A Novel Impedance Definition of a Parallel Plate Pair for an Intrinsic Via Circuit Model

Rigorous analysis of via-plate-pair interactions requires the impedance of a plate pair to be defined in terms of radial transmission lines on perfect magnetic conductor (PMC) ports. The plate domain is not a solid plate pair but one with multiple PMC holes where conventional impedance definitions are not suitable. A new impedance definition is proposed where port voltages and currents are expressed in terms of the inward and outward zero-order modes of a radial transmission line. Radial scattering parameters among multiple radial ports are then introduced and the transforms between the radial scattering and impedance matrices are given. An analytical formula for the radial scattering matrix in a circular plate pair is derived using the addition theorems of cylindrical waves. Furthermore, a boundary integral-equation method is developed to calculate the radial scattering matrix for any irregular plate pair. The method is validated by analytical and numerical simulations as well as measurements.