ECE2205: Circuits and Systems I
Lab 1–1
Department of Electrical and Computer Engineering
University of Colorado at Colorado Springs
"Engineering for the Future"
Lab 1: The Digital Multimeter
1.1 Objective
The objective of this lab is to gain proficiency using a digital multimeter to measure resistance, dc voltage, and dc
current. You will also learn how a real multimeter behaves differently from an ideal multimeter.
1.2 Pre-Lab Preparation
Read the lab overview in section 1.3 and answer the questions below. The instructor is to review your answers before
you begin the lab tasks.
1. What color code designates a 1Ä, 10% resistor?
2. What color code designates a 1kÄ, 5% resistor?
3. What color code designates a 10MÄ, 1% resistor?
4. What is the ideal resistance of a voltmeter?
5. What is the ideal resistance of an ammeter?
6. How do you measure a voltage between two points in a circuit? (draw a diagram)
7. How do you measure a current between two points in a circuit? (draw a diagram)
8. How do you measure the resistance of a circuit element?
Be sure to bring a graphite pencil to the lab!
1.3 Background
The dc power supply and the multimeter. This laboratory assignment will introduce you to two of the laboratory
workhorses: the dc power supply, and the digital multimeter. Each workstation in the electronics lab possesses one
Agilent E3630A triple output dc power supply, drawn in Fig. 1.1, and one Agilent 34401A digital multimeter, drawn
in Fig. 1.2. The multimeter can be used as a voltmeter, ammeter, or ohmmeter, depending on how it is configured.
The workstations have other equipment, which will be investigated in more detail in later labs.
Please be careful with these (and all other) laboratory instruments. They cost thousands of dollars to replace.
A voltmeter is designed to measure the voltage between any two points in a circuit, when the circuit is energized.
If the voltage to be measured is v12 = v1 − v2 , then the black probe is placed on node 2 (corresponding to v2 ) and
the red probe is placed on node 1 (corresponding to v1 ). Since the voltmeter is placed in parallel with a part of the
circuit it potentially can disrupt circuit operation. Ideally, a voltmeter’s resistance is infinite—in which case there
would be no change in circuit operation.
An ammeter is designed to measure current at a point in an energized circuit. To take this reading, the circuit must
be disconnected at the point of interest and the ammeter inserted in series with the circuit at that point. Again,
c 2006, Dr. Gregory L. Plett, ECE Dept., CU Colorado Springs
Lab reader prepared by & Copyright °
Lab 1–2
ECE2205, Lab 1: The Digital Multimeter
Agilent
E3630A 0−6V, 2.5A/0−±20V,0.5A
Triple Output DC Power Supply
Agilent
VOLTAGE ADJUST
VOLTS
AMPS
OVERLOAD
+6V
34401A
Ω 4W Sense/
4W Sense/
Ratio Ref
Ratio Ref
6 1/2 Digit Multimeter
Tracking
+20V
ratio
HI
+20V
200V
Max
−20V
Fixed
+6V
+20V
FUNCTION
OUTPUT
−20V
+6V
COM
+20V
Power
−20V
On
Ω 4W
Period
AC V
Ω 2W
Freq
<
MENU Recall
>
4
CHOICES
The Agilent E3630A triple output dc power supply.
Figure 1.2
RANGE / DIGITS
5
>
Off
On
± 240 VDC MAX TO
Figure 1.1
AC 1
DC V
On/Off
Off
MATH
DC 1
>
METER
Power
Input
d
VΩ
HI
+6V
LEVEL
Cont
6
Auto/
Man
1000V
Max
LO
dB
dBm
Null
Min
Max
LO
Terminals
500Vpk
Max
3A
RMS
I
Auto/Hold
Single
ENTER
TRIG
Shift
LOCAL
Front
Rear
!
Fused on
Rear Panel
The Agilent 34401A digital multimeter.
the ammeter can potentially disrupt circuit operation. Ideally, an ammeter’s resistance is zero—in which case there
would be no change in circuit operation.
An ohmmeter is designed to measure the resistance of a device. To do so, the device must be disconnected from
the circuit (or else the resistance of the device in parallel with the circuit is measured). Two-wire and four-wire
resistance measurement techniques are possible, as discovered in the laboratory exercise.
Resistors. You will also be working with resistors. These are located in the shelving units in the lab. Resistor
values are designated using a color code: see Fig. 1.3. Most resistors have four colored bands. The first three bands
indicate the nominal value of the resistor and the fourth band indicates the manufacturing tolerance in value. The
first two bands form the mantissa, and the third the exponent of 10. Values corresponding to the colored bands are
tabulated in Table 1.1. Many offensive mnemonics exist to help memorize the color bands, but if you want a G-rated
version: “Black Beetles Running On Your Garden Bring Very Good Weather”.
First band: First digit
Second band: Second digit
Third band: Multiplier
Fourth band: Tolerance
Figure 1.3
Table 1.1
Color
Black
Brown
Red
Orange
Yellow
Green
Blue
Violet
Gray
White
Gold
Silver
Resistor color code example.
TABLE OF RESISTOR COLOR BAND VALUES.
First digit
0
1
2
3
4
5
6
7
8
9
NA
NA
Second digit
0
1
2
3
7
5
6
7
8
9
NA
NA
Multiplier
1
10
100
1,000
10,000
100,000
1,000,000
10,000,000
100,000,000
1,000,000,000
0.1
0.01
Tolerance
±20%
±1%
±2%
±3%
±4%
NA
NA
NA
NA
NA
±5%
±10%
The tolerance band is typically either gold or silver. A gold tolerance band indicates that the measured value will
be within 5% of the nominal value. A silver band indicates 10% tolerance. For example a resistor with color code
c 2006, Dr. Gregory L. Plett, ECE Dept., CU Colorado Springs
Lab reader prepared by & Copyright °
Lab 1–3
ECE2205, Lab 1: The Digital Multimeter
brown-black-red-silver indicates a nominal value of 1 kÄ. The first two bands (brown-black) produce the mantissa
(10) and the third band (red) is the exponent of ten (102 = 100). So the value is 10 × 100 = 1, 000Ä or 1kÄ. Since
the tolerance band is silver, we can expect the measured value of the resistor to be between 900Ä and 1100Ä. As
another example, a 47kÄ, 20% resistor has color code: yellow-violet-orange-black.
1.4 Lab Assignment
Task 1: Prelab Certification. Have the Lab Assistant/Instructor review your answers to the prelab assignment
questions and sign the certifications page.
Task 2: Orientation.
instruments:
Visually examine the set of test instruments at your lab station. You should find the following
• Agilent E3630A triple output dc power supply;
• Agilent 33120A function generator;
• Agilent 34401A digital multimeter;
• Agilent 54624A digitizing oscilloscope.
In addition, you should also find a PC and a switch-box that connects the PC to the oscilloscope. You will be using
all of these instruments this semester.
Locate the dc power supply. Examine the controls on its front panel. This is a relatively simple instrument to use.
It is used to provide dc (constant) voltages and currents. It is important to prevent the leads of the dc power supply
from touching each other. When the power supply leads touch, a short circuit is formed which can cause serious
damage to the power supply. Consider what would happen if you shorted the wall socket, or a car battery! Short
circuits can be dangerous, and special care should be taken to avoid them.
Locate the digital multimeter. Examine the controls on its front panel. This instrument is used to measure voltage,
current and resistance. When configured to measure voltage, its function is a voltmeter. Likewise, it may function
as an ammeter or as an ohmmeter.
It will be extremely important that you become comfortable (and proficient!) with the use of all lab test instruments.
Task 3: Measuring Resistance (Two-Wire). The most common way to measure a resistance is to use a two-wire
ohmmeter. The meter places a small voltage across the device under test, measures the current that flows, and uses
Ohm’s law to calculate the resistance.
Agilent
34401A
Ω 4W Sense/
4W Sense/
Ratio Ref
Ratio Ref
6 1/2 Digit Multimeter
Input
d
VΩ
HI
HI
200V
Max
FUNCTION
AC 1
Ω 4W
Period
DC V
AC V
Ω 2W
Freq
On/Off
<
MENU Recall
>
CHOICES
4
Cont
RANGE / DIGITS
5
>
Off
On
MATH
DC 1
>
Power
LEVEL
Figure 1.4
6
Auto/
Man
ENTER
1000V
Max
LO
dB
dBm
Null
Min
Max
LO
Terminals
500Vpk
Max
3A
RMS
I
Auto/Hold
Single
TRIG
Shift
LOCAL
Front
Rear
!
1k Ω
Fused on
Rear Panel
Two-wire resistance measurement setup. A “minigrabber” probe is shown to the right.
1. Select a (nominal) 1kÄ resistor. Record the complete color-code of the resistor you used (and particularly the
tolerance of the resistance).
c 2006, Dr. Gregory L. Plett, ECE Dept., CU Colorado Springs
Lab reader prepared by & Copyright °
Lab 1–4
ECE2205, Lab 1: The Digital Multimeter
2. Use minigrabber probes to connect the multimeter to both terminals of the resistor, as shown in Fig. 1.4.
3. Set the multimeter to measure resistance. To do this, press the softkey labeled “Ä2W”. Determine the actual
value of the resistor. The words “actual” and “measured” may be used interchangeably.
4. Compute the percent difference between the actual (measured) value of the resistor and the nominal value of
1kÄ as indicated by its color code. Record the actual and percent difference values. Hang on to this particular
resistor—you will use it again later.
Task 4: Measuring Resistance (Four-Wire). The two-wire resistance-measurement method works well in most
situations. However, it introduces errors for measuring small resistances (e.g., values less than about 10Ä). The
problem is that you are measuring the resistance of both the device under test and the probe wire leads. The scenario
is illustrated in Fig. 1.5.
i(t)
Test lead 3
R3
i(t) ≈ 0 Test lead 1
i(t) Test lead 1
R1
v(t)
R1
R
Device
under
test
v(t)
R2
i(t) Test lead 2
R
Device
under
test
R2
i(t) ≈ 0 Test lead 2
R4
i(t) Test lead 4
Figure 1.5
Two-wire (left) versus four-wire (right) methods for measuring resistance.
In the two-wire scheme, a voltage is imposed on the test leads and the device under test by the multimeter. Current
flows through the circuit according to the total resistance. The current will be
v(t)
i(t) =
.
R1 + R2 + R
The current is measured and the resistance is estimated as R̂ ≈ v(t)/i(t) = R1 + R2 + R. If the resistance of the
leads is significant compared to the resistance being measured, the two-wire scheme is not adequate.
In the four-wire scheme, a voltage is imposed on one pair of the test leads, again causing a current to flow. While
this current is measured, it is used differently in the calculation. A second pair of test leads connect to the terminals
of the device under test, and the voltage across that pair of test leads is measured. Current flowing through these test
leads is approximately zero since the voltmeter has approximately infinite resistance. Therefore, the true resistance
of the device under test may be much better approximated as R̂ = v(t)/i(t).
1. Select a 1Ä resistor. Record all color bands of the resistor.
2. Repeat the steps from task 3 to measure the resistance using the two-wire method.
3. Now, the four-wire method: Use minigrabber probes to connect the multimeter to both terminals of the resistor
using two pairs of test leads, as shown in Fig. 1.6.
4. Set the multimeter to measure resistance. To do this, press the softkey labeled “shift” and then the softkey
labeled “Ä2W”. This selects the “Ä4W” function. Determine the actual value of the resistor.
c 2006, Dr. Gregory L. Plett, ECE Dept., CU Colorado Springs
Lab reader prepared by & Copyright °
Lab 1–5
ECE2205, Lab 1: The Digital Multimeter
Agilent
34401A
Ω 4W Sense/
4W Sense/
Ratio Ref
Ratio Ref
6 1/2 Digit Multimeter
Input
d
VΩ
HI
HI
200V
Max
FUNCTION
AC 1
Ω 4W
Period
DC V
AC V
Ω 2W
Freq
MENU Recall
On/Off
<
>
CHOICES
4
Cont
RANGE / DIGITS
5
>
Off
On
MATH
DC 1
>
Power
LEVEL
6
Auto/
Man
ENTER
Figure 1.6
1000V
Max
LO
dB
dBm
Null
Min
Max
LO
Terminals
500Vpk
Max
3A
RMS
I
Auto/Hold
Single
TRIG
Shift
LOCAL
Front
Rear
!
1Ω
Fused on
Rear Panel
Four-wire resistance measurement setup.
5. Compute the percent difference between the actual (measured) value of the resistor and the nominal value of
1Ä as indicated by its color code. Record the actual and percent difference values. Compare results measuring
the 1Ä resistor using both methods.
Task 5: Graphite Resistor. You will now create a sequence of carbon resistors. Based on their measured values,
you will draw conclusions about the relationship between their physical dimensions and resistance.
1. Using a pencil, draw a rectangle whose length (approximately 1") is twice its width on a sheet of paper. Fill
in the rectangle with pencil mark. Measure and record the resistance over the length and then over the width
of the graphite resistor.
2. Using a pencil, draw a square whose side-length is approximately 1". Fill in the square with pencil mark.
Measure and record the resistance over the width of the graphite resistor.
3. Based on your measurements, draw conclusions relating the physical dimensions and resistance. Draw resistors with other shapes, if necessary. Record your measurements and conclusions.
Task 6: Biologic Resistor.
1. Holding one probe between the thumb and forefinger of each hand, measure the resistance of your body
between your hands. Squeeze the probes tightly so that good contact is established. Record the value of your
body’s resistance. You should probably use a standard probe tip (cf. Fig. 1.7) to ensure good contact.
2. Considering that a current of 100–200 mA through your heart will almost certainly kill you, how much voltage
across your hands would be lethal?
Figure 1.7
Standard probe to be used to measure the biologic resistor.
Task 7: Measuring Current and Verifying Ohm’s Law.
1. Configure the multimeter to measure voltage by pressing the “DC V” softkey. Configure the meter on the dc
power supply to display the voltage on the +6V output by pressing the “+6V” softkey. Adjust the voltage of
the power supply using the “+6V” knob until it reads 5V. Measure the exact voltage using the multimeter.
2. Assemble the circuit in Fig. 1.8. The figure shows the physical setup of the experiment, with the schematic of
the circuit also shown in the inset. You will use the (nominal) 1kÄ resistor you measured previously.
3. Set the multimeter to measure dc current by pressing the shift softkey followed by the “DC V” softkey (for
the “DC I” function). Make sure that the leads are in the correct jacks in the front panel of the multimeter.
c 2006, Dr. Gregory L. Plett, ECE Dept., CU Colorado Springs
Lab reader prepared by & Copyright °
Lab 1–6
ECE2205, Lab 1: The Digital Multimeter
Agilent
E3630A 0−6V, 2.5A/0−±20V,0.5A
Triple Output DC Power Supply
Agilent
VOLTAGE ADJUST
VOLTS
AMPS
OVERLOAD
+6V
Tracking
+20V
34401A
Ω 4W Sense/
4W Sense/
Ratio Ref
Ratio Ref
6 1/2 Digit Multimeter
ratio
+6V
HI
+20V
200V
Max
−20V
Fixed
+6V
+20V
OUTPUT
−20V
+6V
COM
+20V
FUNCTION
Power
−20V
AC 1
Ω 4W
Period
DC V
AC V
Ω 2W
Freq
On
On/Off
Off
± 240 VDC MAX TO
<
MENU Recall
>
RANGE / DIGITS
4
5
>
Off
On
MATH
DC 1
>
METER
Power
d
Input
VΩ
HI
CHOICES
LEVEL
Cont
6
Auto/
Man
ENTER
1000V
Max
LO
dB
dBm
Null
Min
Max
LO
Terminals
500Vpk
Max
3A
RMS
I
Auto/Hold
Single
TRIG
Shift
LOCAL
Front
Rear
!
Fused on
Rear Panel
1k Ω
5V
Ammeter
1k Ω
Schematic of circuit
Figure 1.8
Setup for verifying Ohm’s law.
4. Measure the current flowing through the resistor. An ammeter measures the current flow from the red probe
to the black probe within the meter. Does this value agree with Ohm’s Law?
5. Measure the current flowing through the resistor in the opposite direction. This is done by reversing the leads
of the ammeter. Does this value agree with Ohm’s Law?
Task 8: Ideal versus Practical Voltmeter An ideal voltmeter has infinite resistance: It is an open circuit. Although it is impossible to make a physical voltmeter with infinite resistance, a well designed voltmeter exhibits a
very large internal input resistance. In some experiments, it is important to take into account the finite, non-ideal,
internal resistance. To determine the internal resistance of the voltmeter, set up the circuit shown in Fig. 1.9. The
voltmeter reads the voltage across itself, which includes its internal resistance. Since the circuit has only a single branch, the current flowing through the resistor also flows through the voltmeter. The current is given by the
equation:
Vs − Vm
,
I =
R
where Vs is the source voltage (nominally 5V in this experiment), Vm is the voltmeter-measured voltage, and R is
the value of the (nominal) 10MÄ resistor. From Ohm’s Law, if we know the current and the voltmeter-measured
voltage, we can compute the voltmeter resistance Rm .
Vm
RVm
Vm
Rm =
= Vs −Vm =
.
I
V
−
V
s
m
R
1. Select a (nominal) 10MÄ resistor. Record all color bands of the resistor.
2. Measure its value using the multimeter. Record this value.
3. Set the power supply to provide 5V (Remember, always measure the voltage provided by the power supply
with the voltmeter. Do not rely on the digital display on the front panel of the power supply.)
4. Assemble the circuit in Fig. 1.9.
5. Record the voltage measured by the voltmeter.
6. Compute the internal resistance of the voltmeter. Record all values.
c 2006, Dr. Gregory L. Plett, ECE Dept., CU Colorado Springs
Lab reader prepared by & Copyright °
Lab 1–7
ECE2205, Lab 1: The Digital Multimeter
Agilent
E3630A 0−6V, 2.5A/0−±20V,0.5A
Triple Output DC Power Supply
Agilent
VOLTAGE ADJUST
VOLTS
AMPS
OVERLOAD
+6V
Tracking
+20V
34401A
Ω 4W Sense/
4W Sense/
Ratio Ref
Ratio Ref
6 1/2 Digit Multimeter
ratio
+6V
HI
+20V
200V
Max
−20V
Fixed
+6V
+20V
OUTPUT
−20V
+6V
COM
+20V
−20V
FUNCTION
Power
AC 1
Ω 4W
Period
DC V
AC V
Ω 2W
Freq
On
On/Off
Off
± 240 VDC MAX TO
<
MENU Recall
>
CHOICES
4
RANGE / DIGITS
5
>
Off
On
MATH
DC 1
>
METER
Power
Input
d
VΩ
HI
LEVEL
Cont
6
Auto/
Man
ENTER
1000V
Max
LO
dB
dBm
Null
Min
Max
LO
Terminals
500Vpk
Max
3A
RMS
I
Auto/Hold
Single
TRIG
Shift
LOCAL
Front
Rear
!
Fused on
Rear Panel
10MΩ
5V
Voltmeter
10MΩ
Schematic of circuit
Figure 1.9
Setup for determining the voltmeter’s internal resistance.
Task 9: Ideal versus Practical Ammeter An ideal ammeter has zero resistance so that the the circuit in which it
has been placed is not disturbed. An ideal ammeter is a short circuit. However, as with the voltmeter, no ammeter
can ever be ideal, and therefore all ammeters have some (hopefully) small internal resistance. To determine the
resistance of the ammeter, we will use the circuit in Fig. 1.8, although with a different value of resistance.
According to Ohm’s Law, the current in this circuit will be I = Vs /Rtot where Rtot = R + Rm . The discrete resistor
R has value (nominally) 100Ä in this experiment. We can re-write this relationship as: I = Vs /(R + Rm ). By using
the known quantities I , Vs and R, we can solve for the unknown quantity Rm . In the procedure that follows it is
extremely important that you take precise and accurate measurements. Record each measurement as precisely as the
instrument will allow.
1. Select a (nominal) 100Ä resistor. Record all color bands. Measure and record its actual value.
2. Measure the voltage across the dc power supply. It should be set to a nominal value of 5V.
3. Assemble the circuit in Fig. 1.8, but substituting the 100Ä resistor for the 1kÄ resistor in the figure.
4. Set the multimeter to the ammeter mode for dc current measurement. Recall this means two things: Place the
test leads in the correct banana jacks on the front panel and press the proper sequence of softkeys.
5. Measure the value of the current using the ammeter and determine the value of Rm . Record all values.
Task 10: Lab report. Submit your results in the form of a typed report. While content is clearly the primary objective, neatness and organization will be weighted significantly in the grading of your lab reports. Circuit diagrams
may be hand-drawn, but wires should be drawn using a straight edge. A good laboratory report is concise while
providing enough detail such that another person could reproduce the results. Another person should be able to read
your lab reports and know what you did and how you did it. Your lab reports should not contain the degree of detail
present in the lab manual. Try to keep your reports as concise as possible without deleting essential information.
Provide minimum procedure statements (e.g., “We obtained four 22 nF capacitors.”). You may assume that the
reader has knowledge and proficiency in the use of the lab instruments. Writing of lab reports is not intended to be
“busy work” in which you simply rephrase what is stated in the lab manual. You should provide data, calculations,
as well as comments, observations, and conclusions to indicate your understanding.
The Department requires formal lab reports which must satisfy the following format rules:
1. Title page: This must include a title, name, course and section name and date of the lab assignment (not the
due date of the lab writeup).
c 2006, Dr. Gregory L. Plett, ECE Dept., CU Colorado Springs
Lab reader prepared by & Copyright °
ECE2205, Lab 1: The Digital Multimeter
Lab 1–8
2. Table of Contents (with page numbers).
3. Introduction: Explain the background and objective of the lab indicating requirements and desired results.
4. Discussion: Discuss the underlying applicable theory and concepts that support the measurements and/or
simulations. Indicate and discuss the measurement/simulation set-up and equipment used.
5. Measurement/Simulation Data and/or Results: Present measurement results in tabular, graphical or numeric
form. Present results from required lab exercises. Organize according to task.
6. Discussion of Measurements: Discuss measured data and results of simulation in context of comparison to
expectation, accuracy, difficulties, etc. Organize according to task.
7. Summary and Conclusions: Discuss findings, explain errors and unexpected results; to what extent were the
objectives achieved?; summarize and indicate conclusions. Organize according to task. Also answer specific
questions (below).
Further requirements on the lab report are:
1. Correct spelling, grammar and punctuation is required.
2. Report must be typed; figures, drawings and equations may be handwritten.
3. Format of references (if any) must conform to IEEE (transactions) standards.
In this lab report, please also address the following questions:
• Suppose you set the voltage of the dc power supply to 5V. You connect it to a circuit and the voltage provided
by the power supply drops to 3V. What happened?
• What is the “resolution” of a digital display? Compare the resolution of the digital display on the front panel
of the dc power supply to the display on the front panel of the multimeter. Why must you use the multimeter
if you wish to set the dc supply to 0.755V?
• In task 6, you measured the dc resistance between your left and right hands. To make this measurement, the
ohmmeter applied a small (known) voltage and measured the resulting current. The ratio of applied voltage to
resulting current is the resistance between the ohmmeter probes (in this case, the resistance between your left
and right hands). Based on the resistance you measured, you calculated the voltage range that would cause
100–200 mA of electric current to flow through your body and termed this “the lethal voltage.” However,
in “real life,” the lethal voltage would be far less than the value you calculated. Voltages above 50V are
considered potentially lethal (really clever people have even been able to kill themselves with lower voltages
than this). You are to explain in detail why the lethal voltage is in fact much less than the value you calculated.
Your explanation should include the change in skin resistance that occurs when an electric shock occurs and
other physiologic effects of electric shock that can be lethal (e.g., pulmonary failure).
• Comment on how close the digital multimeter is to ideal with respect to measuring voltage and current. When
might the meter not be accurate?
c 2006, Dr. Gregory L. Plett, ECE Dept., CU Colorado Springs
Lab reader prepared by & Copyright °