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Some considerations on state equations of linear active networks
Author(s) -
Hirano Kotaro,
Nishi Fumiaki,
Tomiyama ShinIchiro
Publication year - 1974
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.4490020106
Subject(s) - state variable , tree (set theory) , resistor , state (computer science) , mathematics , algebraic equation , series (stratigraphy) , resistive touchscreen , algebraic number , topology (electrical circuits) , mathematical analysis , nonlinear system , computer science , combinatorics , physics , algorithm , voltage , paleontology , quantum mechanics , biology , computer vision , thermodynamics
Abstract It is shown that if there equivalently exist the virtual resistive elements in parallel with the inductive elements of the over‐normal tree of a given linear active network or in series with the capacitive elements of the corresponding co‐tree, an increase in the number of state variables arises. It is also shown that when a virtual resistor equivalently appears in parallel with the distinct resistor in a tree or in series with the distinct resistor in the co‐tree, a decrease in the number of state variables may arise. This is, however, a rare case in the usual types of network. Two algebraic methods for obtaining the state equation of linear active networks are presented. One is useful for the networks in which the decrease in the number of state variables does not arise. From the other, the output equation for the required variables is obtained at the same time as the state equation. Further, the initial values are simply determined without iteration in many cases.