3D dyadic Green´s function for radially inhomogeneous circular ferrite circulator

Here we develop a three dimensional (3D) dyadic recursive Green´s function with elements G/sub ij//sup sv/ suitable for determining the electric field components (E/sub z/, E/sub r/, E/sub /spl phi//) and magnetic field components (H/sub z/, H/sub r/, H/sub /spl phi//) anywhere within a circular, planar (microstrip or stripline) circulator. All of the components are present, although the E/sub z/, H/sub r/, and H/sub /spl phi// components may still be dominant as long as the thickness h of the substrate is small. The recursive nature of G/sub ij//sup sv/ is a reflection of the inhomogeneous region being broken up into one inner disk containing a singularity and N annuli. G/sub ij//sup sv/(r,/spl phi/,z) is found for any arbitrary point (r,/spl phi/,z) within the disk region and within any i th annulus. Specification of G/sub ij//sup sv/, i=E or H, j=H, s=z, v=/spl phi/ 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/sub ij//sup sv/(r,/spl phi/,z) enables S-parameters to be found for three and six port ferrite circulators. 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 behavior in the circulator. The theory is readily adaptable to constructing a computer code for numerical evaluation of finite thickness devices. Also, symmetric port disposition and metallic losses are covered.