Resonant frequency of re-entrant klystron cavity

Resonant frequency of re-entrant klystron cavities is difficult to predict through closed form expressions, since the accurate field profile and their solutions in the resonator volume are not known. Often conflicting requirements need a judicious trade-off between cavity parameters by designer. In absence of knowledge of exact dependence of frequency on geometrical parameters the graphical data is still relied upon. Barroso et al proposed a mathematically simple formulation for calculating the resonant frequency of a cylindrical re-entrant cavity. The frequency equation suggested by Barroso et al is valid for a particular range of cavity dimensions of short cavities. This equation is modified and a closed form expression for resonating frequency of the re-entrant resonator is derived which is applicable to both long and short cavities. The analytical results are compared with earlier reported results and simulation results obtained using Computer Simulation Technology microwave studio.