Driving point impedance of linear antennas in the presence of a stratified dielectric

A linear flat strip antenna lies between several dielectric layers in a direction parallel to the interfaces. Its impedance is formulated variationally as an infinite double integral. For thin half-wave antennas in a homogeneous medium the double integral is evaluated analytically and it gives standard impedance expressions. For antennas of finite width the integrals are evaluated numerically and for a homogeneous medium the impedance has been correlated with the theories of King and Middleton, and Wu, with the impedance computed from a complementary slot antenna and with available measurements. The impedance is also computed for antennas in a dielectric layer, and the decrease of the radiation efficiency observed with increasing electrical thickness of the layer is explained with the increased amounts of surface wave power and in part by local dielectric losses. For insulated antennas located in a dissipative medium the theory presented here yields results in better agreement with measurements than the conventional transmission line theory. The transmission line theory is shown to give too large a resistance and reactance at the full-wave resonant peaks of the impedance and too low a resistance for short antennas.