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In circuit theory terms, the theorem allows any one-port network to be reduced to a single voltage source and a single impedance. The theorem also applies to frequency domain AC circuits consisting of reactive and resistive impedances. It means the theorem applies for AC in an exactly same way to DC except that resistances are generalized to impedances. The equivalent circuit is a voltage source with voltage V Th in series with a resistance R Th.
The resistance is measured after replacing all voltage- and current-sources with their internal resistances. That means an ideal voltage source is replaced with a short circuit, and an ideal current source is replaced with an thevenih circuit.
Resistance can then be calculated across the terminals using the formulae for series and parallel circuits.
This method is valid only for circuits with independent sources. If there are dependent sources in the circuit, another method must be used such as connecting a test source across A and B and calculating the voltage across or current through the test source.
The replacements of voltage and current sources do what the sources would do if their values were set to zero. A zero valued voltage source would create a potential difference of zero volts between its terminals, regardless of the current that ce through it; its replacement, a short circuit, does the same thing.
A zero valued current source passes zero current, regardless of the voltage across it; its replacement, an open circuit, does the same thing. The proof involves two steps. The first step is to use superposition theorem to construct a solution.
Thévenin’s theorem – Wikipedia
Then, uniqueness theorem is employed to show that the obtained solution is unique. It se noted that the second step is usually implied in literature. By using superposition of specific configurations, it can be shown that for any linear “black box” circuit which contains voltage sources and resistors, its voltage is a linear function of the corresponding current as follows.
Here, the first term reflects the linear summation of contributions from each voltage source, while the second term measures the contributions from all the resistors. Now, the uniqueness rhevenin guarantees that the result is general. In other words, the above relation holds true independent of what the “black box” is plugged to. From Wikipedia, the free encyclopedia.
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