Impedance and Effective Resistance of Capacitors With Resistive Top and Bottom Plates

This article presents a distributed analysis of 2-D plate capacitors with resistive top and bottom plates, which results in two coupled partial differential equations in two variables. The exact solutions for the input impedance of a rectangular capacitor are derived for several contacting scenarios. Using frequency power series analysis, we prove the resistance decoupling theorem: the effective (low frequency) series resistance of a plate capacitor is the sum of the effective resistances of the top and bottom plates considered separately. The exact effective resistance can be calculated by assuming a uniform vertical capacitive current flow between the two plates. Based on this theorem, the effective resistance for any contact scenario is derived. Our analysis also results in a geometry-dependent model for the intrinsic base resistance of BJTs that is more accurate than any previous model.