A new simulator for Josephson circuits with lossy transmission lines

A network simulator for Josephson circuits is described, and its performance is compared with SPICE. The proposed simulator can simulate large-scale networks containing either lossy or lossless transmission lines and nonlinear lumped elements such as Josephson junctions. The transmission line treatment is completely general, but with constant distributed parameters, and all lumped elements may be nonlinear. Attention is focused on the simulation of the transmission lines; the technique for this simulation is based on the linearity of the elements of the transmission line. The propagating waves are divided into short pulses represented by the sum of two step functions delayed with respect to each other. The equations for the treatment of the transmission lines are given, and some example simulations are presented. Emphasis is placed on evaluation of the simulator in comparison with SPICE. It is shown that for circuits with long lossy transmission lines the simulator can be appreciably faster than SPICE, in which the lines would have to be represented by a cascade of lumped elements.