Bounded Input Dissipativity of Linearized Circuit Models

We introduce the concept of Bounded Input Dissipativity (BID) for the characterization from an energy perspective of linearized models of nonlinear circuit blocks. Such linearized models are commonly employed in the design of large systems to approximate circuit blocks that operate in the neighborhood of some well-defined and asymptotically stable bias point and lead to a dramatic reduction in circuit simulation runtime. Even if the original circuit block always behaves as a dissipative system, its linearized model may behave as dissipative or non-dissipative depending on the amplitude of its small-signal port voltages and currents, compared to the corresponding constant bias or supply signal components. This paper presents a theoretical framework for the analysis of such a conditional dissipativity and introduces BID criteria based on the feasibility of Bilinear or Linear Matrix Inequalities. These criteria allow to estimate the maximum small-signal input amplitude that guarantees the dissipativity of the linearized model. Various examples demonstrate the validity of the proposed theory, including a test case showing how spurious and physically inconsistent instabilities may arise if the proposed BID conditions are not verified.