Analysis of the dual-polarised patch antenna and two-element array by FDTD

X.X. Yang, S.S. Zhong and G.Q. Zhao

Abstract: The effects of a dual-polarised patch antenna’s structure parameters, such as the width of the feedline, the relative dielectric constant and the depth of the substrate, on the antenna resonant frequency, reflection coefficient and isolation are analysed by means of the FDTD method. The different effects of the structure parameters on the two-element array are compared with that of individual elements. The changes in the array’s coupling with the antenna parameters are also studied by means of the FDTD method.

1 Introduction

Many modern communication systems and remote sensors need dual-polarised antennas with high purity of polarisa- tion to save limited frequency resources and to optimise the whole system. Microstrip antennas have been used in these applications because of their low profile, light weight, small bulk and ease of manufacture and suitability for use in antenna arrays [l-31. Microstrip antennas are usually used as arrays due to the elements’ low gain and in order to obtain the required directivity. Coupling of the array is an important factor to be considered in the process of practical design. Over-coupling may induce mismatch of the antenna’s feed points and cause deteriora- tion of the patterns, gain and purity of polarisation. The preferred dual polarised element is the square patch fed at the centre points of orthogonal edges [4]. However, the effects of the array’s structure parameters on the antenna’s characteristics are different from the effects of the individual elements. This is an important factor for the practical design.

The traditional methods of analysing the elements and the arrays of patch antennas are the transmission theory [5] and the cavity model [6]. The former assimilates the patch to two slits and the latter regards the patch as a cube cavity with magnetic walls all around and electric walls up and down. Both methods obtain analytical expressions under the condition of approximating the patch to a one- or two- dimensional structure whle neglecting the width of the slits and the surface wave, etc. Hence the precision of the expression is poor to some degree and not sufficient for many practical utilities. The Green’s function method [7] and the extended multi-port network method [SI are based on the cavity model, and furthermore, are not convenient to investigate array coupling.

0 IEE, 2002 IEE Proceedings online no. 20020577 doi: IO. 1049/ip-map:20020577 Paper first received 4th September 2001 and in revised form 15th April 2002 X.X. Yang and S.S. Zhong are with the School of Cominunication and Information Engineerins, Shanghai University, 149 Yanchang RD, Shanghai 200072 , People’s Republic of China G.Q. Zhao is with the School of Technology, Shanghai Jiaotong University, Shanghai, People’s Republic of China

Another effective method is full-wave analysis. The finite- difference time-domain method (FDTD) is a new and agile full-wave analysis method. Wide frequency band sweeping can be obtained by one time calculation. To our knowledge, there are very few reported studies of the dual-polarised patch element and array using the FDTD. In ths paper, in- depth investigation is made of the dual-polarised patch antenna and two-element array using the FDTD written in Fortran. The calculated data are compared with published data and with measured data.

2 numerical FDTD model

Theory of dual-polarised patch antenna and the

The dual-polarised patch antenna and two-element array are shown in Figs. la and lb, respectively. For the element, a pair of orthogonal polarised operating modes, TMol and TMlo, having equal amplitude and co-phase, is excited when the square microstrip patch is fed at the centre of adjacent edges. The principle of operation is equivalent to a four-port network. As shown in Fig. IC, SI, and S22 are the reflection losses of the input, S21, and S12 are the isolations of two inputs, and S4, and SQ are the cross-polarisations of the radiated wave. A dual-polarised antenna with good performance should have an excellent input impedance matching network (low Sll and S22), high isolation between the two input ports (low S2, and SI2) and low cross- polarisation of the pattern (low S,, and S32). For the array, low coupling is a further important parameter, S,, in Fig. 16, and is usually denoted C,.

The antenna structure is modelled by means of Yee’s grid [9]. The width of feedline and impedance matching network are modelled by subgridding [lo] in order to adapt the fine structure of different microstrip lines and to improve the numerical precision. Zhao’s excitation source is adopted Ell]. The source plane is placed several grids before the boundary to avoid the transformation from the electric wall to the absorbing boundary, while good numerical precision is gained and CPU time is saved.

The Gaussian pulse in the + z direction (referring to Fig. 14 used as the exciting source has the following expression:

IEE Proc.-Microw. Anfennus P K ~ K J . Vol. 149, No. 516, OctoberlDecember 2002 21 5

I P port 1

-

meas, port 1

I 1 port 1 I I

port 5

a b

polarisation 1

2 'ATE{ polarisation 2

C d

Fig. 1 lence u Element b Two-element array c S-parameter equivalence d Reference co-ordinate

Dud-polurised patch antennu und the S-purumeteer equivu-

Yee's FDTD equation on the source plane is corrected to

where At is the time step, Ax, dy and Az are space steps in the x, y and z directions respectively, the superscripr n is related to time and i, j and k a r e the locations of the :space co-ordina te.

To ensure stability of the numerical calculation, the following criterion must be satisfied.

(3)

where c is the velocity of light. Hence the coarse and fine regions have different spatial and time increments.

The absorbing boundaiy condition (ABC) ha:j an important role in the FDTD method. It determines the precision and usability of the result. Here, The ground plane is assumed to be an ideal conductor. The other five planes in air are truncated by Liao's second-stage ABC [ 121:

We have not found an effective method to simulate the interface of different substrates. Experience indicates that the relative dielectric constant at the air/substrate interface is corrected as:

( 5 ) 1 + E , .

8: = ~

2 The frequency characteristics of the S-parameters of the dual-polarised element and array can be obtained from the ratio of the FFT of the corresponding port's voltage-time wave form:

3 Numerical results

3. I Dual-polarised patch element The dual-polarisation element was built on a home-grown PTFE substrate with 0.8 mm thickness and 2.78 relative dielectric constant. The square patch antenna has an edge length of 15 mm and feedline length of 0.6". The patch is gridded as Ax= Ay = 0.3 mm, Az= 0.2mm. Time step At 0.333 ps. The width T of the Gaussian pulse is 10 ps. The subgridding method is applied on the microstrip feedline and the quarter wavelength impedance converters with Ax = 6 Ax' and Ay' = 6Ay.

The frequency characteristic of the reflection loss SI 1, is plotted in Fig. 2. The measured SIl, of port 1 at 6.06Hz resonant frequency is -35dB and that of port 2 at 5.99GHz is -24.6dB while the calculated value at 6.0 GHz is -40 dB, which shows that the input impedance matchng network of port 1 is better than that of port 2. The frequency characteristic of isolation S2, is shown in Fig. 3, which shows good agreement between measured and calculated data. The measured 365 MHz bandwidth reduc- tion at -30dB indicates that this kind of dual-polarised antenna has high isolation. At the same time, SIl of the

0

-1 0

B " -20

Q -30

-40

meas, port 1

4 5 6 7 8 frequency, GHz

Fig. 2 Frequency characteristic of SI,

-25 m

LY

D - -35

-45

Iy; . . : :

4 5 6 7 8 frequency, GHz

(4) Fig. 3 Frequency churucteristic of S,, + T;34(xm - 4dx, t - A t )

276 IEE Proc.-Microw. Antennas Propag Vol. 149, No. 516, OctoberIDecember 2002

0

0 -

-4

m -

(n= -8

-12

u

-2

-

-

-

-4

m 9 -6

6 -

-8

-10 1 -m- W=l .E mm

-12 ' I I I

4 5 6 7 8 frequency, GHz

Fig. 4 widths W

Frequency characteristic of S I I with d ~ e r e n t feedhilie

-5 r

c? -35 I I-&- W=l.8 mm I - - - W=2.4 mm

-45 t -55 I I I I I

4 5 6 7 8 frequency, GHz

Fig. 5 Frequency characteristic of S,, with dijferent feedline widths W

2 r I

-1 6 1 3 5 7 9 11

frequency, GHz

Fig. 6 Frequency characteristic of SI1 with dijjhrent c,

0 -

-5 -

-10 - m -

+h=2 0 mm

U

-15 -

-20 -

0 -

-5 -

-10 - m U -

-15

-20

-25 I I I I I , I

2 4 6 8 10 frequency, GHz

Frequency characteristic of S,, with dgferent depths h Fig. 7

single polarised patch was calculated and nearly coincides with the solid line in Fig. 2, which shows that another feed port has little influence on the input impedance and resonant frequency of the patch. In other words, this dual-polarised element has high isolation.

Investigations were then made of the effects of design parameters on the dual-polarised patch element with the input impedance matching networks left out. When a given parameter is analysed, the other parameter values remain unchanged.

Fig. 4 plots the frequency characteristics of the reflection loss SI, for different feedline widths W. It can be seen that SI I increases as W increases. However, W has no effect on the centre frequency, 6 GHz, and the -3 dB bandwidths are nearly the same. For example, SI, is -9.7dB for W=0.6mm and -4.1 dB for W= 2.4". The isolation S,, of the dual ports is shown in Fig. 5. For all widths W, the minimum points of S,, occur at the centre frequency and bandwidths at -25 dB are all about 500 MHz.

The significant effects of different E,. on the SI1 values of an element are shown in Fig. 6. With increasing E,., the resonant frequency decreases and the relative bandwidth narrows, which shows the strong resonant trait of the microstrip patch with high relative dielectric constant E,. A patch with high E,. can excite higher order modes. For example, the centre frequency Jb of a patch with E,. = 9.6 is 3.38GHz, while 6.76GHz is the resonant point of the higher mode. Numerical results show that E,. has little influence on the isolation of the dual port at the centre frequency.

Fig. 7 shows the frequency characteristics of SII with different substrate depths. As the thckness increases, the centre frequency decreases and SI I becomes lower. It is also found that a thicker patch has a broader bandwidth, and this is of relevance in engineering applications.

is plotted in Fig. 8. lsolation becomes worse as thickness increases. S,, of the patch with thickness 0.8 mm is -35.2 dB but that for thickness 3.0" is -2.75 dB.

The effect of substrate thickness on

-10 .

e -20 7

G ? .

-30 - h= l 4 mm -h=2 0 mm

- 4 0 1 i ~ 1 1 q ~ t ~ l ~ 1 3 5 7 9 11

frequency, GHz

Fig. 8 Frequency cliaracteristic of'& with d#crent depths h

3.2 Two element array First, the coupling coefficient C, of the linear polarised two- element array in [13] is calculated by means of the proposed FDTD program. Its frequency characteristic is shown in Fig. 9. It can be seen that the FDTD result is close to the measured one and better than the analytical result presented in [ 131, which indicates that the three-dimensional numerical modelling of FDTD is more precise than the two- dimensional theoretical approximation.

This FDTD program is applied to the two-element array of Fig. lb. The element's parameters are the same

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-1 0 calc., [13]

1 3 5 7 9 11 frequency, GHz

Fig. 9 Coupling of two-element array against frequency

0

-2

m

6 U : -4 .... W=l.2 mm

-I- W=l.8 mm

-8 I 8 1

3 5 7 9 11 frequency, GHz

Fig. 10 Array frequency characteristic of SI* with diflerent feedline widths W

previously. The excitation source is located at port 1 while S5, is the coupling coefficient, C,. The different effects of the array’s characteristics from those of the element and the array coupling are described in the following paragraphs.

The frequency characteristic of SI, of the array at different feedline widths is plotted in Fig. 10. It can be seen that the resonant frequency increases with increasing feedline width, which is very different from the beha.viour of the element. Furthermore, the array’s reflection loss SI is higher than that of the element.

The frequency characteristic of the array’s Sll with different relative dielectric E, is plotted in Fig. 11. The interaction between two elements excites other resfonant frequency points, such as 3.3 Ghz for an E, of 1 . I and 9.6 GHz for an E, of 4.2. Furthermore, the array’s reflection loss SI1 is hgher than that of the element.

-12 8 1

2 4 6 8 10 frequency, GHz

Fig. 17 Array frequency characteristic of S I I with dfferent E,

The frequency trend of the array’s SII with different substrate depths h is the same as that of the element apart from the fact that the former is higher than the latter.

In summary, the reflection loss of the array is higher than that of the element and the width of the feedline influences the array’s resonant frequency while it has no influence on that of the element.

Numerical experiments also show that the distance D between elements has almost no influence on reflection loss SI, and the centre frequency, but too short a distance excites other oscillating frequencies near to the centre frequency.

Maximum coupling of the array is not encountered at the centre frequency but at a point soinewhat higher. Coupling decreases with increasing D, as shown in Fig. 12. It can be seen that coupling decreases rapidly from -30 dB when D is greater than the length of the patch. From compactness of the array considerations, a D of about 0.7 A. is acceptable.

* .~ , -4:bl-2: , , , -1: , , , 60

2.1

1.8 50

-45 -1 5 -5

60

- 50 1.84

-42 -40 -38 -36 -34 -32 -30 Cp dB

Fig. 12 coupling

Effects of element disttrnce D and feedline width W oil

The influence of feedline width W on coupling is also plotted in Fig. 12. With widening of W from 0.6” to 2.4mm, the coupling decreases by about 8.5dB. Hence a larger W is preferable, neglecting other factors, such as the radiation of the microstrip line.

The numerical test also shows that depth h has a little effect on coupling. Increasing h from 0.8 mm to 2.0 mm increased coupling by about XdB.

4 Conclusions

The effects of dual-polarised patch antenna structure parameters, such as the width of the feedline, the relative dielectric constant and the depth of the substrate, on the antenna resonant frequency, reflection coefficient and isolation have been analysed in detail by means of the FDTD method. The different effects of the structure parameters on the two-element array are compared with their effects on the element. The influences of antenna parameters on the coupling of the array are also studied. Numerical experiments show that feedline width has little effect on centre frequency and isolation but a large effect on reflection loss. The relative dielectric constant E, strongly influences the centre frequency fo and bandwidth BW: with increasing E,, fb and B W decrease. The effect of substrate depth h is obvious: with increasing h, fo minimises, SI1 reduces and B W increases.

For the two-element array, coupling decreases with increasing element distance D, and decreases rapidly when D is wider than the edge length of the patch. The feedline width W influences the array’s resonant frequencyfo, which

278 IEE Proc.-Microw. Antennus Propciq. Vol. 149, No. 516, OctobedDeceniber 2002

increases as Wincreases. The array’s reflection loss is higher

Further work involves investigating the characteristics of

6 RICHARDS, W.F., Lo, Y.T., and HARRISON, D.D.: ‘An improved theory for microstrip antennas and applications’, IEEE Trans. Antennas Propag., 1981, 29, (l), pp. 3846

7 YANG, x.x., and ZHONG, s.s.: ‘Analysis of two dual-popdrization square-patch antennas’, Microw. Opt. Technol. Lett., 2000, 26, (3), nn. 153-156

than that of the element.

the radiated fields and extension to multi-arrays.

5

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4

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