Preface

The need for a rigorous, yet practical, framework for characterization, modeling, and design of nonlinear electronic components at high frequencies has never been more urgent. The communications revolution is inexorably forcing active devices into more and more strongly nonlinear regimes of operation. This is a consequence of the relentless drive for more efficiency in order to save power, extend battery life, and minimize cooling. The price for efficiency is nonlinearity. Dealing with nonlinearity means that new measurement instrumentation and new modeling and design methodologies are required that go far beyond linear S-parameters. Fortunately, there is an overarching, interoperable paradigm combining all these pieces of the nonlinear puzzle together, seamlessly. The new paradigm is called X-parameters, and that is what this book is about.

The book is intended as a comprehensive introduction to X-parameters. It is aimed at a diverse audience with a wide range of backgrounds. This is quite a challenging undertaking! We are targeting professional microwave engineers, device modeling engineers and scientists, RF and microwave circuit designers, electronic and communications engineers, CAE professionals developing simulator algorithms, and microwave and RF professionals developing new high-speed instrumentation for a wide range of nonlinear characterization applications. The inherent interdisciplinary nature of X-parameters is the prime reason we seek to appeal to this broad audience. The practical solutions based on X-parameters deployed by industry over the past several years depend on contributions in all of these areas.

One of the key features that led to the wide adoption of S-parameters was the availability of hardware and calibration techniques capable of making quick, accurate, and repeatable S-parameter measurements. S-parameters can also be easily extracted in simulation from device or circuit models. In either case, the resulting S-parameters can immediately be used in simulation or design tools. In order to achieve similar success in the nonlinear domain, X-parameters must be easily measured and also easily extracted from simulation.

Measurement hardware

X-parameters, like S-parameters, represent the steady-state behavior of a device in the frequency domain. The linearity assumption of S-parameters, however, greatly simplifies the measurement requirements. The additional capabilities of X-parameters come at the cost of additional complexity in the measurement system as well as the modeling paradigm.

Hardware requirements

X-parameters include cross-frequency terms that capture the distortion products generated by device nonlinearities. In order to measure these terms, the measurement hardware must be capable of measuring coherent cross-frequency phase. Because S-parameters include no cross-frequency interaction (a consequence of the linearity assumption), each frequency may be measured independently with no need for a consistent time base or cross-frequency phase. Since all S-parameters are ratios of waves, there is also no need for accurate measurement of absolute power – only the relative power is needed. As a result, the hardware and calibration techniques developed for S-parameter measurement generally are not sufficient for X-parameter measurement and must be extended to include cross-frequency phase and calibrated absolute power.