The 'frozen operating point' method of small-signal analysis

The method of small-signal analysis of nonlinear time-invariant networks about a fixed operating point is well known. When the bias is time-varying the method remains essentially unchanged. This method has been extensively used in perturbational analysis in optimum control theory. Desoer and Wong have given estimates of the difference between the exact response and that of the linearized network, and have shown that, under certain conditions, the relative difference goes to zero as the small signal goes to zero [1]. In the present work, we show how calculations can be greatly simplified when the bias is slowly varying. Making use of recent results of stability theory, we show that small-signal analysis about the frozen operating point is correct within higherorder terms in the small signal, provided a correction term is inserted in the equation. An important feature of the theory is that its assumptions can often be checked by inspection because it involves only the properties of the frozen network. Section I gives a formal description of the method. In Section II, the method is rigorously analyzed and the results are stated in the form of two assertions.