A mathematical model for the impedance of the cavity-backed slot antenna

A mathematical model is derived that relates the impedance of a cavity-backed slot antenna to that of an identical slot which is free to radiate on both sides of a large ground plane. The model, which utilizes empirical constants from a previous experimental investigation, provides a continuously variable function of frequency and cavity depth for the impedance of a cavity-backed slot of fixed length and cavity cross section. This function is then compared with previously found experimental values and two theoretical solutions, one using a variational method and the other using the complex Poynting theorem.