Circuit models for arrays of Josephson oscillators with loads

Parallel arrays of underdamped Josephson junctions are interesting due to their ability to produce coherent radiation. For a broad range of array parameters, we find that these arrays have solutions which can be represented as traveling waves with a small number of harmonics. We develop equivalent circuits for the DC and AC response using a harmonic balance technique. The reflection and transmission properties at the boundaries are studied by adding a passive terminating load to the array. We also develop a load criteria for optimal output power to both passive and non-linear loads.