My published book titled Parameter Extraction and Complex Nonlinear Transistor Models concerns with the following three key topics:
- Small-signal model parameter extraction
- Large-signal device modeling
- Large-signal measurement techniques
In my first post, dated December 17, 2019, I explained the limitation of using the standard 15-element FET model for modern high power multifinger GaN devices. Similar conclusions can be drawn for single- or two-finger GaAs transistors at high operating frequencies (e.g., 80 GHz).
In my post, dated December 31, 2019, I commented briefly about my motivation to write this book. In this contribution the essential features concerning small-signal model parameter extraction were roughly outlined. The essential point that was highlighted was: instead of choosing arbitrary starting values for the optimization process, these should be carefully selected on the basis of physical device consideration.
In this post I want to address a further interesting aspect. This concerns the in-depth training of anyone involved in microwave transistor development, modeling and high-frequency circuit design. The book gives a broad overview about the diverse model parameter extraction techniques covering both analytical and optimization-based approaches.
Postgraduate students in microwave technology as well as practitioners and physicists in the field learn about the diverse extraction techniques that are thoroughly treated in the book. The underlying mathematical background is described in detail, so that a software implementation is facilitated. But the extraction methods are not only described theoretically. Practical examples of parameter extraction are presented, and pros and cons of the discussed method identified.
As is well known device modeling and model parameter extraction is an inexhaustible field of knowledge that commonly requires much experience to obtain satisfactory interpretable results. Being familiar with the diverse modeling techniques, the book may serve as a guide to select the right extraction method on the basis of device complexity, frequency of operation as well as required extraction accuracy.
As shown, the device model of a low-power field-effect transistor can be approximated by the standard 15-element model at sufficiently low operating frequency. Thus, the classical extraction methods after Dambrine et al. and Berroth et al. can be applied. However, concerning multifinger power devices more complex model topologies are needed to take care for parasitic interelectrode capacitive effects. Regarding single- or two-finger devices at high-frequencies (e.g., 80 GHz and above) stray capacitances have an increasing impact on the device response that must be taken into account by modification and extension of the device equivalent circuit. The book stresses this special point. Beyond conventional low-frequency extraction methods, innovative extraction algorithms are addressed that take these capacitive effects into account.
A wide variety of optimization methods have been proposed so far to deal with this complex extraction problem. To name just a few treated in the book: Descent methods (steepest descent, Newton, Davidon-Fletcher-Powell), nonlinear least-squares data fitting (Gauss-Newton, Levenberg-Marquardt), direct search methods (Hook-Jeeves, Simplex), global optimization (multistart, genetic algorithm, simulated annealing, tree annealing, leaping simplex), and hybrid optimizer.
Standard and advanced extraction methods involving optimization techniques are then discussed in detail and evaluated on the basis of their extraction evidence such as all-at once model parameter extraction, decomposition-based extraction (empirical decomposition, automatic decomposition based on sensitivity analysis), bidirectional search (with detailed mathematical derivation for direct software implementation), pure analytical model parameter extraction, and analytical model parameter extraction using rational functions.
It follows then more advanced extraction methods developed in our research group during the last two decades focusing on the physically reliable model parameter extraction of complex model topologies (three shell model), such as repetitive random optimization and adaptive search space, model parameter extraction with measurement-correlated parameter starting values (“correlated” means that the starting values cannot be defined independently of each other)
Summarizing, the book provides a broad overview and basic understanding of device modeling and extraction methods. It may serve as a guideline for practical application. Regarding teaching in microwave technology, the book has meanwhile proven to be a useful course tool within a short period of time in the international master’s programme Electrical Communication Engineering (ECE) at Kassel University.