# Accurate original synthesis model for microstrip antennas with automatic choice of the shape versus physical and geometrical criteria

Jean-Marc Ribero, Jean-Pierre Damiano, Robert Staraj

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Jean-Marc Ribero, Jean-Pierre Damiano, Robert Staraj. Accurate original synthesis model for microstrip antennas with automatic choice of the shape versus physical and geometrical criteria. Journées Internationales de Nice sur les Antennes (JINA 94), Nov 1994, Nice, France. pp.589-592. hal-04386846

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# ACCURATE ORIGINAL SYNTHESIS MODEL FOR MICROSTRIP ANTENNAS
## WITH AUTOMATIC CHOICE OF THE SHAPE
## VERSUS PHYSICAL AND GEOMETRICAL CRITERIA

J.-M. Ribero, J.-P. Damiano, R. Staraj

Laboratoire d'Electronique - Université de Nice-Sophia Antipolis
URA CNRS 1400 - 250, rue A. Einstein, 06560 Valbonne, France
Tel: + 33.92.94.28.00 - Fax: +33 92.94.28.12

Topic: microstrip antennas

## Abstract

We present an accurate and original synthesis model applied to multilayer probe-fed microstrip antennas. We have developed an original modified Wolff cavity model to obtain, with a low computing time, the optimal size and the shape of the antenna, versus the physical and geometrical parameters, necessary to a good approach. Unpublished results for elliptical and annular ring antennas are presented. We show and discuss numerical and experimental results for different synthesis.

## 1 Introduction

These last years, a great number of models have aimed at determining the electrical characteristics of printed antennas of various shapes with a good agreement with experiments and other rigorous investigations. However, at our knowledge, a synthesis model for multilayer probe-fed microstrip antennas with or without an air-gap taking into account the shape of the element has not been yet published.

We show, figures 1 and 2, the different studied structures. An air-gap enables to obtain exactly the resonant impressed frequency [1,2], the dielectric cover can offer protection against environmental hazards (ice, snow for example) [3 - 5], the ring microstrip antenna can be proposed for dual band operation [6 - 8], and the eccentricity of the elliptical antenna allows us to obtain a wider frequency band and the desired resonant frequency [9 - 11].

For all these reasons, we propose an original synthesis. The analytical model introduced in the synthesis, takes into account all of this parameters and the advantages and drawback of each shape and proposed the best structure possible for each case. Electrical criterias like bandwidth, quality of polarisation, circular polarisation or efficiency versus the shape of the element are associated concurrently with geometrical and physical parameters.

## 2 Symbolic approach

Our theoretical study is achieved from a modified Wolff model [11]. The boundary conditions are taken into account using dynamic permittivity including physical and geometrical parameters and fringing field effects. The calculation of the dynamic edge capacitance is required. It consists in considering the

radiating element as an open microstrip line for which a variational expression of the characteristic impedance allows us to take into account the multilayer lossy structure. The input impedance is determined using one or two equivalent electrical circuits.

The closed-form expressions for the resonant frequency and the input impedance allow us to work in synthesis. For example, the dielectric substrate being given and a set of physical criteria being known, it is easy to compute the dimensions of the patch and the optimal position of the feed to obtain a real part of the impedance equal to 50 Ω, for the impressed resonant frequency.

For example, a microstrip antenna destined to be integrated in an array structure with a small distance between radiating source, should be as small as possible to limitate the coupling effects. Other criterias, like the desired bandwidth, or the resonant frequencies of the superior modes must be taken into account too.

Table 1 gives the performance of modeling. The synthesis was carried out using Quick Basic on 486 DX2 computer. The different calculations were obtained in few seconds.

<table><caption>Table 1: Performances of the modeling
++: excellent +: good -: medium</caption><thead><tr><th>Characteristic</th><th>□</th><th>○</th><th>▷</th><th>○</th><th>○</th></tr></thead><tbody><tr><td>Accuracy</td><td>+</td><td>++</td><td>-</td><td>+</td><td>++</td></tr><tr><td>Calculation time</td><td>++</td><td>++</td><td>+</td><td>+</td><td>-</td></tr></tbody></table>

Table 2 gives a fast view of the advantages that we can expect of each shape, i.e. a large bandwidth at SWR = 1.5, easy circular polarisation.

<table><caption>Table 2: Advantages of each shape</caption><thead><tr><th>Shape</th><th>□</th><th>○</th><th>▷</th><th>○</th><th>○</th></tr></thead><tbody><tr><td>Bandwidth</td><td>-</td><td>+</td><td>-</td><td>+</td><td>+</td></tr><tr><td>Circular Polarisation</td><td>-</td><td>+</td><td>-</td><td>-</td><td>+</td></tr><tr><td>Use of Superior modes</td><td>+</td><td>+</td><td>-</td><td>-</td><td>++</td></tr><tr><td>Metallic relative surface required</td><td>1.85</td><td>1.85</td><td>1.35</td><td>1.46</td><td>1</td></tr><tr><td>Total relative surface required</td><td>1.4</td><td>1.4</td><td>1.01</td><td>1.1</td><td>1</td></tr></tbody></table>
## 3 Results

We present figure 3, the theoretical variations of the characteristic size of the radiating element versus the impressed resonant frequency, for different well-known shapes. For each shape, we indicate the given dimension, for example, disc: diameter 2a, ellipse: the major axis 2a (eccentricity e = 0.745). The ratio for the ellipse (a/b) is equal to 1.5 and for the annular ring r2/r1 = 2. The annular ring takes less space than the others shapes. We have a very good agreement with experiments.

The figure 4 shows the case of an annular ring with a dielectric cover for the first two resonant modes TM11 and TM21. We give the theoretical ratio (r2/r1) versus the desired frequency for r1 = 5 mm and 10 mm. We can notice that the ratio r2/r1 decreases strongly for a small variations of the resonant frequency. Moreover we can choose, according to our specifications, the ratio that we want at a given frequency.

To validate our model of synthesis, we present, for an elliptical radiating element, figure 5 the experimental and theoretical variations of the real part of the input impedance versus frequency. The feed-point (XF) is located at 20 mm from the center. The agreement is excellent. These results are presented for the first time, indeed only the study of resonant frequency was published [10].

The algorithm gives for example the feed position for the desired real part of the input impedance of the ellipse (figure 6).

We show figure 7, for different thickness of air-gap, the variation of the eccentricity e versus the half minor axis b of the ellipse. The bandwidth increases with increase the thickness Ha, for example, for Ha = 0 mm we obtain a bandwidth(BW) equal to 1.6 % (SWR = 1.5) and for Ha = 5 mm BW = 8.9%.

<figure><img src="image_2.png" /><figcaption>Figure 1: Multilayer microstrip antenna</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Figure 2: Various shapes</figcaption></figure>

## 4 Conclusion

We have presented an original synthesis model for multilayer microstrip antennas of different shapes. We have shown that we can determine, when a set of desired parameters is known, the optimal shape and size of microstrip patch to choose.

The knowledge of the advantages and inconveniences of each shape are very important points for synthesis or CAD models. The comparison between theoretical and experimental results shows a very good agreement. Some entirely unpublished results as regards the annular ring and ellipse.

<figure><img src="image_4.png" /><figcaption>Figure 3: Variations of the synthesis size of the radiating element versus resonant frequency</figcaption></figure>

* ○: 2a, △: a, ○: 2r, □: a, ⊙: 2r²
<figure><img src="image_5.png" /><figcaption>Figure 4 : Ratio r2/r1 of annular ring with dielectric cover for TM11 and TM21 versus resonant frequency</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Figure 5 : Real part of the input impedance of ellipse versus frequency</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Figure 6 : Real part of input impedance versus the fed-position for the ellipse</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Figure 7 : Variations of eccentricity for different thickness of air-gap versus half minor axis b of the ellipse</figcaption></figure>

## References

[1] F. Abboud, J.P. Damiano, A. Papiernik, "A new model for calculating the input impedance of coax-fed circular microstrip antennas with and without airgaps", *IEEE Trans.*, 1990, vol.AP-38, pp.1882-1885

[2] J.P. Damiano, A. Papiernik, "A simple and accurate model for the resonant frequency and the input impedance of printed antennas", International Journal of Microwave and Millimeter-Wave Computer-Aided Engineering, 1993, vol.3, n° 4, pp. 350-361

[3] G. Shuxi, M. Yukuan, Z. Shunshi, "The accurate calculation of resonant frequencies of covered circular microstrip disk antennas", *Int. Symp. on Antennas and EM theory*, (ISAE 85), Beijing, China, Aug. 85, pp.205-210

[4] A. K. Bhattacharrya, "Characteristics of circular patch on thick substrate and superstrate", *IEEE Trans.*, 1991, vol. AP-39, No. 9, Sept. 1991, pp.1338-1341

[5] A.K. Verma, Z. Rostamy, "Modify Wolff model for determination of resonance frequency of dielectric covered circular microstrip patch antenna", *Electron. Lett.*, 1991, vol. 27, n° 24, pp.2234-2236

[6] J. Vrba, "Dynamic permittivity of microstrip ring resonator", *Electron. Lett.*, 1979, vol.15, n°16, pp.504-505

[7] A. Das, S.K. Das, "Input impedance of a probe excited circular microstrip ring antenna", *IEE Proc.*, 1985, vol.132, Pt.H, No. 6, pp.384-390

[8] Z. Fan, K.-F. Lee, "Input impedance of Annular-Ring Microstrip Antennas with a Dielectric Cover", *IEEE Trans.*, 1992, vol.AP-40, No. 8, Aug. 92, pp.992-995

[9] M. C. Bailey, M. D. Deshpande, "Analysis of elliptical and circular microstrip antennas using moment method", *IEEE Trans.*, 1985, vol.AP-33, No. 9, pp.954-959

[10] S.R. Rengarajan, "Resonance frequency of elliptical microstrip antennas", *Electron. Lett.*, 1993, vol.29, n°12, pp.1066-1067

[11] R. Staraj, J.P. Damiano, "Simple CAD model for the analysis of disc, elliptical and various ring multilayer microstrip antennas", *ICEAA*, Turin, Italy, Sept. 93, pp.431-434