Phase-Locked Oscillator Optimization for Arrays of Josephson Junctions

An overview of phase locking in two‐dimensional (2D) arrays of identical Josephson junctions is presented. General design criteria are discussed for optimization of power and linewidth. A harmonic balance technique is used to derive an analytic expression for the fundamental power as a function of bias voltage for a single shunted tunnel junction with an external shunt resistor having parasitic inductance. A linear stability analysis is performed on the in‐phase state of 2D arrays in the absence of any external load. Most excitation modes in the 2D array are damped, leading to stable phase locking between parallel junctions within each row; however, within the theoretical model, no mechanisms intrinsic to the array were found to induce phase locking between rows of junctions. The results of these calculations and their impact on and relevance to the design of phase‐locked Josephson oscillators are discussed.

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