  Predicting the performance of traveling-wave parametric amplifiers (TWPAs)
based on nonlinear elements like superconducting Josephson junctions (JJs) is
vital for qubit read-out in quantum computers. The purpose of this article is
twofold: (a) to demonstrate how nonlinear inductors based on combinations of
JJs can be modeled in commercial circuit simulators, and (b) to show how the
harmonic balance (HB) is used in the reliable prediction of the amplifier
performance e.g., gain and pump harmonic power conversion. Experimental
characterization of two types of TWPA architectures is compared with
simulations to showcase the reliability of the HB method. We disseminate the
modeling know-how and techniques to new designers of parametric amplifiers.
