Going Nonlinear

Since the advent of the nonlinear vector network analyzer (NVNA), microwave engineers have become familiar with new terminology regarding nonlinear network parameters such as "X-parameters" (registered trademark of Agilent Technologies), "S-functions", and "waveform engineering/the Cardiff model", as well as new types of equipment used to perform nonlinear characterizations. These nonlinear network parameter approaches have been developed by Root and Verspecht, Verbeyst and Vanden Bossche, and Tasker. Equipment is now commercially avail able to measure these parameters. To date, X-parameters and S-functions have been predominately used to describe amplifiers in system level simulations. Wave form engineering with the Cardiff model has focused on transistor-level amplifier design. Understanding these behavioral modeling approaches allows their application as an effective and time-saving tool for nonlinear power amplifier design. This article examines the X-parameters and S-functions in an effort to provide a working knowledge that will also apply to understanding the other aforementioned approaches.