Embedding impedance approximations in the analysis of SIS mixers

The adequacy of three approximations to J.R. Tucker´s (1979) quantum theory of mixers is examined. They are: (i) the usual three-frequency approximation, which assumes a sinusoidal local oscillator (LO) voltage at the junction and a short-circuit at all frequencies above the upper sideband; (ii) a five-frequency approximation, which allows two LO voltage harmonics and five small-signal sidebands; and (iii) a quasi five-frequency approximation in which five small-signal sidebands are allowed, but the LO voltage is assumed sinusoidal. These are compared with a full harmonic-Newton solution of Tucker´s equations, including eight LO harmonics and their corresponding sidebands, for realistic SIS (superconductor-insulator-superconductor) mixer circuits. It is shown that the accuracy of the three approximations depends strongly on the value of ωR_NC for the SIS junctions used. For ωR_NC values in the range 0.5-10, the range of most practical interest, the quasi five-frequency approximation is a considerable improvement over the three-frequency approximation, giving results very close to those of the eight-harmonic solution, and should be suitable for much design work