Mathematical Modeling of Spherical Microstrip Antennas and Applications

Abstract

Microstrip antennas offer many attractive features and hence it is very challenging to model efficiently their resonance and radiation characteristics (Pozar & Schaubert, 1995). In particular, microstrip antennas composed of perfectly electric conducting (PEC) patches mounted on spherical surfaces possess two basic advantages against the planar ones. First, their curved shape makes them more applicable to real-world moving configurations such as missiles, satellites and aircrafts, where large plane boundaries are usually absent. Second, the frequency scanning problem encountered in case of planar microstrips at low elevations may be overcome due to the conformability of spherical antennas. Apart from these two advantages, spherical microstrip antennas offer (due to their relatively simple geometry) additional attractive features like low cost, light weight, easy fabrication as well as integrability with microwave and millimeter-wave circuits. As far as the metallic patch is concerned, circular or annular-ring ones are preferable for mounting on a spherical body. Interesting design characteristics of microstrip antennas are mainly the complex resonant frequencies, the radiation pattern and the input impedance. An extensive literature survey concerning the analysis of non-planar radiating microstrip structures, as well as the investigations of the aforementioned design characteristics is included in the classic book (Wong, 1999). The mathematical methods, developed for analyzing the behavior of a spherical microstrip, may be categorized as follows: (i) the full-wave approach implements the method of moments (MoM) to approximate the surface current on the PEC patch by means of suitable basis functions (Uwaro & Itoh, 1989; Tam & Luk, 1991; Wong, 1999, Sipus et al., 2003; Giang et al. 2005), (ii) the cavity model analysis assumes that the distance between the substrate and the radiating metallic patch is electrically small, forming a cavity into which the vector of the electric field is independent of the longitudinal coordinate (Lo et al., 1979; Luk & Tam 1991; Chen & Wong, 1994), (iii) the generalized transmission-line model (GTLM) extracts an equivalent circuit for the spherical microstrip, where the line parameters are the electromagnetic fields under the patch (Ke & Kishk, 1991; Kishk, 1993). Regarding the analysis of spherical microstrips, whose circular metallic patch is located inside a coating, composed of an arbitrary number of concentric spherical substrate and superstrate layers, an efficient approach for the analysis of the related resonance and radiation characteristics has been proposed in (Valagiannopoulos & Tsitsas, 2008a; Valagiannopoulos & Tsitsas, 2008b). The generic structure of that microstrip configuration