摘要
模拟集成电路稳态仿真一般采用传统瞬态分析法,故要从初始状态长期积分到稳态,而高Q值、低阻尼电路(诸如LC振荡器)因此求解耗时,成为设计效率的明显瓶颈。该文提出了一种基于Shooting法的高效稳态仿真方法,把周期稳态求解转换为边界值问题,先构造状态转移函数,再用牛顿-拉夫逊迭代法求解,同时配合伪瞬态初始化及自适应阻尼策略,保证快速可靠收敛。更难得的是,基于PyTorch框架构建仿真环境,利用自动微分直接、准确地计算雅可比矩阵,且支持CPU、GPU双重加速。通过对环形振荡器、LC压控振荡器及吉尔伯特混频器三类电路的实验验证,清楚、严谨地证明了所提方法在保证精度的前提下,仿真速度较传统方法提高20~117倍,对高Q值电路有极其突出的加速效果,论证了其在模拟集成电路稳态仿真中的优越性。
Abstract
The steady-state simulation of analog integrated circuits generally adopts the traditional transient analysis method. Therefore, it is necessary to integrate from the initial state to the steady state over a long period of time. For high-Q and low-damping circuits (such as LC oscillators), the solution process is thus time-consuming and becomes a significant bottleneck in design efficiency. This paper proposes an efficient steady-state simulation method based on the Shooting method, converting the periodic steady-state solution into a boundary value problem. Firstly, the state transition function is constructed, and then the Newton-Raphson iterative method is used to solve it. At the same time, pseudo-transient initialization and adaptive damping strategies are combined to ensure rapid and reliable convergence. What's more remarkable is that the simulation environment is built based on the PyTorch framework, using automatic differentiation to directly and accurately calculate the Jacobian matrix, and supporting dual acceleration on CPU and GPU. Through experimental verification of three types of circuits: ring oscillators, LC voltage-controlled oscillators, and Gilbert mixer, it is clearly and rigorously proved that the proposed method, while ensuring accuracy, increases the simulation speed by 20 to 117 times compared to traditional methods. It has extremely prominent acceleration effects for high-Q circuits and demonstrates its superiority in steady-state simulation of analog integrated circuits.
关键词
稳态仿真 /
Shooting法 /
牛顿迭代 /
自动微分 /
模拟集成电路 /
PyTorch
Key words
Steady-state simulation /
Shooting method /
Newton iteration /
Automatic differentiation /
Analog integrated circuits /
PyTorch
湛楠, 陈立军, 李志为.
基于Shooting法的模拟集成电路稳态仿真设计与研究[J]. 集成电路与嵌入式系统. 0 https://doi.org/10.20193/j.ices2097-4191.2026.0039
Simulation-based Design and Research of Steady-State Simulation for Integrated Circuits Using the Shooting Method[J]. Integrated Circuits and Embedded Systems. 0 https://doi.org/10.20193/j.ices2097-4191.2026.0039
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