Examination, Clarification, and Optimization of the Green\´s Function/ $Z$ -Matrix Models and Calculations for Rectangular Planar Microwave Circuits

In this paper, we examine the Green´s function and Z-matrix models commonly used in calculations for microwave planar circuits. We prove, for the first time, the pointwise convergence of the Green´s function and the interchangeability of the integration and infinite summation used in deriving the Z-matrix model. We also show the validity of interchanging the order of the double summation of the Z-matrix. In a related vein, we point out some potential problem of performing series rearrangements in evaluating infinite sums. Through computational analysis, we will demonstrate that a stable and efficient algorithm for the Green´s function and Z-matrix calculations can be optimally obtained for all practical boundary port configurations of rectangular planar circuits.