This article proposes a black-box behavioral modeling framework for analog circuit blocks (CBs) operating under small-signal conditions around nonstationary 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, which considers the time-varying bias components of the port signals as nonstationary parameters. These components are extracted at runtime by a low-pass 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 (LMIs), used as constraints during model construction. Numerical results on various CBs, including voltage regulators, confirm that our approach not only ensures the model stability but also provides speedup in runtime up to two orders of magnitude with respect to full transistor-level circuits.

中文翻译：

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非平稳工作条件下模拟电路块的快速仿真

本文提出了一个黑盒行为建模框架，用于在非平稳工作点周围的小信号条件下运行的模拟电路块 (CB)。这种变化可能是由负载条件的变化引起的，也可能是由用于系统性能优化的操作点的事件驱动更新引起的，例如，以降低功耗。提出了对现有数据驱动参数化降阶建模技术的扩展，该技术将端口信号的时变偏置分量视为非平稳参数。这些组件在运行时由低通滤波器提取，并用于即时更新作为 SPICE 网表实现的降阶状态空间模型的矩阵。我们的主要结果是这种线性参数变化 (LPV) 模型的二次稳定性的正式证明，通过施加特定的模型结构并在正函数的基础上表示传递函数，这些正函数的元素构成了统一的分区。提出的二次稳定性条件可以通过一组有限的小规模线性矩阵不等式 (LMI) 轻松执行，在模型构建期间用作约束。包括电压调节器在内的各种 CB 的数值结果证实，我们的方法不仅确保了模型稳定性，而且相对于完整的晶体管级电路，还提供了高达两个数量级的运行时间加速。提出的二次稳定性条件可以通过一组有限的小规模线性矩阵不等式 (LMI) 轻松执行，在模型构建期间用作约束。包括稳压器在内的各种 CB 的数值结果证实，我们的方法不仅确保了模型的稳定性，而且相对于完整的晶体管级电路，还提供了高达两个数量级的运行时间加速。提出的二次稳定性条件可以通过一组有限的小规模线性矩阵不等式 (LMI) 轻松执行，在模型构建期间用作约束。包括稳压器在内的各种 CB 的数值结果证实，我们的方法不仅确保了模型的稳定性，而且相对于完整的晶体管级电路，还提供了高达两个数量级的运行时间加速。