IMPLICIT 3-D DYADIC GREENS-FUNCTION USING SELF-ADJOINT OPERATORS FOR INHOMOGENEOUS PLANAR FERRITE CIRCULATOR WITH VERTICALLY LAYERED EXTERNAL MATERIAL EMPLOYING MODE-MATCHING

Self-adjoint operators are found for the differential equations descri bing the a-dependent field variation in the medium external to the fer rite microstrip circulator puck, The external medium is, in general, i nhomogeneously layered, consisting of media with permittivity properti es, magnetic properties, or both. Eigenvalue equations characterizing the radially sectioned medium outside the puck are found, as are the e igenvectors. When the z-dependent parts are multiplied with the radial and azimuthal dependences, the complete three-dimensional (3-D) field expressions are determined, Source-constraint equations (representing microstrip lines) driving the circulator are then combined with the m ode-matching technique to obtain in direct space, implicit dyadic Gree n's function elements, Mode orthogonality is employed to encourage spa rsity in matrix system development where appropriate or convenient, Th e implicit Green's function is particularly useful because field infor mation and s-parameters may be found in real space, completely avoidin g typical inverse transformations.