AC Thevenin's Theorem

Any combination of sinusoidal AC sources and impedances with two terminals can be replaced by a single voltage source e and a single series impedance z. The value of e is the open circuit voltage at the terminals, and the value of z is e divided by the current with the terminals short circuited. In this case, that impedance evaluation involves a series-parallel combination.


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AC Thevenin Example

To replace a network by its Thevenin equivalent, compute the Thevenin voltage: the output of the voltage divider formed by Z1 and Z3 . The Thevenin impedance is the impedance looking back from AB with V1 replaced by a short circuit and is therefore a a series-parallel combination.

For impedances
Z1 = + j
Z2 = + j
Z3 = + j
with supply voltage
V1 = V,

the Thevenin voltage would be
VTh = e = + j V
VTh = e =V at degrees.
The Thevenin impedance is
ZTh = + j
ZTh = ohms at degrees.
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AC circuit concepts
 
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