Mathematical approaches to electron device modelling for non-linear microwave circuit design: state of the art and present trends

The accuracy of CAD techniques for the design of non-linear microwave circuits is strongly dependent on the features of the models used for the characterization of electron devices (i.e. MESFET, bipolar transistors, diodes etc...). At present, empirical equivalent circuits are widely used. These models, which are in many cases sufficiently accurate, require, however, quite refined numerical and measurement techniques to extract from measured data the parameters of a model which is strongly dependent on the particular physical structure of each device. Moreover, when using equivalent circuit models, the design of non-linear microwave circuits must be carried out by using numerical optimization techniques. In this respect a simple mathematical model described in the frequency domain in terms of explicit equations between the electrical variables, would be preferable for the designer. Mathematical models, in fact, allow quite easy, direct procedures for circuit design. This paper deals with the problem of mathematical modelling of electron devices operating under large-signal conditions at microwave frequencies. In particular, mathematical models based on the describing-function and Volterra-series approach are considered also taking into account their application to circuit design. The advantages of a recently proposed mathematical modelling approach based on mild assumptions valid for most types of electron devices, are also discussed in the paper.