Microstrip Antennas Conformed onto Spherical Surfaces

Abstract

Microstrip antennas are customary components in modern communications systems, since they are low-profile, low-weight, low-cost, and well suited for integration with microwave circuits. Antennas printed on planar surfaces or conformed onto cylindrical bodies have been discussed in many publications, being the subject of a variety of analytical and numerical methods developed for their investigation (Josefsson & Persson, 2006; Garg et al., 2001; Wong, 1999). However, such is not the case of spherical microstrip antennas and arrays composed of these radiators. Even commercial electromagnetic software, like HFSS® and CST®, do not provide a tool to assist the design of spherical antennas and arrays, i.e., electromagnetic simulators do not have an estimator tool for establishing the initial dimensions of a spherical microstrip antenna for further numerical analysis, as available for planar geometries. Moreover, this software is time-consuming when utilized to simulate spherical radiators, hence it is desirable that the antenna geometry to be analyzed is not too far off from the final optimized one, otherwise the project cost will likely be affected. Nonetheless, spherical microstrip antenna arrays have a great practical interest because they can direct a beam in an arbitrary direction throughout the space, i.e., without limiting the scan angles, differently from the planar antenna behaviour. This characteristic makes them feasible for use in communication satellites and telemetry (Sipus et al., 2006), for example. Rigorous analysis of spherical microstrip antennas and their respective arrays has been conducted through the Method of Moments (MoM) (Tam et al., 1995; Wong, 1999; Sipus et al., 2006). But the MoM involves highly complex and time-consuming calculations. On the other hand, whenever the objective is the analysis of spherical thin radiators, the cavity model (Lima et al., 1991) can be applied, instead of the MoM. However, for both MoM and cavity model, the behaviour of the antenna input impedance and radiated electric field is described by the associated Legendre functions, hence efficient numerical routines for their evaluation are required, otherwise the scope of the antennas analyzed is restricted. In order to overcome the drawbacks described above, a Mathematica®-based CAD software capable of performing the analysis and synthesis of spherical-annular and -circular thin microstrip antennas and their respective arrays with high computational efficiency is presented in this chapter. It is worth mentioning that the theoretical model utilized in the CAD can be extended to other canonical spherical patch geometries such as rectangular or triangular ones. The Mathematica® package, an integrated scientifical computing software with a vast collection of built-in functions, was chosen mainly due to its powerful