Engr228
Lab #3
Spring, 2016
Thévenin and Norton Equivalents
Name _____________________________
Partner(s) _________________________
Grade _______/10
Introduction
Solving electrical networks is often made easier by using Thévenin and Norton equivalent circuits to model an
entire network. The Thévenin and Norton equivalents as shown below are themselves equivalent to each other
as long as VTH = IN RTH . This experiment considers how to determine the parameters of the equivalent circuits
for a T-configuration of resistors attached to a voltage source as shown in step 2 on the following page.
RTH
+
VTH
IN
Thévenin Equivalent
Objectives
•
•
•
Verify Thévenin’s theorem;
Verify Norton’s theorem;
Verify the Maximum Power Transfer theorem.
Equipment
•
•
•
•
•
•
DC Power supply;
Benchtop DMM;
Handheld DMM;
Breadboard;
Decade resistance box;
Assorted resistors.
RTH
Norton Equivalent
Page 2
References
•
•
•
•
Pre-lab #3 assignment;
Circuits text book;
Circuits laboratory instruments hand-out;
Resistor color-code chart.
Procedure
1) Go to the resistor bin and select three resistors with the values shown below. Measure and record their
resistance values. Calculate percentage error using the following formula:
𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒𝐸𝑟𝑟𝑜𝑟 = |(𝑁𝑜𝑚𝑖𝑛𝑎𝑙𝑣𝑎𝑙𝑢𝑒 − 𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑𝑣𝑎𝑙𝑢𝑒)|/(𝑁𝑜𝑚𝑖𝑛𝑎𝑙𝑣𝑎𝑙𝑢𝑒) ∗ 100%
Resistor
Nominal Value
R1
130 Ω
R2
560 Ω
R3
300 Ω
Measured Value
Percentage Error
2) Connect the T-network shown below except initially replace the voltage source with a short circuit and
measure the Thévenin resistance (RTH). This is the resistance seen looking into the circuit from the right,
i.e. into the + and – terminals. Record both the measured and the calculated values.
R1
R3
+
+
V
R2
VT
_
RTH, Measured = __________ Ω RTH, Calculated = __________ Ω
Error = _____________ %
3) Connect the DC voltage source (V) in the network above and adjust its value to 10 volts. Calculate and
measure the open-circuit voltage VT at the output.
VTH, Measured = __________ V VTH, Calculated = __________ V
Error = _____________ %
Page 3
4) Calculate and measure the current (ISC), which is also the Norton current (IN), flowing from the + to the
– terminals at the output.
IN, Measured = ___________ mA IN, Calculated = ___________ mA Error = _____________ %
5) Connect a decade resistance box across the output and measure the voltage VT for values of load
resistance R ranging from 20 Ω to 1000 Ω. Calculate the current through R and the power dissipated in
R for each measurement and fill in the table below.
RΩ
20
35
50
100
200
300
400
500
600
800
1000
VT (V)
I (mA)
P (mW)
6) Using Excel, do a linear regression (least squared error trendline) fit to the (I, VT) data in the table above
to determine the Thévenin voltage, VTH, and the Norton current, IN. The Thévenin voltage is the yintercept, i.e. the open-circuit voltage, and the Norton current is the x-intercept, i.e. the short-circuit
current. Label these points on the graph and record their values below, along with the calculated value
of RTH. Print out a copy of the graph for your lab report.
VTH = __________ V
IN = ___________ mA
RTH = ___________ Ω
r2 = ____________
7) Compare all measured and calculated values in the table below.
VTH
IN
RTH
Measured
Linear Regression
Computation
8) Using values of VTH and RTH from the linear regression analysis, and the equation below, calculate the
power dissipated in the resistor R for all values of R listed in the table in step 5.
Page 4
𝑉@A
𝑃=
𝑅@A + 𝑅
RΩ
20
35
50
100
200
D
𝑅
300
400
500
600
800
1000
P (mW)
9)
Using Excel, plot the calculated power from step 8 above and the measured power from step 5 versus
the load resistance R. Place power on the y-axis and resistance on the x-axis. Use different symbols for
each and identify the curves as calculated and measured. Print out a copy of the graph.
10) From the Thévenin equivalent circuit (using the values of VTH and RTH from the linear regression
analysis in step 7) and the Maximum Power Theorem, calculate the maximum power dissipated by R
and the value of R when this occurs. Compare this result with what you observe from the plot in step 9.
Show your work and the comparison below.
PMAX
PMAX Theorem
Curve of calculated power (eyeball
from graph)
Curve of measured power (eyeball from
graph)
11) State your observations and conclusions concerning this laboratory exercise.
R