Design of a lumped array of Josephson junction oscillators

It is shown that inductively resistively shunted junctions are good candidates for Josephson-junction oscillator arrays. The shunt resonates out the junction intrinsic capacitance, allowing a much higher effective impedance at the resonance frequence, but still with a small shunt resistance giving a narrow linewidth. Compared to resistively shunted junctions they are advantageous for frequencies greater than about 100 GHz, when fewer junctions and lumped arrays can be used, giving larger bandwidths. Design rules that avoid chaotic solutions and optimize output power are given. A design example of an integrated circuit consisting of an SIS-mixer pumped by an array of as few as four junctions at 350 GHz is given. A bandwidth of 160 GHz and a linewidth of 400 kHz should be feasible in a practical situation.<>