Transcript THEVENIN’S THEOREM - City University London

THEVENIN’S THEOREM
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Used to help simplify complex circuits
States that any linear circuit is equivalent to a single
source in series with a single resistance
No matter how complex the circuit and no matter how
many voltage and current sources it contains, it is
equivalent to a real voltage source
We have to replace all of the original circuit lying on
one side or the other of a pair of terminals by its
Thevenin equivalent circuit
The Thevenin equivalent circuit consists of the
Thevenin equivalent voltage, ETH, in series with the
Thevenin equivalent resistance, RTH
The terminals of this ETH and RTH combination coincide
with the terminals of the portion of the circuit of the
original circuit that was replaced
Thevenin and Norton
Equivalent Circuits
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THEVENIN EQUIVALENT CIRCUIT
LAYOUTS
R1
E
R3
RTH
a
R2
a
ETH
R4
R4
b
b
R1
E
x
R2
RTH'
R3
R4
x
ETH'
y
R3
R4
y
Thevenin and Norton
Equivalent Circuits
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PROCEDURE
1. Open-circuit the terminals with respect to which the
Thevenin circuit is desired, i.e. remove all of the
circuitry that will not be replaced by a Thevenin
equivalent, leaving the terminals where it was
connected open-circuited
2. The Thevenin equivalent resistance, RTH, is the total
resistance at the open-circuited terminals when all
voltage sources are replaced by short circuits and all
current sources are replaced by open circuits
3. The Thevenin equivalent voltage, ETH, is the voltage
across the open circuited terminals. We can use
superposition to calculate this
4. Replace the original circuitry by its Thevenin equivalent
circuit with the Thevenin terminals occupying the same
position as the original terminals. The external circuitry
that was removed in step 1 may now be reconnected.
Be certain that the polarity of ETH is such that it
produces current in the external circuitry in the same
direction as the original circuit produced it
Thevenin and Norton
Equivalent Circuits
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NORTON’S THEOREM
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States that any linear circuit is equivalent to a real
current source at a selected set of terminals
Similar to Thevenin’s theorem, except that the voltage
source is replaced by a current source
First find the Thevenin equivalent circuit, then convert it
to an equivalent current source
The Norton equivalent resistance RN = RTH
The Norton equivalent current IN = ETH/RTH
IN is the current that flows in the short circuit connected
across the terminals where the Norton equivalent circuit
is desired
R TH
IN
E TH
RL 
Thevenin and Norton
Equivalent Circuits
RN
RL
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