Frequency dependence of quasi-particle mixers

Since the publication of the original theoretical work on superconductor-insulator-superconductor (SIS) tunnel-junction quasi-particle mixers by Tucker, theoretical attention has largely focused on understanding the physical origin of gain (conversion efficiency greater than unity) in the mixer, the conditions for mixer saturation and the behavior of series arrays of junctions. This work is applicable to frequencies generally much less than the frequency corresponding to the superconducting energy gap. The analysis reported here primarily differs from previous work in that analytic approximations to the quantum mixer theory of Tucker are developed that allow one to derive simple power-law expressions for mixer conversion efficiency and noise temperature due to shot noise over the complete frequency range. These approximations allow one to have a qualitative understanding of frequency-dependent effects in quasi-particle mixers.