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ECE 3300 Lab 2
ECE 1250 Lab 4
Measuring: Voltage
Building: Thevenin Equivalent Circuits
Designing: Voltage Reference
Overview: In Lab 4 you will:
 Build simple linear circuits consisting of v-sources and resistors.
 Measure the output voltage of the linear circuit with various load resistances.
 Find an equivalent Thevenin equivalent circuit consisting of a single voltage
source and resistance that has the same output characteristics as the linear circuit.
 Design a voltage reference whose Thevenin equivalent matches given
specifications.
This lab introduces the idea of Thevenin equivalents, which consist of a single voltage
source and a single resistor. Any linear circuit with two output terminals behaves exactly
like its Thevenin equivalent circuit insofar as its output voltage and current are
concerned. This means that any linear circuit or part of a linear circuit with two wires
connecting it to other circuitry may be replaced by a single voltage source and resistor.
In this lab you will learn how to find the value of that single voltage source (the Thevenin
voltage) and resistance (the Thevenin resistance).
Equipment List:
 MyDAQ board with cables. (You can hook them to the lab computers if you don’t
want to bring your laptop.)
 Multisim software.
 From earlier Labs:
o Protoboard & wire kit
 Additional parts:
o Resistors: 100 kΩ (six)
Safety Precautions:
1) myDAQ power supplies: If you follow the instructions in this lab, your myDAQ
should be perfectly safe, but just be sure you never place a wire directly from a
myDAQ power supply to gnd. Doing so could cause the myDAQ to output too much
current, although the myDAQ probably is designed to handle even this.
2) myDAQ current meter: We are avoiding the use of the myDAQ current meter in this
lab for two reasons: first, a current meter acts like a wire and must be inserted in
series with components of a circuit in order to function properly—if you accidentally
placed the leads across a component you might cause a large current to flow that
might damage the circuit; second, using the current meter requires moving the red
multimeter lead from the voltage plug to the current plug on the myDAQ—we would
rather avoid the hassle! Instead of using the current meter, we use the voltmeter to
measure the voltage drop across a resistor. Then we use Ohm's law to find the current
in the resistor. This is safe and straightforward.
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UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
50 S. Central Campus Dr | Salt Lake City, UT 84112-9206 | Phone: (801) 581-6941 | Fax: (801) 581-5281 | www.ece.utah.edu
ECE 1250 LAB 4
Instructions & Reference Material:
 MyDAQ as voltmeter
https://utah.instructure.com/courses/266578/assignments/1347122
Prelab: Videos and Multisim
1. Review the videos and written material on Thevenin equivalents on the class website.
2. (Optional) You will be faster if you do the Multisim simulations before you come to
lab. If you do not have Multisim running on your PC yet, then just do the Multisim
simulations on the lab computers.
WRITE-UP: In your lab notebook, take notes during the videos and record key
information from reading assignments so you don’t have to go back and watch or
review them again. Make sure to label each section in your notebook with the
same headings as highlighted above and below in yellow as you write the
information mentioned for each write-up section.
Experiment 1: First Thevein equivalent circuit (25 points)
Connect the circuit shown in Fig. 1. In your notebook, figure out what the voltage out of
the circuit will be. Use the node-voltage method with one node at a and the reference
node at b as shown in Fig. 1. Note that at node a, we will have two currents that sum to
zero (since no current flows out of the terminal at a).
Fig. 1. First circuit for which Thevenin equivalent is to be found.
Fig. 2. Thevenin equivalent circuit.
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UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
50 S. Central Campus Dr | Salt Lake City, UT 84112-9206 | Phone: (801) 581-6941 | Fax: (801) 581-5281 | www.ece.utah.edu
ECE 1250 LAB 4
Use your myDAQ voltmeter to measure the actual ±15 V supply voltages and output
voltage. Verify that the measured and predicted values are consistent.
The circuit model of a Thevenin equivalent is shown in Fig. 2. Since the Thevenin
equivalent voltage of your circuit is the same as the voltage you have just measured at the
output, you now know the value of the voltage source, vThev, in the Thevenin equivalent
model of your circuit. That was easy!
To find the Thevenin equivalent resistance of your circuit, you will try two different
methods. For the first method of finding the value of RThev, connect a 100 kΩ resistor
across the circuit output (from a to b), and measure the voltage drop across it. Given
your Thevenin equivalent voltage and the voltage drop across the 100 kΩ resistor, use the
Thevenin equivalent model with symbolic Thevenin resistance, RThev, the voltagedivider formula, and algebra to solve for the value that the RThev must have.
For the second method of finding the value of RThev, disconnect the +15 V and –15 V
power supplies from the circuit. After this is done, make sure the +15 V and –15 V
power supplies do not touch any part of the circuit or each other, or sparks may fly (well,
erroneous readings may occur). On the breadboard, connect a wire from AGND to the
point where the +15 V supply used to come into the circuit, and connect a wire from
AGND to the point where the –15 V supply used to come into the circuit. So the power
supplies have been replaced by wires.
Now switch on the myDAQ resistance meter, and measure the resistance between the
circuit output and AGND. This resistance is the value of RThev. In general, the value of
RThev may be found by replacing voltage sources with wires and current sources with
opens and finding the resistance looking into the output of the circuit. This procedure is
equivalent to turning off the sources in the circuit.
Note in your notebook whether the two values of RThev are consistent. They should be.
WRITEUP: Explain your procedure. Show your measurements and calculations
for the following: vThev calculated, vThev measured, v across added 100 kΩ
resistor, RThev for first method, RThev for second method.
Experiment 2: Thevenin equivalent with added R across output (15 points)
In this part of the lab, you will consider how to modify the Thevenin equivalent when a
resistor is added across the output of a circuit. In Experiment 1, you added a 100 kΩ
resistor across the output of your circuit, obtaining the circuit shown in Fig. 3. Fig. 4
shows the Thevenin equivalent from Experiment 1 with the 100 kΩ resistor added across
the output. Now we want to find the Thevenin equivalent of this new circuit.
Use methods from Experiment 1 to calculate and then measure vThev2 and RThev2 for the
new circuit. Note that you may use the circuit in Fig. 4 instead of the circuit in Fig. 3 for
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UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
50 S. Central Campus Dr | Salt Lake City, UT 84112-9206 | Phone: (801) 581-6941 | Fax: (801) 581-5281 | www.ece.utah.edu
ECE 1250 LAB 4
calculations. Doing so allows you to use a voltage-divider solution to find vThev, which
is the voltage across a and b. Also, RThev is the resistance seen looking into a and b with
vThev replaced by a wire. Verify that your calculated and measured RThev are consistent.
Fig. 3 Second circuit for which Thevenin equivalent is to be found.
=
Fig. 4 Second circuit viewed as first Thevenin equivalent with 100 kΩ added in parallel.
Experiment 3: Thevenin equivalent with added R in series with output (15
points)
Now add another 100 kΩ resistor in series with the output of your circuit, as shown in
Fig. 5. Using the methods you are now familiar with, calculate and measure vThev3 and
RThev3 for the Thevenin equivalent of this new circuit, shown in Fig. 6. If you think
carefully about Fig. 6, you will find that you can find the new Thevenin equivalent from
the previous Thevenin equivalent quite easily.
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UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
50 S. Central Campus Dr | Salt Lake City, UT 84112-9206 | Phone: (801) 581-6941 | Fax: (801) 581-5281 | www.ece.utah.edu
ECE 1250 LAB 4
Fig. 5 Third circuit for which Thevenin equivalent is to be found.
=
Fig. 6 Third circuit viewed as second Thevenin equivalent with 100 kΩ added in series.
Experiment 4: Compare circuit output when loaded by R with Thev equiv
circuit when loaded by R (10 points)
In this experiment, you will verify that a circuit and its Thevenin equivalent have the
same output voltage and current when the load resistance across the output terminals is
varied.
Using the circuit from Fig. 1, place different combinations of 100 kΩ resistors across the
output and measure the voltage drop across the output. Calculate the circuit output
current for each case using Ohm's law. Make a table of the voltage and current values.
Use MATLAB to plot current versus voltage, and use the polyfit function to find and plot
a linear fit to the data.
Make a second plot of output current versus voltage for the Thevenin equivalent of the
circuit in Fig. 1. Use MATLAB and the voltage-divider formula to calculate the output
voltage of the Thevenin equivalent, and use Ohm's law to calculate the output current.
Comment on how the plots compare.
Experiment 5: Design Voltage reference circuit (35 points)
A Thevenin equivalent is a voltage source with an output resistance. We frequently want
to create a voltage source that is different from the value of the power supplies available
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UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
50 S. Central Campus Dr | Salt Lake City, UT 84112-9206 | Phone: (801) 581-6941 | Fax: (801) 581-5281 | www.ece.utah.edu
ECE 1250 LAB 4
in a circuit. Understanding Thevenin equivalents enables us to design such voltage
sources (or "references").
Design a circuit using the myDAQ +15 V power supply and your 100 kΩ resistors with a
Thevenin equivalent of 10 V and 66.6 kΩ. Build the circuit and measure the Thevenin
voltage and resistance.
Extra Credit: Find the voltage for a Thevenin on left driving Thevenin on
right (10 points)
When designing electrical circuits and systems, we can treat a linear circuit's output as a
Thevenin equivalent, and we can also treat a linear circuit's input as a Thevenin
equivalent. If we want to design a large circuit, it becomes essential to think of the
circuit as consisting of building blocks. The Thevenin equivalent allows us to model
circuit outputs and inputs as very simple circuits. This approach, in turn, allows us to
determine how our circuit building blocks behave when connected together. For
example, it allows us to determine how much one circuit loads down the voltage coming
out of a circuit that it is connected to.
Fig. 7 shows one Thevenin equivalent connected to another. This models the connection
of one linear circuit to another. Using the symbolic voltage and resistance names, vTh1,
RTh1, vTh2, and RTh2, find a formula for vo, which is the input voltage to the system on
the right.
Using your myDAQ and breadboard, design and build an example of the circuit in Fig. 7,
and verify your formula for vo. The values of vTh1, RTh1, vTh2, and RTh2 are your choice.
Fig. 7 One Thevenin equivalent connected to another Thevenin equivalent.
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UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
50 S. Central Campus Dr | Salt Lake City, UT 84112-9206 | Phone: (801) 581-6941 | Fax: (801) 581-5281 | www.ece.utah.edu