Efficient impedance coupling formulas for rectangular segment in planar microstrip circuits

A rectangular patch is one of the most common microstrip segments for which the Green´s function is known and is used in the segmentation and desegmentation analysis of complex antenna structures. The coupling impedances between ports on a microstrip segment are derived by integrating the associated Green´s function to obtain a result which involves the evaluation of double infinite series. In this paper the double infinite series is replaced by a single term together with a single infinite series to produce a computationally more efficient formula for the coupling impedance. Three coupling port configurations are examined and in each case numerically efficient formulas are derived.