Dyadic Green's Function Microstrip Circulator Theory for Inhomogeneous Ferrite with and without Penetrable Walls

Abstract

Publisher Summary This chapter focuses on canonically shaped circulators—namely, those with circular symmetry. Great advantage may be taken of mathematical physics tools when restricting the problems examined to canonically shaped objects, such as those with circular symmetry. For electromagnetic circulators, many actual devices possess some degree of circular symmetry, so symmetry restrictions are not unrealistic. As one moves further and further away from simple objects which are symmetrical, (like a circle in a two-dimensional model or a circular cylinder in a three-dimensional model) the ability to derive explicit dyadic Green's functions becomes more difficult. Finally, when the complexity is increased to the extent when the circulator puck (composed of ferrite anisotropic material) is surrounded by layers of substrate material and layers of superstrate material, with radially changing composition, all that is reasonable to seek is an implicit Green's function, which retains some of the features originally employed to find the simpler explicit Green's function, and new aspects found in the mode-matching method. Adding in the mode-matching technique with its variable number of matching modes seems to irrevocably eliminate the ability to solve for explicit dyadic Green's function elements. Systems of equations or equivalently, matrices in matrix equations contain the properties of the environment external to the puck and the manner in which the outlying areas interface with the puck itself. But what is lost in acquiring the field solutions through explicit dyadic Green's functions is gained in treating much more complicated surrounding environments, which still retain circular symmetry.