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ECE 3300 Lab 2
ECE 1250 Lab 4
Name ________________________ Lab Section ___ Student Folder # ____
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 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 measure 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: 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.
Experiment 1: First Thevenin equivalent circuit (25 points)
a. Find the Thevenin Equivalent Voltage (Vth):
For the circuit in Fig. 1, use the node-voltage method to calculate Vab (=Vthev), Vac,
Vad in the circuit. Then, measure these voltages. Record them in Table 1.
Table 1 Voltages & Rthev for circuit in Fig. 1
c
Supply
Supply
Vab=VThev
Vac
Vad
RThev (1)
RThev (2)
d
Calculated
+15V
-15V
Measured
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
b. Find the Thevenin Resistance:
To find the Thevenin equivalent resistance of your circuit, you will try two different
methods.
(1) For the first method of finding the value of RThev, connect a large resistor (100
kΩ is good) across the circuit output (from a to b), and measure the voltage drop
across it. Sketch this resistor in Fig. 2, which now forms a voltage divider. Use
the Thevenin equivalent voltage previously measured, the voltage you just
measured across the 100 kΩ resistor, and the voltage divider equation to
determine RThev. Record this in Table 1.
(2) For the second method of finding the value of RThev, disconnect the +15 V and –
15 V power supplies from the circuit. 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 (c ) where the +15 V supply used to come into the circuit. Connect a
wire from AGND to the point (d) where the –15 V supply used to come into the
circuit. This power supplies have now been replaced by wires. (When you used
this method in homework calculations, you ‘short circuited the power supplies’ to
make this calculation. In real life, we don’t short circuit the supplies (ie. sparks),
but we do replace them with short circuits.) Measure the resistance from a to b.
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. Record this in Table 1.
Are the two values of RThev consistent? They should be.
WRITEUP: Explain the procedures for calculating and measuring the Thevenin
equivalent circuit (voltage and resistance). Show your measurements and
calculations (show your work) for the values above.
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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
Experiment 2: Thevenin equivalent with added R across output (15 points)
Figure 3 Thevenin equivalent from Fig. 2 with a resistor in parallel. Combine these to make a
new Thevenin equivalent circuit, Thev2.
In Experiment 1, you added R=100 kΩ resistor across the output (a-b) of your circuit,
obtaining the circuit shown in Figure 3.In Experiment 2, you will find the new Thevenin
equivalent of the combined circuit in Figure 3. The connection diagram is shown in
Figure 4.
Connect the circuit. Use methods from Experiment 1 to calculate and then measure
vThev2 and RThev2. Note that you may use the circuit in Fig. 3 instead of the circuit in
Figure 4 for calculations. Doing so allows you to use a voltage-divider solution to find
vThev2, which is the voltage across a and b. Also, RThev2 is the resistance seen looking
into a and b with vThev2 replaced by a wire. Record your values below. Verify that your
calculated and measured RThev2 are consistent.
VThev2 =
calculated _____________________
measured ________________________
RThev2 =
calculated _____________________
measured ________________________
Verify that your calculated and measured
RThev are consistent.
Figure 4. Connection of circuit shown in
Figure 3.
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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
Experiment 3: Thevenin equivalent with added R in series with output (15
points)
Figure 5 Thevenin equivalent from Figure 3 with a resistor in series. Combine these to make a new
Thevenin equivalent circuit, Thev3.
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. Record your
values below.
vThev3 =
calculated ________________________
measured ______________________
RThev3=
calculated ________________________
measured ______________________
Figure 6 Connection for circuit shown in
Figure 5.
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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
Experiment 4: Loading 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 (load) resistors
across the output (a-b) and measure the voltage drop across the output (Vab). Calculate
the output current (through your load resistor) for each case using Ohm's law.
WRITEUP: Make a table of the load resistance, 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. Plot the function in a solid line, and your measurements as stars (*).
WRITEUP: Use MATLAB and the voltage-divider formula to calculate the output
voltage of the Thevenin equivalent shown in Figure 2, and use Ohm's law to calculate the
output current. Plot the output current versus voltage on the same plot as above. Use a
different colored dashed line for this output. Label your plots, and include a legend to
explain your line types.
WRITEUP: Explain how to find the Thevenin equivalent circuit (voltage and
resistance) when a resistive load is added. Show your measurements and
calculations (show your work) for the values above.
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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
Experiment 5: Design Voltage reference circuit (35 points)
A Thevenin equivalent is a voltage source with a series output resistance. We frequently
want to create a voltage source that is different from the value of the power supplies
available 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.
WRITEUP: Explain how to design a voltage reference.
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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
Extra Credit: Find the voltage for a Thev on left driving Thev 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.
WRITEUP: Explain your design procedure and give values for the resultant
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