Electronics Lab #5

Thevenin's TheoremOften 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 REQand equivalent battery VEQof 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.

ElectronicsLab5.nb 1

where the equivalent resistance REQand equivalent battery VEQof 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 R3is 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 R2as 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.

ElectronicsLab5.nb 2

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 R2is 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

ElectronicsLab5.nb 3

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)1

REQ

=1

R1

+1

R3

Numerically this is for the case at hand

(2)1

REQ

=1

30, 000 Ω+

1

20, 000 Ω

and Mathematica yields

ElectronicsLab5.nb 4

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 R1and 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

(3)VEQ =R1

R1 + R3

V

For the case at hand, the numerical value of VEQ is

(4)VEQ =30, 000 Ω

30, 000 Ω + 20, 000 Ω12 Volts

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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

(5)i =VEQ

REQ + ROUT

=7.2 V

12, 000 Ω + 50, 000 Ω

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 resis-

tors 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.

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