dc analysis of parallel arrays of two and three Josephson junctions

Arrays of Josephson junctions are becoming of increasing interest, and the dependence of the maximum zero-voltage current on various factors is important in applications. When the array carries the maximum possible zero-voltage current it is said to be in the critical state. Sets of equations describing the critical-state behaviors of arrays of two and three junctions are derived. Account is taken of possible differences of the individual critical currents, self-induced flux, and asymmetric current feed. In a space having the phase differences across the junctions as coordinates, one can construct a locus relating the phase differences that are obtained when the array is in the critical state. It is shown that the periodic, symmetric, and other properties of the various relationships between variables can be inferred from the properties of the phase-difference locus.