# zbMATH — the first resource for mathematics

Structural analysis of electric circuits and consequences. (English) Zbl 1054.94529
Summary: The development of integrated circuits requires powerful numerical simulation programs. Naturally, there is no method that treats all the different kinds of circuits successfully. The numerical simulation tools provide reliable results only if the circuit model meets the assumptions that guarantee a successful application of the integration software. Owing to the large dimension of many circuits (about $$10^7$$ circuit elements) it is often difficult to find the circuit configurations that lead to numerical difficulties. In this paper, we analyse electric circuits with respect to their structural properties in order to give circuit designers some help for fixing modelling problems if the numerical simulation fails. We consider one of the most frequently used modelling techniques, the modified nodal analysis (MNA), and discuss the index of the differential algebraic equations (DAEs) obtained by this kind of modelling.

##### MSC:
 94C99 Circuits, networks
Full Text:
##### References:
 [1] Differential-Algebraic Equations and Their Numerical Treatment, Teubner-Texte zur Mathematik No. 88, BSB B.G. Teubner Verlagsgesellschaft, Leipzig, 1986. · Zbl 0629.65080 [2] The Numerical Solution of Initial Value Problems in Ordinary Differential-Algebraic Equations, North-Holland: Amsterdam, 1989. [3] Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, Springer Series in Computational Mathematics, Vol. 14. Springer: Berlin, Heidelberg, 1991. · Zbl 0729.65051 [4] Bryant, Proceedings of the IEE (GB), Part C 106 pp 174– (1959) [5] Rei?ig, International Journal of Circuit Theory and Applications 27 pp 241– (1999) · Zbl 0921.68004 [6] Brayton, Quarterly of Applied Mathematics 22 pp 1– (1964) [7] Chua, IEEE Transactions Circuit Theory 12 pp 475– (1965) [8] Kuh, Proceedings of the IEEE 53 pp 672– (1965) [9] Ohtsuki, IEEE Transaction Circuit Theory 16 pp 26– (1969) [10] Computer-Aided Analysis of Electronic Circuits. Prentice-Hall: Englewood Cliffs; NJ, 1975. · Zbl 0358.94002 [11] Matsumoto, Journal of Differential Equations 21 pp 179– (1976) · Zbl 0291.34035 [12] Szatkowski, International Journal of Circuit Theory Applications 10 pp 99– (1982) · Zbl 0486.94015 [13] Haggman, IEEE Transactions on CAS 31 pp 1015– (1984) · Zbl 0561.58045 [14] Nishi, IEEE Transactions on Circuits and Systems 31 pp 722– (1984) · Zbl 0547.94021 [15] Hasler, International Journal of Circuits Theory and Applications 14 pp 237– (1986) · Zbl 0621.94022 [16] Theorie nichtlinearer Netzwerke, Springer: Berlin, Heidelberg, New York, 1987. [17] Non-linear Circuits: Qualitative Analysis of Non-linear, Non-Reciprocal Circuits, Wiley: Chichester, 1992. [18] G?nther, Mathematics and Computers in Simulation 39 pp 573– (1995) · Zbl 05475301 [19] G?nther, Zeitschrift f?r Angewandte Mathematik und Mechanik 76 pp 91– (1996) [20] Solution of index-2 differential algebraic equations and its application in circuit simulation. Ph.D. Thesis, Humboldt-University, Berlin, 1996. [21] M?rz, SIAM Journal of Scientific and Statistical Computing 18 pp 139– (1997) · Zbl 0867.65036 [22] Beitr?ge zu Theorie und Anwendung impliziter Differentialgleichungen, Ph.D. Thesis, Technical University, Dresden, 1998. [23] G?nther, Surveys on Mathematics for Industry 8 pp 97– (1999) [24] G?nther, Surveys on Mathematics for Industry 8 pp 131– (1999) [25] Tischendorf, Surveys on Mathematics for Industry 8 pp 187– (1999) [26] The index of the standard circuit equations of passive RLCTG-networks does not exceed 2. Proceedings of the ISCAS’98, vol. 3. 1998; 419-422. [27] Topological analysis for consistent initialization in circuit simulation. Technical Report 99-3, Fachbereich Mathematik, Humboldt-University, Berlin, 1999. [28] Consistent initialization of differential-algebraic equations in circuit simulation. Technical Report 99-5, Fachbereich Mathematik, Humboldt-University, Berlin, 1999. [29] Analyzing the stability behaviour of DAE solutions and their approximations. Technical Report 99-2, Fachbereich Mathematik, Humboldt-University, Berlin, 1999. [30] Basic Circuit Theory, McGraw-Hill: Singapore, 1969. [31] Shichman, IEEE Journal of Solid State Circuits SC-3 pp 285– (1968) [32] M?rz, Acta Numerica pp 141– (1992) [33] Rabier, Differential and Integral Equations 4 pp 563– (1991) [34] Beitrag zur Theorie der Algebrodifferentialgleichungen, Ph.D. Thesis, Technical University Dresden, 1990. [35] Computer-aided analysis of non-linear lumped-distributed multiport networks. IEEE International Symposium on Circuits and Systems, New York, 1992; 428-431.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.