Simple expressions for mutual impedances (dipoles and microstrip elements)

A method of evaluating mutual impedances between thin dipoles is presented. They may be free or printed ones. It involves an asymptotic expansion of a bidimensional Fourier integral. Very simple algebraic expressions are derived, which are convenient for hand calculations. The numerical results are more accurate than previously. The technique is extended to include the presence of an infinite ground plane. Then, using the stationary phase method, simple coupling equations are derived for microstrip elements.