View source for Electrical network

{{short description|Assemblage of connected electrical elements}}
{{For|electrical power transmission grids and distribution networks|Electrical grid}}
{{Refimprove|date=March 2016}}
{{Electromagnetism|cTopic=Network}}
[[File:Ohm's Law with Voltage source TeX.svg|right|thumb|A simple electric circuit made up of a voltage source and a resistor. Here, <math>v=iR</math>, according to [[Ohm's law]].]]

An '''electrical network''' is an interconnection of [[electronic component|electrical component]]s (e.g., [[battery (electricity)|batteries]], [[resistor]]s, [[inductor]]s, [[capacitor]]s, [[switch]]es, [[transistor]]s) or a model of such an interconnection, consisting of [[electrical element]]s (e.g., [[voltage source]]s, [[current source]]s, [[Electrical resistance and conductance|resistance]]s, [[inductance]]s, [[capacitance]]s). An '''electrical circuit''' is a network consisting of a closed loop, giving a return path for the current. Thus all circuits are networks, but not all networks are circuits (although networks without a closed loop are often imprecisely referred to as "circuits"). [[Linear circuit|Linear]] electrical networks, a special type consisting only of sources (voltage or current), linear lumped elements (resistors, capacitors, inductors), and linear distributed elements (transmission lines), have the property that signals are [[Superposition principle|linearly superimposable]].  They are thus more easily analyzed, using powerful [[frequency domain]] methods such as [[Laplace transform]]s, to determine [[direct current|DC response]], [[alternating current|AC response]], and [[transient response]].

A '''resistive network''' is a network containing only resistors and ideal current and voltage sources. [[Network analysis (electrical circuits)|Analysis]] of resistive networks is less complicated than analysis of networks containing capacitors and inductors. If the sources are constant ([[Direct current|DC]]) sources, the result is a DC network. The effective resistance and current distribution properties of arbitrary resistor networks can be modeled in terms of their graph measures and geometrical properties.<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>

A network that contains [[Active component|active]] [[electronics|electronic]] components is known as an ''[[electronic circuit]]''. Such networks are generally nonlinear and require more complex design and analysis tools.

==Classification==

===By passivity===
An active network contains at least one [[voltage source]] or [[current source]] that can supply energy to the network indefinitely. A [[Passivity (engineering)|passive]] network  does not contain an active source.

An active network contains one or more sources of [[electromotive force]]. Practical examples of such sources include a [[Electric battery|battery]] or a [[Electric generator|generator]]. Active elements can inject power to the circuit, provide power gain, and control the current flow within the circuit.

Passive networks do not contain any sources of electromotive force. They consist of passive elements like resistors and capacitors.

===By linearity===
A network is linear if its signals obey the principle of [[Superposition theorem|superposition]]; otherwise it is non-linear.  Passive networks are generally taken to be linear, but there are exceptions.  For instance, an [[inductor]] with an iron core can be driven into [[Saturation (magnetic)|saturation]] if driven with a large enough current.  In this region, the behaviour of the inductor is very non-linear.

===By lumpiness===
Discrete passive components (resistors, capacitors and inductors) are called ''lumped elements'' because all of their, respectively, resistance, capacitance and inductance is assumed to be located ("lumped") at one place.  This design philosophy is called the [[lumped-element model]] and networks so designed are called ''lumped-element circuits''.  This is the conventional approach to circuit design.  At high enough frequencies, or for long enough circuits (such as [[Electric power transmission|power transmission lines]]), the lumped assumption no longer holds because there is a significant fraction of a [[wavelength]] across the component dimensions.  A new design model is needed for such cases called the [[distributed-element model]].  Networks designed to this model are called ''[[distributed-element circuit]]s''.

A distributed-element circuit that includes some lumped components is called a ''semi-lumped'' design.  An example of a semi-lumped circuit is the [[combline filter]].

==Classification of sources==
Sources can be classified as independent sources and dependent sources.

===Independent===
An ideal independent source maintains the same voltage or current regardless of the other elements present in the circuit. Its value is either constant (DC) or sinusoidal (AC). The strength of voltage or current is not changed by any variation in the connected network.

===Dependent===
[[Dependent source]]s depend upon a particular element of the circuit for delivering the power or voltage or current depending upon the type of source it is.

==Applying electrical laws==

A number of electrical laws apply to all linear resistive networks. These include:

* [[Kirchhoff's current law]]: The sum of all currents entering a node is equal to the sum of all currents leaving the node.

* [[Kirchhoff's voltage law]]: The directed sum of the electrical potential differences around a loop must be zero.

* [[Ohm's law]]: The voltage across a resistor is equal to the product of the resistance and the current flowing through it.

* [[Norton's theorem]]: Any network of voltage or current sources and resistors is electrically equivalent to an ideal current source in parallel with a single resistor.

* [[Thévenin's theorem]]: Any network of voltage or current sources and resistors is electrically equivalent to a single voltage source in series with a single resistor.

* [[Superposition theorem]]: In a linear network with several independent sources, the response in a particular branch when all the sources are acting simultaneously is equal to the linear sum of individual responses calculated by taking one independent source at a time.

Applying these laws results in a set of simultaneous equations that can be solved either algebraically or numerically.  The laws can generally be extended to networks containing [[electrical reactance|reactances]].  They cannot be used in networks that contain nonlinear or time-varying components.

==Design methods==
{{Network analysis navigation}}
{{see also|Network analysis (electrical circuits)}}

To design any electrical circuit, either [[Analogue electronics|analog]] or [[Digital circuit|digital]], [[Electrical engineering|electrical engineers]] need to be able to predict the voltages and currents at all places within the circuit.  Simple [[linear circuit]]s can be analyzed by hand using [[Complex number|complex number theory]]. In more complex cases the circuit may be analyzed with specialized [[computer program]]s or estimation techniques such as the piecewise-linear model.

Circuit simulation software, such as [[HSPICE]] (an analog circuit simulator),<ref>{{Cite web|url=https://web.stanford.edu/class/ee133/spice/HSpice.pdf|title=HSPICE|date=1999|website=HSpice|publisher=Stanford University, Electrical Engineering Department}}</ref> and languages such as [[VHDL-AMS]] and [[verilog-AMS]] allow engineers to design circuits without the time, cost and risk of error involved in building circuit prototypes.

==Network simulation software==
More complex circuits can be analyzed numerically with software such as [[SPICE]] or [[GNU Circuit Analysis Package|GNUCAP]], or symbolically using software such as [[SapWin]].

===Linearization around operating point===
When faced with a new circuit, the software first tries to find a [[Steady state|steady state solution]], that is, one where all nodes conform to Kirchhoff's current law ''and'' the voltages across and through each element of the circuit conform to the voltage/current equations governing that element.

Once the steady state solution is found, the ''[[operating point]]s'' of each element in the circuit are known.  For a small signal analysis, every non-linear element can be linearized around its operation point to obtain the small-signal estimate of the voltages and currents.  This is an application of Ohm's Law.  The resulting linear circuit matrix can be solved with [[Gaussian elimination]].

===Piecewise-linear approximation===
Software such as the [[PLECS]] interface to [[Simulink]] uses [[Piecewise linear function|piecewise-linear]] approximation of the equations governing the elements of a circuit.  The circuit is treated as a completely linear network of [[Diode modelling#Mathematically idealized diode|ideal diode]]s.  Every time a diode switches from on to off or vice versa, the configuration of the linear network changes.  Adding more detail to the approximation of equations increases the accuracy of the simulation, but also increases its running time.

==See also==
{{Commons category|Electrical circuits}}
{{Wiktionary|electrical circuit}}

* [[Digital circuit]]
* [[Ground (electricity)]]
* [[Electrical impedance|Impedance]]
* [[External electric load|Load]]
* [[Memristor]]
* [[Open-circuit voltage]]
* [[Short circuit]]
* [[Voltage drop]]

===Representation===
* [[Circuit diagram]]
* [[Schematic]]
* [[Netlist]]

===Design and analysis methodologies===
* [[Network analysis (electrical circuits)]]
* [[Mathematical methods in electronics]]
* [[Superposition theorem]]
* [[Topology (electronics)]]
* [[Mesh analysis]]
* [[Prototype filter]]

===Measurement===
* [[Network analyzer (electrical)]]
* [[Network analyzer (AC power)]]
* [[Continuity test]]

===Analogies===
* [[Hydraulic analogy]]
* [[Mechanical–electrical analogies]]
* [[Impedance analogy]] (Maxwell analogy)
* [[Mobility analogy]] (Firestone analogy)
* [[Through and across analogy]] (Trent analogy)

===Specific topologies===
* [[Bridge circuit]]
* [[LC circuit]]
* [[RC circuit]]
* [[RL circuit]]
* [[RLC circuit]]
* [[Potential divider]]
* [[Series and parallel circuits]]

==References==
{{reflist}}

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[[Category:Electricity]]
[[Category:Electrical engineering]]

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