Fast Simulation of Analog Circuit Blocks under Nonstationary Operating Conditions

This paper proposes a black-box behavioral modeling framework for analog circuit blocks operating under small-signal conditions around non-stationary operating points. Such variations may be induced either by changes in the loading conditions or by event-driven updates of the operating point for system performance optimization, e.g., to reduce power consumption. An extension of existing data-driven parameterized reduced-order modeling techniques is proposed that considers the time-varying bias components of the port signals as non-stationary parameters. These components are extracted at runtime by a lowpass filter and used to instantaneously update the matrices of the reduced-order state-space model realized as a SPICE netlist. Our main result is a formal proof of quadratic stability of such Linear Parameter Varying (LPV) models, enabled by imposing a specific model structure and representing the transfer function in a basis of positive functions whose elements constitute a partition of unity. The proposed quadratic stability conditions are easily enforced through a finite set of small-size Linear Matrix Inequalities (LMI), used as constraints during model construction. Numerical results on various circuit blocks including voltage regulators confirm that our approach not only ensures the model stability, but also provides speedup in runtime up to 2 orders of magnitude with respect to full transistor-level circuits.