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Electrical Engineering Department University of Texas at Arlington
EE 1205 Introduction to
Electrical Engineering
Lab Manual
Howard T. Russell, Jr., PhD V 1.2 August 25, 2011
© 2010 OPALtx
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EE 1205 Introduction to
Electrical Engineering
Lab Manual V 1.2 August 25, 2011
© 2010 OPALtx
Table of Contents Lab Meeting No. 1 Introduction to EE Labs …………………………………………..2 Lab Experiment No. 1 Resistors and Resistor Color Bands .............................................30 Lab Experiment No. 2 Resistor Connections …..………………………………………..32 Lab Experiment No. 3 Ohm’s Law ……………………………………………………...42 Lab Experiment No. 4 Kirchhoff’s Laws ……………………………………………….49 Lab Experiment No. 5 Voltage and Current Maps .……………………………………..59 Lab Experiment No. 6 Network Theorems – Part 1 ……………………………………..68 Lab Experiment No. 7 Cooling Fan Control Circuit ……………………………………..79 Lab Experiment No. 8 Audio Amplifier Networks .……………………………………..84 Appendix 1 Breadboard Layout Examples ………….………………………..86 Appendix 2 Lab Measurement Example …………….………………………..90 Appendix 3 Bills of Material …………….………….………………………..96
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Lab Meeting No. 1 Introduction to EE labs
I. Introduction The objective of this first lab meeting is to introduce beginning EE students to a professional laboratory environment where electronic circuits are built and electrical engineering experiments performed. The following topics will be addressed in this introductory meeting – • an orientation regarding proper behavior and safety while in the lab, • tools and tool box requirements, • lab instruments, • cables, connectors, probes, and wires, • electronic components, parts, and the parts request form, • lab report format, and • useful web sites. II. Lab Orientation All EE 1205 students are required to attend an orientation regarding proper behavior and safety while in the lab. This orientation is presented by the resident lab technicians who are responsible for the maintenance and up-keep of the EE labs in Nedderman Hall. III. Tools and Tool Box (Attachment A) Basic items such as pliers, cutters, and wire strippers are integral components in any electrical engineer’s tool box. These tools are necessary to build circuits and perform experiments in the EE lab. Therefore, it is a mandatory requirement that all EE 1205 students obtain and maintain a tool box containing a set of electrical engineering specific tools. The tool box requirement is not an option and all students must bring their tool box fully loaded to every lab meeting beginning with the second meeting. Students without a tool box on the second and subsequent lab meetings will not be allowed in the lab and will receive a zero for the lab. A list of these tools along with their photographs is included in Attachment A at the end of this document. IV. Lab Instruments (Attachment B) The electrical engineering labs located in rooms NH129, NH129A, NH148, and NH148A are equipped with the most current industry standard test and measurement equipment found in professional electrical engineering companies. Each lab is divided into a series of lab benches with each bench containing the following instruments – • Agilent 34401A 6½ digit multimeter (DMM), • Agilent E3620A dual dc power supply (25V, 1A), • Agilent 54621A 60MHz dual channel oscilloscope, and • Agilent 33120A 15MHz function generator. Most of the experiments performed in EE 1205 will involve the above mentioned instruments to some degree. Data sheets for these instruments are included in Attachment B. V. Cables, Connectors, Probes, and Wires Each lab is equipped with one or more wall-mounted racks containing a variety of cables, connectors, oscilloscope probes, and wires. These connectors provide the necessary electrical connections among the bench instruments and your circuits. VI. Electronic Components, Parts, and the Parts Request Form (Attachment C) A wide assortment of electronic components and parts are available in the EE lab. An extensive list of components and parts can be found on the lab web site www-ee.uta.edu/eelabs2/. Click on ‘parts available’ for a view of the list. The experiments performed in EE 1205 labs involve the use of parts supplied by the lab GTA. In more advanced courses, students will have to order their own parts through the lab by submitting an online parts request form. A copy of this form is shown in Attachment C. Most of the parts listed on the lab web site are considered disposable. This means that once parts are given to the student, the student is allowed to keep and accumulate them. For parts not on the list, a formal written request for these parts may be submitted along with instructor approval to lab personnel. VII. Lab Report Format (Attachment D) Formal lab reports are due typically within one week after each lab experiment. Exceptions are made for more complex and/or extensive lab experiments. The format for lab reports is outlined below.
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• Title Page. Every lab report begins with a title page. This page includes the course and section number, experiment number, experiment title, date the experiment was performed, date the report submitted, and student name and ID number. A sample of the EE 1205 lab report cover page is included in Attachment D. • Introduction. A brief description of the purpose of the lab and a discussion of key information the reader will need to understand the experiment. Give a brief description of the theory the experiment is based upon. • Procedure. Describe how the experiment was performed. List equipment, instruments, and components used in the experiment. Include the theory, equations, and detailed schematics of circuits involved. • Results. Present the results of the experiment with data collected from measurements performed. Data should be professionally and neatly presented in the form of tables, graphs, and plots. • Discussions. Discuss any new ideas and/or questions produced in the experimental process. Comment on the validity, accuracy, and usefulness of the procedure. • Conclusion. A description of what the experiment revealed. Generate a comparison between the expected results based on theory and the actual results. An attempt should be made here to explain any discrepancies between these results. • Appendix. The appendix should contain actual compiled data, notes and comments, equations, sketches, and schematics made during the experiment. • References. List any material contributed from other sources. VIII. Useful Web Sites Mouser Electronics www.mouser.com Jameco Electronics www.jameco.com Marlin P. Jones & Associates, Inc. www.mpja.com Electronics Express/RSR www.elexp.com Nuts and Volts (magazine) www.nutsvolts.com
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Attachment A
Tools and the Tool Box August 2, 2009
Component Example Brand Example Source Price ($)
Suitable container (all-purpose plastic tool box; fishing tackle box)
Keter (13” all-purpose box)
Wal-Mart 3.64
Needle nose pliers (4” to 5”) (Figure 1) Stanley (mini plier set) Wal-Mart 12.88
(set of 6)
Diagonal cutters (4” to 5”) (Figure 2) Stanley (mini plier set) Wal-Mart
Wire strippers (5”) (Figure 3) H-Tools (cutter and stripper, 34-899C)
Fry’s 3.49
Prototype breadboard (6.5” x 2” to 6.5” x 4” with 3 to 5 binding posts) (Figures 4 and 5)
Elenco (Model 9425, 6.5” x 2”, 830 test points)
Fry’s 9.99
Precision screwdriver set (6 to 11 piece set with slotted and Phillips screwdrivers) (Figure 6)
Stanley (6 piece; 4 slotted, 2 Phillips)
Wal-Mart 4.88
22 gauge solid hook-up wire (Figure 7) Fry’s product number: PLU#1615281
Fry’s 2.99
Tax: 3.09
Total: 40.96
Photos
Figure 1
5” needle-nose pliers
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Figure 2
5” diagonal cutters
Figure 3
Wire strippers
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Figure 4
Three binding post breadboard
Figure 5
Three binding post breadboard
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Figure 6
Screwdriver set
Figure 7
22 gauge wire
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Attachment B
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Attachment C
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Attachment D
EE 1205.002
Lab Experiment 2
Resistors and Resistor Color Bands Date experiment performed: June 7, 2010 Date Lab Report submitted: June 14, 2010 Student name: Howard T. Russell, Jr. Student ID: 1000xxxxxxxxx
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Lab Experiment No. 1 Resistors and Resistor Color Bands
I. Introduction Resistors are the most common of electronic components found in many circuits and systems. This lab experiment is designed • to sharpen your skill at reading specified values and tolerances from resistor color bands, and • to introduce you into taking resistor measurements using the DMM. II. Experiment Procedure The lab GTA will give you a numbered plastic bag containing 8 quarter-watt axial-lead (through-hole) metal film resistors of various values and tolerances. Your task is to record the number of your bag at the top of Table 1 shown in Section IV on the following page, and complete the entries in this Table using the resistor color guide and the DMM on the work bench. The procedure for this job is as follows – (a) using only the resistor color guide, fill out columns 2 through 9 for each resistor’s specified value and tolerance;
show your results to the lab GTA before turning on the DMM, (b) power up the DMM and measure the actual resistance of each corresponding resistor; record these values in column
10 of the Table, (c) compute the error in percent (%) between the color band value and the measured value for each corresponding
resistor; record these errors in column 11; use the color band or specified value as the basis for the percent, that is
Measured value Color band valueError % 100%
Color band value
(1)
(d) when you have finished reading color bands and taking measurements, return the bag of resistors to the GTA. The first two rows in Table 1 illustrate an example of the procedure on two resistors Ra and Rb. Resistor Ra in the first row has 4 color bands with colors green (5), brown (1), orange (3), and gold (±5%). The specified value of this resistor is determined from 5 1 000 51a
browngreen orange
R K (2)
with a tolerance of ±5%. However, its value measured with the DMM is 50.5KΩ as is recorded in column 10. The error between its measured and specified values is computed from equation (1) where
50.5 51Error % 100% 0.98%
51
K K
K
(3)
This error is recorded in last column as indicated. The procedure is repeated on resistor Rb which has 5 color bands. The second row of Table 1 contains values for this resistor. Clearly, the differences between the specified and measured values for both resistors are well within specified tolerances. III. Lab Report The report for this lab experiment must be word-processed and contain the following items – • Title Page. • Introduction. • Procedure. • Results. Table 1 neatly and completely filled out with the results of your readings, measurements, and calculations. • Discussions. Provide detailed answers and discussions to the following questions – (a) Are the calculated errors between specified and measured values within specified tolerances? If not,
explain why not. (b) How many resistors had measured values larger than their specified values? (c) How many resistors had measured values smaller than their specified values? (d) Explain reasons for the discrepancies in (b) and (c).
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• Conclusion. Provide detailed answers and discussions to the following questions – (a) In your opinion, is the color band coding of resistors an efficient means of labeling values on quarter-watt
axial-lead resistors? (b) Is this coding method suitable for ⅛ watt or smaller axial-lead resistors? Explain why or why not. (c) What other methods can be used? Explain in detail advantages and disadvantages. • Appendix. • References. IV. Resistor Data
Table 1 Axial-lead resistor values
Bag No.________
R Bands
Color band Color band value (Ω)
Color band
tolerance (%)
Measured value (Ω)
Error (%)
1 2 3 4 5
Ra* 4 green brown orange gold N/A 51K ±5 50.5K -0.98
Rb* 5 red orange violet red brown 23.7K ±1 23.8K +0.42
R1
R2
R3
R4
R5
R6
R7
R8 *Resistor examples
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Lab Experiment No. 2 Resistor Connections
I. Introduction In this lab exercise, you will learn – • how to read schematic diagrams of electronic networks, • how to transform schematics into actual element connections, • correct ways to layout a breadboard connection of a network, • how to connect the DMM for measuring resistance, and • how to combine resistors to establish terminal equivalence. II. Experiment Procedure A collection of resistive networks are given in Figures 1 through 6. The schematic diagram of the network is shown in (a) while the resistor connection is shown in (b) in each Figure. Obtain from the lab GTA all of the resistors required for these experiments. Use these resistors to correctly layout each of these networks on your breadboard. Apply the bench DMM to take measurements and make calculations required to fill out the tables provided with each network. Use specified and calculated values as the basis for percentage variations. (a) Series connection. A series connection of resistors is shown in Figure 1. The schematic diagram of this connection is shown in Figure 1(a) while the actual resistor connection is shown in Figure 1(b). Fill out Table 1 with data obtained below. i. Measure the resistance of each resistor in the series connection. ii. With the specified resistor value as the basis, calculate resistor variations in per-cent (%). iii. Calculate the value of the resistance at the terminals A-B. This is the terminal resistance RAB. iv. Apply the DMM to measure RAB. v. Calculate the variation in RAB in (%). (b) Parallel connection. A parallel connection of resistors is shown in Figure 2. The schematic diagram of this connection is shown in Figure 2(a) while actual resistor connection is shown in Figure 2(b). Fill out Table 2 with data obtained below. i. Measure the resistance of each resistor in the parallel connection. ii. With the specified resistor value as the basis, calculate resistor variations in per-cent (%). iii. Calculate the value of the resistance at the terminals A-B. This is the terminal resistance RAB. iv. Apply the DMM to measure RAB. v. Calculate the variation in RAB in (%). (c) Series/parallel combination. A series connection of parallel resistors is shown in Figure 3. The schematic diagram of this connection is shown in Figure 3(a) while the actual resistor connection is shown in Figure 3(b). Fill out Table 3 with data obtained below. i. Measure the resistance of each resistor in the connection. ii. With the specified resistor value as the basis, calculate resistor variations in per-cent (%). iii. Calculate the value of the resistor Rx that will produce a terminal resistance RAB of 84Ω. iv. Obtain this resistor from the lab GTA and connect it into the network. v. Apply the DMM to measure RAB. vi. Calculate the variation in RAB from 84Ω in (%). (d) Parallel/series combination. A parallel connection of series resistors is shown in Figure 4. The schematic diagram of this connection is shown in Figure 4(a) while the actual resistor connection is shown in Figure 4(b). Fill out Table 4 with data obtained below. i. Measure the resistance of each resistor in the connection. ii. With the specified resistor value as the basis, calculate resistor variations in per-cent (%). iii. Calculate the value of the resistor Rx that will produce a terminal resistance RAB of 1.83KΩ. iv. Obtain this resistor from the lab GTA and connect it into the network. v. Apply the DMM to measure RAB. vi. Calculate the variation in RAB from 1.42KΩ in (%). (e) Combination 1 (Combo 1) connection. A combination connection of resistors in series and parallel is shown in Figure 5. The schematic diagram of this connection is shown in Figure 5(a) while the actual resistor connection is shown in Figures 5(b). Fill out Table 5 with data obtained below.
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i. Measure the resistance of each resistor in the connection. ii. With the specified resistor value as the basis, calculate the resistor variation in per-cent (%). iii. Calculate the value of the resistance at the terminals A-B. This is the terminal resistance RAB. iv. Apply the DMM to measure RAB. v. Calculate the variation in RAB in (%). (f) Combination 2 (Combo 2) connection. Yet another combination connection of resistors in series and parallel is shown in Figure 6. The schematic diagram of this connection is shown in Figure 6(a) while the actual resistor connection is shown in Figures 6(b). Fill out Table 6 with data obtained below. i. Measure the resistance of each resistor in the connection. ii. With the specified resistor value as the basis, calculate the resistor variation in per-cent (%). iii. Calculate the value of the resistance at the terminals A-B. This is the terminal resistance RAB. iv. Apply the DMM to measure RAB. v. Calculate the variation in RAB in (%). III. Lab Report The report for this lab experiment must be word-processed and contain the following items – • Title Page. • Introduction. • Procedure. • Results. • Discussions. (a) Suggest useful applications for the connections studied in this experiment. • Conclusion. Provide detailed comments and discussions on the items listed below for each resistor network.
(a) Are all resistors within tolerance? List those that are not. (b) Account for the difference between measured RAB and calculated RAB (that is, the calculated variation or
tolerance of RAB). (c) Explain how the variation in RAB corresponds to resistor tolerance. (d) Explain how close the calculated values of Rx in the series/parallel and parallel/series connections are to
standard resistor values. Consider resistor tolerance. • Appendix. • References.
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Series Connection
RAB
A
B
21
34
R1 R2
R3
R4R5
3.9K 2K
5.1K
1.2K8.2K
(a)
A
B
1 2
34
R1 R2
R3
R4R5
RAB
(b)
Figure 1 (a) Schematic for the series connection
(b) Component connection diagram
Table 1 Series connection
Resistor (Ri)
Specified value (Ω)
Measured value (Ω)
Variation (%)
R1 3.9K
R2 2K
R3 5.1K
R4 1.2K
R5 8.2K
Terminal resistance
Calculated value (Ω)
Measured value (Ω)
Variation (%)
RAB
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Parallel Connection
A
B
R1 R2 R3 R4 R5
10K 7.5K 15K 3.3K 2.2KRAB
A
B
R1R2 R3 R4 R5RAB
(a) (b)
Figure 2 (a) Schematic for the parallel connection
(b) Component connection diagram
Table 2 Parallel connection
Resistor (Ri)
Specified value (Ω)
Measured value (Ω)
Variation (%)
R1 10K
R2 7.5K
R3 15K
R4 3.3K
R5 2.2K
Terminal resistance
Calculated value (Ω)
Measured value (Ω)
Variation (%)
RAB
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Series/Parallel Connection
Rx
12
15
30
27
56
75
62
82
91
R1
R2
R3
R4
R5
R6
R7
R8
R9
RAB
A
B
12 3
RAB
Rx
R1
R2
R3
R4
R5
R6
R7
R8
R9
A
B
1 2 3
(b)(a)
Figure 3 (a) Schematic for the series/parallel connection
(b) Component connection diagram
Table 3 Series/parallel connection
Resistor (Ri)
Specified value (Ω)
Measured value (Ω)
Variation (%)
R1 15
R2 12
R3 30
R4 27
R5 56
R6 75
R7 62
R8 82
R9 91
Rx
Terminal resistance
Specified value (Ω)
Measured value (Ω)
Variation (%)
RAB 84
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Parallel/Series Connection
R1
7.5K
6.2K
8.2K
9.1K
3.0K
2.7K
5.6K
1.5K
1.2KR2
R3
R5
R6
R4
R7
R8
R9
RxRAB
A
B
R1
R2
R3
R5
R4
R6
R7
R8
R9
Rx
A
B
RAB
(a) (b)
1
2
3
4
6
5 1
2
3
4
5
6
Figure 4
(a) Schematic for the parallel/series connection (b) Component connection diagram
Table 4 Parallel/series connection
Resistor (Ri)
Specified value (Ω)
Measured value (Ω)
Variation (%)
R1 1.5K
R2 1.2K
R3 3K
R4 2.7K
R5 5.6K
R6 7.5K
R7 6.2K
R8 8.2K
R9 9.1K
Rx
Terminal resistance
Specified value (Ω)
Measured value (Ω)
Variation (%)
RAB 1.83K
Combo 1 Connection
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R1
A
3.6K 1.2K 1.8K
1.2K
1.3K
2.2K 2.2K300
1K
1.5K 3K
1K
2K
1K
B
R3 R4
R2
R5
R6
R7 R8
R9
R10
R11
R12 R13
R14
R15
R16
1
2
3
4
5
1.3K
200
6
7
8
RAB 9
Figure 5
(a) Schematic for Combo 1 connection (b) Component connection diagram
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Table 5 Combo 1 connection
Resistor (Ri)
Specified value (Ω)
Measured value (Ω)
Variation (%)
R1 200
R2 1.3K
R3 3.6K
R4 1.2K
R5 1.8K
R6 1.3K
R7 2.2K
R8 2.2K
R9 1.2K
R10 300
R11 1K
R12 1.5K
R13 3K
R14 1K
R15 2K
R16 1K
Terminal resistance
Calculated value (Ω)
Measured value (Ω)
Variation (%)
RAB
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Combo 2 connection
R2
A
B
R3
R1
R4 R5
R6 R7
R8
30K
R9120K
30K
20K
30K
15K
R10 R11
R12
R13 R14
R15
R16
10K
300K
100K
15K
100K
150K
15K
75K
1
4
3
2
5
6
7
8
47K
22K
RAB
Figure 6
(a) Schematic for Combo 2 connection (b) Component connection diagram
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Table 6 Combo 2 connection
Resistor (Ri)
Specified value (Ω)
Measured value (Ω)
Variation (%)
R1 47K
R2 30K
R3 120K
R4 20K
R5 30K
R6 15K
R7 30K
R8 22K
R9 10K
R10 300K
R11 100K
R12 15K
R13 100K
R14 150K
R15 15K
R16 75K
Terminal resistance
Calculated value (Ω)
Measured value (Ω)
Variation (%)
RAB
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Lab Experiment No. 3 Ohm’s Law
I. Introduction In this lab exercise, you will learn – • how to connect the DMM to network elements, • how to generate a VI plot, • the verification of Ohm’s law, and • the calculation of element power. II. Experiment Procedure Schematic diagrams for resistive networks N1 through N5 are shown in Figures 1 through 5 on the following pages. Current directions for each element are shown with line arrows. The actual element connections are also shown. The correct way to connect the DMM as an ammeter (AM) and as a voltmeter (VM) is shown in Figure 1(c) for reference. (a) Resistor VI plot. In network N1, the 10KΩ resistor R1 is connected to the Agilent E3620A power supply. The supply voltage V1 is to be varied from 0 volts to 20 volts with the voltage steps shown in Table 1. i. Measure and record the value of R1. Place the value in Table 1 where indicated. ii. Use the digital multi-meter (DMM) to measure the voltage across and the current through R1 for each value
of V1. Record these measurements in Table 1 where indicated. iii. Use Excel to generate a graph of VR1 (linear scale vertical axis) plotted against IR1 (linear scale horizontal
axis). Calculate the value of the slope of this plot and compare to the measured value of R1. Calculate the difference in percent (DiffR1) between these two values with the measured value as the base. Record these values in Table 1 where indicated.
(b) Verification of Ohm’s law. Networks N2 through N5 contain various combinations of resistors and voltage sources. Data tables are provided for each network. i. For each network, use the digital multi-meter (DMM) to measure the voltage across and the current through
each element (dc voltage sources and resistors), and the value of each resistor. Record these measurements in the tables where indicated. Again, the correct way to connect the DMM as an ammeter (AM) and as a voltmeter (VM) is shown in Figure 1(c).
ii. Verify the validity of Ohm’s law by calculating each resistor current from its measured voltage and the measured value of its resistance. That is, from Ohm’s law,
RiRi
i
V measI calc
R meas (1)
where VRi(meas) is the voltage measured across resistor Ri in volts (V), Ri(meas) is the measured value of
Ri’s resistance in ohms (Ω), and IRi(calc) is the calculated value in amps (A) of the current through Ri. Record these calculated values in the tables where indicated.
iii. Verify the accuracy of Ohm’s law by calculating the percent difference (DiffI) between the measured resistor current (IRi(meas)) and calculated current (IRi(calc)) with the measured value as the base. In other words
% 100%Ri RiI
Ri
I calc I measDiff
I meas
(2)
Record these differences in the tables where indicated. iv. Calculate the power dissipated by each resistor and delivered to or from each voltage source. The power in
Watts (W) delivered to a network element e is computed from e e eP V I (3)
where Ve is the voltage drop across e, Ie is the current through e, and Pe is the power delivered to the
element. If Pe is negative, power is delivered from the element to the network. Calculate Pe using measured variables. Record these powers in the tables where indicated.
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III. Lab Report The report for this lab experiment must be word-processed and contain the following items – • Title Page. • Introduction. • Procedure. • Results. • Discussions. (a) Suggest useful applications for Ohm’s law as studied in this experiment. • Conclusion.
(a) Are all measured and calculated currents within resistor tolerance? List those that are not. (b) Explain how resistor variations produce differences between measured and calculated currents. (c) Which method of determining resistor currents (measurement versus calculation) yields more accurate
results? Explain. (d) Which method is more convenient? Explain. (e) Explain how you would convince your boss (via a sales pitch) to use on method over the other. Strengthen
your sales pitch with solid engineering practice and mathematical reasoning. • Appendix. • References.
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IV. Resistive Networks 1. Network N1.
(a)
V1 R1
1
2N1 R121
(b)
Agilent E3620AV1 V2
DM
M(A
M)
DMM(AM)
DMM(VM)
DMM(VM)
R1 VR1
VV1 V1
IR1
IV1 1
2(c)
10K
10K
Figure 1
(a) Network N1 (b) Component connections
(c) DMM connections
Table 1 Measured variables from N1
V1 (V) VR1 (V) IR1 (A)
0.0
2.5
5.0
7.5
10.0
12.5
15.0
17.5
20.0
R1(meas) (Ω)
Slope of VI plot (Ω)
DiffR1 (%)
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2. Network N2.
(a)
V1
R1
1K
1
4
2
3
R2
R3
2K
3K
9V
N2
Agilent E3620AV1 V2
R1
R2
R3
1
2 3
4
(b)
Figure 2 (a) Network N2
(b) Component connections
Table 2 N2 measured and calculated variables
Element Specified
value Measure
value Ve(meas)
(V) Ie(meas)
(A) Ie(calc)
(A) DiffI (%)
Pe (W)
R1 1KΩ
R2 2KΩ
R3 3KΩ
V1 9V N/A N/A
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3. Network N3.
2
R1
Agilent E3620AV1 V2
R2
R3
1
1
R1 R2 R3V1 5V
2
300K 150K 120K
(a) (b)
N3
Figure 3
(a) Network N3 (b) Component connections
Table 3 N3 measured and calculated variables
Element Specified
value Measure
value Ve(meas)
(V) Ie(meas)
(A) Ie(calc)
(A) DiffI (%)
Pe (W)
R1 300KΩ
R2 150KΩ
R3 120KΩ
V1 5V N/A N/A
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4. Network N4.
Agilent E3620AV1 V2
V1
V2
R1
R2
R3
R2R1
R3
3V
5V
N4
47K
20K
100K
1
1
2
2
3
3
(a) (b)
Figure 4 (a) Network N4
(b) Component connections
Table 4 N4 measured and calculated variables
Element Specified
value Measure
value Ve(meas)
(V) Ie(meas)
(A) Ie(calc)
(A) DiffI (%)
Pe (W)
R1 47KΩ
R2 20KΩ
R3 100KΩ
V1 3V N/A N/A
V2 5V N/A N/A
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5. Network N5.
(b)
Agilent E3620AV1 V2
R1 R2
R3
12
3
4
R1 R2
V2R3V1
1 2 3
4
10K 30K
3K10V
(a)
N5
15V
Figure 5
(a) Network N5 (b) Component connections
Table 5 N5 measured and calculated variables
Element Specified
value Measure
value Ve(meas)
(V) Ie(meas)
(A) Ie(calc)
(A) DiffI (%)
Pe (W)
R1 10KΩ
R2 30KΩ
R3 3KΩ
V1 10V N/A N/A
V2 15V N/A N/A
- 49 -
Lab Experiment No. 4 Kirchhoff’s Laws
I. Introduction In this lab exercise, you will learn – • how to read schematic diagrams of electronic networks, • how to draw and use network graphs, • how to transform schematics into actual component connections, • correct ways to layout a breadboard connection of a network, • how to connect the DMM to network components, and • the verification of KCL and KVL. II. Experiment Procedure Four resistive networks N1 through N4 are shown on the following pages. Each network is accompanied with its oriented graph, a simplified connection diagram, and a photo of its suggested breadboard layout. Your job in this lab experiment is to fill out the three tables included with each network with the following data: (where ‘x’ denotes the network number; eg, x = 1 for network 1, x = 2 for network 2, etc.) (a) Table x.1 (variable map) – measure and record i. the value of each network element, ii. the voltage across each network element with node polarities, and iii. the current through each voltage source with node polarities. (b) Table x.1 (variable map) – calculate and record i. the current through each resistor using Ohm’s law, and ii. the power dissipated by each element. (c) Table x.2 (KCL) – calculate and record i. the total current into each node, ii. the total current out of each node, and iii. verification of KCL at each node. (d) Table x.3 (KVL) – calculate and record i. the total clockwise voltage drop around each circuit, ii. the total counter clockwise voltage drop around each circuit, and iii. verification of KVL for each circuit. III. Lab Report The report for this lab experiment must be word-processed and contain the following items – • Title Page. • Introduction. • Procedure. • Results. • Discussions. (a) Comment with respect to accuracy versus convenience on the application of Ohm’s law to determine
element current. • Conclusion. Provide detailed comments and discussions on the items listed below for each resistor network. (a) Does the total power dissipated equal the total power supplied? Explain why or why not. (b) Are the network laws KCL and KVL verified? Explain any discrepancies. • Appendix. • References.
- 50 -
IV. Resistor Networks
Network N1
v1
v2
eV1 eR1
(a) (b)
R1
1K21
(c)
V1 R1 1K
1
2
10V
Agilent E3620AV1 V2
N1
G1
Figure 1.1
(a) Network N1 (b) Graph G1 of N1
(c) Component connections
Figure 1.2
Breadboard layout of N1
- 51 -
Table 1.1 Voltage, current, and power map for N1
Element
Specified value
Measured value
Element voltage Element current
Element power (W)
Nodes
Measured value (V)
Nodes
Calculated value (A) + − + −
R1 1KΩ
V1 10V 1 2
Table 1.2 Kirchhoff current law
Node Total current into (Iin) (A)
Total current out of (Iout) (A)
KCL (Iin – Iout) (A)
1
2
Table 1.3 Kirchhoff voltage law
Circuit Total cw voltage drop (Vcw) (V)
Total ccw voltage drop (Vccw) (V)
KVL (Vcw – Vccw) (V)
V1, R1
- 52 -
Network N2
Agilent E3620AV1 V2
R1
R2
R3
1
2 3
4
V1
R1
1K
1
4
2
3
R2
R3
2K
3K
9VeV1
v1 v2
v3v4
eR1
eR2
eR3
(a) (b)
(c)
N2G2
Figure 2.1 (a) Network N2
(b) Graph G2 of N2 (c) Component connections
Figure 2.2
Breadboard layout of N2
- 53 -
Table 2.1 Voltage, current, and power map for N2
Element
Specified value
Measured value
Element voltage Element current
Element power (W)
Nodes
Measured value (V)
Nodes
Calculated value (A) + − + −
R1 1KΩ
R2 2KΩ
R3 3KΩ
V1 9V 1 4
Table 2.2 Kirchhoff current law
Node Total current into (Iin) (A)
Total current out of (Iout) (A)
KCL (Iin – Iout) (A)
1
2
3
4
Table 2.3 Kirchhoff voltage law
Circuit Total cw voltage drop (Vcw) (V)
Total ccw voltage drop (Vccw) (V)
KVL (Vcw – Vccw) (V)
V1, R1, R2, R3
- 54 -
Network N3
R1 R2
R3
R4
R5
R6
V1
1 2 3
456
3.9K 1.2K
12K 9.1K
4.7K 2.2K
15V
eR1
eV1
eR2
eR3
eR4
eR5
eR6
v1v2 v3
v4v5v6
Agilent E3620AV1 V2
(a) (b)
N3
G3
R1
R2
R3
R4
R5
R6
1
2
3 4
5
6
(c)
Figure 3.1 (a) Network N3
(b) Graph G3 of N3 (c) Component connections
Figure 3.2
Breadboard layout of N3
- 55 -
Table 3.1 Voltage, current, and power map for N3
Element
Specified value
Measured value
Element voltage Element current
Element power (W)
Nodes
Measured value (V)
Nodes
Calculated value (A) + − + −
R1 3.9KΩ
R2 1.2KΩ
R3 9.1KΩ
R4 2.2KΩ
R5 12KΩ
R6 4.7KΩ
V1 15V 1 6
Table 3.2 Kirchhoff current law
Node Total current into (Iin) (A)
Total current out of (Iout) (A)
KCL (Iin – Iout) (A)
1
2
3
4
5
6
Table 3.3 Kirchhoff voltage law
Circuit Total cw voltage drop (Vcw) (V)
Total ccw voltage drop (Vccw) (V)
KVL (Vcw – Vccw) (V)
V1, R1, R5, R6
R5, R2, R3, R4
V1, R1, R2, R3, R4, R6
- 56 -
Network N4
V1
V2R1
R2 R3
R4
R5R6
R7
1 2 3
456
5V
10V220K
82K 47K
150K
12K
4.7K
3.3K
v1
v2 v3
v4v5
v6
eR1
eR2 eR3
eV1
eV2 eR4
eR5eR6
eR7
(a) (b)
Agilent E3620AV1 V2
13
2
64 5
R1
R2
R3
R4
R5
R6
R7
(c)
N4 G4
Figure 4.1
(a) Network N4 (b) Graph G4 of N4
(c) Component connections
- 57 -
Figure 4.2
Breadboard layout of N4
Table 4.1 Voltage, current, and power map for N4
Element
Specified value
Measured value
Element voltage Element current
Element power (W)
Nodes
Measured value (V)
Nodes
Calculated value (A) + − + −
R1 220KΩ
R2 82KΩ
R3 47KΩ
R4 150KΩ
R5 12KΩ
R6 3.3KΩ
R7 4.7KΩ
V1 5V 1 3
V2 10V 2 5
- 58 -
Table 4.2 Kirchhoff current law
Node Total current into (Iin) (A)
Total current out of (Iout) (A)
KCL (Iin – Iout) (A)
1
2
3
4
5
6
Table 4.3 Kirchhoff voltage law
Circuit Total cw voltage drop (Vcw) (V)
Total ccw voltage drop (Vccw) (V)
KVL (Vcw – Vccw) (V)
R1, R2, V2, R6
V2, R3, R4, R5
R2, V1, R3
R6, R5, R7
- 59 -
Lab Experiment No. 5 Voltage and Current Maps
I. Introduction The purpose of this lab is to gain additional familiarity with making measurements on electrical networks. The experiments involved in this lab address the following topics – (a) reading and understanding a schematic diagram, (b) proper layout of a network on a breadboard, (c) application of electronic test equipment to make voltage and current measurements, (d) generation of a voltage, current, and power map of a network under test (NUT), and (e) performing the least number of measurements necessary to generate the map. The theory and equations associated with these experiments are covered in your class notes. Your job in this session is to build and apply two measurement methods on each of the given networks in order to expand your hands-on experience in working with networks and test equipment. For each network included, make use of the parts supplied by the GTA, and the DMM and dc power supply located on the lab bench. II. Breadboard construction and network measurements The schematics for three resistive networks are shown in Figures 1 through 3. Node ‘0’ is the designated ground or reference node for each network. Each network has three corresponding data tables that are to be filled out. You are to perform the following tasks. (a) Direct measurement method i. Build the network on your breadboard with particular attention paid to strict layout procedures. ii. Measure with the DMM the resistance of each resistor and record it in Table xx1(a) in the column where
indicated. iii. Power the network with the dc power supply set to the specified voltage indicated on the schematic. iv. Use the DMM to measure the voltage drop across each resistor and label on the schematic with a positive sign
(+) the resistor’s positive terminal. Record the voltage reading in Table xx(a) where indicated. v. Complete Table xx(a) entries by computing with Ohm’s law the current through (use the measured resistor
values in Table xx(a)) and the power dissipated by each resistor. Use KCL to compute the current through and the power dissipated by the power supply.
(b) Indirect (node) measurement method i. Using the same network breadboard layout in (a), measure the voltage at each node (Vni) with respect to the
ground node (node ‘0’) and record in Table xx(b) where indicated. Label on the schematic the polarity of the node voltage with a positive (+) or negative (–) sign.
ii. Apply KVL to the node voltages to calculate the voltage across each network resistor. Record the KVL expression and resistor voltage in Table xx(c).
iii. Complete the entries in Table xx(c) by computing with Ohm’s law the current through (use the measured resistor values in Table xx(a)) and the power dissipated by each resistor. Use KCL to compute the current through and the power dissipated by the power supply.
III. An example An example network is worked with the results presented in Tables at the end of this lab statement. Node ‘B’ is the designated ground node for this network. IV. Comparisons, comments and conclusions Compare the voltages, currents and power dissipation in Tables xx(a) and xx(c) for each network. Make comments on which measurement method is more efficient, practical and easier to perform.
1 ‘xx’ refers to the Figure number; ‘1’ for Figure 1, ‘2’ for Figure 2, etc.
- 60 -
Network N1
1
4
32R1 R2
R3
R4
R5
R6
Eps
33K 47K
12K22K
68K 18K
10V
5
6
56K
R7
0
N1 Figure 1
Resistive network N1
Table 1(a) Variable map for network N1 from direct measurements
Component Spec value
Measured value
VRi (V) IRi (A) PRi (W)
R1 33KΩ
R2 47KΩ
R3 12KΩ
R4 18KΩ
R5 56KΩ
R6 68KΩ
R7 22KΩ
Eps 10V
Table 1(b) Node-to-ground voltages
Node i Vni (V)
1
2
3
4
5
6
- 61 -
Table 1(c) Variable map for N1 from node measurements
Component KVL VRi (V) IRi (A) PRi (W)
R1
R2
R3
R4
R5
R6
R7
Eps
- 62 -
Network N2
1
4
32R1 R2
R3
R4
R5
R6
Eps
47K 33K
68K20K
13K 39K
15V
5
0
R7
10K
82K 8.2K
R8 R9
N2 Figure 2
Resistive network N2
Table 2(a) Variable map for network N2 from direct measurements
Component Spec value
Measured value
VRi (V) IRi (A) PRi (W)
R1 47KΩ
R2 33KΩ
R3 68KΩ
R4 39KΩ
R5 20KΩ
R6 13KΩ
R7 10KΩ
R8 82KΩ
R9 8.2KΩ
Eps 15V
Table 2(b) Node-to-ground voltages
Node i Vni (V)
1
2
3
4
5
- 63 -
Table 2(c) Variable map for N2 from node measurements
Component KVL VRi (V) IRi (A) PRi (W)
R1
R2
R3
R4
R5
R6
R7
R8
R9
Eps
- 64 -
Network N3
Eps1
Eps2
R1
R2
R3
R4
R5
R6
R7
R8
R9
1
2
3
4
5
60
12V
12V
100
120
100
1.2K
1.2K
1.8K
2.4K
2.7K
2.4K
Figure 3
Resistive network N3
Table 3(a) Variable map for network N3 from direct measurements
Component Spec value
Measured value
VRi (V) IRi (A) PRi (W)
R1 100Ω
R2 120Ω
R3 100Ω
R4 1.2KΩ
R5 1.8KΩ
R6 1.2KΩ
R7 2.7KΩ
R8 2.4KΩ
R9 2.4KΩ
Eps1 12V
Eps2 12V
Table 3(b) Node-to-ground voltages
Node i Vni (V)
1
2
3
4
5
6
- 65 -
Table 3(c) Variable map for N3 from node measurements
Component KVL VRi (V) IRi (A) PRi (W)
R1
R2
R3
R4
R5
R6
R7
R8
R9
Eps
- 66 -
Example Network
A
B
1 4
32
R1 R2
R3
R4
R5
R6
Vps
10K 3.3K
68056K
56K 51K
10V
Figure 4
Example resistive network
Table 4(a) Variable map for the example network from direct measurements
Component Spec value
Measured value
VRi (V) IRi (A) PRi (W)
R1 10KΩ 9.832KΩ 1.07043 108.87µ 116.53µ
R2 47KΩ 3.2473KΩ 0.17961 55.31µ 9.934µ
R3 12KΩ 674.49Ω 37.316m 55.32µ 2.064µ
R4 18KΩ 49.938KΩ 2.7577 55.22µ 152.29µ
R5 56KΩ 55.538KΩ 2.9745 53.56µ 159.3µ
R6 68KΩ 55.405kΩ 6.0255 108.75µ 655.29µ
Vps 10V 10.09V 10.09 -108.75µ -1.0972m
Table 4(b) Node-to-ground voltages
Node i Vni (V)
1 9.0
2 6.0255
3 8.7832
4 8.8205
A 10.09
- 67 -
Table 4(c) Variable map for example network from node measurements
Component KVL VRi (V) IRi (A) PRi (W)
R1 VA – V1 1.09 110.86µ 120.84µ
R2 V1 – V4 0.17948 55.27µ 9.919µ
R3 V4 – V3 37.316m 55.32µ 2.064µ
R4 V3 – V2 2.7577 55.22µ 152.29µ
R5 V1 – V2 2.9745 53.55µ 159.3µ
R6 V2 6.0255 108.75µ 655.29µ
Eps VA 10.09 (-IR1) -108.97µ -1.0985m
- 68 -
Lab Experiment No. 6 Network Theorems – Part 1
I. Introduction The purpose of this lab is to gain familiarity with several important Electrical Engineering theorems. The experiments performed in this lab involve the following concepts – • voltage and current division, • superposition theorem, and • Thevenin’s theorem. The theory and equations associated with these experiments are covered in your class notes. Your job in this session is to investigate and apply the above theorems on resistive networks to provide a hands-on experience to the theory covered in the lectures on these topics. For each of the networks given below, use the parts supplied by the GTA, and the DMM and dc power supply located on the lab bench. II. Experiment Procedures Procedures for performing experiments on a collection of resistive networks are attached. These experiments involve the theory and applications covered in the lecture on voltage and current division, superposition, and Thevenin’s equivalent. In your lab report, provide detailed answers and discussions to the following – • Discussion. (a) With respect to resistor tolerance, are the results of the measurements within tolerance to calculated values
using specified component values? (b) Explain reasons for any discrepancies between calculated and measured results. (c) How useful are these theorems and operations? Can you think of any specific applications?
- 69 -
III. Voltage Division Part A. Voltage divider network N1. 1. Build network N1 shown in Figure 1 on your breadboard using parts supplied by the GTA. 2. Measure the values of the voltage source Eg1 and each resistor with the DMM and record in Table 1(a) where
indicated. 3. Use the voltage divider operation to do the following: a. calculate voltages V1 through V3 using the specified values for the components and record in Table 1(b), b. calculate the voltages using the measured values for the components and record values in Table 1(b), c. measure with the DMM the voltages on the N1 and record in Table 1(b), and d. calculate the difference in percent (%) between the voltages measured from the network (3c) and those
calculated with specified component values (3a) as the basis, and record in Table 1(b). 4. Provide comments on the accuracy of the voltage divider network N1 for generating precise voltage values with
respect to resistor tolerance.
R1 R2
R3
R4R5
R6
Eg1 12V
V1
V2
V3
15K30K 10K
30K 15K
15K
N1 Figure 1
Network N1
Table 1(a) N1 component values
Component Specified value Measured value
Eg1 12V
R1 30KΩ
R2 15KΩ
R3 10KΩ
R4 30KΩ
R5 15KΩ
R6 15KΩ
- 70 -
Table 1(b) N1 voltage values
Voltage
Calculated from specified R values
(V)
Calculated from measured R values
(V)
Measured from N1
(V)
Difference
(%)
V1
V2
V3
- 71 -
Part B. Application of voltage division. 1. Build network N2 shown in Figure 2(a) on your breadboard using parts supplied by the GTA. 2. Measure the values of each resistor with the DMM and record in Table 2(a) where indicated. 3. Use resistor combination operations to do the following: a. calculate the value of the resistance at terminals A-B of N2 (RAB) using specified component values and
record in Table 2(b), b. calculate the value of RAB using measured component values and record in Table 2(b), and, c. use the DMM to measure the value of RAB and record in Table 2(b). 4. Connect terminals A-B of N2 to the 10V source and RG as shown in Figure 2(b) and do the following: a. select a specified value of RG to be as close as possible to that of the calculated value of RAB; record this
value in Table 2(c), b. obtain this resistor from the GTA, measure its value, measure the value of EG, and record in Table 2(c), c. measure the voltage VAB across terminals A-B of N2 and record in Table 2(c), d. apply the voltage divider operation to calculate the value of RAB using the measured values of EG, RG,
and VAB; record in Table 2(c), and e. calculate the difference in percent between RAB’s DMM measured value (3c) and RAB’s value
calculated from the voltage divider operation (4d), use the DMM value as the basis; record in Table 2(c).
5. Provide comments on the accuracy of voltage division for calculating network input resistance with respect to resistor tolerance.
R2
R1
N2
R3
R5
R7
R4
R8
R6
R9
A
B
1 2
345
15K
30K30K
10K 7.5K 2K
10K24K
2K
RAB
(a)
N2
RG
EG VAB
A
B
(b)
10V
Figure 2
(a) Network N2 (b) Voltage divider with N2
- 72 -
Table 2(a) N2 component values
Component Specified value Measured value
R1 15KΩ
R2 30KΩ
R3 2KΩ
R4 30KΩ
R5 24KΩ
R6 10KΩ
R7 2KΩ
R8 7.5KΩ
R9 10KΩ
Table 2(b) RAB from N2 (Figure 2(a))
Condition RAB (Ω)
Calculated from specified R values
Calculated from measured R values
RAB measured with DMM
Table 2(c) RAB from voltage division (Figure 2(b))
RG specified (Ω)
RG measured (Ω)
EG measured (V)
VAB measured (V)
RAB calculated (Ω)
Difference (%)
- 73 -
IV. Current Division R-2R current divider network N3. 1. Build R-2R network N3 shown in Figure 3 on your breadboard using parts supplied by the GTA. 2. Apply the current division operation to calculate values for the currents listed on the schematic and record in
Table 3. Use specified resistor and voltage source values in these calculations. 3. Measure with the DMM these currents and record their values in Table 3. 4. Calculate the difference in percent (%) between the currents measured from the network (3) and those
calculated with specified component values (2) as the basis, and record in Table 3 where indicated. 5. Provide comments on the accuracy of the current divider network N1 for providing precise binary-weighted
currents resistor scaling and tolerance.
EG
RG2
RG1
R1
R2
R3
R4
R5
R6
R7R8
IG
I1 I3 I5 I7 I8
24V
1K
1K
1K 1K 1K
2K2K
2K2K2K
N3
Figure 3
R-2R network N3
Table 3 N3 currents
Current
Calculated from current division (A)
Measured from N3 (A)
Difference (%)
IG
I1
I3
I5
I7
I8
- 74 -
V. Superposition Part A. Network N4. 1. Build network N4 shown in Figure 4 on your breadboard using parts supplied by the GTA. 2. Measure the values of each resistor with the DMM and record in Table 4(a) where indicated. 3. Perform the following operations. a. With EG1 turned on and operating, measure its value and record in Table 4(a) then turn off voltage source
EG2 by removing it from the connection and replacing it with a short circuit, i. calculate voltage VAB using the specified component values and record in Table 4(b), ii. calculate voltage VAB using the measured component values and record in Table 4(b), iii. measure with the DMM voltage VAB from the breadboard and record in Table 4(b), and iv. calculate the difference in percent (%) between VAB measured and VAB calculated with specified
component values as the basis, and record in Table 4(b). b. With EG2 turned on and operating, measure its value and record in Table 4(a) then turn off voltage source
EG1 by removing it from the connection and replacing it with a short circuit, i. calculate voltage VAB using the specified component values and record in Table 4(b), ii. calculate voltage VAB using the measured component values and record in Table 4(b), iii. measure with the DMM voltage VAB from the breadboard and record in Table 4(b), and iv. calculate the difference in percent (%) between VAB measured and VAB calculated with specified
component values as the basis, and record in Table 4(b). c. Apply the superposition theorem to i. calculate the total voltage for VAB by adding the values calculated from specified component values,
record in Table 4(b), and ii. calculate the total voltage for VAB by adding the values calculated from measured component values,
record in Table 4(b). d. With EG1 and EG2 turned on and operating, i. measure the total voltage VAB directly from N4, and ii. calculate the difference in percent (%) between the total VAB measured from N4 (3di) and the total
VAB calculated with specified component values (3ci) as the basis, and record in Table 4(b). 4. Provide comments on the accuracy of superposition for providing precise voltage measurements and on the
ease of making these measurements.
EG1 EG214V 14V
R1 R2
R3
30K 15K
7.5KVAB
A
B
N4
Figure 4
Network N4
- 75 -
Table 4(a) N4 component values
Component Specified value Measured value
EG1 14V
EG2 14V
R1 30KΩ
R2 15KΩ
Table 4(b) N4 voltages
Voltage
Calculated from specified R values
(V)
Calculated from measured R values
(V)
Measured from N4
(V)
Difference
(%)
VAB (EG2 = 0)
VAB (EG1 = 0)
VAB (total)
- 76 -
Part B. Network N5. 1. Build network N5 shown in Figure 5 on your breadboard using parts supplied by the GTA. 2. Perform the operations similar to those performed in Part A. a. With EG1 turned on and operating, turn off voltage source EG2 by removing it from the connection and
replacing it with a short circuit, measure voltages VAB and VCD, and record in the first column of Table 5. b. With EG2 turned on and operating, turn off voltage source EG1 by removing it from the connection and
replacing it with a short circuit, measure voltages VAB and VCD, and record in the second column of Table 5.
c. Apply the superposition theorem to calculate total measured values for VAB and VCD, and record in the third column of Table 5.
d. With EG1 and EG2 turned on and operating, measure VAB and VCD directly from N5, and record in the fourth column of Table 5.
e. Calculate the difference in percent (%) between VAB and VCD measured directly from N5 (fourth column) and VAB and VCD calculated from superposition (third column) with the measured values as the basis. Record in the last column of Table 5.
3. Provide comments on the accuracy of superposition for providing precise voltage measurements and on the ease of making these measurements.
EG1
EG2
R2
R1
R3 R4R5
R6
R7
A
BC
D8.2K
1K
5.1K 6.8K 4.7K
3.9K
2.7K
15V
12V
N5
Figure 5
Network N5
Table 5 N5 voltages
Voltage
Measured with EG2 = 0
(V)
Measured with EG1 = 0
(V)
Total from superposition
(V)
Total measurement
(V)
Difference
(%)
VAB
VCD
- 77 -
VI. Thevenin’s Equivalent Network N6. 1. Build network N6 shown in Figure 6 on your breadboard using parts supplied by the GTA. 2. Measure the values of the voltage sources and resistors with the DMM, and record in Table 6(a). 3. Apply basic network operations to do the following: a. calculate values for the Thevenin’s voltage source ETH, Thevenin’s resistance RTH, and the current IL
through RL using the specified values of the components and record in Table 6(b), b. calculate values for ETH, RTH, and IL using the measured values of the components and record in Table
6(b), c. apply the DMM on N6 to measure values for ETH, RTH, and IL and record in Table 6(b), and d. calculate the difference in percent (%) between ETH, RTH, and IL measured from the network (c) and those
calculated with specified resistor values (a) as the basis, and record in Table 6b where indicated. 4. Provide comments on the accuracy and convenience of Thevenin’s equivalent for providing precise resistor
currents connected as loads to the network.
EG1 EG220V 10V
R1R2
30K 15KA
B
R3 R4
15K 30K
RL
(a)
(b)
N6
7.5K
RTH
ETH
N6TH
A
B
RL
7.5K
Figure 6
(a) Network N6 (b) Thevenin’s equivalent network
- 78 -
Table 6(a) N6 component values
Component Specified value Measured value
EG1 20V
EG2 10V
R1 30KΩ
R2 15KΩ
R3 15KΩ
R4 30KΩ
RL 7.5KΩ
Table 6(b) N6 Thevenin’s equivalent
Component
Calculated from specified R values
Calculated from measured R values
Measured from N6
Difference (%)
ETH
RTH
IL
- 79 -
Lab Experiment No. 7 Cooling Fan Control Circuit
I. Introduction This lab experience involves a project rather than an experiment. The project is to build and test circuits that use a thermistor to control temperature by activating a cooling fan. II. The Thermistor: Theory of Operation A thermistor is a resistor constructed from special material having a resistivity significantly sensitive to temperature [1,2]. This material allows the resistance of the thermistor to exhibit a predictable variation over a wide range of temperature. These devices are used as temperature sensors, current limiters, bias current compensators, and circuit protectors. The resistance-temperature (RT) characteristics of thermistors are very non-linear. For example, the RT characteristics of one class of thermistors is modeled with an exponential equation derived from the Steinhart-Hart equation for [2]
1 1
o
BT T
t t oR T R T e
(1)
In this equation, T is the ambient temperature in °K, To is the reference or nominal temperature (usually 300.15°K or 27°C), Rt(To) is thermistor resistance at the nominal temperature, and B is a model parameter in °K. The plot of a RT curve for a typical thermistor with a nominal temperature resistance of 6KΩ for two values of B is shown in Figure 1. Over small ranges of temperature, the RT curve exhibits a near straight-line behavior. In these ranges, the resistance of a thermistor can be approximated with a first-order relationship to temperature modeled by
1100t t o oTCR
R T R T T T
(2)
where TCR is the temperature coefficient in %/°C. If the TCR is positive, the thermistor is referred to as a positive temperature coefficient (PTC) device and Rt increases as temperature increases. Conversely, if TCR is negative, then Rt decreases with an increase in temperature and the thermistor is a negative temperature coefficient (NTC) device. The TCR for a typical PTC thermistor is on the order of 0.2%/°C to 0.5%/°C while that for a NTC device is between –5%/°C to –3%/°C. III. Fan Control Circuits There are two versions for the fan control circuit used in this project. The schematic of the first version (Ckt. 1) is shown in Figure 2 where a 5KΩ NTC thermistor RT is connected to a 10KΩ trim pot (R1) to form a voltage divider. The thermistor is placed next to an object (target) whose ambient temperature is to be regulated by the cooling fan. The voltage from the divider provides the excitation (Vin) to the 555 timer which is configured as a Schmitt trigger [3]. Assuming the currents into pins 2 and 6 of the 555 are very small, Vin is expressed as
1
tin CC
t
R TV V
R T R
(3)
where Rt(T) is the temperature dependent resistance of RT. The output of the 555 (Vo) drives a pair of 2N3904 NPN bipolar junction transistors (BJT) Q1 and Q2 to control a cooling fan and the light-emitting diode (LED) D1. The LED provides visual indication of the fan’s condition. The voltage transfer curve (VTC) of the control circuit is shown in Figure 3. At the target’s nominal operating temperature (To), Rt(To) is about 5KΩ such that Vin is slightly larger than 8V which is the ‘high’ threshold voltage (VTH) of the Schmitt trigger. The value for Vin at To can be adjusted by trimming R1. At this point, Vo is approximately equal to zero volts causing Q1 and Q2 to be turned off such that the fan and LED are also turned off. As the target’s temperature begins to increase, Rt(T) begins to decrease causing Vin to decrease as well. When Vin reaches the ‘low’ threshold voltage (VTL), the Schmitt trigger changes state causing Vo to immediately increase to the supply voltage 12V. This voltage is large enough to cause Q1 and Q2 to conduct, and to turn on the fan and the LED. By positioning the fan to direct a flow of cool air toward the target, its temperature will begin to decrease such that Rt(T) and, consequently, Vin will start to increase. When Vin reaches VTH, Vo immediately drops to zero volts which turns Q1 and Q2 off. As a result, the fan and LED are also turned off to complete the operating cycle.
- 80 -
The schematic for the second version (Ckt. 2) of the control circuit is shown in Figure 4. In this circuit, the p-channel junction field-effect transistor (PJFET) J1 and the 10KΩ trim pot R1 make a current source that forces current into the thermistor RT. The operation of this circuit to control the cooling fan is basically identical to that of the first version. IV. Components and Instruments The components and instruments required for this lab are listed below. Components: Resistors: 100Ω 1KΩ (2) 10KΩ trim pot NTC thermistor Capacitors: 0.01µF (2) 10µF Active devices: IC: 555 timer NPN BJT: 2N3904 (2) Red LED PJFET: J271 Instruments: Power supply Multimeter Agilent E3620A Agilent 34401A Additional: 12V cooling fan Breadboard Tool box Hook-up wire V. Project Procedure Both circuit versions described above are to be built and tested in the lab. The following tasks are to be performed. (a) Download, store, and print data sheets for the components listed below NTC502-RC thermistor (Xicon) 555 timer (Fairchild Semiconductor Corp. or National Semiconductor Corp.) NPN BJT 2N3904 (Fairchild Semiconductor Corp.) PJFET J271 (Fairchild Semiconductor Corp.) (b) Obtain a fan from the GTA. Confirm the operation of the fan by connecting it to the Agilent E3620A power
supply. Connect the red lead to positive (+) and the black lead to negative (−). Adjust the voltage to 12V and verify that the fan is operational. If the fan does not operate, obtain another from the GTA. (Note: Be sure to return all fans to the GTA after the project is completed.)
(c) Build Ckt. 1 shown in Figure 2 on your breadboard. Follow the breadboard layout shown in the photo in Figure 5. Place the fan and thermistor connections at the far end of the breadboard for convenient access.
(d) With the power supply voltage Vps of 12V, adjust R1 such that Vin is slightly larger than 8V. Measure and record Vin, and indicate that the fan and LED are off.
(e) Use a heat source (hair dryer) to blow hot air onto the thermistor. Measure and record Vin when the fan and LED turn on. This voltage should be slightly less than 4V.
(f) Remove the heat source and direct the air flow from the fan onto the thermistor. Measure and record Vin as the temperature of the thermistor decreases to nominal. As Vin exceeds 8V, the fan and LED should turn off.
(g) Repeat (c) through (f) for Ckt. 2 shown in Figure 4.
- 81 -
VI. References [1] M. Sapoff and R.M. Oppenheim, “Theory and application of self-heated themistors,” Proc. IEEE, vol. 51, pp.
1292-1305, Oct. 1963. [2] E.A. Boucher, “Theory and applications of thermistors,” Chemical Instrumentation, vol. 44, no. 11, pp.
A935-A966, Nov. 1967. [3] S. Franco, Design with Operational Amplifiers and Analog Integrated Circuits, 3rd Edition, The McGraw-
Hill Companies, Inc., New York, NY, 2002. (ISBN 0-07-232084-2)
50 25 0 25 50 75 100 125 1500.1
1
10
100
1 103
B = 3900KB = 4100K
Temperature (C)
Res
ista
nce
(Koh
ms)
Figure 1
RT curve for a typical thermistor
Vps
12V
2
8
6
1
3555
timer
fan
D1
redLED
R4
C3
R3
C2
Q1 Q2
R1
R2
Rt(T)
10Ktrimpot
5K NTCthermistor
1K1K
0.01F 0.01F100
Agilentpower supply
Vin
Vo
Q1, Q2 - 2N3904
red
black
C110F25V
RT
+VCC
Figure 2
Fan control circuit Ckt. 1 with a thermistor in a voltage divider
- 82 -
Vo
Vin12V
8V4V0V
0V
12V
hysteresis band
fan on
fan off
increasing <---- T ----> decreasing
VTHVTL
Figure 3
Control circuit VTC
Vps
12V
2
8
6
1
3555
timer
fan
D1
redLED
R4
C3
R3
C2
Q1 Q2
R1
R2
Rt(T)
10Ktrimpot
5K NTCthermistor
1K1K
0.01F 0.01F100
Agilentpower supply
Vin
Vo
Q1, Q2 - 2N3904
red
black
C1
10F25V
RT
+VCC
J1
J1 - J271
Figure 4 Fan control circuit Ckt. 2with a
thermistor driven by a current source
- 83 -
Figure 5
Breadboard layout Ckt. 1
- 84 -
Lab Experiment No. 8 Audio Amplifier Networks
I. Introduction The purpose of this lab session is to gain familiarity with several well-known audio amplifier circuits built with standard operational amplifiers (op-amp). Your job in this session is to design (where necessary), build, test, and evaluate each of these circuits in order to expand your hands-on experience in working with the devices. For each network listed below, use TLC274 quad op-amps, standard 5% resistors, a ±5 volt dc power supply, and an ac signal generator. For measurements, use ac voltmeters, DVMs, and oscilloscopes. II. Components and Instruments The components and instruments required for this lab are listed below. Components: Op-amp: TLC274 Resistors 510Ω 5.1KΩ 10KΩ 18KΩ 20KΩ 30KΩ 39KΩ 51KΩ 10KΩ single-turn potentiometer Instruments: Function generator Oscilloscope Agilent 33120A 15MHz Agilent 54621A 60MHz dual-channel Power supply Multimeter Agilent E3620A Agilent 34401A Additional: Breadboard Tool box Hook-up wire Oscilloscope probes III. Lab Assignment Download from the internet the data sheet for the Texas Instrument’s TLC274 quad op-amp. You will need this document for the device pin configuration. Use this op-amp to build and perform measurements on the following amplifier networks. A. Amplifier No. 1. The dual-output audio panpot amplifier (see problem 1.25 Ref .1) shown in Figure 1. Determine
the 1KHz voltage gain at each output as the pot RP is varied over its full range. B. Amplifier No. 2. The bridge amplifier (see problem 1.74 Ref. 1, Ref. 2) shown in Figure 2. Design this amplifier
for a differential output voltage gain of 8. Determine the maximum undistorted peak-to-peak voltage swing across the load resistor RL at 1KHz.
IV. References 1. S. Franco, Design with Operational Amplifiers and Analog Integrated Circuits, 3rd Ed., The McGraw-Hill
Companies, Inc., New York, NY, 2002, (ISBN 0-07-232084-2). 2. NSC data sheet, “LM4991, 3W Audio Power Amplifier with Shutdown Mode”, Audio Power Amplifier Series,
National Semiconductor Corporation, 2003.
- 85 -
R2LR1L R3L
RP
R1R R3R R2R
20K
10K5K+5V
+5V
10K
OAL
OARVoR
VoL
20K
10K5K
Vin
-5V
-5V
right channel
left channel
Figure 1 Audio panpot amplifier
Vin
R1a
10K
R2a
Vo1
Vo2
RL
510
R1b
10K
R2b
OA1
OA2
+5V
+5V
-5V
-5VVo
Figure 2 Bridge amplifier
(aka Boomer Amplifier)
- 86 -
Appendix 1 Breadboard Layout Examples
EE 1205 Bread board layout techniques
September 13, 2008 HTR, Jr.
binding post
(red)binding post
(black)
R1
R2
R3 1K 200K
33K
Figure 1 Resistor network schematic
Figu re 2
Wrong way – off the board with loops
- 87 -
Figure 3
Right way - low to the board and tight
Figure 4
Right way – low to the board and even tighter
- 88 -
Breadboard layout examples HTR, Jr.
February, 25, 2009
- 89 -
- 90 -
Appendix 2 Lab Measurement Example
Lab Measurement Example 1
A
B
1 4
32
R1 R2
R3
R4
R5
R6
Vps
10K 3.3K
68056K
56K 51K
10V
Figure 1
Network schematic
Figure 2
Breadboard layout
- 91 -
Table 1 Voltage, current, and power map
Element
Specified value
Measured value
Element voltage Element current
Element power (W)
Nodes
Measured value (V)
Nodes
Calculated value (A) + − + −
R1 10KΩ 9.8251KΩ
R2 3.3KΩ 3.2624KΩ
R3 680Ω 684.22Ω
R4 51KΩ 50.294KΩ
R5 56KΩ 55.175KΩ
R6 56KΩ 55.158KΩ
Vps 10V A B
Table 2 Kirchhoff current law
Node Total current into (Iin) (A)
Total current out of (Iout) (A)
KCL (Iin – Iout) (A)
1
2
3
4
A
B
- 92 -
Table 3 Kirchhoff voltage law
Circuit Total cw voltage drop (Vcw) (V)
Total ccw voltage drop (Vccw) (V)
KVL (Vcw – Vccw) (V)
Vps, R1, R5, R6
R5, R2, R3, R4
Vps, R1, R2, R3, R4,
R6
- 93 -
Lab Measurement Example 1
Solutions
A
B
1 4
32
R1 R2
R3
R4
R5
R6
Vps
10K 3.3K
68056K
56K 51K
10V
Figure 1
Network schematic
Figure 2
Breadboard layout
- 94 -
Table 1 Voltage, current, and power map
Element
Specified value
Measured value
Element voltage Element current
Element power (W)
Nodes
Measured value (V)
Nodes
Calculated value (A) + − + −
R1 10KΩ 9.8251KΩ A 1 1.09245 A 1 111.1897µ 121.4692µ
R2 3.3KΩ 3.2624KΩ 1 4 0.18271 1 4 56.00478µ 10.23263µ
R3 680Ω 684.22Ω 4 3 38.073m 4 3 55.64438µ 2.118549µ
R4 51KΩ 50.294KΩ 3 2 2.8199 3 2 56.06832µ 158.1071µ
R5 56KΩ 55.175KΩ 1 2 3.0406 1 2 55.10829µ 167.5623µ
R6 56KΩ 55.158KΩ 2 B 6.1287 2 B 111.1117µ 680.9704µ
Vps 10V 10.0147V A B 10.2831 A B -111.4µ −1.145537m
Table 2 Kirchhoff current law
Node Total current into (Iin) (A)
Total current out of (Iout) (A)
KCL (Iin – Iout) (A)
1 (IR1)
111.1897µ (IR2 + IR5) 111.1131µ
76.63n (0.069%)
2 (IR4 + IR5) 111.1766µ
(IR6) 111.1117µ
64.91n (0.058%)
3 (IR3)
55.64438µ (IR4)
56.06832µ −423.9366n
(0.762%)
4 (IR2)
56.00478µ (IR3)
55.64438µ 360.4n
(0.648%)
A 0 (IR1 + Ips) −210.3n
210.3n (0.189%)
B (Ips + IR6) -288.3n
0 −288.3nA (0.259%)
- 95 -
Table 3 Kirchhoff voltage law
Circuit Total cw voltage drop (Vcw) (V)
Total ccw voltage drop (Vccw) (V)
KVL (Vcw – Vccw) (V)
Vps, R1, R5, R6 (VR1 + VR5 + VR6)
10.26175 (Vps)
10.2831 −21.35m (0.208%)
R5, R2, R3, R4 (VR2 + VR3 + VR4)
3.040683 (VR5)
3.0406 83µ
(0.0027%)
Vps, R1, R2, R3, R4, R6
(VR1 + VR2 + VR3 + VR4 + VR6) 10.26183
(Vps) 10.2831
−21.267m (0.207%)
A
B
1 4
32
R1 R2
R3
R4
R5
R6
Vps
10K 3.3K
68056K
56K 51K
10V
Figure 3
Oriented network schematic Total power dissipated by resistors (delivered to resistors) = 1.14046mW Total power delivered by the power supply = 1.145537mW Absolute difference (%) = 5.076µW (0.445%)
- 96 -
Appendix 3 Bills of Material
Lab 2 BOM Lab 2 bill of materials (BOM) – resistor values 12Ω 200Ω 1KΩ (3) 10KΩ (2) 100KΩ (2) 15Ω 300Ω 1.2KΩ (4) 15KΩ (4) 120KΩ 27Ω 1.3KΩ (2) 20KΩ 150KΩ 30Ω 1.5KΩ (2) 22KΩ 300KΩ 56Ω 1.8KΩ 30KΩ (3) 62Ω 2KΩ (2) 47KΩ 75Ω 2.2KΩ (3) 75KΩ 82Ω 2.7KΩ 91Ω 3KΩ (2) 3.3KΩ 3.6KΩ 3.9KΩ 5.1KΩ 5.6KΩ 6.2KΩ 7.5KΩ (2) 8.2KΩ (2) 9.1KΩ Other – 47Ω 4.7KΩ
- 97 -
Lab 3 BOM Lab 3 bill of materials (BOM) – resistor values Network N1: 1KΩ Network N2: 1KΩ 2KΩ 3KΩ Network N3: 120KΩ 150KΩ 300KΩ Network N4: 20KΩ 47KΩ 100KΩ Network N5: 3KΩ 10KΩ 30KΩ
- 98 -
Lab 4 BOM Lab 4 bill of materials (BOM) – resistor values Lab experiment No. 4 resistor list Network N1 Network N2 Network N3 Network N4 1K 1K 1.2K 3.3K 2K 2.2K 4.7K 3K 3.9K 12K 4.7K 47K 9.1K 82K 12K 150K 220K
- 99 -
Lab 5 BOM Lab 5 bill of materials (BOM) – resistor values Lab experiment No. 5 resistor list Network N1 Network N2 Network N3 12K 8.2K 100 (2) 18K 10K 120 22K 13K 1.2K (2) 33K 20K 1.8K 47K 33K 2.4K (2) 56K 39K 2.7K 68K 47K 68K 82K
- 100 -
Lab 6 BOM Lab 6 bill of materials (BOM) – resistor values Lab experiment No. 6 resistor list Voltage divider networks: Network N1 Network N2 10K 2K (2) 15K (3) 7.5K 30K (2) 10K (2) 15K 24K 30K (2) Current divider network: Network N3 1K (5) 2K (5) Superposition networks: Network N4 Network N5 7.5K 1K 15K 2.7K 30K 3.9K 4.7K 5.1K 6.8K 8.2K Thevenin’s equivalent networks: (Same as N4 and N5)
- 101 -
Lab 7 BOM Lab 7 bill of materials (BOM) – component and resistor values Resistors: 100Ω 1KΩ (2) 10KΩ trim pot NTC thermistor Capacitors: 0.01µF (2) 10µF Active devices: IC: 555 timer NPN BJT: 2N3904 (2) Red LED PJFET: J271 Additional: 12V cooling fan
- 102 -
Lab 8 BOM Lab 8 bill of materials (BOM) – component and resistor values
Lab 8 Bill of Materials
Part Description Count
Op-amp TLC274, quad CMOS op-amp, plastic encapsulated
1
Resistor 510Ω, 1/4W, 5%, carbon film resistor 1
Resistor 5.1KΩ, 1/4W, 5%, carbon film resistor 2
Resistor 10KΩ, 1/4W, 5%, carbon film resistor 10
Resistor 18KΩ, 1/4W, 5%, carbon film resistor 2
Resistor 20KΩ, 1/4W, 5%, carbon film resistor 2
Resistor 30KΩ, 1/4W, 5%, carbon film resistor 2
Resistor 39KΩ, 1/4W, 5%, carbon film resistor 2
Resistor 51KΩ, 1/4W, 5%, carbon film resistor 2
Pot 10KΩ, 1/4W, single turn potentiometer 1
Misc. Wire