On The Accuracy of Approximate Methods for Analyzing Cylindrical Dielectric Resonators
The rigorous methods for microwave circuit design often are too complicated for practical purposes. In this paper, various approximate methods available for the analysis of cylindrical dielectric resonators are compared. Improved methods now are available that provide accuracy comparable to that of rigorous methods for the most commonly employed T[E.sub.01[Delta]] mode of resonance.
The limited accuracy of the approximate methods prompted many researchers to revert to rigorous methods for the analysis of cylindrical dielectric resonators in various configurations.[1-4] Although these methods lead to accurate results and provide more information than is possible using approximate methods, rigorous methods have found little use in practical applications because they are quite complicated. Microwave design engineers would be well served with simple-to-use, accurate methods. In this paper, various approximate methods available in the literature for the analysis of cylindrical dielectric resonators are compared. It is concluded that improved approximate methods are now available that provide high accuracy and lead to information available earlier only when using rigorous methods.
Magnetic Wall Model Method
The earliest approach used for analyzing dielectric resonators was the magnetic wall model (MWM) approximation. In this approximation, it is assumed that the walls of the dielectric resonator behave as magnetic walls. A rigorous theory has shown that the MWM approximation is a good approximation only for the T[M.sub.0mn] modes of an isolated cylindrical dielectric resonator. The approximation is not justified for the TE and hybrid modes of the resonator. The method may give small errors for the resonant frequencies of some of these modes, but in these cases the MWM approximation may give highly erroneous results for the field distribution inside the resonator.
All approximate methods start with an assumed simplified field distribution inside the resonator. The validity of any approximate method should be checked not only by comparing the results for the resonant frequencies only, but by determining whether the method is able to predict the field distribution. In principle, it is sufficient to know the fields inside the resonator. The external fields then can be computed from the knowledge of the internal resonator fields by replacing the dielectric resonator by a polarization current source. The internal field distribution must be known in order to compute other characteristics of the resonator, such as energy stored and external fields, including radiated fields and Q-factors. In this respect, the MWM approximation performs quite poorly. Moreover, the MWM approximation is not valid if the resonator is placed in a shielded environment, which is the case in most practical applications.
The T[E.sub.01[Delta]] mode is used most commonly in...