Thevenin's theorem

Brittain, J.E.

doi:10.1109/6.48845

Cited by 56 publications

(24 citation statements)

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“…Its value is identical to the ones obtained by using Green functions [14] or Circuit Theory analysis [1,17]. For example, if all series and parallel impedances between nodes k and l are added, then the final value is equal to the one that is found from equation (11).…”

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confidence: 48%

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General analytical solutions for DC/AC circuit-network analysis

Rubido

Grebogi

Baptista

2017

Eur. Phys. J. Spec. Top.

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Abstract. In this work, we present novel general analytical solutions for the currents that are developed in the edges of network-like circuits when some nodes of the network act as sources/sinks of DC or AC current. We assume that Ohm's law is valid at every edge and that charge at every node is conserved (with the exception of the source/sink nodes). The resistive, capacitive, and/or inductive properties of the lines in the circuit define a complex network structure with given impedances for each edge. Our solution for the currents at each edge is derived in terms of the eigenvalues and eigenvectors of the Laplacian matrix of the network defined from the impedances. This derivation also allows us to compute the equivalent impedance between any two nodes of the circuit and relate it to currents in a closed circuit which has a single voltage generator instead of many input/output source/sink nodes. This simplifies the treatment that could be done via Thévenin's theorem. Contrary to solving Kirchhoff's equations, our derivation allows to easily calculate the redistribution of currents that occurs when the location of sources and sinks changes within the network. Finally, we show that our solutions are identical to the ones found from Circuit Theory nodal analysis.

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confidence: 48%

“…1). In this sense, we are performing a direct calculation of Thévenin theorem [17] without the need for short-circuiting the system. The scientific interest of our solutions comes from establishing a clear relationship between the currents and voltages in DC/AC circuits with the topology invariants of the network.…”

Section: Introductionmentioning

confidence: 99%

General analytical solutions for DC/AC circuit-network analysis

Rubido

Grebogi

Baptista

2017

Eur. Phys. J. Spec. Top.

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“…The well known Thévenin's Theorem of circuit theory [10], [11], [12] follows as a special case of the results developed here. To see this, consider the current dependence relationship of Eqn.…”

Section: Thèvenin's Theorem: a Special Casementioning

confidence: 98%

Linear circuits: A measurement based approach

Layek

Datta

Bhattacharyya

2011

2011 20th European Conference on Circuit Theory and Design (ECCTD)

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“…Thevenin's Theorem [4] follows from (9) with the short circuit current I sc given by I sc = α0 β0 and the open circuit voltage by V oc = α 0 . Thus, the Thevenin equivalent resistance is given by R th = Voc Isc = β 0 and the equivalent Thevenin voltage is V th = V oc .…”

Section: Thevenin Equivalent Circuit Solutionmentioning

confidence: 99%