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A novel approach for analyzing the electromagnetic reflection from stratified anisotropic media

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A

Novel Approach for

Analyzing

the

Electromagnetic Reflection from

Stratified Anisotropic Media

Ming-Shing Lin, Ruey-Beei Wu, and Chun Hsiung Chen Department of Electrical Engineering,

National Taiwan University, Taipei, Taiwan, ROC

ABSTRACT

This paper presents an analysis of plane-wave reflection from stratified anisotropic lossy media.

To this end, an equivalent-transmission-line-circuit (ETLC) model is adopted in the frequency- and time-domain analysis. In this study, the reflec- tion properties of graphite/epoxy, boron/epoxy, Kevlar/epoxy and their hybrid laminated com- posites are investigated in detail.

1. INTRODUCTION

The anisotropic materials such as microstrip substrate, radar absorbing materials, and lami- nated composites are widely employed in many engineering applications

.

The electromagnetic interaction with anisotropic materials thus de- serves intensive investigation. Recently efforts by Morgan [l] and Titchener [2] employed the tran- sition matrix method to study the reflection and transmission phenomena in anisotropic stratified media. The wave-transmission-matrix (WTM) method [3] was also used to solve the laminat- ed and anisotropic composites illuminated by an obliquely incident plane wave. But, these meth- ods cannot get the time-domain solution directly.

The laminated composites are increasingly used as replacement for metals in aircraft and

aerospace applications due to their superior properties in strength-to-weight and modulus-to- weight ratios. Therefore, the reflection problem associated with the anisotropic laminated com- posites needs special attention due to its close re-

lation to the radar-cross-section problem. From the results of [2] and [3], it was suggested that one may use anisotropic media to reduce the re-

flection from metal structure.

In this paper, a novel approach based on the ETLC model is applied to analyze the reflection properties of various laminated composites. The major advantage of ETLC model [4] is that one may directly analyze the problem in both fre- quency and time domains.

2.

ETLC

MODEL

The ETLC model can handle the frequency- and time-domain propagation problem for inho- mogeneous, anisotropic, and transversely lossy slab with permittivity(EgZ), permeability(,uoF), and conductivity(5) tensors of the form

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This model is based on the analogy between field equations and coupled transmission line equa- tions together with suitable boundary conditions. Thus, solving the electromagnetic propagation problem for the stratified anisotropic media is then equivalent to finding the frequency- and time-domain solutions from ETLC model. To facilitate the analysis, the plane wave is decom- posed into El -wave and El-wave components, re- with E-field parallel (or perpendicular) to the 2-2 plane of incidence.

spectively.

T

h

e

Ell-

(or

El-)

wave means the one

Approximating the coupled transmission lines

by cascading lumped T- and R- circuits, one can solve the ETLC model by the circuit analysis pro- grams such as PSPICE. From the output data of PSPICE program, we can get the reflection coef- ficients

Rll,ll, R I I , ~ ,

&,I, and

RI,II,

in frequency

domain, by the following definitions

Pr

U -

P

Here the first subscript “p”=“Il” (or “l.”) de- notes that the incident field E’ is E

-

(or

El-)

wave, and the second subscript uq”=LLll” (or ‘1”)

denotes that the reflected field Er is Ell- (or

El-)

component.

‘ In the time-domain analysis, the transient waveforms for reflected fields t?;,q(t) may be ob- tained for any incident field waveform Et(t). The definitions of “p” and “q” are the same as those defined in the frequency-domain analysis.

3. RESULTS AND DISCUSSIONS

The wave reflection properties of anisotrop- ic laminated composites backed by perfect elec- tric conductor (PEC) (Fig.1) are then ana- lyzed, based on a model which treats each

lamina as a homogeneous and anisotropic sheet. In this study, the reflection proper- ties of graphite/epoxy( G/E), boron/epoxy(B/E),

Kevlar/epoxy(K/E), and hybrid laminated com- posites backed by

PEC

are investigated in detail. Here, we regard the metal foil or metal coating

as a PEC, which is usually used to enhance elec- tromagnetic shielding. The parameters of these composite materials are listed in Table 1. The pa- rameters are described with respect to the com- posite’s principal coordinates (x’, y’, 2’). For the-

oretical analysis, the field quantities and the elec- trical parameters for each layer must be expressed in the global coordinates (x, y, z), since compos- ite layers with different principal axis directions

are to be cascaded [3]. The numerical results are shown in Figs.2

-

3 with oblique Ell-wave and E l - wave incident on the composites ( incidence angle

6 = Oo or 45O ). In the computations of Figs.2

-

3, each lamina has equal thickness and only the fiber orientation pattern [0°/450/900/

-

45O] is considered.

Shown in Fig. 2 are the magnitudes of re- flection coefficients for G/E and B/E laminated composites backed by PEC (laminate thickness

h = 3 x 10-3m

)

with

Ell-

and El-wave inci- dence, respectively. For normal incidence case, the values of

JRl,lI

are smaller than those of lR~,lll in most part of the frequency range. The v ues of

~ R I I , ~ )

and

~R*,II)

for G/E composite are not shown because they are very small

(<

The values of

IRII,II

I

and

lRl,l

I

for B/E are small- er than those for G/E because the conductivity

U=! of B/E is much smaller than that of G/E. In-

teresting phenomenon observed is that there is a deep near 21 GHz in the curves of

IRl,lI

for B/E. Because the intrinsic properties of

K/E

lam- inated composites are nearly isotropic, there is little difference in reflection properties between metal and K/E laminated composites backed by PEC. Therefore, the results for K/E laminated composites backed by PEC are not shown here.

The reflection properties of the hybrid compos- ites with B/E and G/E laminates backed by PEC are also calculated. It is noted that there is only

a little difference in the reflection coefficients be- tween this hybrid composites and the B/E com-

posites backed by PEC. Therefore, the results are

not shown here too.

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In the time-domain analysis, the Gaussian pulse defined by (3) 1 , t > O 0 , t < O u(t) = (4)

Four structures are studied here: (a) free space(FS) in regions I and 11, and G/E laminate in region 111; (b) free space in regions I and 11, and B/E laminate in region 111; (c) free space in region

I, B/E

laminate in region 11, and

G/E

laminate in region 111; and (d) free space in all regions. The structure and results are shown in Fig.3. From the delay time of reflected-wave peaks, one may estimate the reflection points within the struc- ture. It is found that the reflection properties of the hybrid composites with B/E and G/E lami- nates are similar to those of B/E laminated com- posite when the thickness (h) of each region is m. It is also found that little wave energy reaches PEC in cases (a), (b), and (c), therefore, the reflection coefficients of laminated composites without PEC are the same as those with backed PEC. In other words, the reflection properties in cases (a), (b), and (c) are mainly governed by the composites, not by the backed PEC.

4. CONCLUSIONS

From the results obtained, some suggestion-

s may also be made for reducing the reflection coefficients of laminated composites. First, B/E composite is a better selection for the outer lami- nated one. Second, the composites with 45O lam- ina should be employed. Third, if metal coating is necessary for enhancing electromagnetic shield- ing, the coating should be applied on the backside of composites.

5. ACKNOWLEDGMENT

This work was supported by the National Sci- ence Council of the Republic of China under Grant NSC 82-0404-E-002-237.

6. REFERENCES

[l] M. A. Morgan,

D.

L.

Fisher, and E. A. Milne, “Electromagnetic scattering by stratified inho- mogeneous anisotropic media”, IEEE Trans. on

AP,

Vol. AP-35, pp. 191-197, Feb. 1987.

[2] J. B. Titchener and 3.

R.

Willis, “The re- flection of electromagnetic waves from stratifie.d anisotropic media,” IEEE Trans. on AP, Vol. AP-39, pp. 35-39, Jan. 1991.

[3] M. S. Lin and C.

H.

Chen, “Plane-wave shield- ing properties of anisotropic laminated compos- ites,)) IEEE Trans. on EMC., Vol. EMC-35, pp. 21-27, Feb. 1993.

[4] M. S. Lin, C. M. Lin,

R. B.

Wu, and C.

H.

Chen, “Transient Propagation in anisotropic lam- inated composites,” IEEE Trans. Electromagn. Compat., Vol. EMC-35, Aug. 1993.

7. AUTHORS

Ming-Shing Lin, Senior engineer of Aeronauti- cal Research Laboratory (ARL), Taichung, Tai- wan. His current research interests include air- craft system electromagnetic compatibility, air- craft antennas, and electrical and electromagnet- ic properties of composites materials.

Ruey-Beei Wu, Professor of Electrical Engi- neering Department, National Taiwan Universi- ty. He works primarily on the applications of numerical methods to electromagnetic field prob- lems. He has been engaged in researches on di- electric waveguides, wave scattering of anisotrop- ic objects, and interconnection modeling for com- puter packaging.

Chun Hsiung Chen, Professor of Electrical En- gineering Department, National Taiwan Univer- sity. His areas of interest include antenna and waveguide analysis, propagation and scattering of waves, and numerical techniques in electromag- netics.

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Fig.1. Geometry of M-ply laminated compos-

4

E d ites. Po 5.0 5.6 3.6 5.0 5.6 3.6 U . PEC -dU

'c

Fig.2. Reflectivity coefficients of 4-layer

G/E

and B/E laminated composites backed by

PEC.

(a)

Ell-wave incidence,

(b) El-wave in- cidence. I RI 0 . 2 2

-.

',-/- c-- 100 OD 0 20 U ) 60 80

Fig.3. Time-domain response of laminated com- posites with Gaussian pulses ( r =

5 x 10-I2s

,

t o = 5 x 1 0 - I ' ~ ) incident nor- mally. 1 .o hr3:oxio-3"m E'(t) 0.5

-

(a) = FS + FS + G/E (b) = FS t FS + B/E (c) = FS + B/E + WE e --0.5

-

-1.0 40 60 a0 loo 120 la 160 180 Time ( x lO-'*s)

Table 1. Electrical parameters of laminated composites

I I

I

2.0 x 10-8

I

1.0 x 10-9

1

100

數據

Table  1.  Electrical parameters  of  laminated  composites

參考文獻

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