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 their associated fields. Electronic components are mostly industrial products, available in a singular form and are no ...

s (e.g., batteries,

resistor A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active ...

inductor An inductor, also called a coil, choke, or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a ...

capacitor A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passivity (engineering), passive electronic component with two termi ...

switch In electrical engineering, a switch is an electrical component that can disconnect or connect the conducting path in an electrical circuit, interrupting the electric current or diverting it from one conductor to another. The most common type of ...

es,

transistor upright=1.4, gate (G), body (B), source (S) and drain (D) terminals. The gate is separated from the body by an insulating layer (pink). A transistor is a semiconductor device used to Electronic amplifier, amplify or electronic switch, switch e ...

s) or a model of such an interconnection, consisting of

electrical element Electrical elements are conceptual abstractions representing idealized electrical components, such as resistors, capacitors, and inductors, used in the analysis of electrical networks. All electrical networks can be analyzed as multiple electric ...

s (e.g.,

voltage source A voltage source is a two-terminal device which can maintain a fixed voltage. An ideal voltage source can maintain the fixed voltage independent of the load resistance or the output current. However, a real-world voltage source cannot supply u ...

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 dual of a voltage source. The term ''current sink'' is sometimes used for sources fed ...

s, resistances,

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 ...

capacitance Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are ...

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'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear r ...

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 signals with respect to frequency, rather than time. Put simply, a time-domain graph shows how a si ...

methods such as

Laplace transform In mathematics, the Laplace transform, named after its discoverer Pierre-Simon Laplace (), is an integral transform that converts a function of a real variable (usually t, in the ''time domain'') to a function of a complex variable s (in the co ...

s, to determine DC response, AC response, and

transient response In electrical engineering and mechanical engineering, a transient response is the response of a system to a change from an equilibrium or a steady state. The transient response is not necessarily tied to abrupt events but to any event that affe ...

. A resistive circuit is a circuit containing only resistors and ideal current and voltage sources.

Analysis Analysis ( : analyses) is the process of breaking a complex topic or 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 Aristotle (3 ...

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), a 1992 album by Casiopea * Active Records, a record label Ships * ''Active'' (ship), several commercial ships by that name * HMS ''Active'', the name of various ships of the British Roya ...

electronic components is known as an ''

electronic circuit An electronic circuit is composed of individual electronic components, such as resistors, transistors, capacitors, inductors and diodes, connected by conductive wires or traces through which electric current can flow. It is a type of electrical ...

''. Such networks are generally nonlinear and require more complex design and analysis tools.

Classification

By passivity

An active network contains at least one

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 * Passive language, a language from which an interpreter works * Passivity (behavior), the condition of submitting to the influence of on ...

network does not contain an active source. An active network contains one or more sources of

electromotive force In electromagnetism and electronics, electromotive force (also electromotance, abbreviated emf, denoted \mathcal or ) is an energy transfer to an electric circuit per unit of electric charge, measured in volts. Devices called electrical ''transd ...

. Practical examples of such sources include a battery 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

with an iron core can be driven into

saturation Saturation, saturated, unsaturation or unsaturated may refer to: Chemistry * Saturation, a property of organic compounds referring to carbon-carbon bonds **Saturated and unsaturated compounds ** Degree of unsaturation **Saturated fat or fatty aci ...

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, such as electrical circuits, into a topology consisting of discrete e ...

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), 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 on the wave, such as two adjacent crests, tro ...

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 ...

. 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 passive components, such as capacitors, ...

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 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.

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 (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchh ...

: 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 (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchhof ...

: The directed sum of the electrical potential differences around a loop must be zero. *

Ohm's law Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equa ...

: 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, also called the 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 te ...

: 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 containing only voltage sources, current sources and resistances can be replaced at terminals A–B ...

: 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 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, electronic circuits which operate using digital signals **Digital camera, which captures and stores digital i ...

electrical engineers Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...

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 which obeys the superposition principle. This means that the output of the circuit ''F(x)'' when a linear combination of signals ''ax1(t) + bx2(t)'' is applied to it is equal to the linear combination o ...

s can be analyzed by hand using complex number theory. In more complex cases the circuit may be analyzed with specialized computer programs or estimation techniques such as the piecewise-linear model. Circuit simulation software, such as

HSPICE A spice is a seed, fruit, root, bark, or other plant substance primarily used for flavoring or coloring food. Spices are distinguished from herbs, which are the leaves, flowers, or stems of plants used for flavoring or as a garnish. Spices ar ...

(an analog circuit simulator), and languages such as

VHDL-AMS VHDL-AMS is a derivative of the hardware description language VHDL (IEEE standard 1076-1993). It includes analog and mixed-signal extensions (AMS) in order to define the behavior of analog and mixed-signal systems (IEEE 1076.1-1999). The VHDL-A ...

and

verilog-AMS Verilog-AMS is a derivative of the Verilog hardware description language that includes analog and mixed-signal extensions (AMS) in order to define the behavior of analog and mixed-signal systems. It extends the event-based simulator loops of Veril ...

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

GNUCAP GNU Circuit Analysis Package (Gnucap) is a general purpose circuit simulator started by Albert Davis in 1993. It is part of the GNU Project. The latest stable version is 0.35 from 2006. The latest development snapshot (as of November 2017) is fro ...

, 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, 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 In mathematics, Gaussian elimination, also known as row reduction, is an algorithm for solving systems of linear equations. It consists of a sequence of operations performed on the corresponding matrix of coefficients. This method can also be used ...

Piecewise-linear approximation

Software such as the

PLECS PLECS ( Piecewise Linear Electrical Circuit Simulation) is a software tool for system-level simulations of electrical circuits developed by Plexim. It is especially designed for power electronics but can be used for any electrical network. PLEC ...

interface to

Simulink Simulink is a MATLAB-based graphical programming environment for modeling, simulating and analyzing multidomain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block libraries. It offers t ...

uses 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.

References

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

Classification

By passivity

By linearity

By lumpiness

Classification of sources

Independent

Dependent

Applying electrical laws

Design methods

Network simulation software

Linearization around operating point

Piecewise-linear approximation

See also

Representation

Design and analysis methodologies

Measurement

Analogies

Specific topologies

References