Variational methods for nonstandard eigenvalue problems in waveguide and resonator analysis
Abstract
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 functionals for the nonstandard eigenvalues can be constructed. The examples include: cutoff problem of a waveguide with surface reactance, propagation problem of an azimuthally magnetized ferritefilled 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.
 Publication:

IEEE Transactions on Microwave Theory Techniques
 Pub Date:
 August 1982
 DOI:
 10.1109/TMTT.1982.1131221
 Bibcode:
 1982ITMTT..30.1194L
 Keywords:

 Cavity Resonators;
 Eigenvalues;
 Functional Analysis;
 Variational Principles;
 Waveguides;
 Corrugating;
 Electrical Impedance;
 Frequency Response;
 Linear Operators;
 Operators (Mathematics);
 Electronics and Electrical Engineering