ECE 109 Introduction to Electrical Engineering
Laboratory Manual
Prepared by R. Frank Smith
California State Polytechnic University, Pomona
Revised 09/25/2011
Reference Text – Student Reference Manual for Instrumentation Laboratories, Wolf and Smith, Prentice Hall, 2004.
Table of Contents
Exercise 1 – Experimentally Understand Reference
Directions for Voltage and Current
1
Exercise 2 – Ohm’s Law and Resistor Color Codes
7
Exercise 3 – Validation of Kirchhoff’s Laws
8
Exercise 4 – PSpice Computer Exercise
12
Exercise 5 – Design and Analysis of a Variable Voltage
Supply
16
Exercise 6 –Thévenin's, Norton’s and Maximum Power
Theorems
21
Exercise 7 – Operation of an Oscilloscope and Signal
Generator and Response of Meters to
Nonlinear Signals
24
Exercise 8 – Determining Thévenin's Equivalent Circuit of
an Unknown Circuit
30
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page i
ECE 109 Laboratory Exercise 1
Experimentally Understand Reference Directions for Voltage and Current
Laboratory Group (Names) _______________ ______________ _______________ Date Performed _____________
OBJECTIVES

Learn the importance of reference directions for voltage and current

Learn to use an ohmmeter, voltmeter, and ammeter

Learn to calculate power loss in resistors

Learn to identify short circuits and open circuits

Learn to determine an equivalent for unknown circuits.
BACKGROUND
Reference directions for voltage, current, and power are not arbitrary. All meters that measure these
parameters are designed to meet international standards. For example, if you are going to attach a set
of jumper cables between a car with a charged battery and a car with a dead battery, it is extremely
important that the cables be connected in accordance with the established standards. If the batteries
are accidentally reversed there could be an explosion of one or both batteries resulting in a fire and
serious damage to the cars. The jumper cable that is red is connected to the positive terminal of each
battery. The jumper cable that is black is connected to the negative terminal of each battery. This same
color code is used on ammeters, multimeters, power meters, and various other instruments used in
industry. This is no different than measuring the elevation of points on the ground. It is well understood
what is up and what is down. The same principle applies to voltages. It is necessary to understand
whether a voltage is above or below a reference voltage. When you see a stream flowing in the
mountains you know what is upstream and what is downstream. The same principle applies to currents
and a wire. The only difference is that you can't see voltages and you cannot see currents and so you
have to rely on your instruments. Make every effort to make your measurements so that voltages and
currents are typically positive. For example if you live in Los Angeles and wish to drive to San Bernardino
you would not tell a driver to drive minus West to go from Los Angeles to San Bernardino. So why would
an engineer say that he has a battery with a negative voltage or a wire with a negative current. Civil
engineers wouldn't tell a hiker to go minus uphill to reach a destination which is downhill from the hiker.
The accepted standards for voltage and currents are shown in Figure 1. If the product of V and I is
positive then the circuit in the box is a LOAD (for example a resistor). If the product is negative then the
circuit in the box is a source (for example a battery). Notice in the figure that if a positive current goes
into the positive voltage terminal then the circuit is a load otherwise it is a source. If a current is going
into the positive terminal of your car battery then the battery is a load and it is being charged by your
alternator or a battery charger.
If your measuring instrument reads negative, then reverse the leads so that it reads positive. DO NOT
try to work with negative numbers. Do not draw a current arrow in one direction and then say that
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 1
current is flowing in the negative direction. That is left as a trick question on exams. Don’t be fooled by
this technique. The positive lead on a multimeter is RED. The negative lead is black. If the current reads
negative then the current is LEAVING the red lead. If the voltmeter reads positive, then the red lead is
at a higher potential than the black lead. Short circuits have no voltage, but they can have current.
Open circuits can have voltage, but they do not have current.
i
i
+
V
-
Load
-
Load
e.g. resistor or
motor
V
e.g. resistor or
motor
i
+
i
+
V
-
Source
-
Source
e.g. resistor or
motor
V
e.g. resistor or
motor
+
Figure 1. Standards for Voltage and Current.
PROCEDURE
Part 1.
 Construct a series circuit as shown in Figure 2 using the unknown circuits provided by
the instructor.
Figure 2. Series circuit using jumpers.
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 2





Adjust each power supply to 5 volts.
Using your voltmeter to determine the positive terminal (1 or 2). Note it on your
drawing.
Lift the jumper off of T2 and connect it to an ammeter (red) lead and then connect the
black lead of the ammeter to terminal T2. If the ammeter reads positive then the
current is going from T2 to K2.
Now since this is a series circuit then the current must be going in the same direction in
all of the jumpers.
Now that you are an expert in standards which of the circuits are sources and which are
loads. Complete table 1. Measure the source voltage with the power supply connected,
and measure the resistances with the voltage sources disconnected. Never connect an
ohmmeter to a voltage source. You can damage the ohmmeter.
Table 1. Sources and loads in Figure 2.
Circuit
A
E
H
K
T

If a Source what is the Voltage?
If a Load what is the Resistance?
Now that you have all these parameters see if you can draw a schematic of the circuit.
This may be harder than you think. Remember sources ALWAYS have a series
resistance. If you don’t see one on a drawing then it is a make believe circuit.
Figure 3. Draw your Schematic here .
Part 2.

Now construct a parallel circuit as shown in Figure 4.
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 3
Figure 4. Parallel circuit using jumpers.
 Complete Table 2.
Table 2. Sources and loads in Figure 2.
Circuit
K
L
M
N

If a Source what is the Voltage
If a Load what is the Resistance
Now that you have all these parameters see if you can draw a schematic of the circuit.
You really do not know what the equivalent circuit is for the sources. You cannot
determine this until you have had Thévenin’s Theorem which will be covered in a later
experiment.
Figure 5. Draw your Schematic here.
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 4
Part 3.
Using your voltmeter and ammeter determine each circuit component shown in the
series/parallel circuit of Figure 6. Enter values into table 3.
Figure 6. Combination Series and Parallel Circuit.
Table 3. Sources and loads in Figure 6.
Circuit
E
H
K
N

If a Source what is the Voltage? If a Load what is the Resistance?
Now that you have all these parameters see if you can draw a schematic of the circuit.
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 5
Figure 7. Draw your Schematic here.
Questions




What is the difference between conventional current and electron current?
For the series circuit of Figure 2, show that the sum of the voltages around the loop is
zero no matter where you start.
For the parallel circuit of Figure 4, show that the sum of the currents at either node is
zero. A node is where two or more components connect. Draw a circle around each
node and identify them as Node 1 and Node 2.
For the series/parallel circuit of Figure 6, show that the sum of the currents in the
parallel branches is equal to the source current. . This is verification of Kirchhoff’s
Current Law.
Conclusion
Write a professional comprehensive lab report, using a word processor when possible. Show
your results and include a comprehensive conclusion. There are lots of sample lab reports on
the internet. Your report should be such that I can give it to another engineer and they can
duplicate it and verify your findings and conclusion.
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 6
ECE 109 Laboratory Exercise 2
Ohm’s Law and Resistor Color Codes
Laboratory Group (Names) _______________ ______________ _______________
Date ______________
OBJECTIVES

Verify Ohm’s Law

Learn to read resistor color codes

Learn to use an ohmmeter, voltmeter, and ammeter

Learn to calculate power loss in resistors

Learn to construct a simple circuit on a protoboard
BACKGROUND
Resistance Resistors are used for many purposes such as electric heaters, voltage control, and current
control. Resistance values and tolerances vary widely. Resistance tolerances may range from +0.001 to
+20%. The most common types of resistors are carbon composition, wire wound, metal film, carbon
film, steel, and liquid. Their ratings can range from microwatts to megawatts. Variable resistors are
called either potentiometers or rheostats. When used as a potentiometer their output is a variable
voltage. When used as a rheostat they are used to control current. A good reference source for resistor
color codes and other codes is [http://en.wikipedia.org/wiki/Electronic_color_code]. Review this
website before you come to the laboratory. Many types of resistors do not have a color code such as
resistors
made
to
military
specifications
and
surface
mount
resistors
[http://en.wikipedia.org/wiki/Surface-mount_technology]. You might remember the following
mnemonic to help you remember the color versus number code:
Bad (0) Boys (1) Race (2) Our (3) Young (4) Girls (5) But (6) Violet(7) Generally (8) Wins (9).
Black
Brown
Red
Orange
Yellow
Green
Blue
Violet
Grey
White
Most through-hole resistors Figure 1 (a) use either 4 or 5 bands of colors. The 5 band color is usually
used for 1% and 0.1 % resistors. Surface mounted resistors (SMD) either have a printed code or no
markings Figure 1 (c). Typical wattages and sizes are shown in Table 1.
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 7
Table 1. Surface mount resistors.
Package Style
Size(mm)
2512
6.30 x 3.10
2010
5.00 x 2.60
1210
3.20 x 2.60
1206
3.00 x 1.50
0805
2.00 x 1.30
0603
1.50 x 0.08
0402
1.00 x 0.50
0201
0.60 x 0.30
Power Rating
0.5
0.25
0.25
0.125
0.10
0.0625
0.0625 -0.031
0.05
Power When you observe a resistor it is not always possible to predict its wattage by just observing its
size. There are many variables that affect a resistor’s wattage. Some such parameters are size,
mounting, encapsulation, and cooling. There are three ways you can calculate the power being
dissipated in a resistor in this laboratory. See Eq.1. In a thermodynamics' laboratory you could measure
the rise in temperature of water in a calorimeter to determine the power being dissipated by a resistor.
Consider the following design problem. What size (ohms and wattage) resistor would you use for the
heating element in a coffee maker or toaster? Assume 120 VAC and 300 watts.
𝑃=
𝑉2
𝑅
= 𝐼 2 𝑅 = 𝑉∆𝑅 𝐼𝑅
(1)
The resistance of a resistor can be approximated by equation (2):
Resistance (R)=
𝜌𝐿
𝐴
(2)
Where 𝜌 =resistivity of the material; L = length of material; and A is the area of the material. The
material may be solid, liquid, or gaseous. Each of these parameters is often functions of temperature
and stress.
Temperature The first order approximation of resistance change with temperature is defined by
equation (3).
𝑅 = 𝑅𝑜 (1+∝ ∆𝑡)
(3)
Where
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 8
Ro is the resistance at 25 oC
= material temperature coefficient, expressed as ohms/oC or ppm/oC ( parts per million).
t is the change in temperature. It is expressed as ohms/oC
It is very common to use this characteristic of resistors in the design of temperature sensors. Knowing
the variation of resistance with temperature is extremely important in the analysis and design of
electronic circuits.
Liquid is often used for low resistances rated in the megawatts. It quite often consists of two electrodes
in a tank filled with CaCO3. Some typical resistors are shown in Figure 1.
(a)
(b)
(c)
Figure 1. Typical Resistors. (a) 1/8 w to 2 W, (b) 5 W to 25 W, (c) 1/32 W . Very small surface mounted
resistors have no markings and you need a microscope to identify them. The resistors in an IC are
considerably smaller than surface mount resistors.
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 9
PROCEDURE
Part 1. Obtain seven resistors from the stock bins on the 5th floor. Obtain one potentiometer and a
protoboard at an electronic store or from one of the engineering clubs such as SWE in the Engineering
Technology Department, see Figure 2. Record the values of the seven resistors and the potentiometer
and their associated color code if appropriate in Table 2 and perform an error analysis. See your text or
the internet for the color code. Measure each resistor with an ohmmeter then see how that relates to
the color code.
1
3
2
(a)
(d)
(b)
(c)
(e)
Figure 2. Protoboard and potentiometers. (a) Protoboard, (b) Potentiometer, (c) Potentiometer
Diagram, (d) &(e) Assorted Potentiometers.
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 10
Table 2. Resistor color codes and Error Analysis
Measured
Value
Color Code
Theoretical
Value
% error
Experimental
Discrepancy
Part 2. Connect a variable voltage supply to three different resistors and vary the voltage from 0 to 5
volts. Make sure you do not exceed the wattage rating of the resistors. Plot the current versus the
voltage in Figure 3. Label each curve with its resistance value. How does the plot verify Ohm’s Law?
What can you say about the slope of the plots? Calculate the slopes and show that they are equal to
1/R.
Hint: All of the curves go through zero so only one additional point for each resistor is required
to generate the Ohm’s Law curve. Simply set the voltage supply at one voltage for all the
resistors and then measure the current in each resistor. Verify the current using Ohm’s Law.
How do you measure the current through the resistor? How do you calculate the current through a
resistor under test without using an ammeter? For a circuit board with surface mounted resistors you
would usually use the calculation method. Calculation of the measure of uncertainty for each method is
different depending on your method of calculation. A good reference source for error analysis is
[http://www.lhup.edu/~dsimanek/errors.htm]. Currents can also be measured indirectly by measuring
the magnetic field surrounding a resistor using a clamp-on ammeter or a Hall Effect sensor.
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 11
Voltage
Figure 3. Plot of current (mA) versus voltage for verifying Ohm's Law,
𝟏
∆𝒊 = ∆𝒗.
𝒓
Part 3. Connect a small resistor (less than 100 ohms) to the variable power supply. Gradually increase
the voltage and feel, using your finger, the increase in the temperature of the resistor. Only increase the
voltage so that the wattage lost in the resistor is less than 1/3 watt. What voltage created a ¼ watt loss?
At what wattage does the resistor get too hot to touch? Comment on how hot the resistor gets when it
is dissipating 1/4, 1/3, and 1/2 watt. Hint: Power = V2/R. Resistors are available on the 5th floor in the
student work area and stock room. The resistance will change with temperature. Record your values in
Table 3.
CAUTION
Going beyond ¼ watt can cause the resistor to explode or ignite. A 100 ohm resistor will dissipate ¼ watt at 5
volts. You will usually see smoke or fire at ½ watt. Do NOT exceed 8 volts( 0.64 W) for a 100 ohm resistor.
Table 3. Wattage versus resistor temperature
Measured
Calculated
Temperature
Resistance
Voltage
Wattage
None
Warm
Comments
Hot
1/4
1/3
1/2
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 12
Explain how you would determine the power rating of a custom resistor that you just designed for your
company. Write your resistor specifications and its test method.
Part 4.
Connect four resistors in series and four in parallel on your Protoboard. See Figure 4 and Figure 5.
Figure 4. Resistors in parallel and series on a Protoboard.
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 13
The equivalent resistance of resistors in series is Requivalent = R1 + R2 + R3 +R4……
Record your series resistors and observations.
R1 =
R2=
R3=
R4=
Requivalent =
% error = _____________________ based on color code.
% error = _____________________ based on measured values of resistors.
The equivalent resistance of resistors in parallel is
Record your parallel resistors and observations.
R1 =
R2=
R3=
R4=
𝑅𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 =
1
1
1
1
1
+ + +
𝑅1 𝑅2 𝑅3 𝑅4
.
Requivalent =
% error = _____________________ based on color code.
% error = _____________________ based on measured values of resistors.
Conclusion
Write a professional comprehensive lab report, using a word processor when possible. Show
your results and include a comprehensive conclusion. Remember, your report should be such
that it can be given to another research engineer and they should be able to duplicate it and
verify your findings and conclusion.
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 14
ECE 109 Laboratory Exercise 3
Validaton of Kirchhoff’s Laws
Laboratory Group (Names) _______________ ______________ _______________
OBJECTIVE




Verify Kirchhoff’s voltage law
Verify Kirchhoff’s current law
Gain experience in using both an ammeter and voltmeter
Learn to construct simple series and parallel circuits.
BACKGROUND
Gustav Kirchhoff first described his laws in 1845. His first law KCL simply stated is that current
into a node must equal the current leaving a node where a node is the point where two or
more components are connected together. In Figure 1 above, the three currents I1, I2, and I3
leave the top node and go through the three resistors and then merge on the ground circuit.
The voltage across any parallel resistors is always the same. Current through any resistor can
be determined by using Ohm's law.
𝐼=
𝑉 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝑎𝑐𝑟𝑜𝑠𝑠 𝑎 𝑟𝑒𝑠𝑖𝑠𝑡𝑜𝑟
=
𝑅
𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒
or by measuring the current through each resistor using an ammeter.
Kirchhoff's Current Law (KCL)
node.
∑𝒏𝒌=𝟏 𝑰𝒌 = 𝟎 where is the n is the number of branches at a
Kirchhoff's Voltage Law (KVL) ∑𝒏𝒌=𝟏 𝑽𝒌 = 𝟎
(resistors and voltage sources) in a loop.
where is the n is the number of components
Kirchhoff's second law is like going on a hike from your car around a mountain (independent of
path). When you get back to your car, your net change in potential energy is zero. No matter
how you measure voltages around a circuit, when you return to your starting point the change
in voltage is zero.
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 15
PROCEDURE
Part 1 Verify Kirchhoff’s Voltage Law
Construct the series circuit shown in Figure 1 and Figure 2. Label all your components and
show where you will connect your instruments.
Ammeter
B
A
Ammeter
R1
C
10Vdc
V1
10Vdc
V1
R1
R2
I
1
R2
I
2
R3
I
3
D
R3
0
Parallel Circuit
E
Series Circuit
0
Figure 1. Schematics for verifying Kirchhoff's Laws
Figure 2. Protoboard connection for the series and parallel circuits.
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 16
Measure the voltage at each node (A thru E) in your circuit with your black lead connected to E
(ground).
1. Measure the voltages at all of the nodes relative to the power supply ground. The
voltage at a node is not the same as the voltage across a component connected to a
node.
2. Show that the sum of the voltages across all of the components in a loop complies with
Kirchhoff’s voltage law. Show your calculations and show how you connected your
voltmeter.
3. Now measure the same voltages relative to node C (that means that C is where the
black lead of the voltmeter is connected). Show that the sum of these voltages also
comply with Kirchhoff’s voltage law. Some of the voltages will now be negative. Explain
why?
NOTE Remember, the reference node in a circuit can be anywhere you want in a real
circuit.
4. Calculate the power delivered by the power supply. Show that it is equal to the power
consumed by the resistors.
CAUTION Never connect an ammeter in parallel with the component you are trying to measure
the current through. The ammeter is in essence a short circuit and must be in series with the
components through which current is being measured. An error in the connection could
seriously damage the ammeter and the circuit components.
Part 2. Verify Kirchhoff’s Current Law
Connect three resistors in PARALLEL with your power supply, see Figure 1 and Figure 2. Now
measure the current from the power supply. This procedure is NOT shown in Figure 2. It is up
to you to figure out the connection scheme since only the power supply ammeter connection is
shown in Figure 1. You only have one ammeter, see Figure 3. Therefore, rewire each branch
circuit with the ammeter in SERIES with the branch circuit resistor. Verify the ammeter reading
using the calculation method and a voltmeter.
1. Measure the source current and the branch currents I1, I2, and I3. Show that the
currents comply with Kirchhoff’s current law. If you read any negative currents with
your ammeter, what did you do wrong?
2. Calculate the power delivered by the power supply. Show that it is equal to the power
consumed by the three resistors.
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 17
Figure 3. Bench top multimeter. Press appropriate function buttons.
Conclusion
Write a professional comprehensive lab report, using a word processor when possible. Show
your results and include a comprehensive conclusion. Remember, your report should be such
that it can be given to another research engineer and they should be able to duplicate it and
verify your findings and conclusion.
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 18
ECE 109 Laboratory Exercise 4
Computer Analysis of Circuits using PSPice Schematics
Laboratory Group (Names) _______________ ______________ _______________ Date ______
OBJECTIVES



Learn how to initialize the PSpice program and open the Schematic Capture software
Learn how to place, interconnect, and modify circuit component values
Learn how to setup and configure circuit analysis protocols for circuit simulation
Background
PSpice by Cadence is the program used at Cal Poly to simulate analog circuits, digital circuit, and
design printed circuit boards. There are numerous other programs available for students and
professionals to perform the same functions. Some of them are Tina by Texas Instruments,
Electronic Workbench by National Instruments, Micron VX by Simetrix, ICAP/4 by Intusoft, and
Webench by National Semiconductor (now part of Texas Instruments). Most of them have
student versions, but most are not free. There are numerous free versions on the internet, but
they do not have the capabilities or versatility of the full versions.
There are numerous examples on the Internet but most are for older versions of PSpice. In
addition many of them use Netlists instead of Schematic Capture. We will not cover Netlists in
this laboratory exercise.
Using a simulation program to analyze your design is only the first step. The circuit must be
constructed and then tested under operating conditions. You will find that if you are operating
above 10 KHz your circuit on a protoboard usually will not operate as simulated.
You will find that the Cadence software takes a great deal of time to become proficient in its
use. A sample output from Cadence Schematic is shown in Figure 1.
Figure 1. Sample output from Cadence Schematic
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 19
A basic block diagram of Cadence PSpice is shown in Figure 2.
Figure 2. Basic block diagram of Cadence PSpice
PROCEDURE
Analyze at least four circuits from your 109 textbook.
Write a report and attach your PSpice runs.
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 20
ECE 109 Laboratory Exercise 5
Design and Analysis of Voltage Divider and Bridge Circuits
Laboratory Group (Names) _______________ ______________ _______________ Date ______
OBJECTIVES



Gain experience in designing a voltage divider circuit
Gain experience in analyzing a voltage divider circuit
Gain experience in analyzing the effects source variation and load variation referred to
as Source Regulation and Load Regulation (Burden) of a voltage divider circuit
BACKGROUND
Voltage dividers can be used for my applications such as:
o
o
o
o
o
Creating a stable reference voltage
Creating a bias circuit for semiconductors such as common emitter amplifier
Reducing high voltages to smaller voltages
Controlling volume, gain, and current
Controlling negative feedback amplitude for stabilization and gain
Let’s write an equation that defines Vload in Figure 1. Observe that the voltage across a circuit
is just the current through a circuit time its equivalent resistance.
𝑉𝑙𝑜𝑎𝑑 = [
𝑉𝑠𝑜𝑢𝑟𝑐𝑒
𝑅3𝑅4
𝑅1+𝑅2+(
)
𝑅3+𝑅4
𝑅3𝑅4
] [𝑅3+𝑅4]
(1)
For a well-designed circuit we can make the following approximation.
𝑉𝑙𝑜𝑎𝑑 = [
𝑉𝑠𝑜𝑢𝑟𝑐𝑒
𝑅𝑠+𝑅𝐿
] [𝑅𝐿] ≈
𝑉𝑠𝑜𝑢𝑟𝑐𝑒
𝑅2+𝑅3
𝑅3 if you assume that Rs<< R2 and R3<<R4 (2)
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 21
Rs
R2
VLoad
Source
R2
VLoad
Source
R3
R4
Load
R3
Approximate Circuit
Figure 1. Basic voltage divider circuit
In order to make this assumption, Rs is considerably less than R2 and R3 should be 10 times
smaller than R4. A factor of 100 is much better than a factor of 10. With the assistance of some
simple electronic ratios of 1000 can be obtained. In this experiment you will vary these ratios
to determine their effect on the regulated voltage. If you need an extremely tightly regulated
voltage, then you will have to use an electronic regulated supply which is not covered in this
course.
As a designer you will need to find the voltage regulation of your circuit. Voltage regulation
expressed in percent is defined as the variation in the load voltage as the load changes. See
equation 3. A smaller number is better regulation.
𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝑅𝑒𝑔𝑢𝑙𝑎𝑡𝑖𝑜𝑛 (%) =
𝑉𝑜𝑢𝑡 𝑛𝑜 𝑙𝑜𝑎𝑑 −𝑉𝑜𝑢𝑡 𝑓𝑢𝑙𝑙 𝑙𝑜𝑎𝑑
𝑉𝑜𝑢𝑡 𝑛𝑜 𝑙𝑜𝑎𝑑
*100
(3)
The Bridge Circuit was invented by Samuel Christies in 1833 and improved by Charles
Wheatstone in 1843. This circuit topology is used extensively in the field of instrumentation. It
is simply two parallel voltage divider circuits that can be analyzed independently. It is the
voltage difference (Va-Vb Figure 2) between these two voltage dividers that is important. .
Amplifiers are used to increase the size of the error voltage by as much as 1000.
PROCEDURE
Part 1
Construct the circuit shown in Figure 1 with no load connected (R4). Select component values
so that the output is approximately 5 volts when the input voltage is 10. Select two resistors
such that R2/R3 is approximately ½. For example, chose 75  and 150 . Then by equation 2,
the output voltage should be approximately 6.7 vollts. Then connect several load resistors (R4)
ranging from R3 to 1000 R3. Then determine the voltage regulation of the circuit by completing
Table 1.
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 22
Table 1. Voltage Regulator Analysis
VS
R2
R3
R4 (Load)
Vout
Regulation
%
100
1K
10K
1M

Part 2.
Construct the bridge circuit shown in Figure 2. Choose resistors R2, R3, and R4 with the same
value. R1 will be used to simulate a sensor. Choose R1 to be a value close to R2 but LESS than
R2.
Calculate the voltage Va, Vb, and Va-Vb using equation 4. The error voltage of the bridge is VaVb. It is usually input into an amplifier that increases its value before it is input into a
microprocessor. Note that the error voltage (Va-Vb) is directly proportional to the source
voltage. If you increase the source voltage to high then self-heating of the resistors which is
proportional to the square of the source voltage will cause errors.
𝑅2
1
𝑒𝑟𝑟𝑜𝑟 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 = (𝑉𝑎 − 𝑉𝑏) = 𝑉𝑠 (𝑅1+𝑅1 − 2)
(4)
Enter your resistor values into Table 2 then complete the table. Choose two different values for
R1. Calculate the gain so that the output of the amplifier is 5 volts using equation 4.
𝐺𝑎𝑖𝑛 =
R1
𝑉𝑜𝑢𝑡
𝑉𝑎−𝑉𝑏
5
= 𝑉𝑎−𝑉𝑏
(5)
R3
V source
Amplifier
Va
R2
Vb
R4
Figure 2. Bridge circuit
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 23
Table 2. Bridge circuit analysis data
Resistor
Va
R1=
R1 =
R2=R3=R4=
Vs=
Vb
Va-Vb
Gain
Conclusion
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 24
ECE 109 Laboratory Exercise 6
Thévenin and Norton Theorems
Laboratory Group (Names) _______________ ______________ _______________
OBJECTIVES


Learn various ways to measure Thévenin's voltage and resistance.
Validate the maximum power theorem.
BACKGROUND
Thévenin's theorem (1883) states that any linear circuit can be replaced by a single voltage
source and a single series resistance. In 1926 Norton’s Theorem was shown to be equal to
Thévenin’s Theorem, see Figure 1. You might wonder why the 57 year delay between the
theorems. Batteries were easy to construct and incorporate into a circuit. No one knew how to
make a good constant current source. We do not have current sources available in the lab to
verify Norton's theorem, but it can be calculated using Ohm’s Law. Constructing constant
current sources is beyond the scope of this course.
Thévenin's
Resistance
Vout
Vout
Thévenin's
Voltage
Source
=
Norton
Current
Source
Thévenin's
Resistance
Figure 1. Thévenin's and Norton’s equivalent circuits for a Linear Circuit
Thévenin's and Norton’s Theorems are expressed mathematically by equation 1.
𝑟𝑇ℎ𝑒𝑣𝑒𝑛𝑖𝑛 =
𝑣𝑡ℎ𝑒𝑣𝑒𝑛𝑖𝑛
𝑖𝑁𝑜𝑟𝑡𝑜𝑛
𝑣
= 𝑖 𝑜𝑝𝑒𝑛 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 =
𝑠ℎ𝑜𝑟𝑡 𝑐𝑖𝑟𝑐𝑢𝑖𝑡
𝑣𝑜𝑝𝑒𝑛 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 − 𝑣𝑙𝑜𝑎𝑑𝑒𝑑
𝑣𝑙𝑜𝑎𝑑𝑒𝑑
𝑅𝑙𝑜𝑎𝑑
= ℎ𝑎𝑙𝑓 𝑝𝑜𝑤𝑒𝑟 𝑙𝑜𝑎𝑑
(1)
Measuring Vopen circuit just requires a single voltmeter measurement by definition.
CAUTION
Do not attempt to measure I short circuit by shorting your circuit under test. This can be hazardous
to both you and the circuit, especially when testing industrial power circuits.
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 25
Determining the short circuit current is extremely important in the design of power distribution
systems. When you examine the circuit breakers on your home power panel you will notice
that the manufacturer has the Short Circuit capacity prominently displayed on the circuit
breaker. It will be either 5000 A or 10,000 A. For industrial plants it can go as high as 200,000
A. Installing a circuit breaker with a smaller short circuit rating than that which can be supplied
by the utility company can result in an explosion and fire. The short circuit capacity of a circuit
determines the fuse size you use to protect electronic circuits.
Small current sources are frequently used in many electronic circuits and integrated circuits;
however, they are rarely used in industrial power circuits. They are also commonly used to
drive light emitting diodes (LEDs).
The maximum power theorem states that the maximum power will be delivered to a load when
the load resistance is equal to the Thévenin's resistance. This is the basis for selecting the
resistance of a speaker system for a stereo. This assures that in the design stereo systems that
maximize the power will be delivered from the amplifier to the speakers.
PROCEDURE
Part 1
1. Measure the resistor values R1, R2, and R3 using the multimeter. Do not use the color
code to determine the resistance value. Choose three resistors that are reasonably
close in value. Do not pick, for example, 10K, 300, and 100 ohms. You should realize by
now that the resistor color codes are not an accurate way to determine resistor values.
2. Construct the circuit shown in Figure 1 on the protoboard. Using a multimeter, measure
the voltage between points “a” and “b” with NO LOAD connected. Record your
measurement in column 6. This is VThevenin by definition.
3. Remove the 10 Vdc power source and connect a jumper between “1” and “2.” This is
the same as shorting the supply voltage mathematically. Now measure the resistance
between “a” and “b” using your multimeter. By definition this is RThevenin. Record this
value in Table 1. Column 1.
4. Calculate RThevenin by combining the series and parallel resistors with the source disabled
(shorted). Record this value in Table 1. Column 2. Now compare your measured value
and calculated values in order to perform an error analysis. Enter this value in column 3.
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 26
R1
"1"
R2
"a"
V1
Rload
10 Vdc
R3
"2"
"b"
0
Figure 1. Linear resistor network.
5. We are now going to determine RThevenin in another way. Connect a load to the circuit as
shown in Figure 1. For best results the load resistance should be in the same range as
your estimated RThevenin.
6. Now measure the output voltage between “a” and “b” in order to make the
appropriate calculation. Divide this voltage by Rload. This will be the current going
through the Thévenin equivalent circuit.
7. Simply apply Ohm’s Law to find rThevenin..
𝑟𝑇ℎ𝑒𝑣𝑒𝑛𝑖𝑛 =
𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑎𝑐𝑟𝑜𝑠𝑠 𝑟𝑇ℎ𝑒𝑣𝑒𝑛𝑖𝑛 𝑣𝑜𝑝𝑒𝑛 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 − 𝑣𝑙𝑜𝑎𝑑𝑒𝑑
=
𝑣𝑙𝑜𝑎𝑑𝑒𝑑
𝑖𝑟𝑇ℎ𝑒𝑣𝑒𝑛𝑖𝑛
𝑅𝑙𝑜𝑎𝑑
8. How does this RThevenin compare to the value determined in column 2. Calculate %
difference between columns 2 and 4 then enter this value in Table 1, column 5.
Table 1. Measured and calculated data.
1
2
RThevenin
RThevenin
Measured
with sources
removed
(shorted)
Calculated 1
with sources
removed
3
4
% Error
RThevenin
between
measured
and
calculated
Calculated
2
using
Ohm’s
Law and
Rload
5
6
7
8
% Difference
Vab
Vab
% Error
between
calculated 1
and
calculated 2
Measured
Calculated
Thévenin
voltage
measured
and
calculated
Part 2
1. Now construct the network shown in Figure 1, but replace Rload with a
potentiometer connected between “a” and “b.” The equivalent circuit is shown in
Figure 2. We will now determine rthevenin using the potentiometer.
2. Measure the voltage between “a” and “b” as the potentiometer is adjusted.
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 27
3. Adjust the potentiometer wiper until the voltmeter reads VThevenin/2 NOT Vsource/2.
The potentiometer is now set at the maximum power load which is equal to rthevenin
4. Calculate the maximum power delivered to the load using equation (2).
5. Measure the value of the potentiometer and determine how close it is to the value
of rthevenin determined above.
𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑝𝑜𝑤𝑒𝑟 =
𝑉
( 𝑇ℎ𝑒𝑣𝑒𝑛𝑖𝑛 )
2
2
𝑅𝑙𝑜𝑎𝑑
=
2
𝑉𝑎𝑏
R Thevenin
V
R Thevenin
V1
V1
Rload
Thevenin
(2)
𝑅𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑜𝑚𝑒𝑡𝑒𝑟
Rload
V
Thevenin
0
Potentiometer
Wiper
0
Figure 2. Maximum power network.
6. Now prove that this is the load for maximum power. Prove it by measuring the
voltage Vab across the potentiometer after the potentiometer is rotated 1 turn CW.
Then measure the potentiometer resistance at this position. Calculate the power
delivered to the potentiometer using equation (3).
𝑝𝑜𝑤𝑒𝑟 =
(𝑣𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑜𝑚𝑒𝑡𝑒𝑟 ) 2
𝑅𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑜𝑚𝑒𝑡𝑒𝑟
(3)
7. Repeat step 4, but this time rotate the potentiometer 2 turns CCW (1 turn to get
back to the maximum power resistance then one additional turn). Calculate the
power delivered to the potentiometer using equation (3). Compare results.
P1 turn CW= __________
Pmax= _________
This value must be less than Pmax
P2turns CCW= ___________
This value must be less than Pmax
Conclusion
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 28
ECE 231 Laboratory Exercise 7
Oscilloscope/Function Generator Operation and Response of Meters to Nonlinear Signals
Laboratory Group (Names) _______________ ______________ _______________
OBJECTIVES




Gain experience in using an oscilloscope to measure time varying signals.
Gain experience in using a signal generator to create time varying test signals.
Gain experience in properly using an oscilloscope’s controls.
Learn the frequency limitations of instruments to non-linear signals
BACKGROUND
The oscilloscope is primarily a voltmeter for observing time varying signals. It has a fairly low
input impedance of one megohm (1M ) so it cannot be used when a load impedance of this
size would distort the signal being measured. It is an excellent tool for measuring transient
phenomenon such as impact forces on a load cell. Modern oscilloscopes can operate in both a
digital mode and analog mode. They also have built-in computers for doing signal analysis such
as Fourier transforms on the incoming signal. This type of measurement and analysis would be
very useful in measuring impact response of a suspension system. They can also measure
numerous other parameters of an incoming signal.
It is important that you do not indiscriminately turn the controls especially if you have not been
instructed in their use and function. This can prevent the oscilloscope from being able to
properly display an incoming signal. Ask the instructor for assistance if you are having problems
viewing an input signal.
An ideal meter will not disturb the circuit when taking measurements. Multimeters and
oscilloscopes are far from ideal instruments.
You can determine the root-mean-square (rms) value of a sine wave displayed on an
oscilloscope by the following equation: 𝑉𝑟𝑚𝑠 =
𝑉𝑝−𝑝 √2
2
2
= 0.3535𝑣𝑝−𝑝 = 0.707𝑣𝑝 . The rms
value of an input signal is what is digitally displayed by a multimeter. However, not all
multimeters have this capability. They are limited by both waveform and frequency. It is
sometimes possible to determine the algorithm used by a multimeter to determine the rms
value of a waveform.
If you are using one of the new digital oscilloscopes, you can read waveform parameters on the
lower menu which displays Vrms, Vp-p, and frequency. The voltage from a household outlet is
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 29
120 VAC. This is the rms value. The peak value is 1.414 *120= 169.7 voltages. The heating
value of 120 VAC rms is exactly equal to a 120 VDC voltage source such as a photovoltaic panel.
PROCEDURE
Part 1
1. Connect channel 1 of the oscilloscope to the signal generator and to the digital
multimeter (set to voltage). See Figure 1. Make sure that the ground on the
oscilloscope and signal generator are connected together. Both are internally grounded
to the building ground system.
2. Set the signal generator to 1 KHz, 5 V pk-to-pk for each of the following waveforms: sine
wave, triangle wave, and square wave. Increase the frequency to 10 kHz, and then 100
kHz.
3. Plot what you see on the oscilloscope screen in Figure 2.
4. Compare the readings on the multimeter with what you see on the oscilloscope. Place
the results in Table 1. Add dc offset to your input signal and describe what happens on
the oscilloscope. Change the oscilloscope Vertical Mode from GND, to AC, and then to
DC. Describe what happens to the waveform displayed on the oscilloscope with and
without DC offset.
Figure 1. Test Setup
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 30
Time (sec.,msec., sec.)
Figure 2. Oscilloscope Display
Table 1. Measured and calculated results.
Waveform
Oscilloscope
reading Vp-p
Multimeter
reading
Frequency
Sine wave
Sine wave +5dc
Triangular
Square
1 k Hz
1 k HZ
1 kHz
1 kHz
Sine wave
Sine wave +5dc
Triangular
Square
10 kHz
10 kHz
10 kHz
10 kHz
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Calculated RMS
voltage
Page 31
Sine wave
Sine wave +5dc
Triangular
Square
100 kHz
100 kHz
100 kHz
100 kHz
Sine wave
Sine wave +5dc
Triangular
Square
100 MHz
100 MHz
100 MHz
100 MHz
2
Notes: If the amount of heat (joules) generated by a DC source (𝑖𝑑𝑐
𝑅𝑇) it is equal to the heat
𝑇
generated by an ac source over the same period T ,(∫0 𝑅 ∗ 𝑖 2 𝑑𝑡). Equating the energies and
1
𝑇
solving results in 𝐼𝐷𝐶 = 𝑖𝑟𝑚𝑠 = √𝑇 ∫0 𝑖𝑡2 𝑡 𝑑𝑡 . The following are 𝑉𝑟𝑚𝑠 equations for common
waveforms:
Sine wave 𝑉𝑟𝑚𝑠 =
1
𝑝𝑒𝑟𝑖𝑜𝑑 𝑇 𝑜𝑓 𝑜𝑛𝑒 𝑐𝑦𝑐𝑙𝑒
𝑉𝑝−𝑝 √2
2
2
; square wave 𝑉 𝑟𝑚𝑠 = 𝑉𝑝 ; triangle wave 𝑉𝑟𝑚𝑠 =
= 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑜𝑓 𝑤𝑎𝑣𝑒𝑓𝑜𝑟𝑚 (Hz) =
𝑉𝑝−𝑝
(1)
2√3
𝜔 𝑟𝑎𝑑𝑖𝑎𝑛𝑠/𝑠𝑒𝑐𝑜𝑛𝑑
(2)
2𝜋
5. Describe how you measure the frequency of a waveform from the oscilloscope display.
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
6. Why does the multimeter reading decrease as the frequency increases?
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
Hint: The input circuit topology to many analog voltmeters is usually a low pass filter; i.e. it has a
capacitor to ground on the input which short the input signal to ground at high frequencies.
Conclusion
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 32
ECE 109 Laboratory Exercise 8
Determine the Thévenin Equivalent of an Unknown Circuit
Student (Name) _________________________________________________ Pin ___________________
OBJECTIVES



Gain experience in analyzing an unknown circuit
Gain experience drawing a Thévenin’s equivalent circuit of an unknown circuit
Gain experience in proving that a Thévenin’s equivalent circuit behaves the same as an
unknown circuit
PROCEDURE
Part 1


In this exeercise you will be given a circuit that has four (4) terminals, a, b, c, and d.
Your instructor will tell you which two (2) terminals are the input and which two (2) are
the output.

Using the knowledge you gained in Exercise 6, Thévenin's Theorem, determine R
Thevenin
and VThevenin for the unknown circuit with a 5 vdc source.


Each student will perform the experiment by themselves.
You will be graded individually on your ability to:
o
o
o
o
o
o
Setup the experiment
Properly connect the instruments
Properly make measurements
Properly make calculations
Properly write a lab report
Connect a load to your unknown and show that the voltage across the load
matches your predictions.
Rthevenin = ___________________
Rload = ______
Vthevenin = _____________________
Vload = ______ (measured)
Input Terminals _____, _______
Vload = ______ (calculated)
Output Terminals _______, ________
R. Frank Smith, California State Polytechnic University, Pomona, 2011
Page 33