5.8 Assessment of Methods and Summary

Having reviewed the major rigorous analysis methods for both shielded and open DRs, we are now in a position to discuss their merits and shortcomings. In the case of shielded resonators, two competing techniques have emerged, which are applicable to both axisymmetric (m = 0) and hybrid (m ? 1) modes: the radial mode-matching method (Sec. 5.2) and the axial mode matching method (Sec. 5.3). For simplicity, we will refer to these methods in the following discussion as the radial and axial methods, respectively. When applied to a typical DR in a cylindrical cavity (Fig. 5.1), each of these two methods will give sufficiently accurate results, but one of them may require less effort than the other. Systematic convergence studies comparing various techniques have not appeared in the literature, so we have little guidance in this respect. As was discussed in Sec. 5.2, the radial method suffers from a relatively slow convergence for modes with a strong axial component of the electric field, which is singular at the edges of the DR [13,15]. We may speculate that similar difficulty will be encountered in the axial method for modes with strong radial component of the electric field. The source of the difficulty seems to be the fact that in both methods we seek to represent potentially singular functions in terms of continuous waveguide modes.

The relative efficiency of these methods is also likely to vary from case to case, i.e., what is the "best"...