Modeling and Simulation of Nonlinear Systems

Abstract

Perhaps the single greatest justification for the simulation approach to the study of communication systems is the presence of nonlinear elements. In principle, the performance of linear systems can be attacked by analytical means, but the study of nonlinear systems by such means is by and large intractable. Although there have been many analytical studies of one or another nonlinear device, the system context is usually idealized or much simplified compared to realistic scenarios. In addition, it is typical for such analytical formulations to be of such complexity as to require numerical evaluation, a situation which negates the values of analysis-insight and generality. Hence, simulation is generally the appropriate tool for perhaps most nonlinear communication systems because simulation of such systems is no more difficult than for linear systems, given the model. Indeed, the main difficulty i n nonlinear system simulation is obtaining the model itself. Hence, much of the focus in this chapter will be on modeling methodology and on associated measuring techniques for determining parameters of models.In general, a nonlinear system consists of linear and nonlinear elements. Some of the linear elements may be described by linear differential equations, as discussed in the previous chapter, or by other relationships. The nonlinear elements, which are normally relatively few in number, are described by nonlinear functions or nonlinear differential equations relating the input and output of the element. The transform methods described in the previous chapters cannot strictly be applied to nonlinear systems since superposition does not hold in the latter case. The nonlinear system, therefore, generally has to be simulated in the time domain. This applies to the nonlinear part of the system only. The rest of the system can be simulated either in the time domain or the frequency domain (see Figure 5.1), except when it is part of a feedback system. In contrasting linear and nonlinear system simulation, we should make another point. In the linear case, we are generally satified that we will tend to the correct answer under certain limiting conditions (assuming no finite-precision effects), such as letting the sampling interval become smaller and smaller or increasing the duration of a (truncated) finite impulse response. In nonlinear systems, there is no clear set of limiting conditions under which we can assert that the model comes closer to reality, because it is so much more difficult to ascertain the closeness of a nonlinear model to the functioning of the actual device. This reenforces the point made in Chapter 2 about the need to validate simulation models against hardware counterparts. 203 204 Chapter 5 Figure 5.1. Simulation of a nonlinear communication system. Modeling Considerations for Nonlinear SystemsUsually devices used in communication systems such as traveling-wave tube amplifiers (TWTAs) and solid-state power amplifiers (SSPAs) are described by analytical models that typically involve solving a set of si...