Physical Models for Influence of Substrate Permittivity on the Gain of Microstrip Antennas

We propose novel patch antenna models to explain the influence of the dielectric on the antenna gain and radiation pattern. We demonstrate that a patch antenna can be replaced by a set of rectangular loops and sets of horizontal line dipoles, all located in a vacuum. When the relative permittivity of the substrate is close to one, the horizontal dipoles dominate, and the radiation in the horizontal directions is negligible. In contrast, when the relative permittivity is high, the radiation pattern of the antenna resembles the pattern of a loop placed perpendicularly to the ground plane. The developed models explain the gain reduction due to the presence of the dielectric of up to around 4.3 dB (compared with the antenna in a vacuum), which we have confirmed numerically. Another contribution of this communication is the derivation of a simple formula for the gain as a function of the substrate permittivity. Excellent agreement with numerical simulations has been obtained with only a few expansion terms.