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An n-terminal network can, at best, be reduced to n impedances (at worst ()). For a three terminal network, the three impedances can be expressed as a three node delta (Δ) network or four node star (Y) network. These two networks are equivalent and the transformations between them are given below.
1 Network theorems. 2 Network properties. ... Download as PDF; Printable version; ... Network theory is an area of applied mathematics. This page is a list of network ...
Reciprocity of electrical networks is a special case of Lorentz reciprocity, but it can also be proven more directly from network theorems. This proof shows reciprocity for a two-node network in terms of its admittance matrix, and then shows reciprocity for a network with an arbitrary number of nodes by an induction argument.
A simple electric circuit made up of a voltage source and a resistor. Here, =, according to Ohm's law. 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 ...
In direct-current circuit theory, Norton's theorem, also called the Mayer–Norton theorem, is a simplification that can be applied to networks made of linear time-invariant resistances, voltage sources, and current sources. At a pair of terminals of the network, it can be replaced by a current source and a single resistor in parallel.
Tellegen's theorem is extremely general; it is valid for any lumped network that contains any elements, linear or nonlinear, passive or active, time-varying or time-invariant. The generality is extended when W k {\displaystyle W_{k}} and F k {\displaystyle F_{k}} are linear operations on the set of potential differences and on the set of branch ...
The configuration of the network can be anything. Access to the network is provided by a pair of terminals. Designate the voltage measured between the terminals as V θ, as shown in the box on the left side of Figure 2. Fig. 2. Figure used in the proof of Thévenin's theorem.
Simple networks with just a few elements can be dealt with by formulating the network equations "by hand" with the application of simple network theorems such as Kirchhoff's laws. Equivalence is proved between two networks by directly comparing the two sets of equations and equating coefficients. For large networks more powerful techniques are ...