A circuit model for antenna array mutual coupling effects

A Circuit Model for Antenna Array Mutual

Coupling

Effects

Kun-Chou Lee and *TA-Hsiung Chu

Department of Electrical Engineering, National Taiwan University Taipei, Taiwan, Republic of China

I. Introduction

In this paper, a circuit model is developed to represent the input admit- tance of an antenna array with finite elements.

It

consists of a component to represent the input admittance of an isolate antenna element and an infinite shunt components with each to represent different degrees of antenna mutual coupling effects. This model is shown not only to be numerically efficient com- paring to the moment method analysis, but also to give physical insight into the antenna array mutual coupling mechanism.

11. Circuit Model

Consider a finite antenna array of N-dipoles, with each element excited by a voltage Ei respectively. - The resulting feed currents

7, and excitation

voltages are related by

z

7

=

E.

_ -

If all the array elements are identical, the

2 matrix can be written as - Z;,,(g

+

x),

where Z,,, - is the self-impedance of an isolate antenna element, is a unit matrix, and

If;l

is a matrix to represent the antenna array mutual coupling effects with its elements given by

-

-

(1) By applying the bionomial expansion to

Z-l,

we have

Based on the above formulation, the input admittance

vi

of the i-th an- tenna element can be expressed as

where

Therefore, a circuit model composed of a component of self-admittance term

xs0

in shunt with an infinite components Y,@) can be established as shown in Fig.1 to represent the i-th element input admittance

Vn.

Physically, the y i , , component of the model is due to the contribution of the antenna excitation Ei only. The yi'l) is the first-order mutual coupling term, which is due to the direct coupling effects from the other N

-

1 dipoles to the i-th antenna element. The term Mij in (5) means the direct coupling on the i-th dipole from t:he j-th dipole. Similarly, yi") component is the second- order coupling and the term M;j Mjk in ( 6 ) means the "two-trip" coupling from the k-th dipole to the: j-th dipole then to the i-th dipole, as shown in Fig.2. Other shunt components Yf3),

x(*),

...,

can be interpreted in the same manner.

111. Numerical Example

In the numerical study, the array elements are equally spaced by 0.75X in both

6-

and 2-directions, as shown in Fig.3(a). The resulting error of each antenna element input admittance is given as

The

Yezad

in (8) is the exact input admittance which is solved by Pocklington equation using moment method and Galerkin procedure [1][2], while Ymodel is the input admittance calculated using the circuit model.

First, if the mutual coupling effects are completely ignored, Ymodel is identi- cal to the

Xs0.

The resulting percentage error distribution of array elements is shown in Fig.3(b) about 21

%

to 45

%,

and the root mean square error of array admittance is 37.4

%.

In order to identify the antenna array mutual coupling effect, we first apply the circuit model to include only and $). The re- sulting percentage error is shown reduced to about between 5.4 % and 26.5

%

as given in Fig.3(c), and the root mean square error of array input admittance is 13.3 %. Finally, Fig.3(d) shows that the error of input admittance of most elements can be reduced below

7

%, and the root m e a n square error is about

!

-4.23

%

by including the second-order shunt component

Y;:(2).

More accurate results can be achieved as the higher order shunt components considered.

IV. Conclusion

In this paper, a circuit model is developed to represent the input admit- tance of antenna array with finite elements. Physically, this model is equivalent to the Twersky’s treatment of multiple scattering 131. Since the array compu- tation does not involve matrix inversion, it is suitable for large array analysis which the exact antenna array theory is numerically difficult. Furthermore, this model has no limitation on antenna array geometry and excitation.

References

[l] R. F. Harrington, Field Computation by Moment Methods, New York: Macmillan, 1968.

[2] W. L. Stutzman and G. A. Thiele, Antenna Theory and Design, New York: John Wiley & Sons, 1981.

[3] V. Twersky, “Multiple scattering of radiation by arbitrary configuration of parallel cylinders,’

J.

Acoust. Soc. Amer., vol. 24, No. 1, pp. 42-46,

Jan. 1952.

y?

_{e n}

Fig. 1 Circiiit model for the i-th antenna element input admittance.

element i dementi elementk

Fig. 2 Interpretation of miitual conpling mechanism.

Z

Dg

0

i

I I

I

I

II

I I

"4

I

I

I

I

I

II

I I

II I

II

I I I

II

I I

I I I I I I

II I

I

I I I

I

I

I

II

I

I-y

I I I I I I I I I

I

I I

I I I

II

I I

I

Fig. 3 (a) Geometry of a 9 x 9 dipole array: and the pcrccntagc error dis- trihiition of inpiit admittancc hy iising circiiit modcl inchiding (h) sclf-admittancc

v , ~ ~

only, (c)

v,,,

and miitiia~~admittancc term yi"):

and (d)

v , ~ ~

and miitiia~admittancc terms

y ( ' )

and ~ ( ' 1 .