Mixing efficiency of SIS junctions

To evaluate new SIS technologies as low noise mixers we have investigated theoretically the frequency down-conversion efficiency of SIS junctions with IV curves which closely resemble experimentally observed curves. Leakage current and IV curve "sharpness" of the current rise at eV = \Delta_{1} + \Delta_{2} are included as parameters. We have applied a 3-port version of the quantum mixing theory to study the importance of these parameters on conversion efficiency. The results suggest that the leakage conductance should be less than 10% of the normal conductance, that the voltage width of the current rise should be less than 10% of the gap voltage, and that the optimum frequency of operation is near 10% of the gap frequency, eV_{gap}/h .