Explicit efficient coupling impedance formulas for the right-angled isosceles triangle and application to a circularly polarised truncated corners square patch antenna

Formulas for the four possible microstrip coupling impedances between two perimeter ports on a right-angled isosceles triangular microstrip segment are derived by integration of the associated Green's function. The formulas are economised by introducing closed forms of infinite series to give new efficient computational formulas, which are verified experimentally. The variation of input impedance with offset, for a circularly polarised truncated corners square patch antenna, is determined using the segmentation method. Predicted and simulated results shows very good agreement. The area of the perturbation segments increases as a function of offset and this increase reduces the effect of manufacturing errors. A simple matching network for the offset feed is designed for an antenna operating at 2.45 GHz. Predicted, simulated and practical results show good agreement.