- Topology (electronics)
The topology of an electronic circuit is the form taken by the network of interconnections of the circuit components. Different specific values or ratings of the components are regarded as being the same topology.
Strictly speaking, replacing a component with one of an entirely different type is still the same topology. In some contexts, however, these can loosely be described as different topologies. For instance, interchanging inductors and capacitors in a
low-passfilter results in a high-passfilter. These might be described as high-pass and low-pass topologies even though the network topology is identical. A more correct term for these classes of object (that is, a network where the type of component is specified but not the absolute value) is prototype network.
Electronic network topology is related to mathematical topology, in particular, for networks which contain only two-terminal devices, circuit topology can be viewed as an application of
graph theory. In a network analysis of such a circuit from a topological point of view, the network nodes are the vertices of graph theory and the network branches are the edges of graph theory.
Two networks of this kind have the same topology if, and only if, they both have the same mathematical graph. That is, the same nodes are connected to the same branches in both circuits.
Many topology names relate to their appearance when drawn diagramatically. Most circuits can be drawn in a variety of ways and consequently have a variety of names. For instance, the three circuits shown below all look different but have identical topologies.This example also demonstrates a common convention of naming topologies after a letter of the alphabet to which they have a resemblance.
eries and parallel topologies
For a network with two branches, there are only two possible topologies; series and parallel.Even for these simplest of topologies, there are variations in the way the circuit can be presented.
For a network with three branches there are four possible topologies;Note that the parallel/series topology is another representation of the Delta topology discussed below.
Series and parallel topologies can continue to be constructed with greater and greater numbers of branches "ad infinitum". The number of unique topologies that can be obtained from "n" branches is 2n-1. The total number of unique topologies that can be obtained with no more than "n" branches is 2n-1.
Y and Δ topologies
Y and Δ are important topologies in linear network analysis due to these being the simplest possible three-terminal networks. A
Y-Δ transformis available for linear circuits. This transform is important because there are some networks that cannot be analysed in terms of series and parallel combinations. For instance, for this network on the left, consisting of a Y network connected in parallel with a Δ network. Say it is desired to calculate the impedance between two nodes of the network. In many networks this can be done by successive applications of the rules for combination of series or parallel impedances. This is not, however, possible in this case where the Y-Δ transform is needed in addition to the series and parallel rules.
The Y topology is also called star topology. However, star topology may also refer to the more general case of many branches connected to the same node.
imple filter topologies
The topologies shown opposite are commonly used for filter and attenuator designs. The L-section is identical topology to the potential divider topology. The T-section is identical topology to the Y topology. The Π-section is identical topology to the Δ topology.
All these topologies can be viewed as a short section of a
ladder topology. Longer sections would normally be described as ladder topology. These kinds of circuits are commonly analysed and characterised in terms of a two-port network.
Bridge topology is an important topology with many uses in both linear and non-linear applications, including, amongst many others, the
bridge rectifier, the Wheatstone bridgeand the lattice phase equaliser. There are several ways that bridge topology is rendered in circuit diagrams. The first rendering in the diagram above is the traditional depiction of a bridge circuit. The second rendering clearly shows the equivalence between the bridge topology and a topology derived by series and parallel combinations. The third rendering is more commonly known as lattice topology. It is not so obvious that this is topologically equivalent. It can be seen that this is indeed so by visualising the top left node moved to the right of the top right node.
with the input and output ports each consisting of a pair of diagonally opposite nodes. The box topology in the filter topologies section above can be seen to be identical to bridge topology but in the case of the filter the input and output ports are each a pair of "adjacent" nodes. Sometimes the loading (or null indication) component on the output port of the bridge will be included in the bridge topology as shown here.
Bridge T and Twin-T topologies
Bridge T topology is derived from bridge topology in a way explained in the
Zobel networkarticle. There are many derivative topologies also discussed in the same article.There is also a twin-T topology which has practical applications where it is desirable to have the input and output share a common (ground) terminal. This may be, for instance, because the input and output connections are made with co-axial topology. Connecting together an input and output terminal is not allowable with normal bridge topology and for this reason Twin-T is used where a bridge would otherwise be used for balance or null meansurement applications. [Farago, PS, "An Introduction to Linear Network Analysis", pp125-127, The English Universities Press Ltd, 1961.] The topology is also used in the twin-T oscillatoras a sine wave generator. The diagram to the left shows twin-T topology redrawn to emphasise the connection with bridge topology.
Ladder topologycan be extended without limit and is much used in filter designs. There are many variations on ladder topology, some of which are discussed in the Electronic filter topologyand Composite image filterarticles.The balanced form of ladder topology can be viewed as being the graph of the side of a prism of arbitrary order. The side of an anti-prismforms a topology which, in this sense, is an anti-ladder. Anti-ladder topology finds an application in voltage multipliercircuits, in particular the Cockcroft-Walton generator. There is also a full-wave version of the Cockcroft-Walton generator which uses a double anti-ladder topology.
Components with more than two terminals
Circuits containing components with three or more terminals greatly increase the number of possible topologies. Conversely, the number of different circuits represented by a topology diminishes and in many cases the circuit is easily recognisable from the topology even when specific components are not identified.With more complex circuits the description may proceed by specification of a
transfer functionbetween the ports of the network rather than the topology of the components.
Electronic filter topology
Network analysis (electrical circuits)
Wikimedia Foundation. 2010.
Look at other dictionaries:
Multiple feedback topology (electronics) — Multiple feedback topology is an electronic filter topology which is used to implement an electronic filter by adding two poles to the transfer function. A diagram of the circuit topology for a second order low pass filter is shown in the figure… … Wikipedia
Topology (disambiguation) — Topology is a branch of mathematics concerned with spatial properties preserved under bicontinuous deformation (stretching without tearing or gluing); these properties are the topological invariants.Topology may also refer to: *Topology, the… … Wikipedia
Geospatial topology — Topology In a Geographic Information System GIS, topology is a set of rules which define the relationship between points, lines, and polygons. ESRI enables topology generation within their geodatabase feature classes. Network topology explores… … Wikipedia
Electronic filter topology — An elementary filter topology introduces a capacitor into the feedback path of an op amp to achieve an unbalanced active implementation of a low pass transfer function Electronic filter topology defines electronic filter circuits without taking… … Wikipedia
Electrical network — For electrical power transmission grids and distribution networks, see Grid (electricity). A simple electric circuit made up of a voltage source and a resistor. Here, V = iR, according to Ohm s Law. An electrical network is an interconnection of… … Wikipedia
Список награждённых Национальной медалью науки США — Джошуа Ледерберг (справа) получает Национальную медаль науки из рук Президента США Джорджа Буша старшего Список … Википедия
Electric motor — For other kinds of motors, see motor (disambiguation). For a railroad electric engine, see electric locomotive. Various electric motors. A 9 volt PP3 transistor battery is in the center foreground for size comparison. An electric motor converts… … Wikipedia
Distributed element filter — Figure 1. A circuit featuring many of the f … Wikipedia
Mathematics and Physical Sciences — ▪ 2003 Introduction Mathematics Mathematics in 2002 was marked by two discoveries in number theory. The first may have practical implications; the second satisfied a 150 year old curiosity. Computer scientist Manindra Agrawal of the… … Universalium
Translinear circuit — A translinear circuit is a circuit that carries out its function using the translinear principle. These are current mode circuits that can be made using transistors that obey an exponential current voltage characteristic this includes BJTs and… … Wikipedia