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

The use of arrays of injection-locked voltage-controlled oscillators coupled to nearest neighbors has been proposed as a means of controlling the aperture phase of one and two-dimensional (2-D) phased-array antennas. It has been demonstrated both theoretically and experimentally that one may achieve linear distributions of phase across a linear array aperture by injection locking to an external oscillator the end oscillators of an array of a mutually injection-locked oscillators. These linear distributions cause steering of the radiated beam. It is demonstrated theoretically here that one may achieve beamsteering in a similar manner in two dimensions by injecting appropriately phased signals into the perimeter oscillators of a 2-D array. The analysis is based on a continuum representation of the phase previously developed in the context of beamsteering via tuning of the perimeter oscillators.