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Introduction to Switched Circuits | SpringerLink

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Introduction to Switched Circuits

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Book cover Nonsmooth Modeling and Simulation for Switched Circuits

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Abstract

This section is dedicated to introduce simple circuits that contain electronic devices with a nonsmooth current/voltage characteristic. Examples are RLC circuits with so-called ideal diodes, ideal Zener diodes, ideal switches. The main peculiarities of their dynamics are highlighted through detailed analysis. The parallel with simple nonsmooth mechanical systems is made. Last, but not least, the numerical method that will be used in the remainder of the book is introduced.

Good models should describe the real physics only as far as needed and should not carry too much additional ballast, which would slow down the numerical processes necessary to solve them, but would also obscure the desired results… It is a matter of fact that the more compact mathematical formulations yield at the end the better numerical codes.

C. Glocker in Glocker (2005)

An erratum to this chapter can be found at http://dx.doi.org/10.1007/978-90-481-9681-4_9

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Notes

  1. 1.

    In the sequel we shall often neglect the brackets {a} to denote the singletons.

  2. 2.

    See Chap. 2 and (2.23) for details on how to obtain the multivalued mapping \(\mathcal{F}\left( \cdot \right)\) from the nonsmooth part of (1.42).

  3. 3.

    In a system \(\dot{x}(t)=Ax(t)+B\lambda(t)\), w(t)=Cx(t)+D λ(t), with λ(t)∈ℝ, w(t)∈ℝ, the relative degree r is the integer ≥0 such that r=0 if \(D\not=0\), r≥1 if D=0 and CA i−1 B=0 for all i<r, while CA r−1 B≠0.

  4. 4.

    Usually one writes λ instead of v, since this slack variable has the mathematical meaning of a Lagrange multiplier.

  5. 5.

    http://www.cppsim.com/index.html.

  6. 6.

    http://www.lmgc.univ-montp2.fr/~dubois/LMGC90/index.html.

References

  • V. Acary, B. Brogliato, Numerical Methods for Nonsmooth Dynamical Systems: Applications in Mechanics and Electronics. Lecture Notes in Applied and Computational Mechanics, vol. 35 (Springer, Berlin, 2008)

    MATH  Google Scholar 

  • V. Acary, B. Brogliato, D. Goeleven, Higher order Moreau’s sweeping process: mathematical formulation and numerical simulation. Mathematical Programming, Series A 113(1), 133–217 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  • K. Addi, B. Brogliato, D. Goeleven, A qualitative mathematical analysis of a class of linear variational inequalities via semi-complementarity problems: applications in electronics. Mathematical Programming A (2010). doi:10.1007/s10107-009-0268-7

    MATH  Google Scholar 

  • K. Addi, S. Adly, B. Brogliato, D. Goeleven, A method using the approach of Moreau and Panagiotopoulos for the mathematical formulation of non-regular circuits in electronics. Nonlinear Analysis: Hybrid Systems 1(1), 30–43 (2007)

    MathSciNet  MATH  Google Scholar 

  • C. Batlle, E. Fossas, A. Miralles, Generalized discontinuous conduction modes in the complementarity formalism. IEEE Transactions on Circuits and Systems II, Express Briefs 52(8), 447–451 (2005)

    Article  Google Scholar 

  • D. Bedrosian, J. Vlach, Analysis of switched networks. International Journal of Circuit Theory and Applications 20, 309–325 (1992)

    Article  MATH  Google Scholar 

  • D. Biolek, J. Dobes, Computer simulation of continuous-time and switched circuits: limitations of SPICE-family programs and pending issues, in Radioelektronika, 17th Int. Conference, Brno, Czech Republic, 24–25 April 2007

    Google Scholar 

  • W. Bliss, S. Smith, K. Loh, A switched-capacitor realization of discrete-time block filters, in 35th IEEE Midwest Symposium on Circuits and Systems, vol. 1, 9–12 August 1992, pp. 429–432

    Google Scholar 

  • B. Brogliato, Some perspectives on the analysis and control of complementarity systems. IEEE Transactions on Automatic Control 48(6), 918–935 (2003)

    Article  MathSciNet  Google Scholar 

  • B. Brogliato, Absolute stability and the Lagrange-Dirichlet theorem with monotone multivalued mappings. Systems and Control Letters 51, 343–353 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • B. Brogliato, D. Goeleven, The Krasovskii-LaSalle invariance principle for a class of unilateral dynamical systems. Mathematics of Control, Signals and Systems 17(1), 57–76 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  • B. Brogliato, D. Goeleven, Well-posedness, stability and invariance results for a class of multivalued Lur’e dynamical systems. Nonlinear Analysis: Theory, Methods and Applications (2010, in press)

    Google Scholar 

  • B. Brogliato, R. Lozano, B. Maschke, O. Egeland, Dissipative Systems Analysis and Control Theory and Applications, 2nd edn. Communications and Control Engineering (Springer, London, 2007)

    MATH  Google Scholar 

  • K. Camlibel, Complementarity methods in the analysis of piecewise linear dynamical systems, PhD thesis, Katholieke Universiteit Brabant, 2001. ISBN 90 5668 073X

    Google Scholar 

  • M.K. Camlibel, W. Heemels, J. Schumacher, Consistency of a time-stepping method for a class of piecewise-linear networks. IEEE Transactions on Circuits and Systems I 49, 349–357 (2002a)

    Article  MathSciNet  Google Scholar 

  • M. Camlibel, W. Heemels, J. Schumacher, On linear passive complementarity systems. European Journal of Control 8(3), 220–237 (2002b)

    Article  MATH  Google Scholar 

  • A. Carbone, F. Palma, Discontinuity correction in piecewise-linear models of oscillators for phase noise characterization. International Journal of Circuit Theory and Applications 35(1), 93–104 (2006)

    Article  MATH  Google Scholar 

  • L. Chua, A. Dang, Canonical piecewise-linear analysis: Part II—tracing driving-point and transfer characteristics. IEEE Transactions on Circuits and Systems CAS-32(5), 417–444 (1985)

    Article  MATH  Google Scholar 

  • L. Chua, R. Ying, Canonical piecewise-linear analysis. IEEE Transactions on Circuits and Systems CAS-30(3), 125–140 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  • H. Chung, A. Ioinovici, Fast computer aided simulation of switching power regulators based on progressive analysis of the switches’ state. IEEE Transactions on Power Electronics 9(2), 206–212 (1994)

    Article  Google Scholar 

  • L. De Kelper, A. Dessaint, K. Al-Haddad, H. Nakra, A comprehensive approach to fixed-step simulation of switched circuits. IEEE Transactions on Power Electronics 17(2), 216–224 (2002)

    Article  Google Scholar 

  • O. Enge, P. Maisser, Modelling electromechanical systems with electrical switching components using the linear complementarity problem. Multibody System Dynamics 13, 421–445 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  • T. Fujisawa, E. Kuh, T. Ohtsuki, A sparse matrix method for analysis of piecewise linear resistive circuits. IEEE Transactions on Circuit Theory 19(6), 571–584 (1972)

    Article  Google Scholar 

  • C. Glocker, Set-Valued Force Laws: Dynamics of Non-Smooth Systems. Lecture Notes in Applied Mechanics, vol. 1 (Springer, Berlin, 2001)

    Book  MATH  Google Scholar 

  • C. Glocker, Models of non-smooth switches in electrical systems. International Journal of Circuit Theory and Applications 33, 205–234 (2005)

    Article  MATH  Google Scholar 

  • D. Goeleven, Existence and uniqueness for a linear mixed variational inequality arising in electrical circuits with transistors. Journal of Optimization Theory and Applications 138(3), 397–406 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  • D. Goeleven, B. Brogliato, Stability and instability matrices for linear evolution variational inequalities. IEEE Transactions on Automatic Control 49(4), 521–534 (2004)

    Article  MathSciNet  Google Scholar 

  • W. Heemels, B. Brogliato, The complementarity class of hybrid dynamical systems. European Journal of Control 9, 311–349 (2003)

    Article  MATH  Google Scholar 

  • W. Heemels, M. Camlibel, J. Schumacher, A time-stepping method for relay systems, in Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, December 2000, pp. 4461–4466

    Google Scholar 

  • W. Heemels, M. Camlibel, J. Schumacher, On event-driven simulation of electrical circuits with ideal diodes. APII Journal Européen des Systèmes Automatisés, Numéro Spécial ADPM 1, 1–22 (2001)

    Google Scholar 

  • M. Huang, S. Liu, A fully differential comparator-based switched-capacitor δ σ modulator. IEEE Transactions on Circuits and Systems II, Express Briefs 56(5), 369–373 (2009)

    Article  Google Scholar 

  • S. Kang, L. Chua, A global representation of multidimensional piecewise-linear functions with linear partitions. IEEE Transactions on Circuits and Systems CAS-25(11), 938–940 (1978)

    Article  MATH  Google Scholar 

  • T. Kevenaar, D. Leenaerts, A comparison of piecewise-linear model description. IEEE Transactions on Circuits and Systems I, Fundamental Theory and Applications 39(12), 996–1004 (1992)

    Article  MATH  Google Scholar 

  • D. Leenaerts, On linear dynamic complementarity systems. IEEE Transactions on Circuits and Systems I, Fundamental Theory and Applications 46(8), 1022–1026 (1999)

    Article  MATH  Google Scholar 

  • D. Leenaerts, W. Van Bokhoven, Piecewise Linear Modeling and Analysis (Kluwer Academic, Norwell, 1998). ISBN: 0792381904

    Book  MATH  Google Scholar 

  • C. Liu, J. Hsieh, C. Chang, J. Bocek, Y. Hsiao, A fast-decoupled method for time-domain simulation of power converters. IEEE Transactions on Power Electronics 8(1), 37–45 (1993)

    Article  Google Scholar 

  • T. Lukl, J. Vrana, J. Misurec, Scisip—program for switched circuit analysis in matlab, in IEEE International Behavioral Modeling and Simulation Workshop, San Jose, California, 2006, pp. 61–66

    Google Scholar 

  • P. Maffezzoni, L. Codecasa, D. D’Amore, Event-driven time-domain simulation of closed-loop switched circuits. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 25(11), 2413–2426 (2006)

    Article  Google Scholar 

  • D. Maksimovic, A. Stankovic, V. Thottuvelil, G. Verghese, Modeling and simulation of power electronic converters. Proceedings of the IEEE 89(6), 898–912 (2001)

    Article  Google Scholar 

  • K. Mayaram, D. Lee, D. Moinian, J. Roychowdhury, Computer-aided circuit analysis tools for RFIC simulation: algorithms, features, and limitations. IEEE Transactions on Circuits and Systems II, Analog and Digital Signal Processing 47(4), 274–286 (2000)

    Article  Google Scholar 

  • M. Moeller, C. Glocker, Non-smooth modelling of electrical systems using the flux approach. Nonlinear Dynamics 50, 273–295 (2007)

    Article  MATH  Google Scholar 

  • M. Monteiro Marques, Differential Inclusions in Nonsmooth Mechanical Problems. Shocks and Dry Friction. Progress in Nonlinear Differential Equations and Their Applications, vol. 9 (Birkhäuser, Basel, 1993)

    Book  MATH  Google Scholar 

  • A. Opal, Sampled data simulation of linear and nonlinear circuits. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 15(3), 295–307 (1996)

    Article  Google Scholar 

  • M. Parodi, M. Storace, P. Julian, Synthesis of multiport resistors with piecewise-linear characteristics: a mixed-signal architecture. International Journal of Circuit Theory and Applications 33(4), 307–319 (2005)

    Article  MATH  Google Scholar 

  • L. Repetto, M. Parodi, M. Storace, A procedure for the computation of accurate pwl-approximations of non-linear dynamical systems. International Journal of Circuit Theory and Applications 34(2), 237–248 (2006)

    Article  MATH  Google Scholar 

  • S. Stevens, P. Lin, Analysis of piecewise-linear resistive networks using complementarity pivot theory. IEEE Transactions on Circuits and Systems CAS-28(5), 429–441 (1981)

    Article  MATH  Google Scholar 

  • J. Valsa, J. Vlach, Swann—a programme for analysis of switched analogue non-linear networks. International Journal of Circuit Theory and Applications 23, 369–379 (1995)

    Article  Google Scholar 

  • W. van Bokhoven, Piecewise linear modelling and analysis. PhD thesis, Technical University of Eindhoven, TU/e, 1981. Available at alexandria.tue.nl/extra3/proefschrift/PRF3B/8105755.pdf

  • W. van Bokhoven, J. Jess, Some new aspects of P and P 0 matrices and their application to networks with ideal diodes, in IEEE Int. Symp. Circuits and Systems, 1978, pp. 806–810

    Google Scholar 

  • W. van Eijndhoven, A piecewise linear simulator for large scale integrated circuits. PhD thesis, Technical University of Eindhoven, TU/e, 1984

    Google Scholar 

  • M.T. van Stiphout, Plato—a piecewise linear analysis for mixed-level circuit simulation, PhD thesis, Technical University of Eindhoven, TU/e, 1990

    Google Scholar 

  • L. Vandenberghe, B. De Moor, J. Vandewalle, The generalized linear complementarity problem applied to the complete analysis of resistive piecewise-linear circuits. IEEE Transactions on Circuits and Systems 36(11), 1382–1391 (1989)

    Article  MathSciNet  Google Scholar 

  • F. Vasca, L. Iannelli, M. Camlibel, R. Frasca, A new perspective for modelling power electronics converters: complementarity framework. IEEE Transactions on Power Electronics 24(2), 456–468 (2009)

    Article  Google Scholar 

  • J. Vlach, A. Opal, Modern CAD methods for analysis of switched networks. IEEE Transactions on Circuits and Systems I, Fundamental Theory and Applications 44(8), 759–762 (1997)

    Article  MATH  Google Scholar 

  • J. Vlach, K. Singhai, M. Vlach, Computer oriented formulation of equations and analysis of switched-capacitor networks. IEEE Transactions on Circuits and Systems 31(9), 753–765 (1984)

    Article  MATH  Google Scholar 

  • J. Vlach, J. Wojciechowski, A. Opal, Analysis of nonlinear networks with inconsistent initial conditions. IEEE Transactions on Circuits and Systems I, Fundamental Theory and Applications 42(4), 195–200 (1995)

    Article  MATH  Google Scholar 

  • Y. Wang, S. Joeres, R. Wunderlich, S. Heinen, Modeling approaches for functional verification of RF-socs: limits and future requirements. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 28(5), 769–773 (2009)

    Article  Google Scholar 

  • C. Wen, S. Wang, H. Zhang, M. Khan, A novel compact piecewise-linear representation. International Journal of Circuit Theory and Applications 33(1), 87–97 (2005)

    Article  MATH  Google Scholar 

  • K. Yamamura, A. Machida, An efficient algorithm for finding all dc solutions of piecewise-linear circuits. International Journal of Circuit Theory and Applications 36(8), 989–1000 (2008)

    Article  MATH  Google Scholar 

  • F. Yuan, A. Opal, Computer methods for switched circuits. IEEE Transactions on Circuits and Systems I, Fundamental Theory and Applications 50(8), 1013–1024 (2003)

    Article  Google Scholar 

  • L. Zhu, J. Vlach, Analysis and steady state of nonlinear networks with ideal switches. IEEE Transactions on Circuits and Systems I, Fundamental Theory and Applications 42(4), 212–214 (1995)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. INRIA Rhône-Alpes, avenue de l’Europe 655, 38334, Saint-Ismier, France

    Vincent Acary, Olivier Bonnefon & Bernard Brogliato

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  1. Vincent Acary
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Correspondence to Vincent Acary .

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Acary, V., Bonnefon, O., Brogliato, B. (2011). Introduction to Switched Circuits. In: Nonsmooth Modeling and Simulation for Switched Circuits. Lecture Notes in Electrical Engineering, vol 69. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9681-4_1

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  • DOI: https://doi.org/10.1007/978-90-481-9681-4_1

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