A nonlinear transmission line model for simulating distributed SIS frequency multipliers

Superconductor/Insulator/Superconductor (SIS) junctions have extremely nonlinear electrical properties, which makes them ideal for a variety of applications, including heterodyne mixing and frequency multiplication. With SIS mixers, the SIS junctions normally have circular cross-sections, but they can also be fabricated in the form of microstrip transmission lines, known as distributed SIS junctions (DSJs). By using a DSJ as an open-circuit stub, it is possible to create a large SIS junction with a low effective input reactance. This is beneficial for SIS frequency multipliers because their output power is proportional to the area of the junction. It is challenging, however, to simulate the behavior of DSJs because (a) they have to be modeled as transmission lines and (b) the model has to take into account the quasiparticle tunneling current, which is a nonlinear function of the AC voltage. In this paper, we present a new nonlinear transmission line model to accurately describe the behavior of DSJs and to simulate the performance of distributed SIS frequency multipliers (DSMs). This model is compared to experimental data from a recent DSM device and good agreement is found between the DC tunneling currents and the output powers at the second harmonic. Based on this success, an improved DSM design is proposed that has a higher output power and a higher conversion efficiency than previous designs