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An electrical network is an interconnection of
electrical component An electronic component is any basic discrete device or physical entity in an electronic system Electronic may refer to: *Electronics, the science of how to control electric energy in semiconductor *Electronics (magazine), ''Electronics'' (maga ...
s (e.g.,
batteries Battery may refer to: Energy source * Electric battery, an electrochemical device to provide electrical power ** Automotive battery, a device to provide power to certain functions of an automobile ** List of battery types * Energy storage, inclu ...
,
resistor A resistor is a that implements as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to , active elements, and terminate s, among other uses. High-power resistors that can dissipat ...

resistor
s,
inductor An inductor, also called a coil, choke, or reactor, is a passive Passive may refer to: * Passive voice, a grammatical voice common in many languages, see also Pseudopassive (disambiguation), Pseudopassive * Passive language, a language from whi ...

inductor
s,
capacitor A capacitor is a device that stores electric charge in an electric field. It is a passivity (engineering), passive electronic component with two terminal (electronics), terminals. The effect of a capacitor is known as capacitance. While som ...

capacitor
s,
switch In , a switch is an that can disconnect or connect the conducting path in an , interrupting the or diverting it from one conductor to another. The most common type of switch is an electromechanical device consisting of one or more sets of movab ...

switch
es,
transistor upright=1.4, gate Candi bentar, a typical Indonesian gate that is often found on the islands of Java">Indonesia.html" ;"title="Candi bentar, a typical Indonesia">Candi bentar, a typical Indonesian gate that is often found on the islands o ...

transistor
s) or a model of such an interconnection, consisting of
electrical element Electrical elements are conceptual abstractions representing idealized electrical components, such as resistors, capacitor A capacitor is a device that stores electric charge in an electric field. It is a passivity (engineering), passive el ...
s (e.g.,
voltage source A voltage source is a two- terminal device which can maintain a fixed voltage Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential The electric potential (also called the ' ...

voltage source
s,
current source A current source is an electronic circuit that delivers or absorbs an electric current which is independent of the voltage across it. A current source is the duality (electrical circuits), dual of a voltage source. The term ''current sink'' is so ...

current source
s,
resistance Resistance may refer to: Arts, entertainment, and media Comics * Either of two similarly named but otherwise unrelated comic book series, both published by Wildstorm: ** ''Resistance'' (comics), based on the video game of the same title ** ''Th ...
s,
inductance Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The flow of electric current creates a magnetic field around the conductor. The field strength depends on the magnitude of the c ...
s,
capacitance Capacitance is the ratio of the amount of stored on a to a difference in . There are two closely related notions of capacitance: ''self capacitance'' and ''mutual capacitance''. Any object that can be electrically charged exhibits ''self capa ...
s). An electrical circuit is a network consisting of a closed loop, giving a return path for the current.
Linear Linearity is the property of a mathematical relationship (''function Function or functionality may refer to: Computing * Function key A function key is a key on a computer A computer is a machine that can be programmed to carry out se ...
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 linearly superimposable. They are thus more easily analyzed, using powerful
frequency domain In physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or Signal (information theory), signals with respect to frequency, rather than time. Put simply, a time-dom ...
methods such as
Laplace transform In mathematics, the Laplace transform, named after its inventor Pierre-Simon Laplace (), is an integral transform that converts a function of a real variable t (often time in physics, time) to a function of a complex analysis, complex variable s (co ...
s, to determine DC response, AC response, and
transient response In electrical engineering and mechanical engineering Mechanical engineering is an engineering Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including br ...
. A resistive circuit is a circuit containing only resistors and ideal current and voltage sources.
Analysis Analysis is the process of breaking a complexity, complex topic or Substance theory, substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Ari ...
of resistive circuits is less complicated than analysis of circuits containing capacitors and inductors. If the sources are constant ( DC) sources, the result is a DC circuit. 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 contains
active Active may refer to: Music * Active (album), ''Active'' (album), a 1992 album by Casiopea * Active Records, a record label Ships * Active (ship), ''Active'' (ship), several commercial ships by that name * HMS Active, HMS ''Active'', the nam ...
electronic Electronic may refer to: *Electronics Electronics comprises the physics, engineering, technology and applications that deal with the emission, flow and control of electrons in vacuum and matter. It uses active devices to control electron flow b ...
components is known as an ''
electronic circuit 200px, A circuit built on a printed circuit board (PCB). An electronic circuit is composed of individual electronic component An electronic component is any basic discrete device or physical entity in an electronic system used to affect ele ...

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 A voltage source is a two- terminal device which can maintain a fixed voltage Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential The electric potential (also called the ' ...

voltage source
or
current source A current source is an electronic circuit that delivers or absorbs an electric current which is independent of the voltage across it. A current source is the duality (electrical circuits), dual of a voltage source. The term ''current sink'' is so ...

current source
that can supply energy to the network indefinitely. A
passive Passive may refer to: * Passive voice, a grammatical voice common in many languages, see also Pseudopassive (disambiguation), Pseudopassive * Passive language, a language from which an interpreter works * Passivity (behavior), the condition of sub ...
network does not contain an active source. An active network contains one or more sources of
electromotive force In electromagnetism Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force is c ...
. Practical examples of such sources include a
battery Battery may refer to: Energy source * Electric battery, an electrochemical device to provide electrical power ** Automotive battery, a device to provide power to certain functions of an automobile ** List of battery types * Energy storage, inclu ...
or a 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; otherwise it is non-linear. Passive networks are generally taken to be linear, but there are exceptions. For instance, an
inductor An inductor, also called a coil, choke, or reactor, is a passive Passive may refer to: * Passive voice, a grammatical voice common in many languages, see also Pseudopassive (disambiguation), Pseudopassive * Passive language, a language from whi ...

inductor
with an iron core can be driven into 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 The lumped-element model (also called lumped-parameter model, or lumped-component model) simplifies the description of the behaviour of spatially distributed physical systems into a topology s, which have only one surface and one edge, are a k ...
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
power transmission lines Electric power transmission is the bulk movement of electrical energy from a power generation, generating site, such as a power plant, to an electrical substation. The interconnected lines which facilitate this movement are known as a ''transmiss ...

power transmission lines
), the lumped assumption no longer holds because there is a significant fraction of a
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase (waves), phase on the wave, such as two adja ...

wavelength
across the component dimensions. A new design model is needed for such cases called the
distributed-element model : ''This article is an example from the domain of electrical systems, which is a special case of the more general distributed-parameter systems.'' In electrical engineering, the distributed-element model or transmission-line model of electrical El ...
. Networks designed to this model are called ''
distributed-element circuit Distributed-element circuits are electrical circuits composed of lengths of transmission lines or other distributed components. These circuits perform the same functions as conventional circuits composed of Passivity (engineering), passive compone ...
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 In the theory of electrical networks, a dependent source is a voltage source or a current source whose value depends on a voltage or current elsewhere in the network.I. D. Mayergoyz, Wes Lawson ''Basic electric circuit theory: a one-semester text ...
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 Kirchhoff's circuit laws are two equalities that deal with the current and potential difference Voltage, electric potential difference, electromotive force emf, electric pressure or electric tension is the difference in electric potential ...

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 Kirchhoff's circuit laws are two equalities that deal with the current and potential difference Voltage, electric potential difference, electromotive force emf, electric pressure or electric tension is the difference in electric potential ...
: The directed sum of the electrical potential differences around a loop must be zero. *
Ohm's law Ohm's law states that the current Currents or The Current may refer to: Science and technology * Current (fluid) A current in a fluid In physics, a fluid is a substance that continually Deformation (mechanics), deforms (flows) under an ap ...

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 In direct-current circuit theory, Norton's theorem (aka Mayer–Norton theorem) is a simplification that can be applied to networks made of linear time-invariant resistances, voltage sources, and current sources. At a pair of terminals of the n ...
: 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 As originally stated in terms of direct-current resistive circuits only, Thévenin's theorem states that, ''"For any linear electrical network An electrical network is an interconnection of electrical components (e.g., batteries, resist ...
: 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 The superposition theorem is a derived result of the superposition principle motion as superposition of two motions. The rolling motion of the wheel can be described as a combination of two separate motions: translation Translation is th ...
: 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
reactances
reactances
. They cannot be used in networks that contain nonlinear or time-varying components.


Design methods

To design any electrical circuit, either analog or
digital Digital usually refers to something using discrete digits, often binary digits. Technology and computing Hardware *Digital electronics Digital electronics is a field of electronics The field of electronics is a branch of physics and electr ...
,
electrical engineers
electrical engineers
need to be able to predict the voltages and currents at all places within the circuit. Simple
linear circuit A linear circuit is an electronic circuit 200px, A circuit built on a printed circuit board (PCB). An electronic circuit is composed of individual electronic component An electronic component is any basic discrete device or physical entity ...
s can be analyzed by hand using
complex number theory
complex number theory
. In more complex cases the circuit may be analyzed with specialized
computer program In imperative programming, a computer program is a sequence of instructions in a programming language that a computer can execute or interpret. In declarative programming, a ''computer program'' is a Set (mathematics), set of instructions. A comp ...
s or estimation techniques such as the piecewise-linear model. Circuit simulation software, such as
HSPICE A spice is a seed A seed is an embryonic ''Embryonic'' is the twelfth studio album by experimental rock band the Flaming Lips released on October 13, 2009, on Warner Bros. Records, Warner Bros. The band's first double album, it was relea ...
(an analog circuit simulator), and languages such as
VHDL-AMS VHDL-AMS is a derivative of the hardware description language In computer engineering, a hardware description language (HDL) is a specialized computer language used to describe the structure and behavior of electronic circuits, and most commonly ...
and
verilog-AMS Verilog-AMS is a derivative of the Verilog Verilog, standardized as IEEE 1364, is a hardware description language In computer engineering, a hardware description language (HDL) is a specialized computer language used to describe the structure ...
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 A spice is a seed A seed is an embryonic ''Embryonic'' is the twelfth studio album by experimental rock band the Flaming Lips released on October 13, 2009, on Warner Bros. Records, Warner Bros. The band's first double album, it was releas ...

SPICE
or 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 solution
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 {{unreferenced, date=April 2013 The operating point is a specific point within the operation characteristic of a technical device. This point will be engaged because of the properties of the system and the outside influences and parameters. In ele ...
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 Simulink is a MATLAB MATLAB (an abbreviation of "MATrix LABoratory") is a and environment developed by . MATLAB allows manipulations, plotting of and data, implementation of s, creation of s, and interfacing with programs written in o ...

Simulink
uses
piecewise-linear
piecewise-linear
approximation of the equations governing the elements of a circuit. The circuit is treated as a completely linear network of ideal 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 circuitIn theoretical computer science Image:Maquina.png, An artistic representation of a Turing machine. Turing machines are used to model general computing devices. Theoretical computer science (TCS) is a subset of general computer science and mathemati ...
*
Ground (electricity) In electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics The field of electronics is a branch of ...
* Impedance *
Load Load or LOAD may refer to: Aeronautics and transportation *Load factor (aeronautics), the ratio of the lift of an aircraft to its weight *Passenger load factor, the ratio of revenue passenger miles to available seat miles of a particular transpor ...
*
Memristor A memristor (; a portmanteau of ''memory resistor'') is a non-linear terminal (electronics), two-terminal electronic component, electrical component relating electric charge and magnetic flux linkage. It was described and named in 1971 by Leon C ...

Memristor
*
Open-circuit voltage Black curve: The highest possible open-circuit voltage of a Shockley-Queisser model under unconcentrated sunlight, as a function of the semiconductor bandgap">Shockley-Queisser limit">Shockley-Queisser model under unconcentrated sunlight, as a f ...
*
Short circuit A short circuit (sometimes abbreviated to short or s/c) is an electrical circuit An electrical network is an interconnection of electronic component, electrical components (e.g., battery (electricity), batteries, resistors, inductors, capaci ...

Short circuit
*
Voltage drop Voltage drop is the decrease of electrical potential along the path of a current flowing in an electrical circuitCircuit may refer to: Science and technology Electrical engineering * Electrical circuit, a complete electrical network with a ...

Voltage drop


Representation

*
Circuit diagram A circuit diagram (wiring diagram, electrical diagram, elementary diagram, electronic schematic) is a graphical representation of an electrical circuit An electrical network is an interconnection of electrical component An electroni ...

Circuit diagram
*
Schematic A schematic, or schematic diagram, is a representation of the elements of a system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded ...

Schematic
*
Netlist In electronic design Electronic may refer to: *Electronics, the science of how to control electric energy in semiconductor *Electronics (magazine), ''Electronics'' (magazine), a defunct American trade journal *Electronic storage, the storage of ...


Design and analysis methodologies

*
Network analysis (electrical circuits) A network, in the context of electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics The field of ele ...
* Mathematical methods in electronics *
Superposition theorem The superposition theorem is a derived result of the superposition principle motion as superposition of two motions. The rolling motion of the wheel can be described as a combination of two separate motions: translation Translation is th ...
*
Topology (electronics)The topology of an electronic circuit is the form taken by the Network analysis (electrical circuits), network of interconnections of the circuit components. Different specific values or ratings of the components are regarded as being the same topol ...
*
Mesh analysis of the resistor A resistor is a passive two-terminal electrical component that implements electrical resistance In electronics and electromagnetism, the electrical resistance of an object is a measure of its opposition to the flow of ...
*
Prototype filter Prototype filters are electronic filter Electronic filters are a type of signal processing filter in the form of electrical circuits. This article covers those filters consisting of lumped-element model, lumped electronic components, as oppo ...


Measurement

*
Network analyzer (electrical) A network analyzer is an instrument that measures the network parameters of electrical networks. Today, network analyzers commonly measure s–parameters because reflection and transmission Transmission may refer to: Science and technolo ...
*
Network analyzer (AC power) From 1929 to the late 1960s, large alternating current Alternating current (AC) is an electric current which periodically reverses direction and changes its magnitude continuously with time in contrast to direct current Direct current (DC) is ...
*
Continuity test In electronics Electronics comprises the physics, engineering, technology and applications that deal with the emission, flow and control of electrons in vacuum and matter. It uses active devices to control electron flow by amplifier, amplificati ...


Analogies

*
Hydraulic analogy The electronic–hydraulic analogy (derisively referred to as the drain-pipe theory by Oliver Lodge) is the most widely used analogy for "electron fluid" in a metal conductor. Since electric current An electric current is a stream of cha ...
* Mechanical–electrical analogies *
Impedance analogy The impedance analogy is a method of representing a mechanical system by an analogous electrical system. The advantage of doing this is that there is a large body of theory and analysis techniques concerning complex electrical systems, especially i ...
(Maxwell analogy) *
Mobility analogy The mobility analogy, also called admittance analogy or Firestone analogy, is a method of representing a mechanical system by an analogous electrical system. The advantage of doing this is that there is a large body of theory and analysis technique ...
(Firestone analogy) * Through and across analogy (Trent analogy)


Specific topologies

*
Bridge circuit A bridge circuit is a topology In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contai ...

Bridge circuit
*
LC circuit An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit, is an electric circuit consisting of an inductor, represented by the letter L, and a capacitor, represented by the letter C, connected together. The circuit can act ...
*
RC circuit A resistor–capacitor circuit (RC circuit), or RC filter or RC network, is an electric circuit An electrical network is an interconnection of electrical component An electronic component is any basic discrete device or physical entity ...

RC circuit
*
RL circuit A resistor–inductor circuit (RL circuit), or RL filter or RL network, is an electric circuit An electrical network is an interconnection of electrical component An electronic component is any basic discrete device or physical entity i ...
*
RLC circuit An RLC circuit is an electrical circuit An electrical network is an interconnection of electrical component An electronic component is any basic discrete device or physical entity in an electronic system used to affect electrons or thei ...

RLC circuit
*
Potential divider In electronics, a voltage divider (also known as a potential divider) is a passive circuit, passive linear circuit that produces an output voltage (''V''out) that is a fraction of its input voltage (''V''in). Voltage division is the result of distr ...
*
Series and parallel circuits Two-terminal components and electrical networks can be connected in series or parallel. The resulting electrical network will have two terminals, and itself can participate in a series or parallel topology In mathematics Mathemati ...

Series and parallel circuits


References

{{DEFAULTSORT:Electrical Network Electricity Electrical engineering de:Netzwerk (Elektrotechnik)