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 n ...
s (e.g.,
batteries
Battery most often refers to:
* Electric battery, a device that provides electrical power
* Battery (crime), a crime involving unlawful physical contact
Battery may also refer to:
Energy source
*Automotive battery, a device to provide power t ...
,
resistors,
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 c ...
s,
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 passive electronic component with two terminals.
The effect of ...
s,
switches,
transistors) or a model of such an interconnection, consisting of
electrical elements (e.g.,
voltage sources,
current sources,
resistances,
inductances,
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 ...
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 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 ...
s, to determine
DC response,
AC response, and
transient response.
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 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 contains at least one
voltage source or
current source that can supply energy to the network indefinitely. A
passive network does not contain an active source.
An active network contains one or more sources of
electromotive force. Practical examples of such sources include a
battery
Battery most often refers to:
* Electric battery, a device that provides electrical power
* Battery (crime), a crime involving unlawful physical contact
Battery may also refer to:
Energy source
*Automotive battery, a device to provide power t ...
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 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 c ...
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 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 generating site, such as a power plant, to an electrical substation. The interconnected lines that facilitate this movement form a ''transmission network''. This is ...
), 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, tr ...
across the component dimensions. A new design model is needed for such cases called the
distributed-element model. Networks designed to this model are called ''
distributed-element circuits''.
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 tex ...
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: 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 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,
electrical engineers need to be able to predict the voltages and currents at all places within the circuit. Simple
linear circuits can be analyzed by hand using
complex number theory. In more complex cases the circuit may be analyzed with specialized
computer program
A computer program is a sequence or set of instructions in a programming language for a computer to Execution (computing), execute. Computer programs are one component of software, which also includes software documentation, documentation and oth ...
s or estimation techniques such as the piecewise-linear model.
Circuit simulation software, such as
HSPICE (an analog circuit simulator),
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.
Network simulation software
More complex circuits can be analyzed numerically with software such as
SPICE
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 a ...
or
GNUCAP, or symbolically using software such as
SapWin
Symbolic Analysis Program for Windows (SAPWIN) is a proprietary symbolic circuit simulator written in C++ for the Microsoft Windows operating systems Vista, 7.0 and 8.1. Unlike more common numerical circuit simulators (such as Simulation Program w ...
.
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 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 el ...
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
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. PL ...
interface to
Simulink 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.
See also
*
Digital circuit In theoretical computer science, a circuit is a model of computation in which input values proceed through a sequence of gates, each of which computes a function. Circuits of this kind provide a generalization of Boolean circuits and a mathemati ...
*
Ground (electricity)
*
Impedance
*
Load
*
Memristor
*
Open-circuit voltage
*
Short circuit
A short circuit (sometimes abbreviated to short or s/c) is an electrical circuit that allows a current to travel along an unintended path with no or very low electrical impedance. This results in an excessive current flowing through the circu ...
*
Voltage drop
Representation
*
Circuit diagram
*
Schematic
*
Netlist
Design and analysis methodologies
*
Network analysis (electrical circuits)
*
Mathematical methods in electronics
Mathematical methods are integral to the study of electronics.
Mathematics in electronics
Electronics engineering careers usually include courses in calculus (single and multivariable), complex analysis, differential equations (both ordinary an ...
*
Superposition theorem
*
Topology (electronics)
*
Mesh analysis
*
Prototype filter
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 of electrical networks are easy to measure at hig ...
*
Network analyzer (AC power)
*
Continuity test
In electronics, a continuity test is the checking of an electric circuit to see if current flows (that it is in fact a complete circuit).
A continuity test is performed by placing a small voltage (wired in series with an LED or noise-producing c ...
Analogies
*
Hydraulic analogy
*
Mechanical–electrical analogies
Mechanical–electrical analogies are the representation of mechanical systems as electrical networks. At first, such analogies were used in reverse to help explain electrical phenomena in familiar mechanical terms. James Clerk Maxwell introduce ...
*
Impedance analogy (Maxwell analogy)
*
Mobility analogy (Firestone analogy)
*
Through and across analogy
Prepositions and postpositions, together called adpositions (or broadly, in traditional grammar, simply prepositions), are a class of words used to express spatial or temporal relations (''in'', ''under'', ''towards'', ''before'') or mark various ...
(Trent analogy)
Specific topologies
*
Bridge circuit
A bridge circuit is a topology of electrical circuitry in which two circuit branches (usually in parallel with each other) are "bridged" by a third branch connected between the first two branches at some intermediate point along them. The bridge ...
*
LC circuit
*
RC circuit
A resistor–capacitor circuit (RC circuit), or RC filter or RC network, is an electric circuit composed of resistors and capacitors. It may be driven by a voltage or current source and these will produce different responses. A first order RC ...
*
RL circuit
*
RLC circuit
An RLC circuit is an electrical circuit consisting of a resistor (R), an inductor (L), and a capacitor (C), connected in series or in parallel. The name of the circuit is derived from the letters that are used to denote the constituent compon ...
*
Potential divider
In electronics, a voltage divider (also known as a potential divider) is a 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 distributing the inp ...
*
Series and parallel circuits
References
{{DEFAULTSORT:Electrical Network
Electricity
Electrical engineering
de:Netzwerk (Elektrotechnik)