Simulating the behaviour of travelling wave superconducting parametric amplifiers using a commercial circuit simulator

Kinetic inductance travelling wave parametric amplifiers (KI-TWPAs) have been simulated using Keysight's Advanced Design System. A lumped element representation of a superconducting transmission line has been developed using nonlinear inductor elements to represent the current dependency of the intrinsic kinetic inductance. This provides a fast, simple and easily modifiable method for analysing the parametric processes that occur in nonlinear kinetic inductance devices, such as parametric oscillators or amplifiers while also allowing the accompanying RF network to be optimised. This methodology is used to model the behaviour of a select number of KI-TWPA designs operating in the 3-wave mixing (3WM) and 4-wave mixing (4WM) regimes. S-parameters and dispersion properties are extracted from large signal S-parameter simulations, and the gain curve of each amplifier design is generated from harmonic balance simulations. The results are compared to the gain expression from the analytic solutions of the coupled mode equations while making reference to the gain curves of the equivalent KI-TWPAs from literature.