introduction to electrical engineering lab manual engineering department university of texas at...

Electrical Engineering Department University of Texas at Arlington

EE 1205 Introduction to

Electrical Engineering

Lab Manual

Howard T. Russell, Jr., PhD V 1.3 August 26, 2012

© 2010 OPALtx

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EE 1205 Introduction to

Electrical Engineering

Lab Manual V 1.3 August 26, 2012

© 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, • useful web sites, and • lab rules. 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 IX. Lab Rules 1. Regardless of the lab section, student attendance in all EE 1205 labs is mandatory and not an option. You must

attend each and every lab meeting for the entire time the lab is scheduled to be in session. 2. As indication of your attendance, you must sign and write the time of day on the lab attendance sheet provided

at the beginning of each lab. If your signature and time stamp are not on the attendance sheet, you are considered to be absent and not in attendance for that lab meeting.

3. Do not sign for your lab partner(s) if they are not in attendance. 4. You must bring your tool box containing all required tools to each and every lab meeting. This is mandatory

and not an option. The presence of your tool box will be checked off on the lab attendance sheet by the lab instructor or GTA. If you are in the lab without your tool box, you are considered to be absent and not in attendance for that lab meeting.

5. You are responsible for obtaining and applying data sheets for any and all components used in the lab experiments.

6. It is mandatory that the circuits you build and layout for the lab experiments work and perform as designed. This is not an option. You are responsible for trouble shooting your circuits and correcting any problems that cause them not to work.

7. Lab partners are well-advised to divide all tasks involved in lab experiments in an equal manner in order to gain experience in performing these tasks. For example, swap breadboard layout and measurement tasks so each partner becomes equally familiar with these jobs.

8. Formal lab reports are due on the date indicated. Reports submitted after the due date are considered late. Any late lab reports will not be counted in your lab grade.

9. A hands-on lab examination will be given at the end of the semester. This exam will be given to each student on a one-to-one basis with the instructor and/or GTA. The exam will test your ability and skills to

• read a schematic diagram, • build a circuit on a breadboard, • measure voltage, current, and resistance, and • properly use and apply lab equipment. 10. Performance on the lab exam along with lab attendance and tool box is counted in the total lab grade. 11. If necessary, exceptions, additions, modifications, inclusions, and details to these and all other lab rules will be

provided prior to or during the lab.

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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 orangeR K= Ω = Ω (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 KKΩ− Ω

= ⋅ ≅ −Ω

(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

3.9KΩ 2KΩ

5.1KΩ

1.2KΩ8.2KΩ

(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

10KΩ 7.5KΩ 15KΩ 3.3KΩ 2.2KΩRAB

A

B

R1 R2 R3 R4 R5RAB

(a) (b)

Figure 2 (a) Schematic for the parallel connection


Table 2 Parallel connection

Resistor (Ri)


Measured value (Ω)

Variation (%)

R1 10K

R2 7.5K

R3 15K

R4 3.3K

R5 2.2K

Terminal resistance


Measured value (Ω)

Variation (%)

RAB

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Series/Parallel Connection

Rx

12Ω

15Ω

30Ω

27Ω

56Ω

75Ω

62Ω

82Ω

91Ω

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


Table 3 Series/parallel connection

Resistor (Ri)


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


Measured value (Ω)

Variation (%)

RAB 84

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Parallel/Series Connection

R1

7.5KΩ

6.2KΩ

8.2KΩ

9.1KΩ

3.0KΩ

2.7KΩ

5.6KΩ

1.5KΩ

1.2KΩR2

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)


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


Measured value (Ω)

Variation (%)

RAB 1.83K

Combo 1 Connection

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R1

A

3.6KΩ 1.2KΩ 1.8KΩ

1.2KΩ

1.3KΩ

2.2KΩ 2.2KΩ300Ω

1KΩ

1.5KΩ 3KΩ

1KΩ

2KΩ

1KΩ

B

R3 R4

R2

R5

R6

R7 R8

R9

R10

R11

R12 R13

R14

R15

R16

1

2

3

4

5

1.3KΩ

200Ω

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)


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


Measured value (Ω)

Variation (%)

RAB

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Combo 2 connection

R2

A

B

R3

R1

R4 R5

R6 R7

R8

30KΩ

R9120KΩ

30KΩ

20KΩ

30KΩ

15KΩ

R10 R11

R12

R13 R14

R15

R16

10KΩ

300KΩ

100KΩ

15KΩ

100KΩ

150KΩ

15KΩ

75KΩ

1

4

3

2

5

6

7

8

47KΩ

22KΩ

RAB

Figure 6

(a) Schematic for Combo 2 connection (b) Component connection diagram

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Table 6 Combo 2 connection

Resistor (Ri)


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


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)

10KΩ

10KΩ

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

1KΩ

1

4

2

3

R2

R3

2KΩ

3KΩ

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

300KΩ 150KΩ 120KΩ

(a) (b)

N3

Figure 3




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

- 47 -

4. Network N4.

Agilent E3620AV1 V2

V1

V2

R1

R2

R3

R2R1

R3

3V

5V

N4

47KΩ

20KΩ

100KΩ

1

1

2

2

3

3

(a) (b)

Figure 4 (a) Network N4

(b) Component connections



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

- 48 -

5. Network N5.

(b)

Agilent E3620AV1 V2

R1 R2

R3

12

3

4

R1 R2

V2R3V1

1 2 3

4

10KΩ 30KΩ

3KΩ10V

(a)

N5

15V

Figure 5




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

1KΩ21

(c)

V1 R1 1KΩ

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

1KΩ

1

4

2

3

R2

R3

2KΩ

3KΩ

9VeV1

v1 v2

v3v4

eR1

eR2

eR3

(a) (b)

(c)

N2 G2

Figure 2.1 (a) Network N2

(b) Graph G2 of N2 (c) Component connections

Figure 2.2


- 53 -


Element

Specified value

Measured value


Element power (W)

Nodes

Measured value (V)

Nodes


R1 1KΩ

R2 2KΩ

R3 3KΩ

V1 9V 1 4





1

2

3

4





V1, R1, R2, R3

- 54 -

Network N3

R1 R2

R3

R4

R5

R6

V1

1 2 3

456

3.9KΩ 1.2KΩ

12KΩ 9.1KΩ

4.7KΩ 2.2KΩ

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


- 55 -


Element

Specified value

Measured value


Element power (W)

Nodes

Measured value (V)

Nodes


R1 3.9KΩ

R2 1.2KΩ

R3 9.1KΩ

R4 2.2KΩ

R5 12KΩ

R6 4.7KΩ

V1 15V 1 6





1

2

3

4

5

6





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

10V220KΩ

82KΩ 47KΩ

150KΩ

12KΩ

4.7KΩ

3.3KΩ

v1v2 v3

v4v5v6

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



Element

Specified value

Measured value


Element power (W)

Nodes

Measured value (V)

Nodes


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 -





1

2

3

4

5

6





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

33KΩ 47KΩ

12KΩ22KΩ

68KΩ 18KΩ

10V

5

6

56KΩ

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

47KΩ 33KΩ

68KΩ20KΩ

13KΩ 39KΩ

15V

5

0

R7

10KΩ

82KΩ 8.2KΩ

R8 R9

N2 Figure 2





R1 47KΩ

R2 33KΩ

R3 68KΩ

R4 39KΩ

R5 20KΩ

R6 13KΩ

R7 10KΩ

R8 82KΩ

R9 8.2KΩ

Eps 15V


Node i Vni (V)

1

2

3

4

5

- 63 -

Table 2(c)

Variable map for N2 from node measurements


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

100Ω

120Ω

100Ω

1.2KΩ

1.2KΩ

1.8KΩ

2.4KΩ

2.7KΩ2.4KΩ

Figure 3





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


Node i Vni (V)

1

2

3

4

5

6

- 65 -

Table 3(c) Variable map for N3 from node measurements


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

10KΩ 3.3KΩ

680Ω56KΩ

56KΩ 51KΩ

10V

Figure 4

Example resistive network

Table 4(a) Variable map for the example network from direct measurements



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


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


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 R2R3

R4 R5

R6

Eg1 12V

V1

V2

V3

15KΩ30KΩ 10KΩ

30KΩ 15KΩ

15KΩ

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

15KΩ

30KΩ30KΩ

10KΩ 7.5KΩ 2KΩ

10KΩ24KΩ

2KΩ

RAB

(a)

N2

RG

EG VAB

A

B

(b)

10V

Figure 2

(a) Network N2 (b) Voltage divider with N2

- 72 -



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)



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

1KΩ

1KΩ

1KΩ 1KΩ 1KΩ

2KΩ2KΩ

2KΩ2KΩ2KΩ

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

30KΩ 15KΩ

7.5KΩVAB

A

B

N4

Figure 4

Network N4

- 75 -



EG1 14V

EG2 14V

R1 30KΩ

R2 15KΩ

Table 4(b) N4 voltages

Voltage


(V)


(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 R4 R5

R6

R7

A

BC

D8.2KΩ

1KΩ

5.1KΩ 6.8KΩ 4.7KΩ

3.9KΩ

2.7KΩ

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

30KΩ 15KΩA

B

R3 R4

15KΩ 30KΩ

RL

(a)

(b)

N6

7.5KΩ

RTH

ETH

N6TH

A

B

RL

7.5KΩ

Figure 6

(a) Network N6 (b) Thevenin’s equivalent network

- 78 -



EG1 20V

EG2 10V

R1 30KΩ

R2 15KΩ

R3 15KΩ

R4 30KΩ

RL 7.5KΩ

Table 6(b) N6 Thevenin’s equivalent

Component



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

oB

T Tt 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 oTCRR 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

R4C3

R3

C2

Q1 Q2

R1

R2

Rt(T)

10KΩtrimpot

5KΩ NTCthermistor

1KΩ1KΩ

0.01μF 0.01μF100Ω

Agilentpower supply

Vin

Vo

Q1, Q2 - 2N3904

red

blackC1

10μF25V

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

R4C3

R3

C2

Q1 Q2

R1

R2

Rt(T)

10KΩtrimpot

5KΩ NTCthermistor

1KΩ1KΩ

0.01μF 0.01μF100Ω

Agilentpower supply

Vin

Vo

Q1, Q2 - 2N3904

red

black

C1

10μF25V

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

20KΩ

10KΩ5KΩ+5V

+5V

10KΩ

OAL

OAR VoR

VoL

20KΩ

10KΩ5KΩ

Vin

-5V

-5V

right channel

left channel

Figure 1 Audio panpot amplifier

Vin

R1a

10KΩ

R2a

Vo1

Vo2

RL

510Ω

R1b

10KΩ

R2b

OA1

OA2

+5V

+5V

-5V

-5VΔVo

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 1KΩ 200KΩ

33KΩ

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

10KΩ 3.3KΩ

680Ω56KΩ

56KΩ 51KΩ

10V

Figure 1

Network schematic

Figure 2

Breadboard layout

- 91 -

Table 1 Voltage, current, and power map

Element

Specified value

Measured value


Element power (W)

Nodes

Measured value (V)

Nodes


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




1

2

3

4

A

B

- 92 -

Table 3 Kirchhoff voltage law




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

10KΩ 3.3KΩ

680Ω56KΩ

56KΩ 51KΩ

10V

Figure 1

Network schematic

Figure 2

Breadboard layout

- 94 -

Table 1 Voltage, current, and power map

Element

Specified value

Measured value


Element power (W)

Nodes

Measured value (V)

Nodes


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




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




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

10KΩ 3.3KΩ

680Ω56KΩ

56KΩ 51KΩ

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






Pot 10KΩ, 1/4W, single turn potentiometer 1

Misc. Wire

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