EMBEDDING IMPEDANCE APPROXIMATIONS IN THE ANALYSIS OF SIS MIXERS

Tucker's quantum theory of mixers is the basis for almost all analysis and design of SIS (Superconductor-Insulator-Superconductor) mixers. T his paper examines the adequacy of three approximations to Tucker's th eory: (i) the usual three-frequency approximation which assumes a sinu soidal LO voltage at the junction, and a short-circuit at all frequenc ies above the upper sideband, (ii) a five-frequency approximation whic h 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. Thes e are compared with a full harmonic-Newton solution of Tucker's equati ons, including eight LO harmonics and their corresponding sidebands, f or realistic SIS mixer circuits. It is shown that the accuracy of the three approximations depends strongly on the value of omegaR(N)C for t he SIS junctions used. For large omegaR(N)C, all three approximations approach the eight-harmonic solution. For omegaR(N)C values in the ran ge 0.5 to 10, the range of most practical interest, the quasi five-fre quency approximation is a considerable improvement over the three-freq uency approximation, and should be suitable for much design work. For the realistic SIS mixers considered here, the five-frequency approxima tion gives results very close to those of the eight-harmonic solution.