A Theoretical Treatment of the Frequency Entrainment of a Reflex Klystron

Abstract

The frequency entrainment of a reflex klystron is studied in a fundamental way by setting up the differential equation which describes the oscillation of the klystron cavity under application of an external signal. Under such a condition that the oscillator runs at its normal operation with no electronic susceptance and with matched loading, the problem is shown to be essentially analogous to the simmilar one in an ordinary vacuum-tube oscillator of lower frequency range. Within this limitation on the operation condition the bandwidth of frequency entrainment is estimated in relation to the power ratio of the externally applied signal and the output of the normally operating klystron oscillator. Phase retardation of the cavity oscillation in the entrained klystron from the phase of the externally applied signal is investigated. In connection with this subject, the self-excited oscillation of the reflex klystron is also introductively treated from the standpoint of the theory of nonlinear oscillation.