An efficient formula for the input impedance of a microstrip right-angled isosceles triangular patch antenna

Input impedance formulas for feed positions first, on the vertical side, and second, on the hypotenuse, are obtained from coplanar microstrip circuit analysis. The formulas that involve both single and double infinite series are economized by introducing closed forms of the infinite series. These new formulas are verified by comparison with practical results and a simulation based on full wave analysis.