Optimal partial filling of microstrip antennas with dielectric and magnetic substrates

In this paper we study microstrip antenna miniaturization using partial filling of the antenna volume with dielectric and magnetic materials. With the help of analytical formulae derived for the antenna element non-uniformly filled with two arbitrary materials we seek for the optimal voltage and current distributions in the antenna element in terms of the minimized radiation quality factor. Qualitative design rules are given, and a miniaturization example is provided where the antenna performance is compared for different filling patterns. Results given by the analytical model are verified with numerical simulations and in the case of partial dielectric filling also with experiments.