Symbolic Sensitivity Analysis Enhanced by Nullor Model and Modified Coates Flow Graph

Asenova, Irina; Balik, Franciszek

doi:10.1007/978-3-319-75157-3_5

Cited by 2 publications

(2 citation statements)

References 13 publications

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“…(1,2) (9,9) in Equation ( 14). The matrix (1) H(9)| (1,2) (9,9) is formed by eliminating the first row and the ninth column of matrix M 1,1 (A a ), which removes the incoming branches of input node x 1 and outgoing branches of backward node x 9 . The product term (a 9,1 )•det( (1) H( 9…”

Section: )|mentioning

confidence: 99%

“…In the past several decades, flow graph analysis has been widely used in electrical engineering [1][2][3][4][5][6], computer science, biological science [7], and for solving economic problems. Furthermore, the applications of graph theory in conjunction with symbolic network analysis [8,9] and the computer-aided simulation of electronic circuits [10] have been widely encountered in recent years.…”

Section: Introductionmentioning

confidence: 99%

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A Matrix Approach for Analyzing Signal Flow Graph

2020

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Mason’s gain formula can grow factorially because of growth in the enumeration of paths in a directed graph. Each of the (n − 2)! permutation of the intermediate vertices includes a path between input and output nodes. This paper presents a novel method for analyzing the loop gain of a signal flow graph based on the transform matrix approach. This approach only requires matrix determinant operations to determine the transfer function with complexity O(n3) in the worst case, therefore rendering it more efficient than Mason’s gain formula. We derive the transfer function of the signal flow graph to the ratio of different cofactor matrices of the augmented matrix. By using the cofactor expansion, we then obtain a correspondence between the topological operation of deleting a vertex from a signal flow graph and the algebraic operation of eliminating a variable from the set of equations. A set of loops sharing the same backward edges, referred to as a loop group, is used to simplify the loop enumeration. Two examples of feedback networks demonstrate the intuitive approach to obtain the transfer function for both numerical and computer-aided symbolic analysis, which yields the same results as Mason’s gain formula. The transfer matrix offers an excellent physical insight, because it enables visualization of the signal flow.

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Section: )|mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Matrix Approach for Analyzing Signal Flow Graph

2020

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Efficient generation of compact symbolic network functions in a nested rational form

Filaretov

Gorshkov

2020

Circuit Theory & Apps

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SummaryThis paper presents the extension of generalized parameter extraction method for direct circuit function generation in a fully symbolic form of rational expressions or a nested s‐expanded polynomial. The new formula for implicit extraction of parameters that allows effective factoring by grouping of determinants of circuits containing any linear models of active elements, such as controlled sources, nullors, and pathological mirrors, is proposed. The concept of nullor with parameter is used for implicit extraction. The rules of optimal selection of parameters for extraction are presented. The proposed algorithm of symbolic analysis is implemented in the CirSym program, which is available online. The paper discusses the results of automatic analysis of several large active circuits, as well as determinants of matrixes and passive topologies, in terms of compact size and minimization of the number of arithmetic operations. Experimental results demonstrate that the expressions of determinants derived by CirSym are more compact than the results of the factorization algorithms of commercial computer algebra systems. The comparison with several other symbolic analysis algorithms shows that CirSym is the only available program that provides the exact calculation of the symbolic function of large circuits in the s‐expanded form with every coefficient being a compact‐nested expression.

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Symbolic Sensitivity Analysis Enhanced by Nullor Model and Modified Coates Flow Graph

Cited by 2 publications

References 13 publications

A Matrix Approach for Analyzing Signal Flow Graph

A Matrix Approach for Analyzing Signal Flow Graph

Efficient generation of compact symbolic network functions in a nested rational form

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