Calculation of Eigenmode Fields in RF-Resonators using Coupled S-Parameter Calculation
Usually, eigenfrequencies and eigenmodes of rf-structures are computed numerically by dedicated programs like MAFIA or Microwave StudioTM 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 S-Parameter Calculation (CSC) based on the well known S-parameter formalism was developed. The properties of the whole rf-structure are determined by subdividing it into several smaller subsections and computing their S-parameters. 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 S-parameter-matrix 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 S-parameters of one cell have to be calculated. In our case this is performed by Microwave StudioTM 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 4-cell chain as a function of the cell-to-cell-angle. Further investigations show rotation of the orientation of the electric field of the dipole-eigenmodes along the resonator chain.
1. Microwave Studio V4.3, MAFIA V4.108, CST GmbH, Büdinger Str 2a, D-64289 Darmstadt, Germany.
2. H.-W. Glock, K.Rothemund, U. van Rienen, “CSC – A Procedure for Coupled S-Parameter Calculations”, IEEE Trans. Magnetics, vol. 32, pp. 3111-3113, Mar. 2002
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