Numerical recipes in Pascal: the art of scientific computing
Numerical recipes in Pascal: the art of scientific computing
Proceedings of the 1996 IEEE/ACM international conference on Computer-aided design
Efficient methods for simulating highly nonlinear multi-rate circuits
DAC '97 Proceedings of the 34th annual Design Automation Conference
Numerical Initial Value Problems in Ordinary Differential Equations
Numerical Initial Value Problems in Ordinary Differential Equations
Computer-Aided Analysis of Electronic Circuits: Algorithms and Computational Techniques
Computer-Aided Analysis of Electronic Circuits: Algorithms and Computational Techniques
Robust, stable time-domain methods for solving MPDEs of fast/slow systems
Proceedings of the 41st annual Design Automation Conference
An efficient and robust technique for tracking amplitude and frequency envelopes in oscillators
ICCAD '05 Proceedings of the 2005 IEEE/ACM International conference on Computer-aided design
A versatile time-domain approach to simulate oscillators in RF circuits
IEEE Transactions on Circuits and Systems Part I: Regular Papers
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Fourier-envelope algorithms are an important component of the mixed-signal/RF verification toolbox. In this paper, we address the unpredictability and lack of robustness that has been reported for these algorithms. We show that the problem stems from fast oscillations in envelopes that are expected to be slowly varying. We demonstrate that this is related to the fact that the envelope equations are always stiff, whether or not the underlying system is. We show that careful choice of envelope initial conditions is necessary to obtain useful solutions, and propose two techniques for finding good initial conditions. Applying these, and solving the envelope equations with stiffly-stable numerical methods, we improve the robustness and reliability of Fourier-envelope methods. We illustrate the new methods with a direct-downconversion mixer circuit.