Circuit Analysis of Eddy Currents

Abstract

Maxwell's equations govern the eddy-current phenomenon, and are the starting point of this analysis. It is shown that Maxwell's equations, as applied to steady-state ac conditions, can be transformed to a Fredholm-type integral equation in eddy-current density. In turn, it is demonstrated that the method of subareas can be used to solve the Fredholm equation. This approach leads to the familiar circuit-analysis concepts of resistance and inductance in finite coupled circuits. The coupledcircuit method can be utilized in cases of complex, mixed boundary conditions without difficulty, as is illustrated by an example of the eddy-current losses in a conducting disk of finite thickness and finite radius, in the presence of a current-carrying loop. Experimental data is presented which confirms the theory, for a range of disk thicknesses. References are included to previous work.