Spherical waves representation of the Green's functions in the far field zone of printed antennas

The field problem for microwave and millimeter wave printed circuits and antennas is commonly approached with the aid of potential functions that are formulated in the spectral domain. In the space domain the latter are expressed like Sommerfeld integrals assessable only numerically. However, analytic asymptotic expressions are available for the far field problem. The present work presents a new expression for the Green's functions far field contribution that is a superposition of outgoing spherical waves and presents several useful feature for the analysis and synthesis of patch antennas.