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THEVENIN'S THEOREM

The theoretical foundations of linear circuit theory rest on Maxwell’s theory of electromagnetism. In its more applied form, circuit theory rests on the key concepts of Kirchoff’s Laws, impedance, Ohm’s Law (in its most general sense by encompassing impedances), and the Principle of Superposition. From this foundation, any linear circuit can be solved: Given a specification of all sources in the circuit, a set of linear equations can be found and solved to yield any voltage and current in the circuit. One of the most surprising concepts to arise from linear circuit theory is the equivalent circuit: 

Thevenin’s theorem permits the reduction of a two-terminal dc network with any number of resistors and sources (Complex Circuit) to one Equivalent circuit having only one source and one internal resistance in a series configuration shown below


In circuit theory, Thévenin's theorem for linear electrical networks states that any combination of voltage sources, current sources, and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R. For single frequency AC systems the theorem can also be applied to general impedances, not just resistors. The theorem was first discovered by German scientist Hermann von Helmholtz in 1853,[1] but was then rediscovered in 1883 by French telegraph engineer Léon Charles Thévenin (1857–1926)

Léon Charles Thévenin (30 March 1857, Meaux, Seine-et-Marne - 21 September 1926, Paris) was a French telegraph engineer who extended Ohm's law to the analysis of complex electrical circuits.

Thevenin’s theorem is a popular theorem, used often for analysis of electronic circuits.  Its theoretical value is due to the insight it offers about the circuit. This theorem states that a linear circuit containing one or more sources and other linear elements can be represented by a voltage source and a resistance. Using this theorem, a model of the circuit can be developed based on its output characteristic. Let us try to  find  out what Thevenin’s  theorem is  by using an investigative approach.

Thevenin's Theorem states that it is possible to simplify any linear circuit, no matter how complex, to an equivalent circuit with just a single voltage source and series resistance connected to a load. The qualification of "linear" is identical to that found in the Superposition Theorem, where all the underlying equations must be linear (no exponents or roots). If we're dealing with passive components (such as resistors, and later, inductors and capacitors), this is true. However, there are some components (especially certain gas-discharge and semiconductor components) which are nonlinear: that is, their opposition to current changes with voltage and/or current. As such, we would call circuits containing these types of components, nonlinear circuits.

In the previous 3 tutorials we have looked at solving complex electrical circuits using Kirchoff´s Circuit Laws, Mesh Analysis and finally Nodal Analysis but there are many more "Circuit Analysis Theorems" available to calculate the currents and voltages at any point in a circuit. In this tutorial we will look at one of the more common circuit analysis theorems (next to Kirchoff´s) that has been developed, Thevenins Theorem.

Thevenin’s theorem is a popular theorem, used often for analysis of electronic circuits. Its theoretical value is due to the insight it offers about the circuit. This theorem states that a linear circuit containing one or more sources and other linear elements can be represented by a voltage source and a resistance. Using this theorem, a model of the circuit can be developed based on its output characteristic. Let us try to find out what Thevenin’s theorem is by using an investigative approach. 

Thevenin’s theorem states that a two terminal circuit containing voltage sources, current sources, and resistors can be modeled as a voltage source in series with a resistor.  The benefit of using a Thevenin equivalent is that it makes analyzing how a circuit interacts with other circuits a much simpler process.  Consider the circuit below.  Suppose you want to know the loaded voltage of the circuit (VL) for three different loads connected to nodes a and b.  The three loads are 200 Ω,  2 kΩ, and 20 kΩ.  How fast could you find each Vab?

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