Formulas for the Maximum Radiated Power Density at Broadside in Lossy Fabry-Perot Cavity Antennas

The leaky-wave analysis of lossless Fabry-Perot cavity antennas (FPCAs) reveals that the maximum radiated power at broadside is reached at the leaky cutoff, i.e., when the leaky phase and attenuation constant of the fundamental TE-TM leaky-mode pair excited in the structure are equal to each other. Formulas for optimizing the cavity height to reach the leaky cutoff at the design frequency were previously provided under one of these two assumptions: i) the radiated power at broadside is dominated by the leaky-wave contribution, and ii) the structure is lossless. Here, a new formula is derived to accurately optimize the cavity height for maximum radiated power density at broadside which accounts for both dielectric and ohmic losses. The formula is based on the expression of the total pattern radiated by a lossy FPCA, and thus remains accurate even when the leaky-wave contribution does not dominate the aperture field.