Network Analog Solution of Skin and Proximity Effect Problems

Abstract

The general problem of skin effect in conductors of arbitrary shape may be formulated as a partial differential equation in the magnetic vector potential and a set of integral conditions on the field. Such systems of equations are not analytically easily tractable, but may be solved by constructing a resistive-capacitive analog network of infinite extent. This paper describes a method of mapping such an infinite network onto two finite networks by means of a simple conformal transformation. With a suitable choice of network size and parameter values, solution of skin and proximity effect problems is then possible to any desired accuracy. A network suitable for a certain class of problems is described, and skin effect resistance ratios obtained from the analog compared with experimental data. Excellent agreement results within the design limits of the analog. Current distribution within any given conductor, or among a set of conductors, is directly measurable by this method, and is illustrated by sample results.