Fast Harmonic Balance of SIS Mixers with Multiple Junctions and Superconducting Circuits

We have extended the spectral domain harmonic balance method of Withington and Kollberg [1] to handle quasiparticle mixer circuits of arbitrary complexity containing any number of superconducting tunnel junctions. Our algorithm uses a multidimensional Newton-Raphson technique to achieve rapid convergence, even when many harmonics are included in the analysis. Another improvement is to perform all linear circuit calculations using the scattering matrix representation typical of modern circuit modeling techniques. This algorithm has been implemented as part of an extensive C++ class library for modeling the signal and noise performance of superconducting heterodyne receivers (SuperMix). Using the common, free C++ compiler ”g++” (Free Software Foundation), impressive results can be achieved on modern workstations of moderate capability. Such speeds will make complex nonlinear optimization calculations a routine part of SIS receiver design.