Electrical network

For electrical power transmission grids and distribution networks, seeElectrical grid.

Anelectrical networkis an interconnection ofelectrical components(e.g.,batteries,resistors,inductors,capacitors,switches,transistors) or a model of such an interconnection, consisting ofelectrical elements(e.g.,voltage sources,current sources,resistances,inductances,capacitances). Anelectrical circuitis 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" ).Linearelectrical 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 arelinearly superimposable.They are thus more easily analyzed, using powerfulfrequency domainmethods such asLaplace transforms,to determineDC response,AC response,andtransient response.

A simple electric circuit made up of a voltage source and a resistor. Here,$v=iR$,according toOhm's law.

Aresistive networkis a network containing only resistors and ideal current and voltage sources.Analysisof resistive networks is less complicated than analysis of networks containing capacitors and inductors. If the sources are constant (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.

A network that containsactiveelectroniccomponents is known as anelectronic circuit.Such networks are generally nonlinear and require more complex design and analysis tools.

Classification

By passivity

An active network contains at least onevoltage sourceorcurrent sourcethat can supply energy to the network indefinitely. Apassivenetwork does not contain an active source.

An active network contains one or more sources ofelectromotive force.Practical examples of such sources include abatteryor agenerator.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 ofsuperposition;otherwise it is non-linear. Passive networks are generally taken to be linear, but there are exceptions. For instance, aninductorwith an iron core can be driven intosaturationif 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 calledlumped elementsbecause all of their, respectively, resistance, capacitance and inductance is assumed to be located ( "lumped" ) at one place. This design philosophy is called thelumped-element modeland networks so designed are calledlumped-element circuits.This is the conventional approach to circuit design. At high enough frequencies, or for long enough circuits (such aspower transmission lines), the lumped assumption no longer holds because there is a significant fraction of awavelengthacross the component dimensions. A new design model is needed for such cases called thedistributed-element model.Networks designed to this model are calleddistributed-element circuits.

A distributed-element circuit that includes some lumped components is called asemi-lumpeddesign. An example of a semi-lumped circuit is thecombline 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 sourcesdepend 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 containingreactances.They cannot be used in networks that contain nonlinear or time-varying components.

Design methods

Linearnetwork analysis
Elements
Components
Series and parallel circuits
Impedance transforms
Generator theorems	Networktheorems
Network analysis methods
Two-port parameters

See also:Network analysis (electrical circuits)

To design any electrical circuit, eitheranalogordigital,electrical engineersneed to be able to predict the voltages and currents at all places within the circuit. Simplelinear circuitscan be analyzed by hand usingcomplex number theory.In more complex cases the circuit may be analyzed with specializedcomputer programsor estimation techniques such as the piecewise-linear model.

Circuit simulation software, such asHSPICE(an analog circuit simulator),and languages such asVHDL-AMSandverilog-AMSallow 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 asSPICEorGNUCAP,or symbolically using software such asSapWin.

Linearization around operating point

When faced with a new circuit, the software first tries to find asteady state solution,that is, one where all nodes conform to Kirchhoff's current lawandthe 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, theoperating pointsof 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 withGaussian elimination.

Piecewise-linear approximation

Software such as thePLECSinterface toSimulinkusespiecewise-linearapproximation of the equations governing the elements of a circuit. The circuit is treated as a completely linear network ofideal diodes.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

• Digital circuit
• Ground (electricity)
• Impedance
• 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