Generalization of the linearized discrete model of coupled oscillator arrays to account for coupling delay

Arrays of mutually injection locked oscillators have been proposed as a means of providing properly phased excitations for the elements of a phased array antenna. Analysis of such oscillator arrays has typically made use of Van der Pol's oscillator model and Adler's theory of injection locking resulting in a system of nonlinear differential equations for the phases of the oscillators. The solution resulting from a linearization of this formulation is noncausal because it does not account for time delay in the interoscillator coupling. The present analysis extends the linearlized formulation to account for coupling delay and thus yields a causal solution.