Topology (electrical circuits)

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. Topology is not concerned with the physical layout of components in a circuit, nor with their positions on a circuit diagram, similarly to the mathematic concept of topology it is only concerned with what connections exist between the components. There may be numerous physical layouts and circuit diagrams that all amount to the same topology. 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. Topology is not concerned with the physical layout of components in a circuit, nor with their positions on a circuit diagram, similarly to the mathematic concept of topology it is only concerned with what connections exist between the components. There may be numerous physical layouts and circuit diagrams that all amount to 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. 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. Standard graph theory can be extended to deal with active components and multi-terminal devices such as integrated circuits. Graphs can also be used in the analysis of infinite networks. The circuit diagrams in this article follow the usual conventions in electronics; lines represent conductors, filled small circles represent junctions of conductors, open small circles represent terminals for connection to the outside world. In most cases, impedances are represented by rectangles. A practical circuit diagram would use the specific symbols for resistors, inductors, capacitors etc., but topology is not concerned with the type of component in the network so the symbol for a general impedance has been used instead. The Graph theory section of this article gives an alternative method of representing networks. 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 in figure 1.1 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. Greek alphabet letters can also be used in this way, for example Π (pi) topology and Δ (delta) topology. For a network with two branches, there are only two possible topologies: series and parallel.