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Higher‐order differentiation of network functions using signal flow graphs
Author(s) -
Osowski Stanislaw
Publication year - 2012
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.766
Subject(s) - signal flow graph , automatic differentiation , numerical differentiation , signal (programming language) , function (biology) , flow (mathematics) , order (exchange) , computer science , network analysis , basis (linear algebra) , derivative (finance) , electronic circuit , algorithm , mathematics , topology (electrical circuits) , mathematical analysis , combinatorics , physics , engineering , geometry , finance , quantum mechanics , evolutionary biology , electrical engineering , economics , computation , biology , programming language , financial economics
SUMMARY This paper presents the application of signal flow graphs (SFG) in the calculation of higher‐order derivatives (sensitivities) of the linear circuit functions. The idea of exact differentiation of the circuit functions is based on the adjoint networks, translated into SFG language. Thanks to its application, it is possible to calculate the exact value of any order derivative of circuit function without knowing this function in explicit form. Moreover, these derivatives can be determined on the basis of analysis of only two graphs (circuits): the original and adjoint one. We show that the SFG approach to the sensitivity calculation allows to reduce greatly the complexity of calculations. Copyright © 2011 John Wiley & Sons, Ltd.