ME 530.241: Electronics and Instrumentation
Lab 3: Thévenin and Norton Equivalent Circuits.
Louis L. Whitcomb∗
Department of Mechanical Engineering
The Johns Hopkins University
Spring 2011
Revision 1
Apparatuses
DC power supply, multimeter, leads, breadboard.
Components Various resistors.
Overview The purpose of this lab is to validate experimentally basic concepts of Thévenin and Norton
equivalent circuits.
d
a
b
e
Vo = Va -Vc
c
Figure 1: A simple resistor network.
• In your previous lab, 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.
∗ Copyright
c Louis L. Whitcomb — do not reproduce without permission.
2004-2011 1
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Pre-Lab Exercises
It is a good idea for you to keep a photocopy or a scan of your pre-lab exercises so that you can refer to
them when performing and writing up the lab exercises.
For the following questions, Refer to your lecture notes and Chapter 3 of [1].
1. Solve exercise 3.7 of [1] using the principle of superposition.
2. Exercise 3.40 of [1].
3. Exercise 3.51 of [1].
4. Find the Norton equivalent circuit as seen by the 3 Ω resistor for the circuit of Figure 3.51 of [1].
5. Consider a power supply that has a Thévenin equivalent circuit with Thévenin voltage VS and Thévenin
resistance RS . Consider the case where this power supply is providing power to a resistive load with
resistance RL .
(a) Derive the symbolic expression for power consumed by the resistive load, PL as a function of VS ,
RS , and RL .
(b) Derive the symbolic expression for the value of RL that enables the load resistor to have maximum
power.
(c) Derive the symbolic expression for power sourced by the power supply PS as a function of VS ,
RS , and RL .
(d) Derive the symbolic expression for efficiency of the system as a function of VS , RS , and RL , where
efficiency is defined as the ratio of power consumed by the resistive load, PL , to power sourced by
the power supply PS .
(e) For the specific case of VS = 12V , RS = 2Ω, plot the following values vary when RL varies
between 0Ω and 10Ω using Matlab, Excel, or your favorite other program:
i. PL vs RL .
ii. PS vs RL .
iii. E vs RL .
(f) For the specific numerical value of RL where peak power is being delivered to the load (from
question 5e):
i. How many watts of power are being consumed by the load (numerical answer)?
ii. How many watts of power are being sourced by the power supply (numerical answer)?
iii. What efficiency is achieved (numerical answer)?
6. This question relates to “Section 2: Thévenin and Norton Equivalent Circuits”. Assume that Vs1 ,
Vs2 , R1 , R2 , R3 , R4 , and R5 are known. You will need to refer to those expressions throughout this
laboratory.
(a) Derive expressions for VOC and and ISC (see Figure 2(A,B)).
(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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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.
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.
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 approve your power supply and breadboard before proceeding.
4. Turn on the power supply, and adjust Vs1 = Vs2 = 5V . Measure and record the voltages using your
multimeter.
Vs1 =
Vs2 =
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.
5. 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
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6. 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 5?
7. Draw and label the Thévenin equivalent circuit.
8. Draw and label the Norton equivalent circuit.
9. From the point of view of the a and c nodes, what, if any, is the difference between the Thévenin and
Norton equivalent circuits and the original circuits?
10. Construct a new circuit: the Thévenin equivalent circuit that you designed in question 7.
Your circuit should use a single power supply set to the Thévenin voltage that you specifie in question 7,
and a single resistor that is closest to the Thévenin equivalent resistance that you specified in question
7.
(a) Measure the following for this Thévenin equivalent circuit:
VOC =
ISC =
11. Compare the open circuit voltage and short-circuot current for the circuit shown in Figure 1 with the
open circuit voltage and short-circuot current for the Thévenin equivalent circuit.
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 3: Thévenin and Norton 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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