Two-dimensional array beam scanning via externally and mutually injection locked coupled oscillators

Stephan (1986) proposed an approach to one dimensional (linear) phased array beam steering which requires only a single phase shifter. This involves the use of a linear array of voltage controlled electronic oscillators coupled to nearest neighbor. The oscillators are mutually injection locked by controlling their coupling and tuning appropriately. Stephan´s approach consists of deriving two signals from a master oscillator, one signal phase shifted with respect to the other by means of a single phase shifter. These two signals are injected into the end oscillators of the array. The result is a linear phase progression across the oscillator array. Thus, if radiating elements are connected to each oscillator and spaced uniformly along a line, they will radiate a beam at an angle to that line determined by the phase gradient which is, in turn, determined by the phase difference between the injection signals. The beam direction is therefore controlled by adjusting this phase difference. Pogorzelski and York presented a formulation which facilitates theoretical analysis of the above beam steering technique. Using this formulation, the Stephan beam steering technique can be generalized to two-dimensional arrays in which the beam control signals are applied to the oscillators on the perimeter of the array. In this paper the continuum model for this two-dimensional case is developed and the dynamic solution for the corresponding aperture phase function is obtained The corresponding behavior of the resulting far-zone radiation pattern is displayed as well.