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2014 | OriginalPaper | Buchkapitel

2. Mathematical Modeling and Analysis of Nonlinear Time-Invariant RLC Circuits

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Abstract

We give a basic and self-contained introduction to the mathematical description of electrical circuits that contain resistances, capacitances, inductances, voltage, and current sources. Methods for the modeling of circuits by differential–algebraic equations are presented. The second part of this paper is devoted to an analysis of these equations.

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Literatur
1.
Zurück zum Zitat Agricola, I., Friedrich, T.: Global Analysis: Differential Forms in Analysis, Geometry and Physics. Oxford University Press, Oxford (2002) Agricola, I., Friedrich, T.: Global Analysis: Differential Forms in Analysis, Geometry and Physics. Oxford University Press, Oxford (2002)
2.
Zurück zum Zitat Anderson, B.D.O.: Minimal order gyrator lossless synthesis. IEEE Trans. Circuit Theory CT-20(1), 10–15 (1973) Anderson, B.D.O.: Minimal order gyrator lossless synthesis. IEEE Trans. Circuit Theory CT-20(1), 10–15 (1973)
3.
Zurück zum Zitat Anderson, B.D.O., Newcomb, R.W.: Lossless n-port synthesis via state-space techniques. Technical Report 6558-8, Systems Theory Laboratory, Stanford Electronics Laboratories (1967) Anderson, B.D.O., Newcomb, R.W.: Lossless n-port synthesis via state-space techniques. Technical Report 6558-8, Systems Theory Laboratory, Stanford Electronics Laboratories (1967)
4.
Zurück zum Zitat Anderson, B.D.O., Newcomb, R.W.: Impedance synthesis via state-space techniques. Proc. IEEE 115, 928–936 (1968) Anderson, B.D.O., Newcomb, R.W.: Impedance synthesis via state-space techniques. Proc. IEEE 115, 928–936 (1968)
5.
Zurück zum Zitat Anderson, B.D.O., Vongpanitlerd, S.: Scattering matrix synthesis via reactance extraction. IEEE Trans. Circuit Theory CT-17(4), 511–517 (1970) MathSciNet Anderson, B.D.O., Vongpanitlerd, S.: Scattering matrix synthesis via reactance extraction. IEEE Trans. Circuit Theory CT-17(4), 511–517 (1970) MathSciNet
6.
Zurück zum Zitat Anderson, B.D.O., Vongpanitlerd, S.: Network Analysis and Synthesis. Prentice Hall, Englewood Cliffs (1973) Anderson, B.D.O., Vongpanitlerd, S.: Network Analysis and Synthesis. Prentice Hall, Englewood Cliffs (1973)
7.
Zurück zum Zitat Andrasfai, B.: Graph Theory: Flows, Matrices. Taylor & Francis, London (1991) MATH Andrasfai, B.: Graph Theory: Flows, Matrices. Taylor & Francis, London (1991) MATH
8.
Zurück zum Zitat Arnol’d, V.I.: Ordinary Differential Equations. Undergraduate Texts in Mathematics. Springer, Berlin (1992). Translated by R. Cooke MATH Arnol’d, V.I.: Ordinary Differential Equations. Undergraduate Texts in Mathematics. Springer, Berlin (1992). Translated by R. Cooke MATH
9.
Zurück zum Zitat Bächle, S.: Numerical solution of differential–algebraic systems arising in circuit simulation. Doctoral dissertation (2007) Bächle, S.: Numerical solution of differential–algebraic systems arising in circuit simulation. Doctoral dissertation (2007)
10.
Zurück zum Zitat Berger, T.: On differential–algebraic control systems. Doctoral dissertation (2013) Berger, T.: On differential–algebraic control systems. Doctoral dissertation (2013)
11.
Zurück zum Zitat Berger, T., Reis, T.: Zero dynamics and funnel control for linear electrical circuits. J. Franklin Inst. (2014, accepted for publication) Berger, T., Reis, T.: Zero dynamics and funnel control for linear electrical circuits. J. Franklin Inst. (2014, accepted for publication)
12.
Zurück zum Zitat Bodestedt, M., Tischendorf, C.: PDAE models of integrated circuits and perturbation analysis. Math. Comput. Model. Dyn. Syst. 13(1), 1–17 (2007) MathSciNetCrossRefMATH Bodestedt, M., Tischendorf, C.: PDAE models of integrated circuits and perturbation analysis. Math. Comput. Model. Dyn. Syst. 13(1), 1–17 (2007) MathSciNetCrossRefMATH
13.
Zurück zum Zitat Brenan, K.E., Campbell, S.L., Petzold, L.R.: Numerical Solution of Initial-Value Problems in Differential–Algebraic Equations. North-Holland, Amsterdam (1989) MATH Brenan, K.E., Campbell, S.L., Petzold, L.R.: Numerical Solution of Initial-Value Problems in Differential–Algebraic Equations. North-Holland, Amsterdam (1989) MATH
14.
Zurück zum Zitat Cauer, W.: Die Verwirklichung der Wechselstromwiderstände vorgeschriebener Frequenzabhängigkeit. Arch. Elektrotech. 17, 355–388 (1926) CrossRef Cauer, W.: Die Verwirklichung der Wechselstromwiderstände vorgeschriebener Frequenzabhängigkeit. Arch. Elektrotech. 17, 355–388 (1926) CrossRef
16.
Zurück zum Zitat Chua, L.O., Desoer, C.A., Kuh, E.S.: Linear and Nonlinear Circuits. McGraw-Hill, New York (1987) MATH Chua, L.O., Desoer, C.A., Kuh, E.S.: Linear and Nonlinear Circuits. McGraw-Hill, New York (1987) MATH
17.
Zurück zum Zitat Conway, J.B.: A Course in Functional Analysis. Graduate Texts in Mathematics, vol. 96. Springer, New York (1985) MATH Conway, J.B.: A Course in Functional Analysis. Graduate Texts in Mathematics, vol. 96. Springer, New York (1985) MATH
18.
Zurück zum Zitat Deo, N.: Graph Theory with Application to Engineering and Computer Science. Prentice-Hall, Englewood Cliffs (1974) Deo, N.: Graph Theory with Application to Engineering and Computer Science. Prentice-Hall, Englewood Cliffs (1974)
19.
Zurück zum Zitat Desoer, C.A., Kuh, E.S.: Basic Circuit Theory. McGraw-Hill, New York (1969) Desoer, C.A., Kuh, E.S.: Basic Circuit Theory. McGraw-Hill, New York (1969)
20.
Zurück zum Zitat Estévez Schwarz, D.: A step-by-step approach to compute a consistent initialization for the MNA. Int. J. Circuit Theory Appl. 30(1), 1–16 (2002) CrossRefMATH Estévez Schwarz, D.: A step-by-step approach to compute a consistent initialization for the MNA. Int. J. Circuit Theory Appl. 30(1), 1–16 (2002) CrossRefMATH
21.
Zurück zum Zitat Estévez Schwarz, D., Lamour, R.: The computation of consistent initial values for nonlinear index-2 differential–algebraic equations. Numer. Algorithms 26(1), 49–75 (2001) MathSciNetCrossRefMATH Estévez Schwarz, D., Lamour, R.: The computation of consistent initial values for nonlinear index-2 differential–algebraic equations. Numer. Algorithms 26(1), 49–75 (2001) MathSciNetCrossRefMATH
22.
Zurück zum Zitat Estévez Schwarz, D., Tischendorf, C.: Structural analysis for electric circuits and consequences for MNA. Int. J. Circuit Theory Appl. 28(2), 131–162 (2000) CrossRefMATH Estévez Schwarz, D., Tischendorf, C.: Structural analysis for electric circuits and consequences for MNA. Int. J. Circuit Theory Appl. 28(2), 131–162 (2000) CrossRefMATH
23.
Zurück zum Zitat Günther, M., Feldmann, U.: CAD-based electric-circuit modeling in industry I. Mathematical structure and index of network equations. Surv. Math. Ind. 8, 97–129 (1999) MATH Günther, M., Feldmann, U.: CAD-based electric-circuit modeling in industry I. Mathematical structure and index of network equations. Surv. Math. Ind. 8, 97–129 (1999) MATH
24.
Zurück zum Zitat Günther, M., Feldmann, U.: CAD-based electric-circuit modeling in industry II. Impact of circuit configurations and parameters. Surv. Math. Ind. 8, 131–157 (1999) MATH Günther, M., Feldmann, U.: CAD-based electric-circuit modeling in industry II. Impact of circuit configurations and parameters. Surv. Math. Ind. 8, 131–157 (1999) MATH
25.
Zurück zum Zitat Hairer, E., Lubich, Ch., Roche, M.: The Numerical Solution of Differential–Algebraic Equations by Runge–Kutta Methods. Lecture Notes in Mathematics, vol. 1409. Springer, Berlin (1989) Hairer, E., Lubich, Ch., Roche, M.: The Numerical Solution of Differential–Algebraic Equations by Runge–Kutta Methods. Lecture Notes in Mathematics, vol. 1409. Springer, Berlin (1989)
26.
Zurück zum Zitat Ho, C.-W., Ruehli, A., Brennan, P.A.: The modified nodal approach to network analysis. IEEE Trans. Circuits Syst. CAS-22(6), 504–509 (1975) Ho, C.-W., Ruehli, A., Brennan, P.A.: The modified nodal approach to network analysis. IEEE Trans. Circuits Syst. CAS-22(6), 504–509 (1975)
27.
Zurück zum Zitat Ilchmann, A., Reis, T.: Surveys in Differential–Algebraic Equations I. Differential–Algebraic Equations Forum, vol. 2. Springer, Berlin (2013) CrossRefMATH Ilchmann, A., Reis, T.: Surveys in Differential–Algebraic Equations I. Differential–Algebraic Equations Forum, vol. 2. Springer, Berlin (2013) CrossRefMATH
28.
Zurück zum Zitat Ipach, H.: Graphentheoretische Anwendungen in der Analyse elektrischer Schaltkreise. B.Sc. Thesis (2013) Ipach, H.: Graphentheoretische Anwendungen in der Analyse elektrischer Schaltkreise. B.Sc. Thesis (2013)
29.
Zurück zum Zitat Iwata, S., Takamatsu, M., Tischendorf, C.: Tractability index of hybrid equations for circuit simulation. Math. Comput. 81(278), 923–939 (2012) MathSciNetCrossRefMATH Iwata, S., Takamatsu, M., Tischendorf, C.: Tractability index of hybrid equations for circuit simulation. Math. Comput. 81(278), 923–939 (2012) MathSciNetCrossRefMATH
30.
Zurück zum Zitat Jackson, J.D.: Classical Electrodynamics, 3rd edn. Wiley, New York (1999) MATH Jackson, J.D.: Classical Electrodynamics, 3rd edn. Wiley, New York (1999) MATH
31.
Zurück zum Zitat Jänich, K.: Vector Analysis. Undergraduate Texts in Mathematics. Springer, New York (2001). Translated by L. Kay CrossRef Jänich, K.: Vector Analysis. Undergraduate Texts in Mathematics. Springer, New York (2001). Translated by L. Kay CrossRef
32.
Zurück zum Zitat Johnson, D.E., Johnson, J.R., Hilburn, J.L.: Electric Circuit Analysis, 2nd edn. Prentice-Hall, Englewood Cliffs (1992) Johnson, D.E., Johnson, J.R., Hilburn, J.L.: Electric Circuit Analysis, 2nd edn. Prentice-Hall, Englewood Cliffs (1992)
33.
Zurück zum Zitat Kunkel, P., Mehrmann, V.: Differential–Algebraic Equations. Analysis and Numerical Solution. EMS, Zürich (2006) CrossRefMATH Kunkel, P., Mehrmann, V.: Differential–Algebraic Equations. Analysis and Numerical Solution. EMS, Zürich (2006) CrossRefMATH
34.
Zurück zum Zitat Küpfmüller, K., Kohn, G.: Theoretische Elektrotechnik und Elektronik: Eine Einführung. Springer, Berlin (1993) CrossRef Küpfmüller, K., Kohn, G.: Theoretische Elektrotechnik und Elektronik: Eine Einführung. Springer, Berlin (1993) CrossRef
35.
Zurück zum Zitat Lamour, R., März, R., Tischendorf, C.: Differential Algebraic Equations: A Projector Based Analysis. Differential–Algebraic Equations Forum, vol. 1. Springer, Heidelberg (2013) Lamour, R., März, R., Tischendorf, C.: Differential Algebraic Equations: A Projector Based Analysis. Differential–Algebraic Equations Forum, vol. 1. Springer, Heidelberg (2013)
36.
Zurück zum Zitat Markowich, P.A., Ringhofer, C.A., Schmeiser, C.: Semiconductor Equations, 1st edn. Springer, Wien (1990) CrossRefMATH Markowich, P.A., Ringhofer, C.A., Schmeiser, C.: Semiconductor Equations, 1st edn. Springer, Wien (1990) CrossRefMATH
37.
Zurück zum Zitat Marsden, J.E., Tromba, A.: Vector Calculus. W. H. Freeman, New York (2003) Marsden, J.E., Tromba, A.: Vector Calculus. W. H. Freeman, New York (2003)
38.
Zurück zum Zitat März, R., Estévez Schwarz, D., Feldmans, U., Sturtzel, S., Tischendorf, C.: Finding beneficial DAE structures in circuit simulation. In: Krebs, H.J., Jäger, W. (eds.) Mathematics—Key Technology for the Future—Joint Projects Between Universities and Industry, pp. 413–428. Springer, Berlin (2003) März, R., Estévez Schwarz, D., Feldmans, U., Sturtzel, S., Tischendorf, C.: Finding beneficial DAE structures in circuit simulation. In: Krebs, H.J., Jäger, W. (eds.) Mathematics—Key Technology for the Future—Joint Projects Between Universities and Industry, pp. 413–428. Springer, Berlin (2003)
39.
Zurück zum Zitat Newcomb, R.W.: The semistate description of nonlinear time-variable circuits. IEEE Trans. Circuits Syst. CAS-28, 62–71 (1981) MathSciNetCrossRef Newcomb, R.W.: The semistate description of nonlinear time-variable circuits. IEEE Trans. Circuits Syst. CAS-28, 62–71 (1981) MathSciNetCrossRef
41.
Zurück zum Zitat Rabier, P.J., Rheinboldt, W.C.: A geometric treatment of implicit differential–algebraic equations. J. Differ. Equ. 109(1), 110–146 (1994) MathSciNetCrossRefMATH Rabier, P.J., Rheinboldt, W.C.: A geometric treatment of implicit differential–algebraic equations. J. Differ. Equ. 109(1), 110–146 (1994) MathSciNetCrossRefMATH
42.
Zurück zum Zitat Reis, T.: Systems theoretic aspects of PDAEs and applications to electrical circuits. Doctoral dissertation, Fachbereich Mathematik. Technische Universität, Kaiserslautern, Kaiserslautern (2006) Reis, T.: Systems theoretic aspects of PDAEs and applications to electrical circuits. Doctoral dissertation, Fachbereich Mathematik. Technische Universität, Kaiserslautern, Kaiserslautern (2006)
43.
Zurück zum Zitat Reis, T.: Circuit synthesis of passive descriptor systems: a modified nodal approach. Int. J. Circuit Theory Appl. 38, 44–68 (2010) CrossRefMATH Reis, T.: Circuit synthesis of passive descriptor systems: a modified nodal approach. Int. J. Circuit Theory Appl. 38, 44–68 (2010) CrossRefMATH
44.
Zurück zum Zitat Reis, T., Stykel, T.: PABTEC: passivity-preserving balanced truncation for electrical circuits. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 29(10), 1354–1367 (2010) CrossRef Reis, T., Stykel, T.: PABTEC: passivity-preserving balanced truncation for electrical circuits. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 29(10), 1354–1367 (2010) CrossRef
45.
Zurück zum Zitat Reis, T., Stykel, T.: Lyapunov balancing for passivity-preserving model reduction of RC circuits. SIAM J. Appl. Dyn. Syst. 10(1), 1–34 (2011) MathSciNetCrossRefMATH Reis, T., Stykel, T.: Lyapunov balancing for passivity-preserving model reduction of RC circuits. SIAM J. Appl. Dyn. Syst. 10(1), 1–34 (2011) MathSciNetCrossRefMATH
46.
Zurück zum Zitat Riaza, R.: Time-domain properties of reactive dual circuits. Int. J. Circuit Theory Appl. 34(3), 317–340 (2006) CrossRefMATH Riaza, R.: Time-domain properties of reactive dual circuits. Int. J. Circuit Theory Appl. 34(3), 317–340 (2006) CrossRefMATH
47.
Zurück zum Zitat Riaza, R.: Differential–Algebraic Systems. Analytical Aspects and Circuit Applications. World Scientific, Basel (2008) CrossRefMATH Riaza, R.: Differential–Algebraic Systems. Analytical Aspects and Circuit Applications. World Scientific, Basel (2008) CrossRefMATH
48.
Zurück zum Zitat Riaza, R.: Dynamical properties of electrical circuits with fully nonlinear memristors. Nonlinear Anal., Real World Appl. 12(6), 3674–3686 (2011) MathSciNetCrossRefMATH Riaza, R.: Dynamical properties of electrical circuits with fully nonlinear memristors. Nonlinear Anal., Real World Appl. 12(6), 3674–3686 (2011) MathSciNetCrossRefMATH
49.
Zurück zum Zitat Riaza, R.: Surveys in differential–algebraic equations I. In: DAEs in Circuit Modelling: A Survey. Differential–Algebraic Equations Forum, vol. 2, pp. 97–136. Springer, Berlin (2013) Riaza, R.: Surveys in differential–algebraic equations I. In: DAEs in Circuit Modelling: A Survey. Differential–Algebraic Equations Forum, vol. 2, pp. 97–136. Springer, Berlin (2013)
50.
Zurück zum Zitat Riaza, R., Encinas, A.J.: Augmented nodal matrices and normal trees. Math. Methods Appl. Sci. 158(1), 44–61 (2010) MathSciNetMATH Riaza, R., Encinas, A.J.: Augmented nodal matrices and normal trees. Math. Methods Appl. Sci. 158(1), 44–61 (2010) MathSciNetMATH
51.
Zurück zum Zitat Riaza, R., Tischendorf, C.: Qualitative features of matrix pencils and DAEs arising in circuit dynamics. Dyn. Syst. 22(2), 107–131 (2007) MathSciNetCrossRefMATH Riaza, R., Tischendorf, C.: Qualitative features of matrix pencils and DAEs arising in circuit dynamics. Dyn. Syst. 22(2), 107–131 (2007) MathSciNetCrossRefMATH
52.
Zurück zum Zitat Riaza, R., Tischendorf, C.: The hyperbolicity problem in electrical circuit theory. Math. Methods Appl. Sci. 33(17), 2037–2049 (2010) MathSciNetCrossRefMATH Riaza, R., Tischendorf, C.: The hyperbolicity problem in electrical circuit theory. Math. Methods Appl. Sci. 33(17), 2037–2049 (2010) MathSciNetCrossRefMATH
53.
Zurück zum Zitat Riaza, R., Tischendorf, C.: Semistate models of electrical circuits including memristors. Int. J. Circuit Theory Appl. 39(6), 607–627 (2011) CrossRefMATH Riaza, R., Tischendorf, C.: Semistate models of electrical circuits including memristors. Int. J. Circuit Theory Appl. 39(6), 607–627 (2011) CrossRefMATH
54.
Zurück zum Zitat Riaza, R., Tischendorf, C.: Structural characterization of classical and memristive circuits with purely imaginary eigenvalues. Int. J. Circuit Theory Appl. 41(3), 273–294 (2013) CrossRef Riaza, R., Tischendorf, C.: Structural characterization of classical and memristive circuits with purely imaginary eigenvalues. Int. J. Circuit Theory Appl. 41(3), 273–294 (2013) CrossRef
55.
Zurück zum Zitat Shockley, W.: The theory of p–n junctions in semiconductors and p–n junction transistors. Bell Syst. Tech. J. 28(3), 435–489 (1947) CrossRef Shockley, W.: The theory of pn junctions in semiconductors and pn junction transistors. Bell Syst. Tech. J. 28(3), 435–489 (1947) CrossRef
56.
Zurück zum Zitat Simeon, B.: Computational Flexible Multibody Dynamics: A Differential–Algebraic Approach. Differential–Algebraic Equations Forum, vol. 3. Springer, Heidelberg-Berlin (2013) CrossRef Simeon, B.: Computational Flexible Multibody Dynamics: A Differential–Algebraic Approach. Differential–Algebraic Equations Forum, vol. 3. Springer, Heidelberg-Berlin (2013) CrossRef
57.
Zurück zum Zitat Sternberg, S., Bamberg, P.: A Course in Mathematics for Students of Physics, vol. 2. Cambridge University Press, Cambridge (1991) Sternberg, S., Bamberg, P.: A Course in Mathematics for Students of Physics, vol. 2. Cambridge University Press, Cambridge (1991)
58.
Zurück zum Zitat Takamatsu, M., Iwata, S.: Index characterization of differential–algebraic equations in hybrid analysis for circuit simulation. Int. J. Circuit Theory Appl. 38, 419–440 (2010) MATH Takamatsu, M., Iwata, S.: Index characterization of differential–algebraic equations in hybrid analysis for circuit simulation. Int. J. Circuit Theory Appl. 38, 419–440 (2010) MATH
59.
Zurück zum Zitat Tao, T.: Analysis II. Texts and Readings in Mathematics, vol. 38. Hindustan Book Agency, New Delhi (2009) MATH Tao, T.: Analysis II. Texts and Readings in Mathematics, vol. 38. Hindustan Book Agency, New Delhi (2009) MATH
60.
Zurück zum Zitat Tischendorf, C.: Mathematische Probleme und Methoden der Schaltungssimulation. Unpublished Lecture Notes Tischendorf, C.: Mathematische Probleme und Methoden der Schaltungssimulation. Unpublished Lecture Notes
61.
Zurück zum Zitat Tooley, M.: Electronic Circuits: Fundamentals and Applications. Newnes, Oxford (2006) Tooley, M.: Electronic Circuits: Fundamentals and Applications. Newnes, Oxford (2006)
62.
Zurück zum Zitat van der Schaft, A.J.: L 2-Gain and Passivity Techniques in Nonlinear Control. Lecture Notes in Control and Information Sciences, vol. 218. Springer, London (1996) CrossRefMATH van der Schaft, A.J.: L 2-Gain and Passivity Techniques in Nonlinear Control. Lecture Notes in Control and Information Sciences, vol. 218. Springer, London (1996) CrossRefMATH
63.
Zurück zum Zitat van der Schaft, A.J.: Surveys in differential–algebraic equations I. In: Port-Hamiltonian Differential–Algebraic Equations. Differential–Algebraic Equations Forum, vol. 2, pp. 173–226. Springer, Berlin (2013) van der Schaft, A.J.: Surveys in differential–algebraic equations I. In: Port-Hamiltonian Differential–Algebraic Equations. Differential–Algebraic Equations Forum, vol. 2, pp. 173–226. Springer, Berlin (2013)
64.
65.
Zurück zum Zitat Wedepohl, L.M., Jackson, L.: Modified nodal analysis: an essential addition to electrical circuit theory and analysis. Eng. Sci. Educ. J. 11(3), 84–92 (2002) CrossRef Wedepohl, L.M., Jackson, L.: Modified nodal analysis: an essential addition to electrical circuit theory and analysis. Eng. Sci. Educ. J. 11(3), 84–92 (2002) CrossRef
67.
Zurück zum Zitat Willems, J.C.: Realization of systems with internal passivity and symmetry constraints. J. Franklin Inst. 301, 605–621 (1976) MathSciNetCrossRefMATH Willems, J.C.: Realization of systems with internal passivity and symmetry constraints. J. Franklin Inst. 301, 605–621 (1976) MathSciNetCrossRefMATH
Metadaten
Titel
Mathematical Modeling and Analysis of Nonlinear Time-Invariant RLC Circuits
verfasst von
Timo Reis
Copyright-Jahr
2014
DOI
https://doi.org/10.1007/978-3-319-08437-4_2