Symbolic Analysis of Large Circuits Using Discrete Wavelet Transform

Authors: Ali Al-Ataby , Fawzi Al-Naima

Abstract:

Symbolic Circuit Analysis (SCA) is a technique used to generate the symbolic expression of a network. It has become a well-established technique in circuit analysis and design. The symbolic expression of networks offers excellent way to perform frequency response analysis, sensitivity computation, stability measurements, performance optimization, and fault diagnosis. Many approaches have been proposed in the area of SCA offering different features and capabilities. Numerical Interpolation methods are very common in this context, especially by using the Fast Fourier Transform (FFT). The aim of this paper is to present a method for SCA that depends on the use of Wavelet Transform (WT) as a mathematical tool to generate the symbolic expression for large circuits with minimizing the analysis time by reducing the number of computations.

Keywords: Numerical Interpolation, Sparse Matrices, SymbolicAnalysis, Wavelet Transform.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1072223

References:

[1] P. M. Lin, Symbolic Network Analysis, Elsevier Science Publishers, 1991, ch. 1.
[2] G. Gielen and W. Sansen, Symbolic Analysis for Automated Design of Analog Integrated Circuits, Kluwer Academic Publishers, 1991, ch. 3.
[3] H. Floberg, Symbolic Analysis in Analog Integrated Circuit Design, Kluwer Academic Publishers, 1997, ch.2.
[4] X. Wang and L. Hedrich, "Hierarchical symbolic analysis of analog circuits using two-port networks", 6th WSEAS International Conference on Circuits, Systems, Electronics, Control & Signal Processing, Cairo, Egypt, 2007.
[5] V. Fernández, P. Wambacq, G. Gielen, A. Rodríguez-Vázquez, and W. Sansen, "Symbolic analysis of large analog integrated circuits by approximation during expression generation", Proc. Int. Symposium on Circuits and Systems, London, pp.25-28, June 1994.
[6] G. Gielen, P. Wambaq, and W. Sansen, "Symbolic analysis methods and applications for analog circuits: a tutorial overview", Proc. IEEE, Vol. 82, No.2, February 1994.
[7] K. Singhal and J. Vlach, "Symbolic analysis of analog and digital circuits", IEEE Transactions on Circuits and Systems, Vol. CAS-24, No.11, November 1977.
[8] K. S. Yeung, "Symbolic Network Function Generation Via Discrete Fourier Transform", IEEE Transactions on Circuits and Systems, Vol. CAS-31, No. 2, 1984.
[9] J. Vlach and K. Singhal, Computer Methods for Circuit Analysis and Design, Van Nostrand-Reinhold, 1993.
[10] K. Singhal and J. Vlach, "Generation of immittance functions in symbolic form for lumped distributed active networks", IEEE Transactions on Circuits and Systems, Vol. CAS-21, No.1 January 1974.
[11] K. Yeung and F. Kumbi, "Symbolic matrix Inversion with application to electronic circuits", IEEE Transactions on Circuits and Systems, Vol. CAS-35, No.2, February 1988.
[12] S. Burrus, R. A. Gopinath, and H. Guo, Introduction to Wavelets Transforms, Prentice-Hall, 1998, ch. 4.
[13] E. Newland, An Introduction to Random Vibrations, Spectral and Wavelet Analysis, Longman Scientific and Technical, 1993, ch.7.
[14] H. P. William , T. V. William, A. T. Saul, and P. F. Brian, Numerical Recipe, The Art of Scientific Computing, Third Edition, Cambridge, 2007.
[15] I. Daubechies, "Orthonormal bases of compactly supported wavelets", Comm. Pure Appl. Math., Vol. 41, 1988, pp. 906-966.
[16] P. Kumar and R. Senani, "Bibliography on nullors and their applications in circuit analysis, synthesis and design", Analog Integrated Circuits and Processing, 33, 65-76, Kluwer Academic Publishers, 2002.
[17] E. Tlelo-Cuautle, C. Sanchez-Lopez, and F. Sandoval-Ibarra, "Symbolic analysis: a formulation approach by manupulation data structures", IEEE SCAS, Vol. IV, pp.640-643, 2003.
[18] E. Tlelo-Cuautle, A. Quintanar-Ramos, G. Gutierrez-Perez, an M. Gonzalez de la Rosa," SIASCA: Interactive system for the symbolic analysis of analog circuits", IEICE Electronic Express, Vol. 1, No.1, pp.19-23, April 2004.
[19] Wai Kai Chen, The Circuits and Filters Handbook, CRC Press, 2003. ISBN´╝Ü 0-8493-0912-3, ch.6.
[20] M. A. Al-Taee, F. M. Al-Naima, and B. Z. Al-Jewad, Optimized sparse storage mode for symbolic analysis of large networks, Advances in Engineering Software, Vol.38, No.2, Feb. 2007, pp.112-120.
[21] M. A. Al-Taee, F. M. Al-Naima, and B. Z. Al-Jewad, Symbolic analyzer for large lumped and distributed networks, Chapter 23 in the Book: Symbolic - Numeric Computations, Wang, Dongming, Zhi, Li- Hong (Eds.), Series: Trends in Mathematics, pp. 375-394, Birkhauser Verlag Basel, Switzerland, Feb 2007.