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Top1. Introduction
The study of microstrip patch resonators has made great progress in recent years. Compared with conventional antennas, microstrip patch resonatos have more advantages and better prospects. They are lighter in weight, low volume, low cost, low profile, smaller in dimension and case of fabrication and conformity (Sidharath & al, 2013). Over the last two decades, microwave resonators have become an important subject of interest, they were introduced in 1972 (Howell, 1972) and were used in a variety of applications including sensors, filters, oscillators, frequency meters and tuned amplifier (Pozar, 1990). Resonator elements based on microstrip technology are conformable and have minimized shape, low weight and cost. Hence, they are commonly used in many commercial applications in the industry, such as mobile satellite communications or direct broadcast satellite services, but also as nondestructive testing sensors for material evaluation.
Patch resonator performances, such as resonant frequency and quality factor, are strongly dependant of the dielectric parameters of the different materials involved in their structure. In microwave systems applications, dielectrics for substrate and superstrate are realized with very low losses materials to obtain the best performances. When used as sensors, some of the dielectric layers can be constituted with unknown material; the change in the resonator parameters, mainly frequency shift and increase of the quality factor, are related to the complex permittivity of this unknown material. In this particular application, a patch sensor may be used to assess permittivity of particular layers by comparison between patch measured parameters with a reference structure and those obtained with the unknown material. Accuracy between modeling of the structures and measurements data is strongly necessary to obtain, by solving the inverse problem, good values of the dielectric parameters of the unknown material, or to highlight local variations of the dielectric permittivity.
Microwave sensors can be designed and according to the given specifications can take any form and shapes. In many applications the microwave sensor is in the form of a patch resonator. Some of these resonators were fabricated onto substrate or onto multilayer substrate. In order to accurately predict the characteristic of these resonators, several methods of analyses were employed. In most applications, the analyses require to solve the electromagnetic fields in each layer (Wan Ali, 2003).
This paper presents a theoretical development backed with experimental work, it is focused on the exhaustive comparison between a theoretical modeling of a Rectangular Patch Resonator (RPR), Electromagnetic simulations with commercial software's and measurements on selected structures. RPR's have been studied extensively using rigorous full-wave analysis and various types of current expansion functions (Bouttout & al, 2000, Newman & al, 1987, Tounsi & al, 2006). The proposed theoretical analysis is based on the Moment Method (MoM) which is considered as a standard procedure to solve problems (Essid & al, 2009, Hassani & al, 2008, Mittra & al, 2008, Liu & al, 2009) such as the fundamental quantity of interest, namely the electric current distribution on the patch surface, from which all the other required resonator parameters can be obtained (Bouttout & al, 2000, Mathis & al, 1998). In the literature, three types of entire domain basis functions are widely used to expand the patch currents. While, the first two types of basis functions involve a set of sinusoidal cavity modes without edge conditions (sbf-wo-ec) (Mathis & al, 1998, Wong & al, 1993) and with edge conditions (sbf-w-ec) (Wong & al, 1993), and in order to incorporate the edge conditions (cp-ec), the third one consists of Chebyshev polynomials combinations with weighting factors (Row & al, 1993). The accuracy of these theoretical results has been compared with electromagnetic simulations with HFSS and CST software's and previous published works.
Four RPR prototypes have been realized with different substrate thicknesses, with and without superstrate. In order to quantify the effects of the results dispersion due to the real physical dimensions of the resonators, all their dimensions have been carefully measured. These values have been introduced for comparison in the EM simulators as a new set of parameters. This procedure gives an estimation of the variation of the results due to geometrical dimensions of the resonators.