Compact expressions for radiated fields of patch antennas

Theoretical expressions for the fields radiated by microstrip antennas have been developed extensively since the late 1970s. The general nature of the analysis is to formulate the solution for the fields into Sommerfeld-like integrals that uniquely meet the boundary conditions of the problem. The solution, in integral form, can then be evaluated using asymptotic techniques such as stationary phase or saddle point integration. The resulting expressions are described and presented here in a compact format. Although not new information, the organization of the expressions lends insight into why certain blind angles (associated with surface waves) are seen in either the E- or H-planes in patch array configurations.