Norton’s Theorem statement
Statement for DC
Norton’s theorem states that any two terminal
linear network having number of
voltage sources,
current sources and
resistances can be replaced by a simple equivalent circuit consisting of a single current source, I
N in parallel with a resistance R
N. Whereas the value of the current source, I
N is the short circuit
current through terminals of the network when the terminals are shorted and the Norton’s resistance, R
N is the equivalent resistance measured between the terminals when all
independent sources are turned off; i.e the independent
ideal voltage source is replaced by a short circuit and ideal current source with open circuit.
Statement for AC
Norton’s theorem states that any two terminal linear network having number of voltage sources, current sources and impedances can be replaced by a simple equivalent circuit consisting of a single current source, IN in parallel with an impedance ZN. Whereas the value of the current source, IN is the short circuit current through the terminals of the network and the Norton’s impedance, ZN is the equivalent impedance measured between the terminals of the networks when all independent sources are turned off.
Norton’s Equivalent
The below figures show the Norton’s equivalent circuit.
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| Norton's equivalent for AC |
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| Norton's equivalent circuit for DC |
Procedure for Finding the Norton’s equivalent
The following circuit is considered for finding the Norton’s equivalent.
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| Main Circuit for analysis |
For finding the Norton’s current, replace the load with a short circuit as in the below figure and find the
current through the short circuited path. This givens the Norton’s current I
N.
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| Circuit for finding Norton's current, IN |
For finding the Norton’s resistance remove the load and turn off all the independent sources. The given circuit has two sources namely one current source and one voltage source. Replacing the current source with open circuit and voltage source with a short circuit leads to the following circuit. Find the equivalent resistance between the terminals from the obtained circuit. This gives the Norton’s resistance RN.
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| Circuit for finding Norton's resistance |
Form the Norton’s equivalent from the above obtained values of I
N and R
N.
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| Norton's equivalent |
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