CHARACTERIZATIONS OF NETWORKS

Over the past two decades, we have witnessed a rapid development of solid-state technology with its apparently unending proliferation of new devices. Presently available solid-state devices such as the transistor, the tunnel diode, the Zener diode, and the varactor diode have already replaced the old vacuum tube in most practical network applications. Moreover, the emerging field of integrated circuit technology threatens to push these relatively recent inventions into obsolescence. In order to understand fully the network properties and limitations of solid-state devices and to be able to cope with the applications of the new devices yet to come, it has become increasingly necessary to emphasize the fundamentals of active network theory that will transcend the advent of new devices and design tools.

The purpose of this chapter is to introduce many fundamental concepts used in the study of linear active networks. We first introduce the concepts of portwise linearity and time invariance. Then we define passivity in terms of the universally encountered physical quantities time and energy, and show that causality is a consequence of linearity and passivity. This is followed by a brief review of the general characterizations of w-port networks in the frequency domain. The translation of the time-domain passivity criteria into the equivalent frequencydomain passivity conditions is taken up next. Finally, we introduce the discretefrequency concepts of passivity. The significance of passivity in the study of active networks is that passivity is the formal negation of activity.