General Treatment of Klystron Resonant Cavities

Klystron resonant cavities are treated for general cases and their equivalent circuits are theoretically determined, which allows a fairly accurate estimate of resonant properties. It is shown that a reentrant cavity is expressed as a low-frequency series LCR_se circuit or a shunt LCR_sh circuit, taking L as the inductance of a toroidal coil with one turn and with a cross section the same as the cavity, C as the gap capacitance plus the equivalent capacitance of the cavity, and R_se or R_sh as the equivalent series or shunt resistance of the cavity at resonance. The introduction of the equivalent cavity capacitance has proved to be very effective. The formulas derived here enable one to calculate the resonant frequency within an error of a few per cent and the shunt resistance and the Q within an error of several tenths of a per cent in most cases, and thus should prove to be very useful to the designer of microwave circuits.