Title :
Generalized reaction and unrestricted variational formulation of cavity resonators. II. Nonorthogonal and free-boundary mode-matching method
Author :
Shams-Zadeh-Amiri, Ali M. ; Safavi-Naeini, Safieddin ; Chaudhuri, Sujeet K. ; Sabry, Ramin
Author_Institution :
Dept. of Electr. & Comput. Eng., Waterloo Univ., Ont., Canada
fDate :
11/1/2002 12:00:00 AM
Abstract :
For pt. I see ibid., vol. 50, no. 11, p. 2480-90 (2002). This paper addresses a systematic method whereby the conventional mode-matching method is generalized to the cases where the set of modes used for the field expansion within a cavity resonator are relaxed to be orthogonal or satisfy any specific boundary conditions. It is shown that this approach is based on the unrestricted variational formulation of a cavity resonator. Reciprocity theorem and generalized reaction are the mathematical foundations of this new formulation. We have shown that the conventional mode-matching method is a special case of this generalized formulation and indeed is variational in nature. More precisely, we have proven that, if the field distribution obtained based on the conventional mode-matching method is used as a trial one in some variational formulas, the resonant frequency will be the same as the one obtained by the mode-matching method.
Keywords :
cavity resonators; eigenvalues and eigenfunctions; electromagnetic field theory; mode matching; variational techniques; boundary conditions; cavity resonator; eigenvalue problem; field distribution; field expansion; generalized mode-matching method; generalized reaction; reciprocity theorem; resonant frequency; unrestricted variational formulation; Boundary conditions; Cavity resonators; Dielectric losses; Eigenvalues and eigenfunctions; Electromagnetic waveguides; Microwave filters; Mode matching methods; Rectangular waveguides; Resonant frequency; Resonator filters;
Journal_Title :
Microwave Theory and Techniques, IEEE Transactions on
DOI :
10.1109/TMTT.2002.804520