Effect of Coupling Phase on Mutual Injection Locking Range in Coupled Oscillator Arrays

The performance of a coupled oscillator array depends critically on the coupling network. Determination of the optimal coupling phase depends on the oscillator equivalent circuit and the location of mutual coupling between the oscillators. In this paper, the authors examine the effects of coupling phase on the mutual injection locking range. Three element coupled oscillator arrays (COAs) were mutually coupled at two different locations, with each coupling location presenting a different resonance to the coupling network, and the optimal coupling phase required to generate a linear phase shift in the range of $-90^{circ}$ to 90$^{circ}$ was determined. For each coupling location, when the coupling phase was off by 180$^{circ}$ , the arrays were shown to lock with a limited range and operate in a mode other than the in-phase mode.