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Modified Nodal Approach to Network Analysis and Design

IP.com Disclosure Number: IPCOM000080507D
Original Publication Date: 1973-Dec-01
Included in the Prior Art Database: 2005-Feb-27
Document File: 5 page(s) / 87K

Publishing Venue

IBM

Related People

Brennan, PA: AUTHOR [+3]

Abstract

The method by which circuit equations are formulated in a computer program is the key to a computer aided design program for integrated circuits. Such a description needs to be flexible, computationally efficient and economical with storage. Among the approaches presently used, the model method has been implemented in programs like "BIAS-3" as shown in "Computer-Aided Design and Device Modeling", W. T. McCalla, and W. G. Howard, IEEE International Solid State Circuits Conference Digest, Lewis Winner, N. Y., 1970, p.82; and CANCER Computer Analysis of Nonlinear Circuits Excluding Radiation'', R. A. Rohrer, L. W. Nagel, R. Meyer and L. Weber, IEEE International Solid State Circuits Conference Digest, Lewis Winner, N. Y., 1972, p.124.

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Modified Nodal Approach to Network Analysis and Design

The method by which circuit equations are formulated in a computer program is the key to a computer aided design program for integrated circuits. Such a description needs to be flexible, computationally efficient and economical with storage. Among the approaches presently used, the model method has been implemented in programs like "BIAS-3" as shown in "Computer-Aided Design and Device Modeling", W. T. McCalla, and W. G. Howard, IEEE International Solid State Circuits Conference Digest, Lewis Winner, N. Y., 1970,
p.82; and CANCER Computer Analysis of Nonlinear Circuits Excluding Radiation'', R. A. Rohrer, L. W. Nagel, R. Meyer and L. Weber, IEEE International Solid State Circuits Conference Digest, Lewis Winner, N. Y., 1972,
p.124. The tableau method as discussed in "The Sparse Tableau Approach to Network Analysis and Design", G. D. Hachtel, R. K. Brayton and T. G. Gustavson, IEEE Transactions on Circuit Theory, Vol. GT-18, No. 1, January 1971, pp. 101-114, has been implemented in "ECAP II, An Electronic Circuit Analysis Program", F. H. Branin, G. R. Hogsett, L. E. Kugel and R. L. Lunde, IEEE Spectrum, Vol. 6, No. 6, June, 1972.

Here, a modification is proposed which eliminates some of the inefficiencies inherent in the nodal formulation and is called the modified nodal approach (MNA). The MNA is first of all applicable to all three types of analysis, AC, DC and transient. Secondly, problems in the handling of voltage sources and current controlled nonlinear elements in the nodal method are eliminated, without a large increase in solution complexity. Finally, the formulation given here is computationally fast and has only moderate storage requirements. This is an important consideration for an environment where storage is limited, as is the case for smaller computers or for present APL terminals.

Changes in the nodal equations have been proposed before. However, they result in either a much more complex formulation, e.g., by hybrid nodal-loop equations as shown in "Computer-Aided Design: Analyzing circuits by Number",
F. Branin, Computer-aided design REPRINTED

FROM Electronic, McGraw Mill, 1971, or introduce undesirable elements such as negative resistances as discussed in "Behandlung idealer gesteuerter Quellen bei der Netzwerkanalyse mit Digitalrechnern" NTZ, Vol. 1, pp. 8-10, 1970.

The modified nodal algorithm is summaraized next. Only the changes from the usual nodal approach are stated. The starting unknowns are the node - common datum voltages V = V(1), V(2)...V(n).

(1) For each voltage source E(i) (dependent or independent) connected between the nodes i and j (Fig. 1) in the network, an additional equation is introduced which is V(i)-V(j)-E(i)=0. Further as an additional unknown, the current IE(1), through the voltage source is introduced. IE(1) represents the branch current between nodes i and j in the nodal equations for changes in nodes i and j.

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(2) For...