Systems theory approach to analog circuit design

Analog circuits and and their interconnections, broadly called analog systems, are indispensable components of modern communication and electronic systems as well as electronic converters used in power systems. Almost all such circuits are built using active devices which require an external excitation for their operation. Active devices exhibit large sensitivity of performance to variations of sources, device parameters, operating conditions such as temperature and their operation is often unstable or required to be kept sufficiently stable. Active devices are also difficult to model accurately especially at high frequencies where they are often operated. To harness superior properties of active devices and circuits it is thus necessary to embed such circuits within systems which provide stable operation along with desired level of sensitivity reduction and desired response over a wide band. While interconnections of passive systems is always stable this is not so for active systems. This is in fact the reason why stability is never a requirement in passive circuit design. On the other hand an improperly designed interconnection of stable active circuits may even result in deterioration of stability and sensitivity. Hence for active circuit design it is necessary to build a mathematically rigorous theory of designing interconnections which will provide structure of interconnections for stablility and facilitate solution of performance optimization problems. For passive circuit synthesis a state space based systems theory approach is proposed in [4]. In case of active networks the problem of compensation design is also important apart from a purely synthesis problem, both of which require a rigorous stabilization theory. Purpose of this article is to propose such a stabilization theory in the formalism of factorization theory of feedback systems and show how this leads to an H∞ formulation of the sensitivity reduction problem. Application of fedback control for design of amplifiers has a long history even before the book by Bode [1]. This work can be considered as one of the early attempts at designing active circuits using feedback control concepts. Feedback theory has subsequently enormously advanced and has provided solutions of several problems of control theory (broadly known as H∞ feedback control theory [8]). This theory has also found wide and successful applications in engineering. However an application of these advances to the problem of designing active circuits and systems is seldom found in the literature. Much of the analog