Calculation of Eigenmode Fields in RFResonators using Coupled SParameter Calculation
Usually, eigenfrequencies and eigenmodes of rfstructures are computed numerically by dedicated programs like MAFIA or Microwave Studio^{TM} by discretizing the geometry. If fine details or slight geometry deviations have to be taken into account, the number of mesh points easily becomes too high even for modern computer hardware. Therefore a procedure called Coupled SParameter Calculation (CSC) based on the well known Sparameter formalism was developed. The properties of the whole rfstructure are determined by subdividing it into several smaller subsections and computing their Sparameters. This can be done numerically by any field solving code or, for some special sections like waveguides and shorts, analytically. Additionally, symmetries of the whole structure or of individual subsections can be exploited to reduce the overall numerical effort. CSC allows to calculate the entire Sparametermatrix of an open structure. If all external ports are closed, the eigenfrequencies and the wave amplitudes of the eigenmodes are given as result of the CSC procedure. As an example of a closed structure a chain of weak elliptically deformed resonator cells will be presented. All the cells are of identical shape, which means, only the Sparameters of one cell have to be calculated. In our case this is performed by Microwave Studio^{TM} considering the first pair of degenerated dipole modes. Neighbouring cells are rotated by a certain angle with respect to each other. Fig. 1 shows a chain of four cells, the arrows denote the rotation of the reference frame from cell to cell. The scattering parameters of the rotating section as well as the ones of the shorts at both ends of the chain can be determined analytically. In a first step CSC is used to determine the resonant frequencies of the whole 4cell chain as a function of the celltocellangle. Further investigations show rotation of the orientation of the electric field of the dipoleeigenmodes along the resonator chain.
REFERENCES 1. Microwave Studio V4.3, MAFIA V4.108, CST GmbH, Büdinger Str 2a, D64289 Darmstadt, Germany. 2. H.W. Glock, K.Rothemund, U. van Rienen, “CSC – A Procedure for Coupled SParameter Calculations”, IEEE Trans. Magnetics, vol. 32, pp. 31113113, Mar. 2002


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