Linear and nonlinear device models are the building blocks of most RF and microwave designs. S-parameters are often used to represent linear devices. As a “black-box” model, they can easily be obtained using a vector network analyzer and distributed for simulation. S-parameters use superposition to equate the linear relationship between incident and reflected waves at all of the device’s ports. Nonlinear devices, however, distort waveforms such that their behavior cannot be represented through superposition or S-parameters.

Historically, nonlinear devices have been represented in simulation by compact empirical or analytical SPICE models that operate in the time domain. Today’s high-frequency circuit simulators analyze the linear portions of the network in the frequency domain and the nonlinear components in the time domain, resolving the two through an iterative technique called harmonic balance.

The process of developing a compact model, be it empirical or analytical, is costly, time consuming, and potentially exposes the device maker’s intellectual property. More importantly, since most compact model parameters are extracted from linear 50 ohm, S-parameters and DC IV (static and pulsed) data, their ability to predict behavior under extreme nonlinear conditions or non-50 ohm terminations may be questionable. The cost of model development is not trivial, and the resulting quality and availability varies among integrated device manufacturers.