Frequency Modulation and Control by Electron Beams

General formulas for the effect of electron beams on resonant systems in terms of frequency shift and change in Q are derived from the point of view of lumped circuits and from a general electromagnetic field standpoint. A way of introducing the electrons has been found which materially enhances their effectiveness in producing a shift of frequency in a resonant system. Measurements of the frequency shift produced by such an electron beam in a typical geometry were made which check well with values calculated from the general theory. Possible amplitude and phase distortions are calculated when such a beam is used to frequency-modulate a system, and these are found to be negligibly small, even for very high modulating frequencies. It is shown that this method of frequency control is ideally suited for frequency modulation or automatic frequency stabilization of continuous-wave magnetron oscillators using negative-grid-controlled electron beams for controlling the frequency of oscillations.