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{{For|electrical power transmission grids and distribution networks|Grid (electricity)}}
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[[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]].]]
{{Unreferenced|date=January 2007}}
 
An '''electrical network''' is an interconnection of [[electrical element]]s such as [[resistor]]s, [[inductor]]s, [[capacitor]]s, [[voltage source]]s, [[current source]]s and [[switch]]es. An '''electrical circuit''' is a network consisting of a closed loop, giving a return path for the current. [[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 circuit''' is a circuit containing only resistors and ideal current and voltage sources.  [[Network analysis (electrical circuits)|Analysis]] of resistive circuits is less complicated than analysis of circuits containing capacitors and inductors.  If the sources are constant ([[Direct current|DC]]) sources, the result is a [[direct current circuit|DC circuit]].
 
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 is a network that consists of at least one active source like a [[voltage source]] or [[current source]]
 
A passive network is a network which does not contain any active device.
 
===By linearity===
A [[linear circuit]] is a circuit which is composed entirely of independent sources, linear dependent
sources and linear passive elements or a combination of these.
(A network is said to be linear if it obeys the principles of homogeneity{{clarify|reason=In what sense is homogeneity (physics) a requirement for linearity?|date=September 2013}} and superposition).
Otherwise it is called a non-linear network.
 
==Classification of sources==
Sources can be classified as independent sources and dependent sources
 
===Independent Sources===
Ideal Independent Source maintains 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 connected network.
 
===Dependent Sources===
[[Dependent Sources]] depend upon a particular element of the circuit for delivering the power or voltage or current depending upon the type of source it is.
 
==Electrical laws==
A number of electrical laws apply to all electrical networks.  These include:
*[[Kirchhoff's circuit laws#Kirchhoff's current law|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 circuit laws#Kirchhoff's voltage law|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 talking one independent source at a time.  
==Design methods==
 
{{Network analysis navigation}}
 
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. [[Linear circuit]]s, that is, circuits with the same input and output frequency, can be analyzed by hand using [[Complex number|complex number theory]]. Other circuits can only be analyzed with specialized [[software program]]s or estimation techniques such as the piecewise-linear model.
 
Circuit simulation software, such as [[HSPICE]], 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.
 
* See also [[Network analysis (electrical circuits)]].
 
Other more complex laws may be needed if the network contains nonlinear or [[Reactance (electronics)|reactive]] components.  Non-linear self-regenerative [[Heterodyne|heterodyning]] systems can be approximated. Applying these laws results in a set of [[simultaneous equations]] that can be solved either algebraically or numerically.
 
==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 points''' 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==
{{div col|colwidth=20em}}
* [[Bridge circuit]]
* [[Digital circuit]]
* [[Circuit diagram]]
* [[Circuit theory]]
* [[Diode bridge]]
* [[Quiescent current]]
* [[Ground (electricity)]]
* [[Hydraulic analogy]]
* [[Electrical impedance|Impedance]]
* [[External electric load|Load]]
* [[Mathematical methods in electronics]]
* [[Memristor]]
* [[Netlist]]
* [[Network analyzer (electrical)]]
* [[Network analyzer (AC power)]]
* [[Open-circuit voltage]]
* [[LC circuit]]
* [[RC circuit]]
* [[RL circuit]]
* [[RLC circuit]]
* [[Lumped element model]] and [[distributed element model]]
* [[Potential divider]]
* [[Prototype filter]]
* [[Schematic]]
* [[Series and parallel circuits]]
* [[Short circuit]]
* [[Superposition theorem]]
* [[Topology (electronics)]]
* [[Continuity test]]
* [[Voltage drop]]
* [[Mesh analysis]]
{{div col end}}
{{Portal bar|Electronics}}
 
== External links ==
{{Commons category|Circuit diagrams|electric circuits}}
{{Wiktionary|electrical circuit}}
 
{{DEFAULTSORT:Electrical Network}}
[[Category:Electricity]]
[[Category:Electrical engineering]]
 
[[de:Netzwerk (Elektrotechnik)]]

Revision as of 18:42, 2 March 2014

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