ANALYSIS OF MICROSTRIP PATCHES ANTENNAS ARRAY BY USING A NEW BOND GRAPH TECHNOLOGY

This study is the only one that combines the micros trip patch antennas representing the microwave doma in and the bond graph technique representing the autom atic domain. In this study, we propose a new methodology to analyses the microstrip patch antenn as arrays: It is the bond graph technique and the w ave scattering formalism. This method helps us to achie ve our purpose which is to improve the analysis and comprehension of patch antenna arrays as the result s fo nd show.


INTRODUCTION
Recently, microstrip patch antennas arrays have become a research topic among researches for the development of a new wireless communication technology. The highest gain of this type of antennas could be achieved by using a limited number of patch characterized by low profile, low volume, light weight and low fabrication cost. Moreover, this antenna has a planar configuration which can be mounted easily on all surfaces Ambresh et al. (2010). In this study, we propose the bond graph approach because this latter seems a very powerful technique to model and analyses microwave systems Paynter (1992) It also permits us to show up the cause/effect relations in different parts of patch antenna arrays thanks to the causality assignment. At the beginning of this article, we will determine the simple and the precise electric model from the geometric measurements of one patch antenna Mehouachi et al. (2012a;2012b). Then, we will move to the construction of the bond graph of this model. After that, we will transform this last model to the reduced bond graph model to determine the scattering matrix that allows us to find the reflection and transmission coefficients. Every time, we add another patch without forgetting to solve the problem of adaptation. We have to repeat the same gait for each patch added and to decompose each model into several submodel to simplify the modeling. Finally, we will repeat simulation with the conventional method which is simulation using ADS. By the end, we will compare the results found of the two methods.

GEOMETRIC STRUCTURS PROPOSED OF PATCH ANTENNA ARRAY
We propose a linear antenna array consisting of four patches. First, we start with a single patch and we add successively another element after the simulation to obtain the best gain. The antenna is characterized by a substrate material with a thickness H = 3.2 mm, a relative permittivity ε r = 2.6, loss (tangδ) = 0.002 and it has an edge L = W2 = 36 mm Mehouachi et al. (2012a) W3 = 10 mm. Figure 1 shows a linear array consisting of n antennas deposited along the axis Ox.
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Fig. 1. Linear array antenna with n elements
Initially, we begin by determining the bond graph model of this array with four elements. To make this bond graph model rigorous, we will consider the adaptation between radiating elements using quarter-wave transformers.

Determining Model Band Graph of the Antenna 2.1.1. Model Band Graph of Narrow Microstrip Lines
There are two interests of inserting these quarter wavelength transformers between the radiating element and the feed line. The first interest is to achieve a successive impedance transformation which is necessary for adapting it to all the points in the network. The second is to perform the adaptation of the antenna 50 Ω at the excitation points Houssini (2009). Figure 2 shown a narrow microstrip lines and its equivalent electric element. Figure 3 present a bond graph model of a narrow microstrip lines.
With I is the inductive element.

Model Band Graph of Rectangular Patch
Also the rectangular patch can translate by the bond graph model shown by Fig. 4 Mehouachi et al. (2012b).
In order to determine the value of L and the parameters of the patch, we use the following Equation 1 to 11 Mehouachi et al. (2012a): x 0 is the position of the probe on the patch according to the x axis.
After taking into account the adaptation of feeding to the radiating element, the previous models help us to determine the general model of linear antenna array consists of four elements fed in series. Figure 5 shows the band graph model of this antenna.

Scattering Band Graph Model of Antenna
The bond graph is widely used for modeling the physical system which operates in low frequency. This technique is based on the exchange of energy to model and simplify complex systems. Mr Hichem Taghouti and Mr Abdelkader Mami have developped this approach in Taghouti and Mami (2009;

so that
Science Publications AJAS the bond graph becomes capable to model the highest frequency systems. The bond graph model of our antenna array is shown in Fig. 6.
We can make a decomposition of the bond graph shown above Mehouachi et al. (2012a) and the new model is shown in Fig. 7.
The reduced and causal bond graph model can be decomposed in four sub-models Taghouti and Mami (2010;2011) as shown in Fig. 8.
Each sub-model can be simplified by the reduced bond graph model with effort-flow causality Taghouti and Mami (2009). All this is summarized in Fig. 9.
For this type of reduced and causal bond graph, we will have the following matrix Mehouachi et al. (2012a); Taghouti and Mami (2012) Equation 12: The matrix H is presented by the following Equation 13 to 17: R 0 = The scaling resistance and s = The Laplace operator Hij represent the integro-differentiels operators associated to the causal ways connecting the port P j to the port P i and obtained by the general form given below Equation 18 and 19:  The equivalent model electrical of a serial array antennas consists is inspired from the electrical model of patch antenna described by Ferchichi et al. (2009). This model is represented by Fig. 10. The values of resistors, capacitors and inductors are given by the same equation used in the bond graph method.

RESULTS
The use of this new bond graph technology allows us to get the following results, which are given by the Fig. 11-18 which show reflection and transmissions coefficients of the antenna array after development a program in maple.
If we use the conventional method, we find the following results. Figures 19-26 show reflections and transmissions coefficients of the antenna array simulated under HP-ADS.
Through the previous results, we notice that the traditional method (simulations under HP-ADS) and the method of scattering bond graph have almost the same bandwidth and the same desired resonant frequency f r = 2.45 GHz. According to Fig. 11-18, we also find the coefficients of transmission and coefficient of reflection its almost identical to those simulated by the conventional method shown by Fig. 18-26.
Other hand, the physical interpretation of the above results shows that the antenna's gain is proportional to the number of patches: Using a single patch the gain is about -8.5 dB but if we use four patches, antenna's gain become at the order of -17.5 dB as shown in Fig. 17. So, we can choose the number of elements in our antenna array according to the gain we want.

DUSCUSSION
This new bond graph technology, which was started in research works of Taghouti and Mami (2010); Khamailia et al. (2013) by simple electronic circuits will be extended by applying the formula given in Equation 25 for the modeling and simulation even antennas that contains à high number of patches, contrary to the work carried out by Ambresh et al. (2010), Ferchichi et al. (2009 and others who have limited the simulation of patches antennas to HFSS or HP-ADS softwares.
We note also that the simulation time is very different between the two methods. The simulation time by using the ADS softwares is about more than 60 seconds especially if we choose a high resolution but the bond graph method takes 5 seconds.

CONCLUSION
An analysis of microstrip antenna in linear array using the method of scattering bond graph was presented and was presented and explained briefly. Results are almost the same results obtained with the conventional method but with greater precision. Furthermore, our method takes into account the exchange of power between the different elements of the antenna array. This new type of analysis enables us to get the best results in a more economical and easier way. For the simulation, we need a simple programming under Maple without the need of the HP-ADS software. The proposed method is very useful due to its simplicity, the reduced cost, reduced simulation time and the possibility to control antenna parameters. These benefits are very important in our field of study. In our future work, we will extend our method to simulate different forms of patches even those that are very complicated as array of bwe tie antenna and we will determine also their radiation pattern.

ACKNOWLEDGMENT
We would like to thank especially Prof. MAMI Abdelkader for the time and guidance given throughout the all carried out works, without forgetting the members of the unit of electronics and high frequency Science Publications AJAS circuits and all those who contributed and aided for this study in particularly LACS members (Laboratory of analysis and command systems).