Analysis of the Frequency Locking Region of Coupled Oscillators Applied to 1-D Antenna Arrays

During the past decade, coupled oscillators have shown their efficiency as simple methods for phase control in microwave antenna arrays, and hence as alternatives to conventional electronic beam steering methods. In this paper, a new writing of the nonlinear equations proposed by R. York to describe the oscillators locked states is presented. This has allowed the elaboration of a CAD tool which provides, in a considerably short simulation time, the frequency locking region of the coupled oscillators. This region is plotted versus the oscillators' tunings referred to the resonant frequency of the coupling circuit. A prototype circuit consisting of a five oscillators array is currently under test to validate the theory.