Solvability and error bounds for nonlinear circuits containing operational amplifiers

Although an operational amplifier is a nonlinear device, the existing methods of analysis of circuits with operational amplifiers view it as a linear element which possibly has an infinite gain. As a result, it is not clear to what extent the results thus obtained hold. In this paper we construct a general model of a (nonlinear) circuit containing operational amplifiers. Viewing such a network as an interconnection of a multiport withn operational amplifiers, we give conditions for solvability (i.e., for the existence of an input-output operator), and establish estimates for the error incurred by replacing such a system by an idealized system whose operational amplifiers have infinite gain. In this way we determine ranges for variables within which the traditional linear analysis gives results that fulfill given accuracy requirements.