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Electronics Lab #5
Thevenin's Theorem
Often you deal with a complicated electronic circuit. It is often the case that the behavior of one
particular component is crucial. For example, you could have an stereo amplifier connected to a speaker.
You would NOT be particularly interested in how the amplifier works in detail and you would only be
interested in how the amplifier interacts with the speaker. For your purposes, the amplifier is a "black
box" that produces some effect at the output terminals and the speaker is connected across the output
terminals. A diagram of the situation appears
The speaker serves to convert electrical energy into acoustic energy with an electromagnet near a metallic
diaphragm but for our purposes it is simply a resistance Routput . Thevenin's theorem says we can replace
the entire amplifier by an effective or equivalent battery (or voltage source) VEQ in series with and
effective or equivalent resistance REQ . Thus the above diagram appears according to Thevenin's theorem
where the equivalent resistance REQ and equivalent battery VEQ of the amplifier are in series with the
output resistance ROUT . The claim is that any complicated circuit having resistors and batteries can be
represented by a Thevenin equivalent circuit like that drawn above. We do NOT prove the theorem here
(this is a subject in an electrical engineering course) and we simply show it is true for an example.
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where the equivalent resistance REQ and equivalent battery VEQ of the amplifier are in series with the
output resistance ROUT . The claim is that any complicated circuit having resistors and batteries can be
represented by a Thevenin equivalent circuit like that drawn above. We do NOT prove the theorem here
(this is a subject in an electrical engineering course) and we simply show it is true for an example.
Thevenin's theorem for a circuit having resistors in series
and parallel
A previous lab lecture solved the circuit below using conventional methods. The circuit has three
resistors: R1 and R2 are in parallel while R3 is in series with the parallel combination.
Suppose the same two resistors as before, R1 = 30, 000 W and R2 = 50, 000 W are in parallel, and this
combination is in series with R3 = 20, 000 W The battery voltage is V-12 Volts as before. In a previous
la using simple reduction methods we obtained the current through R2 as i2 =0.12 ma. Here we show that
Thevenin's theorem gives the same result for the current as an illustration of Thevenin's theorem. Since
we are focusing only on the current through the resistor R2 we relabel it the output resistance ROUT .
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Thevenin's theorem claims the above circuit can be replaced by an equivalent or effective circuit
indicated below:
Notice the equivalent voltage VEQ is NOT the original battery voltage and the equivalent resistance REQ
is NOT simply R1 or R2 or R3 . We now give Thevenin's prescription for calculating REQ and VEQ .
Calculate the Equivalent Resistance REQ
Thevenin's theorem says you calculate the effective or equivalent resistance REQ by (1) removing
the battery from the ORIGINAL circuit and (2) replacing the battery by a short circuit wire. Also, the (3)
output resistance R2 is removed from the circuit. The resistance measured at the output terminals is REQ
operationally (experimentally) and theoretically. The original circuit appears after the above operations
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The above circuit is equal to the circuit below of two resistors in parallel:
At first, you might not believe these two circuits are equal electrically. To convince yourself of this fact
make sure to understand that the connections of the two resistors to terminal A are the same in both
circuits and the connections to terminal B are the same in both circuits.
The equivalent resistance is the of two resistors in parallel, that is
1
REQ
=
1
R1
+
1
(1)
R3
Numerically this is for the case at hand
1
REQ
=
1
30, 000 W
and Mathematica yields
+
1
20, 000 W
(2)
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1
30 000
+
1
20 000.
0.0000833333
and further taking the reciprocal
REQ =
1
0.000083
12 048.2
Thus the equivalent resistance for this circuit is REQ =12 kW.
Calculate the Equivalent Voltage VEQ
Thevenin's theorem says you calculate the effective or equivalent voltage VEQ by (1) returning the
battery from the ORIGINAL circuit and (2) removing the output resistor ROUT =R2 . The equivalent
battery VEQ is the voltage measured or calculated at the output terminal as indicated below:
Resistors R1 and R3 are in series and the voltage is measured across R1 . The above circuit is effectively a
voltage divider so the equivalent or effective voltage VEQ is
VEQ =
R1
R1 + R3
V
(3)
For the case at hand, the numerical value of VEQ is
VEQ =
30, 000 W
30, 000 W + 20, 000 W
12 Volts
(4)
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Mathematica yields
VEQ =
30 000
30 000 + 20 000.
12
7.2
so VEQ =7.2 Volts.
The Thevenin circuit for this problem
The Thevenin equivalent circuit for this problem with the numerical values used appears
It is now an easy matter to calculate the current through the output resistor and one obtains via Ohm's law
i=
VEQ
REQ + ROUT
=
7.2 V
12, 000 W + 50, 000 W
(5)
Mathematica yields
7.2
12 000 + 50 000
0.000116129
Thus using the Thevenin's theorem we obtain the output current i=0.12 ma which is the same number as
obtained using the simple series and parallel circuit analysis. This example should give you more
confidence in the Thevenin theorem; however, you should work other examples and show that the simple
direct method and Thevenin's theorem both give the same answers. Thevenin's theorem is a powerful and
useful means of dealing with complex circuits if you want to focus on the behavior of one circuit element.
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Experiments You Should Do
Series and Parallel Resistors Circuit: Pick three resistors from your parts box in the 10,000W range. (It
would be helpful if these were the same three resistors you used in the last laboratory.) Measure the
resistances using the Ohmmeter and make sure the values agree with the color code. Connect the resistors in series and parallel as indicated in the above discussion. Measure the equivalent resistance using
Thevenin's procedure and see that this resistance agrees with what you expect from numerical calculation.
Measure the equivalent voltage using Thevenin's procedure and see that this voltage agrees with what you
expect from numerical calculation. Finally use Ohm's law to calculate the current through the output
resistor and see that this current agrees with the value of the current measured with an ammeter. You can
also measure and calculate the output voltage across the output resistor.