# Multilayer Microstrip Equivalent Antenna Analysis using Finite Difference Time Domain Method

DOI : 10.17577/IJERTCONV4IS24005

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#### Multilayer Microstrip Equivalent Antenna Analysis using Finite Difference Time Domain Method

P. Elamaran*

Department of ECE,

University college of Engineering Pattukkottai, Thanjavur, Tamil Nadu, India.

G. Srivatsun

Department of ECE,

P.S.G College of technology, Coimbatore, Tamil Nadu, India.

Abstract:-Microstrip equivalent antenna used in radio communication is presented. Finite difference time domain (FDTD) method is used for analyzing microstrip antenna which is based on multilayer multipermittivity dielectric substrate. FDTD method is used for modifying equivalent iterative formula in the condition of cylindrical coordinate system. The mixed substrate which consists two kinds of media (one of them is air) takes the place of original single substrate. The results ofmicrostrip equivalent antenna simulation show that the resonant frequency of equivalent antenna is similar to that of the prototype original antenna. The validity of analysis can be validated by means of antenna resonant frequency formula. The radiation pattern of two antennas show that same radiation pattern and gain. This method can be used to reduce the weight and increase the efficiency of compact antenna, which is significant to the design of missile-borne antenna in military applications.

Keywords-Microstrip antenna; FDTD; multilayer; military applications.

1. EQUIVALENT ANTEENA STRUCTURE AND FDTD ANALYSIS

In1966, K.S. Yee introduced the theory of FDTD [5].FDTD is a novel method which can be used to intuitively and succinctly explain the Maxwell's equations. In this method, the electric field and magnetic field are included in a three-dimensionalModel (Yee cell). This model is used for solving all the problem of electromagnetic field. A circular antenna is easily integrated into a warhead of bomb compared to rectangle antenna. So the formulae in References [6,7]should be amended in the cylindrical coordinatesystem (see Fig. 1).

1. INTRODUCTION

In recent years, antenna has been important module for military antennas [1,7]. Particularly for missile- borne antenna which required to be small in size and light in weight. The microstripantenna [2] has many advantages, such as, small size ,light weight and planar structure. Many work has been doneon its miniaturization [3,4].But few research concentrated on decreasing the weight of antenna and leaving its basic parameters unchanged under the conditions of same size and thickness.

In this work, another model design is proposed. The aims of this work are: a) to conserve the shape of

Fig. 1. Yee cell.

+1 ( + 1 , , )=2 ( + 1 , , )

antenna; b) to conservethe of antenna electromagnetic

2

2+ 2

parameters; and c) to decrease the weight of antenna. For

1

+ 1 1

1

+ 1 1

this, a substrate with low permittivity and high dielectric permittivity media is taken the place of the original substrate, in which air is used as a lower dielectric

+ 2 Ã— [

2+

2(+2,+2,) 2(+2,2,) (+1)

2

2

+ +

+ +

1 1

permittivity media (high dielectric permittivity media can be any mediaas its dielectric permittivity is higher than original media). The introduction of the air media can effectively decrease the weight of antenna in proposed model. The analysis of equivalent antenna is based on FDTD.

2(+1,,+1) 2(+1,,1)

2 2 2 2

2 2 2 2

].(1)

+1

1 1 2

1 1

1

+ 1 1

+1 1 1

2 (, +

, + ) = 2 (, + , +

2

2(+2,+2,) 2(+2,2,)

2 2 2+ 2

2 + [

(+1)

(,+1,+1)(+1,,+1)

2

1) 2

[

2 2 2

2 2+

+1 1

1

)

)

1 + 1 1

1

1

2(+2,,+2) 2(+2,,2)]

(,+2,+1)(,+2,)](2)

Equations(1) and (2) are electric and magnetic fields equation for Yee cell.

Two medium exist in Yee grid (the permittivitys are r1; r2).From Ampere circuital theorem, we have,

(8)

After the simplification, the equivalent permittivity can be obtained

+

= + (3)

= 11 1

1

1+ 12 1

1 2

Assuming that the magnetic conductivities of two dielectric media are the same. It can be known from the

(9)

boundary condition of electromagnetic field that the normal component of magnetic field on the Interface between the two media is continuous, in cylindrical coordinate system [8]; Equation (3) could be rewritten as

r

r

Hdl = Hn+0.5(i, j + 0.5, k)r

Through the analysis mentioned above, the structure of antenna substrate can be designed, as shown in Fig. 2.

In FDTD iteration,

Hn+0.5(i, j + 0.5, k)r

r

r

Hn+0.5(i, j 0.5, k)r

+ Hn+0.5(i, j + 0.5, k) . . . (4)

+1

1 +1

2(, , ) =

2 [ (, , ) + (, , )](5)

The right hand side equation (5) can be extended to

Fig. 2. Structure of substrate.

=

=

=1

=1

2. DISCUSSION OF SIMULATION

(,,)

(,,)

+1(,,)

Ã— [11111 +

](6)

Through the above analysis, FR4 substrate is

12 1

12..+

chosen for original substrate. The basic parameters of antenna are r= 4:4, R =14 mm, h =2 mm, r= 12 mm.

=

=1 =1

+1(, , )

Equation (10) shows the relationship between two medium.Fig.3 shows the prototype antenna design. Table 1 lists the parameters of equivalent antennas.

= (,,)

2 + 2 = 2

2 1 1

2 2

Ã— 111111

+ [12112

+ ]

(7)

1+2=R (10)

 r1 r2 R1 R2 A 12.8 1 8.56 6.42 B 9.7 1 9.8 5.0
 r1 r2 R1 R2 A 12.8 1 8.56 6.42 B 9.7 1 9.8 5.0

Substituting equations (4), (6) and (7) into Eq. (3), we have,

+1 1

2

( + 2 , , ) =

2+ ( +

1 , , ) +

2

TABLE 1: PARAMETERS OF EQUIVALENT ANTENNAS

Fig .3.Prototype antenna design

Fig. 4 shows that the resonant frequency of original antenna is 3.2 GHz, and the resonant frequencies of the equivalent antennas A and B are also remain unchanged. It can be concluded from the resonant frequency formula that the permittivity is the only factor which has effect on resonant frequency when the radius of radiation patch and the working mode remain the same. So two media can be treated s a singlemedium which has a same permittivity as that of original medium. The results prove the accuracy of FDTD analysis. Because the position of feed point was not changed in simulation, the S11 parameters of the equivalent antenna deteriorated compared to the original antenna. So the equivalent antenna is not exactly equal to the original antenna.

Fig. 4.Resonant frequencies of three antennas.

The parameters can be improved by changing the position of feed point. Fig. 5 shows the S11 parameters after changing the position of feed point.

Fig. 5.S11 with different feed feint.

Fig. 6 and 7 show the radiation patterns of equivalent antenna and original antenna. It can be seen from Fig. 6 and 7 that the direction and co polarization of equivalent antenna are similar to those of the original one. This shows that the equivalent antenna can replace the original antenna.

3. CONCLUSION

A method for decreasing the weight of antenna was proposed in the paper. By means of analysis based on FDTD, air medium and a higher permittivity medium are introduced to take the place of original substrate. The simulation results show that resonant frequency, radiation pattern and gain of equivalent antenna did not change. The air media can be used to reduce the weight of antenna.

REFERENCES

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4. Yee KS. Numerical solution of initial boundary value problems involving Maxwell equations in isotropic media. IEEE Trans Antennas Propagate 1966; 14(3):302e7

5. Taflove A, Hagness SC. Computational electrodynamics: the finite difference time domain method. 2nd ed. Norwood, MA: ArtechHoose; 2000.

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9. yun-xing yang, hui-changzhao*, cui di. analysis of equivalent antenna based on FDTD method, elsevier b.v.,2014