ABSTRACT
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.
- E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. D. Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen. LAPACK Users' Guide, 3rd ed. Society for Industrial and Applied Mathematics, Philadelphia, PA, 1999. Google ScholarDigital Library
- ATLAS. http://math-atlas.sourceforge.net/.Google Scholar
- L. S. Blackford, J. Demmel, J. Dongarra, I. Duff, S. Hammarling, G. Henry, M. Heroux, L. Kaufman, A. Lumsdaine, A. Petitet, R. Pozo, K. Remington, and R. C. Whaley. An updated set of Basic Linear Algebra Subprograms (BLAS). ACM Transactions on Mathematical Software, 28:135--151, 2002. Google ScholarDigital Library
- W. Dong and P. Li. Hierarchical harmonic-balance methods for frequency-domain analog-circuit analysis. IEEE Trans. Computer-Aided Design, 26:2089--2101, Dec. 2007. Google ScholarDigital Library
- P. Feldmann, B. Melville, and D. Long. Efficient frequency domain analysis of large nonlinear analog circuits. In Proceedings of the IEEE 1996 Custom Integrated Circuits Conference, pages 461--464, 1996.Google ScholarCross Ref
- R. Freund, G. H. Golub, and N. M. Nachtigal. Iterative solutions of linear systems. Acta Numerica, pages 57--100, 1991.Google Scholar
- R. J. Gilmore and M. B. Steer. Nonlinear circuit analysis using the method of harmonic balance, a review of the art. Part I. Introductory concepts. International Journal on Microwave and Millimeter Wave Computer Aided Engineering, 1, Jan. 1991.Google Scholar
- Intel. http://www.intel.com/cd/software/products/asmo-na/eng/307757.htm.Google Scholar
- K. S. Kundert, J. K. White, and A. L. Sangiovanni-Vincentelli. Steadystate methods for simulating analog and microwave circuits. Kluwer, Boston, MA, 1990.Google ScholarCross Ref
- P. Li and L. T. Pillegi. Efficient harmonic balance simulation using multi-level frequency decomposition. In IEEE/ACM International Conference on Computer Aided Design, pages 677--682, 2004. Google ScholarDigital Library
- D. Long, R. Melville, K. Ashby, and B. Horton. Full-chip harmonic balance. In Proceedings of the IEEE 1997 Custom Integrated Circuits Conference, pages 379--382, 1997.Google ScholarCross Ref
- R. C. Melville, P. Feldmann, and J. Roychowdhury. Efficient multi-tone distortion analysis of analog integrated circuits. In Proceedings of the IEEE 1995 Custom Integrated Circuits Conference, pages 241--244, 1995.Google ScholarCross Ref
- O. Nastov, R. Telichevesky, K. Kundert, and J. White. Fundamentals of fast simulation algorithms for RF circuits. Proceedings of the IEEE, 93:600--621, Mar. 2007.Google ScholarCross Ref
- J. Roychowdhury. Efficient methods for simulating highly nonlinear multi-rate circuits. In Proceedings 34th Design Automation Conference, pages 269--274, 1997. Google ScholarDigital Library
- J. Roychowdhury. Analyzing circuits with widely separated time scales using numerical PDE methods. IEEE Trans. Circuits Sys. I, 48:578--594, May 2001.Google ScholarCross Ref
- Y. Saad. Iterative methods for sparse linear systems. Society for Industrial and Applied Mathematics, 1996. Google ScholarDigital Library
- R. Telichevesky, K. Kundert, I. Elfadel, and J. K. White. Fast simulation algorithms for RF circuits. In Proceedings of the IEEE 1996 Custom Integrated Circuits Conference, pages 437--444, 1996.Google ScholarCross Ref
- V. Rizzoli, C. Cecchetti, A. Lipparini, and F. Mastri. General-purpose harmonic balance analysis of nonlinear microwave circuits under multitone excitation. IEEE Trans. Microwave Theory Tech, 1, Jan. 1991.Google Scholar
Index Terms
- A robust and efficient harmonic balance (HB) using direct solution of HB Jacobian
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