Simultaneous Formulation of the Theoretical Equations for Conductor Currents and Displacement Currents and Method of Three Dimensional Calculations

Abstract

We propose theoretical formulation to connect the integral equations of conductor currents and differential equations of displacement currents in order to develop analytical techniques related to high-frequency electrical characteristics for noise and surge protection designs. Discretization of the obtained equations by the finite element method leads to only one matrix equation of 3D space and second-time derivative with the unknowns of current vector potentials because the displacement currents can be eliminated. In the frequency domain, the frequency characteristics of displacement currents in insulators and currents in conductors as well as impedances can be obtained with this method. To verify this method, we developed a 3D high-frequency currents calculation program. We calculated the impedances of test objects, and compared them with our measured impedances. The results were as follows. (1) The calculated resonance and anti-resonance frequencies of a simple 1D transmission line were within a 4.5% difference off measured ones below 1GHz. (2) The first resonance frequency of an LCR series circuit formed by the parasitic capacitance of a commercial power module was calculated by taking into account the wiring shape, and this frequency matched the measured value within 4.2%. These results validate our theoretical formulation and method.