Rough Conductor Modeling Through State-Space Formulation

Abstract

Based on the state-space formulation, the exact analytical solution of the magnetic-field distribution inside a rough conductor trace is presented. The infinite Dyson’s series, a well-known tool for describing the interaction picture of a quantum system in the field of quantum electrodynamics (QED), is used to derive the magnetic-field evolution inside a rough conductor, starting from the conductor rough surface up to a far distance inside the conductor or equivalently a mathematical infinity. Validity of the obtained values from the first-, second-, and third-order approximations of the proposed series is proven by comparing with very recent research works. In addition, based on the first-order approximation, a very compact matrix identity is presented for the calculation of the state-space evolution matrix. The obtained values of the rough conductor surface impedance from dc up to 100 GHz are in excellent agreement with those obtained by the finite-difference (FD) method and other recently published solutions.