Equations system constructors of hierarchical circuits play a central role in device modeling, nonlinear equations solving, and circuit design automation. However, existing constructors present limitations in applications to different extents. For example, the costs of developing and reusing device models -- especially coarse-grained equivalent models of circuit modules -- remain high while parameter sensitivity analysis is complex and inefficient. Inspired by differentiable programming and leveraging the ecosystem benefits of open-source software, we propose an equations system constructor using the computational graph representation, along with its JSON format netlist, to address these limitations. This representation allows for runtime dependencies between signals and subcircuit/device parameters. The proposed method streamlines the model development process and facilitates end-to-end computation of gradients of equations remainders with respect to parameters. This paper discusses in detail the overarching concept of hierarchical subcircuit/device decomposition and nested invocation by drawing parallels to functions in programming languages, and introduces rules for parameters passing and gradient propagation across hierarchical circuit modules. The presented numerical examples, including (1) an uncoupled CMOS model representation using "equivalent circuit decomposition+dynamic parameters" and (2) operational amplifier (OpAmp) auto device sizing, have demonstrated that the proposed method supports circuit simulation and design and particularly subcircuit modeling with improved efficiency, simplicity, and decoupling compared to existing techniques.

翻译：层次化电路的方程系统构造器在器件建模、非线性方程求解及电路设计自动化中发挥着核心作用。然而，现有构造器在不同程度上存在应用局限性。例如，器件模型（尤其是电路模块的粗粒度等效模型）的开发和复用成本仍然较高，而参数灵敏度分析则复杂且低效。受可微分编程的启发并利用开源软件的生态优势，我们提出了一种采用计算图表示的方程系统构造器及其JSON格式网表，以应对这些局限。该表示方法支持信号与子电路/器件参数之间的运行时依赖关系。所提方法简化了模型开发流程，并实现了方程残差对参数梯度的端到端计算。本文通过类比编程语言中的函数，详细阐述了层次化子电路/器件分解与嵌套调用的总体概念，并介绍了跨层次电路模块的参数传递与梯度传播规则。所展示的数值算例包括：（1）采用“等效电路分解+动态参数”的非耦合CMOS模型表示，以及（2）运算放大器（OpAmp）自动器件尺寸设计，这些算例证明所提方法能够支持电路仿真与设计，特别是在子电路建模方面，相较于现有技术具有更高的效率、简洁性和解耦性。