Pin Impedance Based Figure of Merit with Mutual Coupling (PMC-FOM) for Assessment of A Decoupling Capacitor on Polygonal Parallel Plates

A novel pin impedance-based figure of merit with mutual coupling (PMC-FOM) is proposed for effectiveness assessment of a decoupling capacitor. The algorithm is based on the relative location of the capacitor on parallel plates and takes into account mutual coupling by extending the existing scalar expressions to matrix relations. New analytical relations are developed for the calculation of derivatives as required for the iterative solution of the problem. The relations for resonant parallel plates of regular shapes are extended to the practical case of polygonal shapes. It is demonstrated that a capacitor's effective zone can hardly be delimited with a simple circle when mutual interaction with other capacitors is considered. In fact, the presence of other capacitors deforms the circular zone to an irregular contour. The proposed method is analyzed with several benchmark examples and the results are validated for efficiency and accuracy by comparing with alternate methods including a commercial electromagnetic (EM) simulator.