On the Effective Range of Decoupling Capacitors Including Mutual Coupling

A method is proposed to calculate the effectiveness of a decoupling capacitor in the presence of other capacitors. The previously developed scalar expressions for calculating the effective radius of a capacitor in isolation are extended to matrix relations which account for mutual coupling. In the same vein, the scalar operations are substituted by their matrix counterparts including the calculation of derivatives using matrix calculus techniques which are required for the iterative solution of the problem. The proposed method is tested on a sample case and the results are observed to compare favorably against those from a numerical electromagnetic (EM) simulator.