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Thévenin's Theorem
As originally stated in terms of direct-current resistive circuits only, Thévenin's theorem states that ''"For any linear electrical network containing only voltage sources, current sources and resistances can be replaced at terminals A–B by an equivalent combination of a voltage source Vth in a series connection with a resistance Rth."'' * The equivalent voltage ''V''th is the voltage obtained at terminals A–B of the network with terminals A–B open circuited. * The equivalent resistance ''R''th is the resistance that the circuit between terminals A and B would have if all ideal voltage sources in the circuit were replaced by a short circuit and all ideal current sources were replaced by an open circuit. * If terminals A and B are connected to one another, the current flowing from A to B will be ''V''th/''R''th. This means that ''R''th could alternatively be calculated as ''V''th divided by the short-circuit current between A and B when they are connected together. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kirchhoff's Circuit Laws
Kirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchhoff. This generalized the work of Georg Ohm and preceded the work of James Clerk Maxwell. Widely used in electrical engineering, they are also called Kirchhoff's rules or simply Kirchhoff's laws. These laws can be applied in time and frequency domains and form the basis for network analysis. Both of Kirchhoff's laws can be understood as corollaries of Maxwell's equations in the low-frequency limit. They are accurate for DC circuits, and for AC circuits at frequencies where the wavelengths of electromagnetic radiation are very large compared to the circuits. Kirchhoff's current law This law, also called Kirchhoff's first law, or Kirchhoff's junction rule, states that, for any node (junction) in an electrical circuit, the sum of currents ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Millman's Theorem
In electrical engineering, Millman's theorem (or the parallel generator theorem) is a method to simplify the solution of a circuit. Specifically, Millman's theorem is used to compute the voltage at the ends of a circuit made up of only branches in parallel. It is named after Jacob Millman, who proved the theorem. Explanation Let e_k be the generators' voltages. Let R_k be the resistances on the branches with voltage generators e_k. Then Millman states that the voltage at the ends of the circuit is given by: :v=\frac . That is, the sum of the short circuit currents in branch divided by the sum of the conductances in each branch. It can be proved by considering the circuit as a single supernode. Then, according to Ohm and Kirchhoff, the voltage between the ends of the circuit is equal to the total current entering the supernode divided by the total equivalent conductance of the supernode. The total current is the sum of the currents in each branch. The total equivalent c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum Power Transfer Theorem
In electrical engineering, the maximum power transfer theorem states that, to obtain ''maximum'' external power from a power source with internal resistance, the resistance of the load must equal the resistance of the source as viewed from its output terminals. Moritz von Jacobi published the maximum power (transfer) theorem around 1840; it is also referred to as "Jacobi's law". The theorem results in maximum ''power'' transfer from the power source to the load, and not maximum ''efficiency'' of useful power out of total power consumed. If the load resistance is made larger than the source resistance, then efficiency increases (since a higher percentage of the source power is transferred to the load), but the ''magnitude'' of the load power decreases (since the total circuit resistance increases). If the load resistance is made smaller than the source resistance, then efficiency decreases (since most of the power ends up being dissipated in the source). Although the total power dis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extra Element Theorem
The Extra Element Theorem (EET) is an analytic technique developed by R. D. Middlebrook for simplifying the process of deriving driving point and transfer functions for linear electronic circuits. Much like Thévenin's theorem, the extra element theorem breaks down one complicated problem into several simpler ones. Driving point and transfer functions can generally be found using Kirchhoff's circuit laws. However several complicated equations may result that offer little insight into the circuit's behavior. Using the extra element theorem, a circuit element (such as a resistor) can be removed from a circuit and the desired driving point or transfer function found. By removing the element that most complicates the circuit (such as an element that creates feedback), the desired function can be easier to obtain. Next two correctional factors must be found and combined with the previously derived function to find the exact expression. The general form of the extra element theorem i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electromagnetism Uniqueness Theorem
The electromagnetism uniqueness theorem states the uniqueness (but not necessarily the existence) of a solution to Maxwell's equations, if the boundary conditions provided satisfy the following requirements: # At t=0, the initial values of all fields (, , and ) everywhere (in the entire volume considered) is specified; # For all times (of consideration), the component of either the electric field or the magnetic field tangential to the boundary surface (\hat n \times \mathbf or \hat n \times \mathbf, where \hat n is the normal vector at a point on the boundary surface) is specified. Note that this theorem must not be misunderstood as that providing boundary conditions (or the field solution itself) uniquely fixes a source distribution, when the source distribution is outside of the volume specified in the initial condition. One example is that the field outside a uniformly charged sphere may also be produced by a point charge placed at the center of the sphere instead, i.e. t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superposition Theorem
The superposition theorem is a derived result of the superposition principle suited to the network analysis of electrical circuits. The superposition theorem states that for a linear system (notably including the subcategory of time-invariant linear systems) the response (voltage or current) in any branch of a bilateral linear circuit having more than one independent source equals the algebraic sum of the responses caused by each independent source acting alone, where all the other independent sources are replaced by their internal impedances. To ascertain the contribution of each individual source, all of the other sources first must be "turned off" (set to zero) by: * Replacing all other independent voltage sources with a short circuit (thereby eliminating difference of potential i.e. ''V''=0; internal impedance of ideal voltage source is zero (short circuit)). * Replacing all other independent current sources with an open circuit (thereby eliminating current i.e. ''I''=0; int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Norton Equivalent Circuit
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. For alternating current (AC) systems the theorem can be applied to reactive impedances as well as resistances. The Norton equivalent circuit is used to represent any network of linear sources and impedances at a given frequency. Norton's theorem and its dual, Thévenin's theorem, are widely used for circuit analysis simplification and to study circuit's initial-condition and steady-state response. Norton's theorem was independently derived in 1926 by Siemens & Halske researcher Hans Ferdinand Mayer (1895–1980) and Bell Labs engineer Edward Lawry Norton (1898–1983). To find the equivalent, the Norton current ''I''no is calculated as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parallel Resistors
A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active elements, and terminate transmission lines, among other uses. High-power resistors that can dissipate many watts of electrical power as heat may be used as part of motor controls, in power distribution systems, or as test loads for generators. Fixed resistors have resistances that only change slightly with temperature, time or operating voltage. Variable resistors can be used to adjust circuit elements (such as a volume control or a lamp dimmer), or as sensing devices for heat, light, humidity, force, or chemical activity. Resistors are common elements of electrical networks and electronic circuits and are ubiquitous in electronic equipment. Practical resistors as discrete components can be composed of various compounds and forms. Resisto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parallel (operator)
The parallel operator (also known as reduced sum, parallel sum or parallel addition) \, (pronounced "parallel", following the parallel (geometry)#Symbol, parallel lines notation from geometry) is a function (mathematics), mathematical function which is used as a shorthand in electrical engineering, but is also used in kinetics (physics), kinetics, fluid mechanics and financial mathematics. The name ''parallel'' comes from the use of the operator computing the combined resistance of Resistor#Series and parallel resistors, resistors in parallel. Overview The parallel operator represents the multiplicative inverse, reciprocal value of a sum of reciprocal values (sometimes also referred to as the "reciprocal formula" or "harmonic series (mathematics), harmonic sum") and is defined by: :\begin \parallel: &&\overline \times \overline &\to \overline \\ &&(a, b) &\mapsto a \parallel b = \frac = \frac, \end with \overline = \mathbb\cup\ being the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
