Efficient methods for simulating highly nonlinear multi-rate circuits
DAC '97 Proceedings of the 34th annual Design Automation Conference
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
An updated set of basic linear algebra subprograms (BLAS)
ACM Transactions on Mathematical Software (TOMS)
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Efficient harmonic balance simulation using multi-level frequency decomposition
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
Hierarchical Harmonic-Balance Methods for Frequency-Domain Analog-Circuit Analysis
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Proceedings of the International Conference on Computer-Aided Design
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In this paper we introduce a new method of performing direct solution of the harmonic balance Jacobian. For examples with moderate number of harmonics and moderate to strong nonlinearities, we demonstrate that the direct solver has far superior performance with a moderate increase in memory compared to the best preconditioned iterative solvers. This solver is especially suited for Fourier envelope analysis where the number of harmonics is small, circuits are nonlinear and Jacobian bypass can be used for additional speed. For examples with large number of harmonics and moderate to strong nonlinearities, the performance advantage is maintained but the memory requirements increase. We propose efficient preconditioners based on direct solution of harmonic balance matrices which provide the user with a memory-speed trade-off.