A Circuit Model of Transverse Electric Eddy-Current Problems in Magnetic Rings

A circuit model consisting of inductance-resistance ladder network to solve the transverse electric eddy-current problems was proposed. The general idea is to divide the region to be solved into a number of eddy shells, which are modeled by a series of coils magnetically coupled with each other. Detailed discussions of the model were made under two special cases where analytical solutions are available. First, it was proved in theory that the limit form of the recursive formula of the circuit model is identical with the Maxwell equations. Next, numerical accuracy of the model was evaluated by making comparison between the circuit solutions and the analytical solutions. It turns out that when the width of each shell is less than the skin depth, the results match the analytical solutions quite well. The proposed circuit model could find its application in the simulation of very fast transient overvoltage mitigation by magnetic rings, where analytical solutions do not exist and other commonly used numerical methods cost too much calculation amount.