Theory of Frequency Modulation Noise in Tubes Employing Phase Focusing

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Abstract
Oscillators employing phase focusing such as magnetrons have fairly well defined spokes whose rotational speed is proportional to the oscillation frequency. Each spoke is composed of a finite number of electrons having random velocities and consequently is subject to random fluctuations about a mean position. This spoke ``jitter'' leads to fluctuations in the oscillation frequency resulting in frequency modulation noise. It is the theoretical evaluation of the parameters of this noise as affecting the power spectrum of the oscillator output that is of interest here. The theoretical results compare favorably with the measured power spectrum of a voltage-tunable magnetron. The application of the formulas require an estimate of electron temperature although no attempt is made to evaluate this temperature. Amplitude fluctuation noise appears to be relatively unimportant in continuous-wave phase-focused oscillators.