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Variational Methods for Nonstandard Eigenvalue Problems in Waveguide and Resonator Analysis

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The nonstandard (general) eigenvalue problem is defined in operator form by L (Lambda) f = 0 and B (Lambda) f = 0, where L and B are linear operators, and for a standard problem L is a linear function of the parameter Lambda and B does not depend on Lambda. It is shown by examples, that nonstandard problems arise in electromagnetic problems, and a unified variational principle is formulated from which stationary functional for the nonstandard eigenvalues can be constructed. The examples include cutoff problem of a waveguide with surface reactance, propagation problem of an azimuthally magnetized ferrite-filled waveguide, the cutoff problem of a corrugated waveguide and the problem of a material insert in a resonator. It is demonstrated with these simple but nontrivial examples that the present method leads to a good engineering accuracy with very elementary test functions.

Published in:

IEEE Transactions on Microwave Theory and Techniques  (Volume:30 ,  Issue: 8 )