C. N. R. Rao, FRS, for his kind help, valuable suggestions, and encouragement. The authors also wish to thank Professor R. P. Shenoy and Professor M. Satyam for their kind help.