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-pass filter results in a high-pass filter. 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.
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Mathematical topology
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.
Topology names
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.
Series 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 transform is 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.
Simple 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
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 bridge and 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.
It is normal to call a network bridge topology only if it is being used as a two-port network 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 network article. 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 measurement applications.[1] The topology is also used in the twin-T oscillator as a sine wave generator. The diagram to the left shows twin-T topology redrawn to emphasise the connection with bridge topology.
Infinite topologies
Ladder topology can 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 topology and Composite image filter articles.
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-prism forms a topology which, in this sense, is an anti-ladder. Anti-ladder topology finds an application in voltage multiplier circuits, 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.
Infinite topologies can also be formed by cascading multiple sections of some other simple topology, such as lattice or bridge-T sections. Such infinite chains of lattice sections occur in the theoretical analysis and artificial simulation of transmission lines, but are rarely used as a practical circuit implementation.
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.
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With more complex circuits the description may proceed by specification of a transfer function between the ports of the network rather than the topology of the components.
See also
References
- ^ Farago, PS, An Introduction to Linear Network Analysis, pp125-127, The English Universities Press Ltd, 1961.
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