A Complete Variational Method for Capacitance Extractions

In the past, coupling capacitances between conductors was extracted using charge distributions directly. In this paper a set of new generalized variational formulas are derived. They are complete since they are valid not only for self-capacitances, but also for mutual capacitances. As for the realistic numerical implementation, elastance matrices become asymmetrical because of numerical method used. Then a more general variational formula is derived to account for the asymmetrical elastance matrix case. By these novel formulas the computational accuracy can be significantly improved compared to the conventional capacitance extraction method.