A simplified theory of coupled oscillator array phase control

Linear and planar arrays of coupled oscillators have been proposed as means of achieving high power rf sources through coherent spatial power combining (Mink, 1986 and York, 1993). In such-applications, a uniform phase distribution over the aperture is desired. However, it has been shown that by detuning some of the oscillators away from the oscillation frequency of the ensemble of oscillators, one may achieve other useful aperture phase distributions Liao and York, 1993). Notable among these are linear phase distributions resulting in the steering of the output rf beam away from the broadside direction. The theory describing the operation of such arrays of coupled oscillators is quite complicated since the phenomena involved are inherently nonlinear. This has made it difficult to develop an intuitive understanding of the impact of oscillator tuning on phase control and has thus impeded practical application. In this work a simplified theory is developed which facilitates intuitive understanding by establishing an analog of the phase control problem in terms of electrostatics.