  Kinetic inductance travelling wave parametric amplifiers (KI-TWPAs) have been
simulated using Keysight's Advanced Design System (ADS). 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. Results of these 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.
