Inductance of perfectly conducting foils including spiral inductors

A numerical method for calculating the lumped inductance parameters of perfectly conducting foils (i.e., current sheets) is presented. A quasi-static analysis for computing the inductance for foils arbitrarily shaped in three dimensions is described. The vector current distribution on the structure is solved in terms of a scalar current potential function. The method of moments is utilized to solve the integral equation. Numerical results are also presented. The strength of this technique is that a bound on the numerical accuracy can be provided. The relative error provides not only a self-consistency check, but also the accuracy with which the numerical values have been computed. Foil structures which can be approximated accurately with a triangular patch model and whose terminal edge current distributions are known can be analyzed with this method. The method yields results with reasonable accuracy as long as the quasi-static conditions are met and the size of the structure is within prescribed limits. The method has the capability of providing an accuracy check on the numerical values of the inductance. This can be achieved by evaluating the inductance on two different contours.