Symbolic Analysis of Large Circuits Using Discrete Wavelet Transform
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.
[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.
[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.
@article{"International Journal of Electrical, Electronic and Communication Sciences:58220", author = "Ali Al-Ataby and Fawzi Al-Naima", title = "Symbolic Analysis of Large Circuits Using Discrete Wavelet Transform", 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.", volume = "3", number = "4", pages = "831-7", }
