X ‐Parameters

Abstract

X‐parameters are a rigorous superset of S‐parameters that are applicable to linear and nonlinear radio‐frequency (RF) and microwave components, excited by small and large signals. X‐parameters reduce exactly to S‐parameters in the small‐signal limit. Unlike S‐parameters, X‐parameters contain detailed and useful information including magnitudes and phases of distortion products generated by the nonlinear component in response to large‐signal stimuli. In fact, the framework of X‐parameters unifies linear S‐parameters, load‐pull measurements of power amplifiers, multiport nonlinear measurements of frequency translation devices (e.g., mixers), and calibrated nonlinear waveform measurements in a consistent, rigorous, scalable formalism and solution suite. X‐parameters provide a powerful and eminently practical solution to many previously unsolved problems, significantly advancing the state of the art in characterization, modeling, and design of nonlinear RF and microwave components and systems. X‐parameters enable a predictable and hierarchical design methodology for nonlinear systems based only on the knowledge of the X‐parameters of their constituent components and their connectivity. X‐parameters can be applied wherever linear S‐parameters are currently used for active or nonlinear devices and components, but with more benefit. X‐parameters do for nonlinear characterization, modeling, and design of nonlinear microwave and RF components and systems what S‐parameters do for linear components and systems. This article reviews the basic concepts and formalism of X‐parameters. It describes several practical use cases and enumerates many of the major benefits and their significance. A discussion of the measurements is provided, as well as a description of the file format for convenient reference.