Transient sensitivity analysis aims to obtain the gradients of objective functions (circuit performance) with respect to design or variation parameters in a simulator, which can be widely used in yield analysis and circuit optimization, among others. However, the traditional method has a computational complexity of $O\mathsf{}\mathrm{(}{N}^{\mathrm{2}}\mathrm{)}$ for objective functions containing circuit states at $N$ time points. The computational complexity is too expensive for large $N$, especially in time-frequency transform. This paper proposes a many-time-point sensitivity method to reduce the computational complexity to $O\mathsf{}\mathrm{(}N\mathrm{)}$ in multiparameter many-time-point cases. The paper demonstrates a derivation process that improves efficiency by weighting the transfer chain and multiplexing the backpropagation process. We also proposed an early-stop method to improve efficiency further under the premise of ensuring accuracy. The algorithm enables sensitivity calculation of performances involving thousands of time points, such as signal-to-noise and distortion ratio and total harmonic distortion, with significant speed improvements.

Building a post-layout simulation performance model is essential in closing the loop of analog circuits, but it is a challenging task because of the high-dimensional space and expensive simulation cost. To facilitate efficient modeling, this paper proposes a Global Mapping Model Fusion (GMMF) technique. The key idea of GMMF is to reuse the schematic-level model trained by the Artificial Neural Network (ANN) algorithm, and combine it with few mapping coefficients to build the post-simulation model. Furthermore, as an efficient global optimization algorithm, differential evolution is applied to determine the optimal mapping coefficients with few samples. In GMMF, only a small number of mapping coefficients are unknown, so the number of post-layout samples needed is significantly reduced. To enhance practical utility of the proposed GMMF technique, two specific mapping relations, i.e., linear or weakly no-linear and nonlinear, are carefully considered in this paper. We conduct experiments on two topologies of two-stage operational amplifier and comparator in different commercial processes. All the simulation data for modeling are obtained from a parametric design framework. A more than 5 $\mathrm{\times }$ runtime speedup is achieved over ANN without surrendering any accuracy.