### Abstract

Original language | English |
---|---|

Pages (from-to) | 1829-1844 |

Number of pages | 16 |

Journal | The European Physical Journal. Special Topics |

Volume | 226 |

Issue number | 9 |

Early online date | 21 Jun 2017 |

DOIs | |

Publication status | Published - Jun 2017 |

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**General analytical solutions for DC/AC circuit-network analysis.** / Rubido, Nicolas; Grebogi, Celso; Baptista, Murilo S.

Research output: Contribution to journal › Article

*The European Physical Journal. Special Topics*, vol. 226, no. 9, pp. 1829-1844. https://doi.org/10.1140/epjst/e2017-70074-2

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TY - JOUR

T1 - General analytical solutions for DC/AC circuit-network analysis

AU - Rubido, Nicolas

AU - Grebogi, Celso

AU - Baptista, Murilo S.

N1 - All authors thank the Scottish University Physics Alliance (SUPA) support. NR also acknowledges de support of PEDECIBA, Uruguay. MSB acknowledges the support of EPSRC grant Ref. EP/I032606/1. Open access via Springer Compact Agreement.

PY - 2017/6

Y1 - 2017/6

N2 - 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.

AB - 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.

U2 - 10.1140/epjst/e2017-70074-2

DO - 10.1140/epjst/e2017-70074-2

M3 - Article

VL - 226

SP - 1829

EP - 1844

JO - The European Physical Journal. Special Topics

JF - The European Physical Journal. Special Topics

SN - 1951-6355

IS - 9

ER -