THEORY AND NUMERICAL-CALCULATIONS FOR RADIALLY INHOMOGENEOUS CIRCULARFERRITE CIRCULATORS

This paper presents a new theory for the operation of microstrip and s tripline circulators, specially set up to permit radial variation of a ll the magnetic parameters. A computer code, taking only a few seconds per calculated point on a modest computer, was developed from the the ory, and calculated results are given. In the theory we develop a two- dimensional (2-D) recursive Green's function G suitable for determinin g the electric field E(a) anywhere within a microstrip or stripline ci rculator. The recursive nature of G is a reflection of the inhomogeneo us region being broken up into one inner disk containing a singularity and N annuli, G has the correct properties to allow matching to the e xternal ports, thereby enabling s-parameters to be found for a three-p ort ferrite circulator. Because of the general nature of the problem c onstruction, the ports may be located at arbitrary azimuthal angle phi and possess arbitrary line widths. Inhomogeneities may occur in the a pplied magnetic field H-app, magnetization 4 pi M(s), and demagnetizat ion factor N-d. All magnetic inhomogeneity effects can be put into the frequency dependent tensor elements of the anisotropic permeability t ensor. Numerical results are presented for the simpler but immensely p ractical case of symmetrically disposed ports of equal widths taking i nto account these radial inhomogeneities. Studies of breaking up the a rea into 1, 2, and 5 annuli are undertaken to treat specific inhomogen eous problems. The computer code which evaluates the recursive Green's function is very efficient and has no convergence problems.