THEORY OF PHASE-LOCKING IN GENERALIZED HYBRID JOSEPHSON-JUNCTION ARRAYS

A recently proposed scheme for the analytical treatment of the dynamic s of two-dimensional hybrid Josephson-junction arrays is extended to a class of generalized hybrid arrays with ''horizontal'' shunts involvi ng a capacitive as well as an inductive component. This class of array s is of special interest, because the internal cell coupling has been shown numerically to favor in-phase synchronization for certain parame ter values. As a result, we derive limits on the circuit design parame ters for realizing this state. In addition, we obtain formulas for the flux-dependent frequency including flux-induced switching processes b etween the in-phase and antiphase oscillation regime. The treatment co vers unloaded arrays as well as arrays shunted via an external load.