Network analysis (electrical circuits): Difference between revisions

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|'''[[Port (circuit theory)|Port]]'''||Two terminals where the current into one is identical to the current out of the other.

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|'''[[Electrical circuit|Circuit]]'''||A current from one terminal of a [[generator (circuit theory)|generator]], through load component(s) and back into the other terminal. A circuit is, in this sense, a one-port network and is a trivial case to analyse. If there is any connection to any other circuits then a non-trivial network has been formed and at least two ports must exist. Often, "circuit" and "network" are used interchangeably, but many analysts reserve "network" to mean an idealised model consisting of ideal components.<ref>{{cite journal |author=Belevitch V |title=Summary of the history of circuit theory |journal=Proceedings of the IRE |volume=50 |issue=5 |pages=849 |date=May 1962 |doi=10.1109/JRPROC.1962.288301 |s2cid=51666316 |author-link=Vitold Belevitch }} cites {{cite journal |title=IRE Standards on Circuits: Definitions of Terms for Linear Passive Reciprocal Time Invariant Networks, 1960 |journal=Proceedings of the IRE |volume=48 |issue=9 |pages=1609 |date=September 1960 |doi=10.1109/JRPROC.1960.287676 }}to justify this definition.<br />[[Sidney Darlington]] {{cite journal |author=Darlington S |title=A history of network synthesis and filter theory for circuits composed of resistors, inductors, and capacitors |journal=IEEE Trans. Circuits and Systems |volume=31 |issue=1 |pages=4 |year=1984 |doi= 10.1109/TCS.1984.1085415}}<br />follows Belevitch but notes there are now also many colloquial uses of "network".</ref>

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|'''[[Transfer function]]'''||The relationship of the currents and/or voltages between two ports. Most often, an input port and an output port are discussed and the transfer function is described as gain or attenuation.

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:<math>V_\mathrm{s} = RI_\mathrm{s}\,\!</math> or <math>I_\mathrm{s} = \frac{V_\mathrm{s}}{R}</math>

* [[ThéveninNorton's theorem]] states that any two-terminal linear network can be reduced to an ideal voltagecurrent generator plusand a seriesparallel impedance.

* [[NortonThévenin's theorem]] states that any two-terminal linear network can be reduced to an ideal currentvoltage generator andplus a parallelseries impedance.

*

*[[Thévenin's theorem]] states that any two-terminal linear network can be reduced to an ideal voltage generator plus a series impedance.

*

==Simple networks==

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==Choice of method==

Choice of method<ref>{{cite book |author=Nilsson, J W, Riedel, S A |title=Electric Circuits |publisher=Pearson Prentice Hall |year=2007 |isbn=978-0-13-198925-2 |edition=8th |pages=112–113 |url=https://books.google.com/books?id=sxmM8RFL99wC&q=112&pg=PA112 }}</ref> is to some extent a matter of taste. If the network is particularly simple or only a specific current or voltage is required then ad-hoc application of some simple equivalent circuits may yield the answer without recourse to the more systematic methods.

* [[Nodal analysis]]: The number of voltage variables, and hence simultaneous equations to solve, equals the number of nodes minus one. Every voltage source connected to the reference node reduces the number of unknowns and equations by one.

* [[NodalMesh analysis]]: The number of voltagecurrent variables, and hence simultaneous equations to solve, equals the number of nodes minus onemeshes. Every voltagecurrent source connectedin to the referencea nodemesh reduces the number of unknowns and equations by one. Mesh analysis can only be used with networks which can be drawn as a [[Planar graph|planar]] network, that is, with no crossing components.<ref>{{cite book |author=Nilsson, J W, Riedel, S A |title=Electric Circuits |publisher=Pearson Prentice Hall |year=2007 |isbn=978-0-13-198925-2 |edition=8th |page=94 |url=https://books.google.com/books?id=sxmM8RFL99wC&pg=PA94 }}</ref>

* [[Superposition theorem|Superposition]] is possibly the most conceptually simple method but rapidly leads to a large number of equations and messy impedance combinations as the network becomes larger.

*[[Mesh analysis]]: The number of current variables, and hence simultaneous equations to solve, equals the number of meshes. Every current source in a mesh reduces the number of unknowns by one. Mesh analysis can only be used with networks which can be drawn as a [[Planar graph|planar]] network, that is, with no crossing components.<ref>{{cite book |author=Nilsson, J W, Riedel, S A |title=Electric Circuits |publisher=Pearson Prentice Hall |year=2007 |isbn=978-0-13-198925-2 |edition=8th |page=94 |url=https://books.google.com/books?id=sxmM8RFL99wC&pg=PA94 }}</ref>

* [[Effective medium approximations]]: For a network consisting of a high density of random resistors, an exact solution for each individual element may be impractical or impossible. Instead, the effective resistance and current distribution properties can be modelled in terms of [[Graph (discrete mathematics)|graph]] measures and geometrical properties of networks.<ref>{{Cite journal|last1=Kumar|first1=Ankush|last2=Vidhyadhiraja|first2=N. S.|last3=Kulkarni|first3=G. U .|year=2017|title=Current distribution in conducting nanowire networks|journal=Journal of Applied Physics|volume=122|issue=4|pages=045101|doi=10.1063/1.4985792|bibcode=2017JAP...122d5101K}}</ref>

*[[Superposition theorem|Superposition]] is possibly the most conceptually simple method but rapidly leads to a large number of equations and messy impedance combinations as the network becomes larger.

*[[Effective medium approximations]]: For a network consisting of a high density of random resistors, an exact solution for each individual element may be impractical or impossible. Instead, the effective resistance and current distribution properties can be modelled in terms of [[Graph (discrete mathematics)|graph]] measures and geometrical properties of networks.<ref>{{Cite journal|last1=Kumar|first1=Ankush|last2=Vidhyadhiraja|first2=N. S.|last3=Kulkarni|first3=G. U .|year=2017|title=Current distribution in conducting nanowire networks|journal=Journal of Applied Physics|volume=122|issue=4|pages=045101|doi=10.1063/1.4985792|bibcode=2017JAP...122d5101K}}</ref>

==Transfer function==

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==See also==

{{div col |colwidth=14em |content=

* [[Bartlett's bisection theorem]]

* [[Equivalent impedance transforms]]