Lumped-element circulator optimization

A detailed theoretical model for lumped-element circulators is used as the basis for a synthesis procedure in which the various circuit parameters are determined so that the lossless three-port junction is a perfect circulator at the desired design frequency with maximum bandwidth for a given size of the ferrite disk. Theoretical expressions for the internal and external permeabilities are derived from the Landau-Lifshitz equations. The y-connected lumped-element circulator is then analyzed on the basis of a very general equivalent circuit, which applies to ferrite samples of arbitrary spheroidal shape. Theoretical expressions for the impedance matrix of the ferrite-loaded junction are derived, and the scattering matrix is calculated. An algorithm for finding consistent sets of parameter values that will result in perfect circulation (in the lossless case) at any desired design frequency is used. Optimization for maximal bandwidth at given design frequency is obtained by imposing the additional constraint that the frequency derivatives of the phases of the eigenvalues of the scattering matrix are equal at the design frequency. Sample results are provided that demonstrate the validity of the approach.<>