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 Greenʹs 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 Greenʹs 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.