An analysis of mode-locked arrays of automatic level control oscillators

The locking region for beat frequency entrained, or mode-locked arrays of discrete microwave oscillators, is exceedingly small, which presents great difficulty in array design. This paper shows that introducing a time-delayed gain control loop can enhance the entrainment region and that this region is maximized for a coupling phase of 90 degrees. For this value of coupling phase the location, size, shape, and orientation of the stable mode locking region is derived for arrays of arbitrary size. A study of the dependence of the stable mode locking region on the number of array elements shows that the region becomes highly eccentric as the number increases, thus making array tuning difficult and causing high sensitivity to particular oscillator tuning errors. The analysis is confirmed with a low frequency realization of a three-element array