FVCC Engineering Laboratory
Thevenin’s Theorem
Using Multisim and Excel
J.K. Boger∗
September 16, 2013
1
Objective
Use a computer circuit simulation program to investigate resistor circuits used in power supplies. Investigate the optimum power output from a modeled power supply, learn that complicate power supplies
can be reduced to a simple model called a Thevenin equivalent, and investigate the loading effect on a
large voltage divider circuit. We will use Multisim and Excel for data analysis and presentation.
1
2
∗
Learn to analyze series-parallel circuits
Check our circuits on Multisim
jboger@fvcc.edu
1
FVCC EELE 101
3
4
5
6
7
2
Thevenin’s Theorem: Computer Simulation Lab
2
Plot power dissipated by a load against resistance to find maximum power transfer
Find the Thevenin equivalent for a circuit
Measure power in the simulation for many different load resistances
Learn to use Multisim
Learn to use Excel to plot data
Equipment
The basic equipment for this experiment is as follows:
1
2
3
Multisim
Excel
Theory
Voltage dividers are basic circuits with a voltage source connected to two or more resistors in series.
It was an easy matter to calculate the voltage across each resistor and it was suggested in an earlier
lab that this circuit could be used as a power supply with multiple voltage outputs. But when we
actually hook-up a load external to the voltage divider, we change the behavior of our circuit. This lab
will attempt to explore the problem of loading the circuit. In doing so, we will see that the effect is
small if the load resistor is large relative to the resistors in the voltage divider. Additionally, to simplify
circuits, we will explore the concept of a Thevenin equivalent. Finally, we’ll see that maximum power
transfer occurs in circuits when the load resistor is in series with the Thevenin equivalent internal source
resistance and equal to it.
3.1
The Loaded Voltage Divider
When two or more resistors are connect in series with a voltage source, the resistors step the voltage
down or divide the voltage. The formula for this division is given by equation 1. This voltage is available
for us to use if we simply tap the circuit just before, and just after the resistor R1.
VR1 = Vsource
R1
(R1 + R2 + . . .)
(1)
Tapping the voltage means wiring a load resistor in parallel with R1. Naturally this changes R1 which
is something we can calculate using our formulas for series and parallel resistors. The rule for resistors
in parallel is that the net resistance drops below the resistance of the smallest resistor in the parallel
combination. In short, the load causes R1 to be effectively reduced which in turn couples into equation 1
FVCC EELE 101
Thevenin’s Theorem: Computer Simulation Lab
3
to reduce the voltage available at the R1 taps. While annoying, we will find that the effect is not so
large that we abandon the use of this circuit for dividing voltages.
3.2
Thevenin’s Theorem
Thevenin’s theorem is a way to model a complicated circuit composed of many resistors and even many
sources[1, p. 244]. We can replace the complicated circuit with an equivalent circuit with one voltage
and one resistor in series with that voltage. This is the Thevenin equivalent circuit.
The Thevenin equivalent voltage (Vth ) is the open circuit voltage between two specified
output terminals in a circuit.
The Thevenin equivalent resistance (Rth ) is the total resistance appearing between two
specified output terminals in a circuit with all sources replaced by short circuits. (For real
voltage sources we would replace the source with their internal resistance values.)
These two statements constitute the prescription for finding the values of voltage and resistance in a
Thevenin model. It also possible to measure the values. To do this we will find the open circuit voltage
by measuring the terminals of interest with a multimeter. Then load the terminals with a resistor RL
and measure the current through that resistor. This is the equivalent current. The internal resistance is
then found by starting with equation 2 and completing the derivation with equation 3.
Vth = (Rth + RL ) IL
(2)
Vth
− RL
(3)
IL
In these equations Vth , Rth are the Thevenin voltage equivalent and the Thevenin resistance. IL is
the resistance in the load. In summary, measure the open circuit voltage at the terminals of interest,
measure the load resistance and measure the current in that load resistor when hooked up to the circuit.
Then use equation 3.
Rth =
3.3
Maximum Power Transfer
Since we now know how to reduce complicated circuits to their Thevenin equivalent, we can add in the
maximum power transfer theorem. The maximum power transfer theorem can be stated as:
For a given source voltage, maximum power is transferred to a load when the load resistance
is equal to the Thevenin equivalent internal source resistance.
To test this, simply build a DC powered circuit with two series resistors. Plug in various values of
resistance and measure the voltage and current in the resistor. Calculate power using P = V I.
FVCC EELE 101
4
Thevenin’s Theorem: Computer Simulation Lab
4
Procedure
4.1
Maximum Power Transform Determination
In this part of the lab, we’ll build a simple model where the DC voltage source is constant and has
some internal resistance in series. We’ll then connect various resistors to this power source and measure
the power dissipated by the load. Plot the data in Excel and determine which resistance dissipates the
maximum power.
1. Open Excel and build the data table shown in Table 1
2. Open Multisim and build the circuit shown in figure 1.
3. Select the load resistance by double clicking the element on the diagram and changing the properties. Start with 10[Ω].
4. Collect voltage and current data by running the simulation. The run button is the toggle switch
in the upper right corner.
5. Put your data in an Excel spreadsheet which is to match Table 1.
6. Change your load resistance value, and continue collecting data to fill out the entire data table.
The last resistance value should be 300[Ω].
7. Use Excel to plot the data. Power should be on the vertical axis and resistance should be on the
horizontal axis
8. Determine what value of load resistance results in maximum power delivered.
4.2
Thevenin Equivalent
We will use the power and ease of the circuit simulator to find the Thevenin equivalent of the circuit[2]
in figure 2, and then prove that the equivalent circuit behaves precisely as the original circuit under
various loads. Then find the Thevenin equivalent of the Wheatstone bridge circuit shown in figure 3.
1. Open a new sheet in Multisim
2. Build the circuit shown in figure 2.
3. Measure the open circuit voltage and record this as Thevenin voltage.
4. Choose a small resistor and connect it across the terminals.
FVCC EELE 101
Thevenin’s Theorem: Computer Simulation Lab
Figure 1: Circuit in Multisim pane used to determine maximum power output
5
FVCC EELE 101
Thevenin’s Theorem: Computer Simulation Lab
R_1
R_2
270!
560!
A
6
A
XMM2
10 V
R_3
680!
150!
XMM1
B
B
Th_A
Th_A
Original Circuit
XMM4
150!
Th_V
XMM3
Th_B
Th_B
Thevenin Equivalent Circuit
Figure 2: A complex source-resistor circuit and its Thevenin equivalent circuit
5. Put a current meter in series with this small resistor.
6. Use equation 3 to calculate Thevenin resistance.
7. Build a Thevenin equivalent circuit using the source voltage and resistance found.
8. Run the simulation and show that the complex circuit and the Thevenin circuit behave identically.
9. Repeat this exercise Thevenizing the circuit in figure 3
4.3
The Loaded Voltage Divider
In this section of the lab we will build a voltage divider and then measure the changes in its behavior
as load resistors are added. Our goal is to build the circuit shown in Figure 4. We will then use
the simulation to fill out the data table shown. There are numerous ways to build this circuit in the
simulation. As shown, connector pins are shown. You can get to these pins and connectors by right
clicking while the mouse pointer is in the circuit diagram. The pins allow you to create a much cleaner
circuit rather than trying to make connected loops.
1. Open Excel and build the data table shown in Table 2.
FVCC EELE 101
Thevenin’s Theorem: Computer Simulation Lab
R1
7
R2
A
B
V1
12 V
R4
R3
Figure 3: Thevenize this Wheatstone bridge circuit
2. Open the circuit simulation software by National Instruments.
3. In Multisim, build the circuit shown in figure 4.
(a) choose resistors from ”basic” components on the left side of the screen
(b) choose DC power supply from ”sources” on the left side of the screen
(c) choose ground from ”sources”.
(d) get the multimeters from the pallet on the right side of the screen. Place the component on
the diagram and double click it to open the front panel of the multimeter. There you can
choose to either measure voltage or current just like a real multimeter. You can leave this
panel open, since you’ll read your data directly from the multimeters.
(e) You can wire your components together simply by positioning the mouse over a junction on
the diagram ( e.g. end of the resistor ). Sometimes the wires connect in ways that appear
sloppy. You can fix this by adding a junction to the circuit exactly where you want a wire
to connect. Right clicking while in the circuit diagram will bring up the pallet which has
junctions.
4. Fill out the data table for this circuit by running the simulation. Note, the circuit must have a
ground to run. The run button is a toggle switch in the upper right of the simulation screen.
Table 2
5. Calculate the ”no load” output voltages at pins 1,2 3. Do this algebraically. Use Excel to calculate
numeric values
FVCC EELE 101
Thevenin’s Theorem: Computer Simulation Lab
8
6. Measure the same ”no load” output voltages at pins 1,2 and 3 using the simulation.
7. Connect one 10[M Ω] load to Pin 2 being sure to run this connection through an ammeter. Leave
the other pins unconnected. (of course leave the voltmeter connected to these pins so we can
measure the voltage.
8. With Pin 2 loaded, measure the output voltages on all pins. Compare the voltage on pin 2 to the
voltage on this pin when no loads are connected.
9. Compare calculated values to measured values. Do this by calculating the percent difference
between the two. The formula is given in given in eq. 4.
10. Measure the current running through pin 2 and the 10[M Ω] resistive load.
11. Fill out the rest of the data table
%dif f =
(V2noload − V2load )
× 100
V2noload
(4)
References
[1] T. L. Floyd and D. M.Buchla. Electronic Fundamentals 8th edition. Prentice Hall.
[2] D. M.Buchla. Experiments in Electronics Fundamentals and Electric Circuits Fundamentals. Prentice
Hall.
Revision date: September 16, 2013
FVCC EELE 101
Thevenin’s Theorem: Computer Simulation Lab
Voltage Divider Circuit
9
Measurement
XMM1
XMM2
XMM3
XMM4
Pin1
Pin1
R1
Pin2
Pin3
Pin4
Pin2
220k!
R2
220k!
V1
12 V
Pin3
R3
220k!
XMM7
XMM5
XMM6
Pin2
Pin3
Pin4
Out2
Out3
Out4
Pin4
Loads
R4
220k!
Out2
R5
10.0M!
Out3
R6
10.0M!
Figure 4: Basic voltage divider circuit
Out4
R7
10.0M!
FVCC EELE 101
Thevenin’s Theorem: Computer Simulation Lab
Table 1: Power Data
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FVCC EELE 101
Thevenin’s Theorem: Computer Simulation Lab
11
Table 2: Loaded Voltage divider data
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