A compact recursive trans-impedance Green´s function for the inhomogeneous ferrite microwave circulator

A detailed analytical investigation of the circular ferrite circulator is provided in this paper. The ferrite is assumed to be radially inhomogeneous as a result of an azimuthally invariant demagnetization field. The cavity model of Bosma and the stratified ferrite model of Krowne and Neidert are used to construct a compact recursive Green´s function in terms of wave impedances and azimuthal modes. The Green´s function logarithmic singularity is treated separately and extracted to improve the convergence characteristics of the modal series. The impedance parameters of the circulator are obtained via an integration of the Green´s function and its singular term; to obtain the scattering parameters, various matrix manipulations of the impedance parameters are invoked. Data are provided and compared with independent sources to demonstrate the veracity of the Green´s function approach. Finally, a circulator design is offered using the Green´s function method and scattering-parameter data associated with that design are compared with data from a three-dimensional finite-element electromagnetic simulation of a microstrip circulator. The correlation between both data sets further supports the validity of the inhomogeneous cavity model and the Green´s function approach.