Mutual Coupling Effect of Microstrip Antenna Array

Procedia Engineering 29 (2012) 1984 – 1988

1877-7058 ? 2011 Published by Elsevier Ltd.

doi:10.1016/j.proeng.2012.01.248Available online at https://www.sodocs.net/doc/1f11484554.html, vailable online at https://www.sodocs.net/doc/1f11484554.html,

2012 International Workshop on Information and Electronics Engineering (IWIEE)

Mutual Coupling Effect of Microstrip Antenna Array

Rao Jia-ren 1, Zong Peng, Darwin R. Becerra

College of Astronautics, Nanjing University of Aeronautics and Astronautics (NUAA)

29 Yudao Street, Nanjing,210016, P. R. China.

Abstract

Microstrip patch antenna is widely used due to the advantages such as small size and mass. However, when the patches are close to each other, the mutual coupling can’t be neglected. So RWG (Rao-Wilton-Glisson) and Method of Moments are chosen as the basic algorithm, then the mutual coupling can be visualized by the means of mutual impedance. Furthermore, a model of linear array antenna consists of five microstrip patch antennas is built, which works on 4.25GHz, then a Matlab simulation is done, and the mutual coupling effect of microstrip patch antenna array is verified efficiently.

? 2011 Published by Elsevier Ltd.

Key words: pahsed array antenna; RWG; microstrip patch; mutual coupling;

1. Introduction

Antenna plays an important role in communication, sonar, spaceflight and some other fields, at the same time, the increasing intensity of electronic equipment calls for demanding antennas, so EMI (Electro Magnetic Compatibility) can not be neglected. For antenna array, close distance between two elements can lead to mutual coupling of energy, which can have direct and bad effect on the gain, signal to noise ratio, pattern of antenna, this problem can make the designed antenna different from the fact one, and sometimes it is even intolerable. We can study the mutual coupling between patches beginning with the analysis of mutual impedance, choosing precise model and algorithm can offer better service for looking into the mutual coupling effects. Combining RWG and MoM (Method of Moments) to analysis mutual impendence and pattern of microstrip patch antenna array can study antenna mutual coupling efficiently.

1

Tel: +86150********

E-mail address: raojiaren19871210@https://www.sodocs.net/doc/1f11484554.html,

1985

Rao Jia-ren et al. / Procedia Engineering 29 (2012) 1984 – 19882. Ideal pattern of array

For the field-strength ideal microstrip antenna array,(,)()N f f f θφθ=?, we can find that it consists of two parts, that is to say, the field of a antenna array is equal to the field of a single patch ()f θ multiplied by the array factor N f . Here , the field of a single patch depends on the pattern function characteristics of the concrete antenna, however, the array factor has relation with the relative position and amplitude rather than the pattern function characteristics, so it is can be formulated by point sources. Fig.1 is a point source array.

2.1 Pattern function characteristics of microstrip patch antenna

Microstrip patch antenna can be seen as a dielectric-loaded cavity with two perfectly conducting electric walls. In ideal case, the normalized E-plane electric field function of microstrip patch antenna is [1]

()cos(sin )2

E L f k θθ= (1) The normalized H-plane magnetic field function is

()sin (sin /2)c o s /(sin /2)H f kW kW θθθθ= (2)

2.2 Array factor of antenna array

There are several common styles of antenna array: liner array, rectangular array and circular array, all of them can be seen as point sources. Field in viewpoint is the total contribution of all elements, so, to find

Figure 1: Linear array aligned along the x-axis

As we can see, fig.1 shows a linear antenna array, it consists of N elements aligned along the x -axis with the same distance d, and cos kd ψγβ=+, then the array factor can be computed by [2]

(1)1N

j n N n n f I e ψ?==∑ (3)

When the excitation of the elements are the same, and n 1I =, then, the array factor can be simplified to follow form:

sin(/2)sin(/2)

N N f ψψ= (4) Furthermore, when the elements align along the x -axis, cos sin cos γθφ=; When the elements align along the y -axis, cos sin sin γθφ=; When the elements align along the z -axis, cos cos γθ=.

1986 Rao Jia-ren et al. / Procedia Engineering 29 (2012) 1984 – 1988

3. Calculation of mutual coupling

When the patches are far away from each other, the mutual coupling effect can be neglected; however, when they are close to each other, this problem must not be lost of sight. I n the antenna array, each element can be seen as an open circuit, which includes electromagnetic coupling effect. So, when antenna array transmits signals, there is not only feed current included in surface current, but also the scatter current caused by nearby elements. When receiving signals, the antenna elements not only affected by incident waves, they may also be affected by nearby elements. I n short, energy mutual coupling effect exists in antenna array, and this effect can directly lead to the distortion pattern.[3] Microstrip patch antenna array is discussed in this paper as an important content. It consists of metal

patch, dielectric substrate, ground and coaxial probe, the metal patch is equivalent to parallel microstrip. Mutual impendence between two microstrip patches can be solved by MoM, and it is given by ''*21(,)(,)(,)4ij i x y x y j x y x y Z J k k G k k J k k dk dk π+∞+∞?∞?∞

=?∫∫u u r uu r (5) Where the strength of current 'J uu r is the Fourier transform of basic function J uu r

:

()'(,)(,)x y j k x k y xi x y xi J k k J x y e dxdy +∞+∞+?∞?∞=∫∫uu u r uu u r (6)

All together ()'(,)(,)x y j k x k y yi x y yi J k k J x y e dxdy +∞+∞+?∞?∞=∫∫uuu r uuu r (7)

Where, (,)(,)(,)

i xi yi J x y J x y J x y =uur uuu r uuu r And in expression (5),'''(,)(,)(,)i x y xi x y yi x y J k k J k k J k k =uu r uuu r uuu r ,'

''(,)(,)(,)

j x y xj x y yj x y J k k J k k J k k =uu r uuu r uuu r

To form a hypothesis, the magnetic permeability of air is 0μ, permittivity is 0ε, and the permittivity of

dielectric is ε, the relative dielectric constant is r ε, then 0r εεε=, the dielectric loss tan is ta n δ, then the component x x G of spectral domain dielectric layer Green function (,)x y G k k is ()222200211010()cos()()sin(),r x x xx x y e m

jZ k k k k d jk k k k d G k k k TT ε?+?=? (8) Where

222101,Im {}0r k k k εβ=?<;222202,Im {}0k k k β=?< 1121cos()sin()e T k k d jk k d =+;2111cos()sin()m r T k k d jk k d ε=+

222x y k k β=

+

;002k πλ==,2w f π=

;0Z =According to above analysis, mutual coupling between microstrip patches is represented with mutual impendence. In actual engineering, mutual coupling can be showed visually through the pattern.[4]

4. Simulation based on RWG

4.1 RWG

The first step of RWG is to divide the antenna surface into a number of triangles; the two adjacent triangles share the same edge, which constitute the RWG edge (one positive and one negative).According

1987

Rao Jia-ren et al. / Procedia Engineering 29 (2012) 1984 – 1988to RWG, the mutual coupling between two RWG edges is obtained, and then it can be represented with

mutual coupling. Here, we propose the feed voltage is 1V, phase is 0, mn ±A is used to denote induction magnetic vector potential from edge n to edge m, mn ±Φdenotes the scalar potential. Then [()()()()]422n n n n

mn n n m n n n m n T T n n l l g dS g dS A A μπ+?

±+±?±+?+∫∫A ρr r ρr r (9) 1[()()]4n n n

n

mn m n m n T T n n l l g dS g dS j A A πωε+?

±±±+?=??∫∫Φr r (10) where, ()jk c m n

m n c m n

e g ?±±±

?=?r r

r

r

r So, the mutual impendence between two RWG edges can be calculated by

[(/2/2)]c c mn m mn m mn m mn mn Z l jw ++???+=

?+?+

?A A ρρΦΦ (11) 4.2 MATLAB simulation

Linear array is adopted as an example to do simulation, the size of each microstrip patch designed in this paper is 10cm ×4cm ×2cm, and the dielectric constant is 1, five patches align along x-axis as fig.2 shows, the distance between two adjacent patches is 2cm.

(a) (b)

Figure 2: (a) Structure diagram of five patches array, (b) Current distribution of five patches array

Figure 3: (a) Pattern in yz plane considering mutual coupling, (b) Pattern in yz plane of ideal case

Based on RWG, MATLAB simulation is done. The stepping phase shifting is 0°, frequency is

4.25GHz, then the current distribution can be obtained, it given in fig.2 (b), where, the color is whiter, and the current magnitude is higher. And the far-field radiation power pattern of microstrip patch array antenna is given by fig.3.

1988Rao Jia-ren et al. / Procedia Engineering 29 (2012) 1984 – 1988

According to the calculation, in ideal case, gain of the microstrip patch antenna array is 4.8db. By using RWG and MoM, the gain of considering mutual coupling is 1.9db. According to above simulation, a conclusion can be drawn that mutual coupling effect can lead to the decline of antenna gain, and also make the practical pattern very different from the ideal pattern, or make the pattern function characteristic be worse.

5. Conclusions

Analysis of antenna mutual coupling always needs some electromagnetic numerical algorithms. MoM is a common one. There RWG methods divide the antenna surface into a number of small triangles, by this way we can analyze the current distribution and pattern function characteristic of all kinds of antenna, so it is benefit for the analysis of mutual coupling, and that algorithm is accurate.

By introducing the MoM and RWG methods to quantitatively analyze the pattern function characteristic of microstrip antenna array, comparison between the ideal pattern and the pattern considering mutual coupling is made, and it is proved to have a big difference between them, the most obvious influence is that the antenna gain declines when mutual coupling exists in any case, of course there are some other influences, the mutual coupling effect may also give rise to side lobe level raise. By these ways, we can learn that the pattern function characteristic of microstrip patch antenna array accurately which lays a good foundation for the compensation of the mutual coupling.

References

[1] Zhang Qing, Zong Peng. Analysis of array’s direction characteristics of mutual coupling based on RWG. Modern Radar, 2010,32(6): 73-76.

[2] Hoi-Shun LUi, Han Tat Hui, Mook Seng Leong. A note on the mutual-coupling problems in transmitting and receiving antenna arrays. IEEE Antennas and Propagation Magazine, 2009, 51(5): 171-176.

[3] Ramesh Garg, Prakash Bhartia , Inder Bahl. Microstip antenna design handbook[M]. Londn: Arech House,2001.

[4] Mark S. Gatti, Robert Navarro, Andre Jongeling. Arraying performance of a 3-Antenna demonstration array for deep space communications. IEEEAC, 2010, 1-10.