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TUlE-4 3 D DYADIC GREEN ' S FUNCTION FOR RADIALLY INHOMOGENEOUS CIRCULAR FERRITE CIRCULATOR
| Content Provider | Semantic Scholar |
|---|---|
| Author | Krowne, Clifford M. |
| Copyright Year | 2004 |
| Abstract | Here we develop a three dimensional (3D) dyadic recursive Green's function with elements Gr suitable for determining the electric field components Fz, Er, E@) and magnetic field components (HZ, Hr, HQ) anywhere within a circular, planar ( microstrip or stripline) circulator. All of the components are present, although the EZ. Hr, and HQ components may still be dominant as long as the thickness h of the substrate is small. The recursive nature of G!y is a reflection of the inhomogeneous region being broken up into one inner disk containing a singularity and N annuli. G6( r, $9 z, is found for any arbitrary point ( r, Q, z) within the disk region and within any i th annulus. Specification of Gr , i = E or H, j = H, s = z, v = Q 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?( rl $1 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. INTRODUCTION As discussed in a previous paper [l], the ferrite research and development community, which has focused on producing ferrite based circulators, has been in need of simple but accurate ways of calculating performance when the device is subject to radial variation of the bias field H, ferrite material magnetization 4rcM,, and demagnetization factor Nd. The two dimensional recursive Green's function employed in [l] allowed the inhomogeneous boundary valued problem, subject to inhomogeneities in parameters, to be solved in an orderly and systematic fashion. It utilized an integral-discretization mapping operator and finally resulted in scattering parameters being expressed for a three port circulator with unsymmetrically disposed ports. The theory requires the circulator region to be broken up into two different zones. The inner zone is made up of a disk containing the origin point and the outer zone is segmented or divided up into annuli, each one of unequal radial extent, layered as in an onion. Numerical calculations, based upon a FORTRAN computer code developed from the theory, show that a few seconds are required per frequency point to obtain results including s-parameters. In contrast, two and three dimensional finite element ( FE) and finite difference ( FD) analyses are hundreds to thousands of times slower. Because of the success of the 2D approach, we develop here a completely new dyadic Green's function theory to describe the fields within a circulator of finite thickness. Integral-discretization operators will be employed, and spectral summation over the doubly infinite domain of azimuthal integers n will be maintained. However, because of the 3D nature of the construction, neglect of some of the field components won't be necessary any more. Although most circulators are built to be thin in terms of electrical wavelengths compared to their planar extent, assumptions requiring the thickness h to approach zero to apply a 2D model will no longer be required. Thus the actual effects of a finite thickness substrate on the circulator behavior will now be possible. The one characteristic radial propagation constant found in the 211 model now will break up into two radial propagation constants, both affected by the allowed normal z-directed propagation constant k,. The problem is no longer reducible to or described by a single governing equation, but rather by two coupled governing equations which always stitch the field components together. Thus, TEM, TM, and TE modes are not allowed in relation to any coordinates and no coordinate transformations will ever allow such modes to be found. Because of the impossibility of finding such simple modes, a much more involved approach to solving the 3D problem nnust be enlisted. Eventually, we show how these new dyadic Green's functions may br. utili& to determine circulator s-parameters. 3D THEORY The theory, briefly, starts with coupled radial Helmholtz equations stated in streamlined form as ( see Figure 1 for perspective sketch of the circulator, with thickness in the z direction exaggerated) |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://ia601506.us.archive.org/zipview.php?file=10.1109@mwsym.1996.508477.pdf&zip=/3/items/ieee-us-government-works-dir/ieee-us-government-works-dir.zip |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
