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Node Elimination
The star-mesh transform, or star-polygon transform, is a mathematical circuit analysis technique to transform a resistive network into an equivalent network with one less node. The equivalence follows from the Schur complement identity applied to the Kirchhoff matrix of the network. The equivalent impedance betweens nodes A and B is given by: :z_\text = z_\text z_\text \sum\frac, where z_\text is the impedance between node A and the central node being removed. The transform replaces ''N'' resistors with \fracN(N - 1) resistors. For N > 3, the result is an increase in the number of resistors, so the transform has no general inverse without additional constraints. It is possible, though not necessarily efficient, to transform an arbitrarily complex two-terminal resistive network into a single equivalent resistor by repeatedly applying the star-mesh transform to eliminate each non-terminal node. Special cases When ''N'' is: # For a single dangling resistor, the transform eli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circuit Analysis
A network, in the context of electrical engineering and electronics, is a collection of interconnected components. Network analysis is the process of finding the voltages across, and the currents through, all network components. There are many techniques for calculating these values. However, for the most part, the techniques assume linear components. Except where stated, the methods described in this article are applicable only to ''linear'' network analysis. Definitions Equivalent circuits A useful procedure in network analysis is to simplify the network by reducing the number of components. This can be done by replacing physical components with other notional components that have the same effect. A particular technique might directly reduce the number of components, for instance by combining impedances in series. On the other hand, it might merely change the form into one in which the components can be reduced in a later operation. For instance, one might transform a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Network Analysis (electrical Circuits)
A network, in the context of electrical engineering and electronics, is a collection of interconnected components. Network analysis is the process of finding the voltages across, and the currents through, all network components. There are many techniques for calculating these values. However, for the most part, the techniques assume linear components. Except where stated, the methods described in this article are applicable only to ''linear'' network analysis. Definitions Equivalent circuits A useful procedure in network analysis is to simplify the network by reducing the number of components. This can be done by replacing physical components with other notional components that have the same effect. A particular technique might directly reduce the number of components, for instance by combining impedances in series. On the other hand, it might merely change the form into one in which the components can be reduced in a later operation. For instance, one might transform a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schur Complement
In linear algebra and the theory of matrices, the Schur complement of a block matrix is defined as follows. Suppose ''p'', ''q'' are nonnegative integers, and suppose ''A'', ''B'', ''C'', ''D'' are respectively ''p'' × ''p'', ''p'' × ''q'', ''q'' × ''p'', and ''q'' × ''q'' matrices of complex numbers. Let :M = \left begin A & B \\ C & D \end\right/math> so that ''M'' is a (''p'' + ''q'') × (''p'' + ''q'') matrix. If ''D'' is invertible, then the Schur complement of the block ''D'' of the matrix ''M'' is the ''p'' × ''p'' matrix defined by :M/D := A - BD^C. If ''A'' is invertible, the Schur complement of the block ''A'' of the matrix ''M'' is the ''q'' × ''q'' matrix defined by :M/A := D - CA^B. In the case that ''A'' or ''D'' is singular, substituting a generalized inverse for the inverses on ''M/A'' and ''M/D'' yields the generalized Schur complement. The Schur complement is named after Issai Schur who used it to prove Schur's lemma, although it had been used previous ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Star-mesh Transform
The star-mesh transform, or star-polygon transform, is a mathematical circuit analysis technique to transform a resistive network into an equivalent network with one less node. The equivalence follows from the Schur complement identity applied to the Kirchhoff matrix of the network. The equivalent impedance betweens nodes A and B is given by: :z_\text = z_\text z_\text \sum\frac, where z_\text is the impedance between node A and the central node being removed. The transform replaces ''N'' resistors with \fracN(N - 1) resistors. For N > 3, the result is an increase in the number of resistors, so the transform has no general inverse without additional constraints. It is possible, though not necessarily efficient, to transform an arbitrarily complex two-terminal resistive network into a single equivalent resistor by repeatedly applying the star-mesh transform to eliminate each non-terminal node. Special cases When ''N'' is: # For a single dangling resistor, the transform elim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Y-Δ Transform
The Y-Δ transform, also written wye-delta and also known by many other names, is a mathematical technique to simplify the analysis of an electrical network. The name derives from the shapes of the circuit diagrams, which look respectively like the letter Y and the Greek capital letter Δ. This circuit transformation theory was published by Arthur Edwin Kennelly in 1899. It is widely used in analysis of three-phase electric power circuits. The Y-Δ transform can be considered a special case of the star-mesh transform for three resistors. In mathematics, the Y-Δ transform plays an important role in theory of circular planar graphs. Names The Y-Δ transform is known by a variety of other names, mostly based upon the two shapes involved, listed in either order. The Y, spelled out as wye, can also be called T or star; the Δ, spelled out as delta, can also be called triangle, Π (spelled out as pi), or mesh. Thus, common names for the transformation include wye-delta or delta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Network Analysis (electrical Circuits)
A network, in the context of electrical engineering and electronics, is a collection of interconnected components. Network analysis is the process of finding the voltages across, and the currents through, all network components. There are many techniques for calculating these values. However, for the most part, the techniques assume linear components. Except where stated, the methods described in this article are applicable only to ''linear'' network analysis. Definitions Equivalent circuits A useful procedure in network analysis is to simplify the network by reducing the number of components. This can be done by replacing physical components with other notional components that have the same effect. A particular technique might directly reduce the number of components, for instance by combining impedances in series. On the other hand, it might merely change the form into one in which the components can be reduced in a later operation. For instance, one might transform a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electrical Circuits
An electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sources, current sources, resistances, inductances, capacitances). An electrical circuit is a network consisting of a closed loop, giving a return path for the current. 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 transforms, 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 of resistive circuits is less complicated t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circuit Theorems
Circuit may refer to: Science and technology Electrical engineering * Electrical circuit, a complete electrical network with a closed-loop giving a return path for current ** Analog circuit, uses continuous signal levels ** Balanced circuit, paths are impedance-matched ** Circuit analysis, the process of finding the voltages across, and the currents through, every component in an electrical circuit ** Circuit diagram, a graphical representation of an electrical circuit ** Digital circuit, uses discrete signal levels ** Electronic circuit, contains "active" (nonlinear) electronic components capable of performing amplification, computation, and data transfer *** Asynchronous circuit, or self-timed circuit, a sequential digital logic circuit that is not governed by a clock circuit or global clock signal *** Integrated circuit, a set of electronic circuits on a small "chip" of semiconductor material **** Mixed-signal integrated circuit, contains both analog and digital signals * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
