Anisotropic recursive dyadic Green's function 3D theory for a radially inhomogeneous microstrip circular ferrite circulator

摘要

Here we develop a three-dimensional (3D) dyadic recursive Green's function with elements G_ij~st suitable for determining the electric field component E_z and magnetic field component Hφ anywhere within a circular, planar (microstrip or stripline) circulator. All of the other components may also be found, as none are zero in the 3D model which includes a finite thickness h of the substrate. The recursive nature of G_ij~st is a reflection of the inhomogeneous region being broken up into one inner disk containing a removable singularity and N annuli. G_ij~st(r, φ, z) is found for any arbitrary point (r, φ, z) within the disk region and within any ith annulus. Specification of G_ij~st, i = E, j = H, s = z, t = φ or z, at the circulator diameter r = R leads to the determination of the circulator s-parameters. The ports have been separated into discretized ports with elements (subports) and continuous ports. It is shown how G_EH~zt(R, φ, z) enables s-parameters to be found for a simple case of a three port ferrite circulator. Because of the general nature of the problem construction, the ports may be located at arbitrary azimuthal angle φ and possess arbitrary line widths. Inhomogeneities can occur because of variations in the applied magnetic field H_app, magnetization 4πM_s, and demagnetization factor N_d. All inhomogeneity effects are put into the frequency-dependent tensor elements of the anisotropic permeability tensor P. Because of the z-variation present in the finite thickness model, TEM, TM, and TE modal decompositions are not allowed for the 3D analysis, and instead it is found that new coupled governing equations describe the field behaviour in the circulator. The theory is readily adapted to constructing a computer code for numerical evaluation of finite thickness devices. Published in 1999 by John Wiley & Sons, Ltd. This article is a US Government work and is in the public domain in the U.S.