  Cylindrical re-entrant cavities are unique three-dimensional structures that
resonate with their electric and magnetic fields in separate parts of the
cavity. To further understand these devices, we undertake rigorous analysis of
the properties of the resonance using in-house developed Finite Element Method
(FEM) software capable of dealing with small gap structures of extreme aspect
ratio. Comparisons between the FEM method and experiments are consistent and we
illustrate where predictions using established lumped element models work well
and where they are limited. With the aid of the modeling we design a highly
tunable cavity that can be tuned from 2 GHz to 22 GHz just by inserting a post
into a fixed dimensioned cylindrical cavity. We show this is possible as the
mode structure transforms from a re-entrant mode during the tuning process to a
standard cylindrical Transverse Magnetic (TM) mode.
