Electrical network

An electrical network or electrical circuit is an interconnection of electrical elements such as resistors, inductors, capacitors, diodes, switches and transistors. It can be as small as an integrated circuit on a silicon chip, or as large as an electricity distribution network.
A circuit is a network that has a closed loop i.e. a return path. A network is a connection of 2 or more simple circuit elements, and may not be a circuit.
The goal when designing electrical networks for signal processing is to apply a predefined operation on potential differences (measured in volts) or currents (measured in amperes). Typical functions for these electrical networks are amplification, oscillation and analog linear algorithmic operations such as addition, subtraction, multiplication, division, differentiation and integration.
In the case of power distribution networks, engineers design the circuit to transport the energy as efficiently as possible while at the same time taking into account economic factors, network safety and redundancy. These networks use components such as power lines, cables, circuit breakers, switches and transformers.
To design any electrical circuits, electrical engineers need to be able to predict the voltages and currents in the circuit. Linear circuits can be analysed to a certain extent by hand because complex number theory gives engineers the ability to treat all linear elements using a single mathematical representation.
A number of electrical laws apply to all electrical 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 circuit must be zero.
 Ohm's law: the voltage across a resistor is the product of its resistance and the current flowing through it.
 the Ydelta transform
 Norton's theorem: any twoterminal collection of voltage sources and resistors is electrically equivalent to an ideal current source in parallel with a single resistor.
 Thevenin's theorem: any twoterminal combination of voltage sources and resistors is electrically equivalent to a single voltage source in series with a single resistor.
 Millman's method: the voltage on the ends of branches in parallel is equal to the sum of the currents flowing in every branch divided by the total equivalent conductance.
 See also Analysis of resistive circuits.
Other more complex laws may be needed if the network contains nonlinear or reactive components. Nonlinear selfregenerative hetrodyning systems can be approximated. Applying these laws results in a set of simultaneous equations that can be solved either by hand or by a computer.
Network simulation software
In more complex circuits, engineers need to turn to circuit simulation software. SPICE is the most famous of these.
Linearization around operating point
When faced with a new circuit, the software first tries to find a steady state solution. This is a solution 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 nonlinear element can be linearized around its operation point to obtain the smallsignal estimate of the voltages and currents. This is an application of Ohm's Law. The resulting linear circuit matrix can be solved with GaussJordan elimination.
Piecewise linear approximation
This type of simulator uses piecewise linear approximations of the equations governing the elements of a circuit. This approximation comes down to splitting the circuit into two parts: a completely linear network with a number of terminals that connect to ideal diodes. Every time a diode switches from on to off or vice versa, the linear network is configured differently. Increasing the accuracy of the simulation can be achieved by adding more detail to the approximation of the equations, this will increase the running time of the simulation. This flexibility allows an engineer to make a tradeoff between simulation time and the precision of the results, something that is not easily done with the previous simulation technique.
See also
 Analysis of resistive circuits
 Alternating current
 Balancing network
 Digital circuit
 Diode bridge
 Direct current
 Quiescent current
 Ground (electricity)
 Impedance
 Load
 Netlist
 Network
 RC circuit
 RLC circuit
 Potential divider
 Schematic
 Series and parallel circuits
 SPICE
 Tesla coil
 Continuity test
External link
 All About Circuits (http://www.allaboutcircuits.com) Offers a complete guide to electric circuits including experiments
 Circuit simulator with voltage and current visualization (http://www.falstad.com/circuit/)
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