Quality Factors of Unloaded Evanescent Mode Resonators

New general relation for unloaded Q-factors (Qu) of resonators realized by a lumped capacity or its equivalent which is connected in a section of a waveguide below cutoff is briefly derived and its applications are shown in this paper. This relation expresses the dependence of Qu both on terminations of such resonator, i.e. on the kind of its limiting walls in the given waveguide, and on its length, which can be optimized in the case of electric limiting walls. An useful special form of the derived relations agtees with the simplier formulae given in [1] or [2] for sufficiently long resonators, but it is often substantially more precise for relatively short resonators.