ME 530.241: Electronics and Instrumentation
Lab 2: Resistor Networks and Equivalent Circuits
Louis L. Whitcomb∗
Department of Mechanical Engineering
The Johns Hopkins University
Spring 2010
Revised Feb 22, 2010 - question 2.2 is revised.
Apparatuses
DC power supply, multimeter, leads, breadboard.
Components Various resistors.
Overview The purpose of this lab is to validate experimentally basic concepts from resistor network
analysis, including Kirchhoff’s laws, the node-voltage method, and Thévenin and Norton equivalent circuits.
In this lab, we will use the circuit below to explore the basics of resistor networks.
d
a
b
e
Vo = Va -Vc
c
Figure 1: A simple resistor network.
• In your prelab, you should have derived mathematical expressions for Va , Vb , Vc , and Vo assuming that
Vs1 , Vs2 , R1 , R2 , R3 , R4 , and R5 are known. You will need to refer to those expressions throughout
this laboratory.
• When taking measurements, use consistent significant digits, include units, and carry these through to
your calculations.
• Your power supply should remain off until asked to turn it on.
∗ 2010
c
Louis L. Whitcomb, Kyle B. Reed, and Noah J. Cowan – do not reproduce without permission.
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Pre-Lab Exercises
For the following questions, assume that Vs1 , Vs2 , R1 , R2 , R3 , R4 , and R5 are known. You will need to refer
to those expressions throughout this laboratory. Refer to your lecture notes and Chapter 3 of [1].
1. Exercise 3.1 of [1].
2. Exercise 3.7 of [1].
3. Exercise 3.8 of [1].
4. This question relates to “Part 1: Nodal Analysis” of the Lab 2; see Figure 1 of Lab 2.
(a) By inspection, what are the voltages at nodes b, d, and e (relative to ground, −|).
(b) Using the Node Voltage method, setup a system of linear equations in terms of nodes a and c.
(c) Solve the system of equations to find mathematical expressions for Va and Vc .
(d) Derive and expression for Vo , in terms of known quantities.
5. Exercise 3.51 of [1].
6. Find the Norton equivalent circuit as seen by the 3 Ω resistor for the circuit of Figure 3.51 of [1].
7. Exercise 3.54 of [1].
8. This question relates to “Part 2: Thévenin and Norton Equivalent Circuits” of Lab 2.
(a) Derive expressions for VOC and and ISC (see Figure 2(A,B) from Lab 2).
(b) Derive expressions for the Thévenin voltage and resistance, VT and RT .
(c) Derive expressions for the Norton current and resistance, IN and RN .
(d) Draw the Thévenin and Norton equivalent circuits. From the point of view of the a and c nodes,
what, if any, is the difference between the equivalent circuits and the original circuits?
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Nodal Analysis
1. Your TA will provide you with 5 resistors. Using the color code, determine the nominal value of each
resistor, and decide which one you will use for R1 , R2 , . . . , R5 . Measure and report the actual value of
each.
R1 =
R2 =
R3 =
R4 =
R5 =
Nominal
R1 =
R2 =
R3 =
R4 =
R5 =
Measured (use for calculations)
2. Determine and note in your lab report the correct way to configure your DC supply for the circuit
shown in Figure 1: ”Indep.”, ”Series”, or ”Parallel” mode. Also note any necessary jumper connections
between the power sources and to earth ground. Keep in mind that we may want Vs1 and Vs2 to be
different values. Set your DC supply so that the “+” (red) terminal of the leftmost variable supply
is internally connected to the “−” (black) terminal of the rightmost variable supply. Determine and
note in your lab report the correct way to configure your DC supply for the circuit we are building:
“Indep.”, “Series”, or “Parallel” mode.
3. Construct the circuit:
• Using a banana-to-banana jumper, connect the center power terminal to earth ground. Earth
ground is the green terminal; note that both green terminals are internally connected to the
chassis, as well as the “third prong” of the three-pronged power plug.
• Bring the three voltages (−Vs2 , GND, +Vs1 ) down to your breadboard using an intelligent color
scheme, and further bring these down to three bus lines on your breadboard.
• Using your jumper kit and five resistors, carefully construct the circuit in Figure 1. It is particularly important to lay this circuit out logically to simplify debugging and measurements.
• Your TA must sign off on your power supply and breadboard before proceeding.
4. Turn on the power supply, and adjust Vs1 to the lower of you and your partner’s birth months, and
set Vs2 to the other partner’s birth month. For example, if your birth months were December and
January, then you would set Vs1 to approximately 1V, and Vs2 to approximately 12V. Measure and
record the voltages using your multimeter.
Vs1 =
Vs2 =
5. Comparing theory and experiment for node voltages.
• Use the above values for resistances and sources into your formulas from your prelab and obtain
theoretical values for all of your node voltages.
• Using your multimeter, measure these voltages. Report these measurements in your report. When
measuring the node voltages with
a multimeter, you will keep the negative (black) test lead
connected to the ground node, −|.
Va =
Vb =
Vc =
Vd =
Ve =
Theoretical values
Va =
Vb =
Vc =
Vd =
Ve =
Measured values
Do these match with the theoretical? Report the percent error.
6. Comparing theory and experiment for Vo .
• Now, compute Vo from your formulas that use resistances and source values.
• Now, compute Vo from the fact that Vo = Va − Vc , using your measured values of Va and Vc .
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• Finally, measure Vo directly.
Vo =
Theoretical value computed from on sources and resistances
Vo =
Theoretical value from measured node voltages
Vo =
Directly measured using your multimeter
• Compare these (% error) in your lab report.
• Demonstrate measuring Va , Vc , and Vo to your TA.
7. Now, repeat the nodal measurements
of question 5, above, except place the black “−” lead at node e
instead of the ground node, −|. Measure the relative voltages of all of these nodes relative to node e:
Vae =
Vbe =
Vce =
Vde =
Vee =
VGNDe =
How do these relate to the nodal measurements made in question 5? Show your work.
8. † What was the point of this entire question (clear, two to three sentence explanation).
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Thévenin and Norton Equivalent Circuits
From your prelab, you should have formulas that relate all of the values in your circuit to the Thévenin and
Norton equivalent circuits. From your prelab, you should have expressions for VOC and and ISC assuming
that Vs1 , Vs2 , R1 , R2 , R3 , R4 , and R5 are known. You will need to refer to those expressions throughout
this laboratory.
d
a
b
e
(A)
d
a
b
VOC
e
c
(B)
I SC
c
Figure 2: Theoretically determining the Thévenin and Norton equivalent circuits. (A) Circuit for determining
the open-circuit voltage. (B) Circuit for determining the short-circuit current.
1. Use your measured values for Vs1 , Vs2 , R1 , R2 , R3 , R4 , and R5 to determine the theoretical values for
the following quantities:
VOC =
ISC =
VT =
RT =
IN =
RN =
Theoretical quantities
2. Measure VOC and ISC using your multimeter, appropriately configured. Then, use these data to
determine all of the following quantities.
VOC =
ISC =
VT =
RT =
IN =
RN =
Experimentally determined quantities
Derived directly from experimental quantities
How do these compare with the theoretical quantities from question 1?
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3. In your report, draw the Thévenin and Norton equivalent circuits. From the point of view of the a and
c nodes, what, if any, is the difference between the equivalent circuits and the original circuits?
4. † Again, what was the point of this section? (Two to three clear and concise sentences.)
REMEMBER
• Note your lab partner’s secret code on your lab report as well as your lab station number.
• Return all electronic test equipment and components to their proper location.
• Remember to show your work.
• Typewritten reports are not required, but messy or disorganized reports are unacceptable.
• Clean up your workstation to perfection when you are done.
• Get your station checked off by your TA.
References
[1] Giorgio Rizzoni. Fundamentals of Electrical Engineering. McGraw Hill, New York, 2009.
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ME 530.241 Lab 2: Resistor Networks
and Equivalent Circuits
My Secret Code
My Partner’s Secret Code
Lab Date
Lab Station Number
Today’s Date
:
:
:
:
:
You must have the T.A. inspect your lab station at the end of your lab session.
T.A. Signature and Date
:
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