Determination of the Green's function in the spectral domain using a matrix method: Application to radiators or resonators immersed in a complex anisotropic layered medium

A planar structure having arbitrarily located conductor patches immersed in complex anisotropic layered media presents a very general field problem. This problem is solved here by a rigorous formulation technique characterizing each layer by a
6 \times 6
tensor and finding the appropriate Fourier transformed Green's function matrix
G
of
2n \times 2n
size. The technique finds a set of field eigenvectors for each layer. Using
G
, a method of moments numerical solution for radiation characteristics of probe fed patch(es) can be had in the spectral domain employing, for example, a zero reaction method. Variation of real frequencies of the driving probe fed signal is allowed by that approach. Those workers desirous of radiator or resonator fields and frequency behavior at only selected resonant frequencies can use
G
to derive a matrix
S_{X}
given here. Setting the determinant of
S_{X}
equal to zero yields complex resonant frequency solutions, and the field solutions as a consequence to the nonprobe fed or free standing patch structure. The method is very versatile and can handle a large class of microwave or millimeter wave integrated circuit or monolithic circuit problems, no matter how simple or complex as long as they possess planar layers.