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Abstract

Electrical noise sets a fundamental limit on the performance of electronic systems, particularly in high-sensitivity applications such as radio-frequency receivers. As circuit complexity continues to grow, there is a critical need for faster and more scalable noise analysis methods in circuit simulators. Although time-domain transient noise analysis offers broader applicability than frequency-domain and time-domain steady-state noise analysis, it is typically more computationally expensive, especially for large circuits. This challenge is intensified by flicker noise, whose inclusion in a time-domain circuit formulation greatly increases the effective size of the system. To address these efficiency problems, this dissertation presents several transient noise analysis methods. Using parallel computing and innovative continuous-time and discrete-time modeling approaches, these methods achieve significant improvements in computational efficiency compared to state-of-the-art methods.

Covariance analysis is an effective technique for simulating transient noise in small subblocks of larger circuit designs due to its accuracy and reasonable simulation times. However, its computational efficiency deteriorates as circuit size increases. To improve scalability and reduce simulation times, this dissertation first presents a parallel covariance analysis method. It also introduces a new flicker noise time-domain circuit representation that mitigates the added system complexity associated with modeling flicker noise sources in covariance analysis. Furthermore, an adjoint-based approach is offered to improve the computational efficiency of the parallel covariance analysis method. This dissertation then presents a charge-based covariance analysis method that models nonlinear capacitors using charge rather than voltage in a linearized time-domain noise-perturbed circuit formulation. This approach achieves higher numerical accuracy than traditional capacitance-based methods, allowing larger simulation step sizes and consequently reducing simulation times. Finally, a charge-based covariance analysis method derived using implicit numerical schemes for stochastic differential equations is introduced. By modeling the discrete-time evolution of the covariance, this method provides a more computationally efficient and scalable alternative to continuous-time formulations.