EE 1205 Introduction to Electrical Engineering Lab Manual

EE 1205 Introduction to Electrical Engineering Lab Manual Howard T. Russell, Jr., PhD V 1.3 August 26, 2012 © 2010 OPALtx Electrical Engineering Depa...
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EE 1205 Introduction to Electrical Engineering Lab Manual Howard T. Russell, Jr., PhD V 1.3 August 26, 2012 © 2010 OPALtx

Electrical Engineering Department

 

University of Texas at Arlington

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. - 2 - 

 

• 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 Jameco Electronics Marlin P. Jones & Associates, Inc. Electronics Express/RSR Nuts and Volts (magazine)

www.mouser.com www.jameco.com www.mpja.com www.elexp.com 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

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) Prototype breadboard (6.5” x 2” to 6.5” x 4” with 3 to 5 binding posts) (Figures 4 and 5) Precision screwdriver set (6 to 11 piece set with slotted and Phillips screwdrivers) (Figure 6) 22 gauge solid hook-up wire (Figure 7)

H-Tools (cutter and stripper, 34-899C) Elenco (Model 9425, 6.5” x 2”, 830 test points)

Fry’s

3.49

Fry’s

9.99

Stanley (6 piece; 4 slotted, 2 Phillips)

Wal-Mart

4.88

Fry’s product number: PLU#1615281

Fry’s

2.99 Tax: Total:

Photos

Figure 1 5” needle-nose pliers

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Price ($)

3.09 40.96

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 Error ( % ) =

Measured value − Color band value ⋅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 Ra = 5N

1N

000 N Ω = 51K Ω

(2)

green brown orange

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 Error ( % ) =

50.5 K Ω − 51K Ω ⋅100% ≅ −0.98% 51K 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.________ Color band

1

2

3

4

5

Color band value (Ω)

Color band tolerance (%)

Measured value (Ω)

Error (%)

R

Bands

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. - 32 - 

 

i. ii. iii. iv. v.

Measure the resistance of each resistor in the connection. With the specified resistor value as the basis, calculate the resistor variation in per-cent (%). Calculate the value of the resistance at the terminals A-B. This is the terminal resistance RAB. Apply the DMM to measure RAB. 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 1 R1

1

R2

A 3.9KΩ

A

2

R1

2 R2

2KΩ R3

RAB 8.2KΩ

5.1KΩ

RAB

R3

1.2KΩ

B 4

R5

R4

3

B

R5

R4 4

(a)

(b)

Figure 1 (a) Schematic for the series connection (b) Component connection diagram Table 1 Series connection Resistor (Ri)

Specified value (Ω)

R1

3.9K

R2

2K

R3

5.1K

R4

1.2K

R5

8.2K

Terminal resistance

Calculated value (Ω)

Measured value (Ω)

Variation (%)

Measured value (Ω)

Variation (%)

RAB

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3

Parallel Connection A A R1

R2

R4

R3

R5

RAB

RAB 10KΩ

7.5KΩ

15KΩ

3.3KΩ

R1

R2

R3

2.2KΩ

B B

(a)

(b)

Figure 2 (a) Schematic for the parallel connection (b) Component connection diagram Table 2 Parallel connection Resistor (Ri)

Specified value (Ω)

R1

10K

R2

7.5K

R3

15K

R4

3.3K

R5

2.2K

Terminal resistance

Calculated value (Ω)

Measured value (Ω)

Variation (%)

Measured value (Ω)

Variation (%)

RAB

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R4

R5

Series/Parallel Connection R6

R1 15Ω

Rx A

2

R3

75Ω

30Ω

62Ω

R4

R6 R3 R1

R7

3

1

A 12Ω R2

27Ω

82Ω

56Ω

R8

RAB

Rx

R7 2

1 R2

R9

B

(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)

R1

15

R2

12

R3

30

R4

27

R5

56

R6

75

R7

62

R8

82

R9

91

Measured value (Ω)

Variation (%)

Measured value (Ω)

Variation (%)

Rx Terminal resistance

Specified value (Ω)

RAB

84

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R8

R9

91Ω

B

3

R5

RAB R5

R4

 

Parallel/Series Connection

R6

R6

7.5KΩ

4

R3 A

R3

R1

A

RAB B

4

3.0KΩ

R1 Rx

1.5KΩ

2

1

2.7KΩ

5

3

8.2KΩ

R4

1.2KΩ

R2

2

R8

RAB

1

Rx

5

R4

R2 R5

R7

6.2KΩ

R7

3

R8

6

5.6KΩ

B R9

9.1KΩ

6

R5

R9

(a)

(b)

Figure 4 (a) Schematic for the parallel/series connection (b) Component connection diagram Table 4 Parallel/series connection Resistor (Ri)

Specified value (Ω)

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

Measured value (Ω)

Variation (%)

Measured value (Ω)

Variation (%)

Rx Terminal resistance

Specified value (Ω)

RAB

1.83K Combo 1 Connection - 37 - 

 

R1

R9

1

5

A 1.2KΩ

200Ω R3

R4

R5 1.2KΩ

3.6KΩ

R11

2

R15

6 R12

1.3KΩ

R6

RAB

1KΩ

1.8KΩ

R13 1.5KΩ 7

R8 2.2KΩ

1KΩ

R14 2.2KΩ 300Ω

1.3KΩ B R2

4

R10

Figure 5 (a) Schematic for Combo 1 connection (b) Component connection diagram

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8

9 3KΩ

3

R7

2KΩ

R16

1KΩ

Table 5 Combo 1 connection Resistor (Ri)

Specified value (Ω)

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 (%)

Measured value (Ω)

Variation (%)

RAB

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Combo 2 connection R1

1

A 47KΩ R3

R2

120KΩ

10KΩ

R9

R13

R14 100KΩ

30KΩ 2 4 R4

RAB

R5

R10

30KΩ

20KΩ

7 R11

100KΩ

R15

300KΩ 3

8

5 R6

R7 15KΩ

15KΩ

R12

30KΩ R8

B 22KΩ

6

Figure 6 (a) Schematic for Combo 2 connection (b) Component connection diagram

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15KΩ

R16

75KΩ

150KΩ

Table 6 Combo 2 connection Resistor (Ri)

Specified value (Ω)

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 (%)

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, I Ri ( calc ) =

VRi ( meas )

(1)

Ri ( meas )

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 Diff I ( % ) =

I Ri ( calc ) − I Ri ( meas ) I Ri ( meas )

⋅100%

(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 Pe = Ve ⋅ I e

(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. - 42 - 

 

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. 1.

Resistive Networks Network N1. 1 Agilent E3620A V1 10KΩ

R1

V1

N1

V2

2

R1 1

2

(a)

(b) DMM (AM)

IV1

1 IR1 DMM (AM)

DMM (VM)

VV1

V1 R1

VR1 DMM (VM)

10KΩ

2 (c)

Figure 1 (a) Network N1 (b) Component connections (c) DMM connections Table 1 Measured variables from N1 V1 (V)

VR1 (V)

IR1 (A)

Slope of VI plot (Ω)

DiffR1 (%)

0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 R1(meas) (Ω)

- 44 - 

 

2.

Network N2. Agilent E3620A R1

1

V1

2

V2

1KΩ V1

R2

9V

2KΩ

1

4

R3 R1 N2

4

3KΩ

R3

3 2

3 R2

(a)

(b)

Figure 2 (a) Network N2 (b) Component connections Table 2 N2 measured and calculated variables Element

Specified value

R1

1KΩ

R2

2KΩ

R3

3KΩ

V1

9V

Measure value

Ve(meas) (V)

Ie(meas) (A)

- 45 - 

 

Ie(calc) (A)

DiffI (%)

N/A

N/A

Pe (W)

3.

Network N3. Agilent E3620A V1

V2

1

V1

5V

R1

R2

R3 R1

300KΩ

150KΩ

120KΩ 1

2

N3

R2

2

R3 (b)

(a)

Figure 3 (a) Network N3 (b) Component connections Table 3 N3 measured and calculated variables Element

Specified value

R1

300KΩ

R2

150KΩ

R3

120KΩ

V1

5V

Measure value

Ve(meas) (V)

Ie(meas) (A)

- 46 - 

 

Ie(calc) (A)

DiffI (%)

N/A

N/A

Pe (W)

4.

Network N4. 1 Agilent E3620A V1 V1

3V

47KΩ

R1

2 V2

5V

N4

V2

R2

R3

100KΩ 1

20KΩ

R1

R2

3

2 3

R3

(a)

(b)

Figure 4 (a) Network N4 (b) Component connections Table 4 N4 measured and calculated variables Element

Specified value

R1

47KΩ

R2

20KΩ

R3

100KΩ

V1 V2

Measure value

Ve(meas) (V)

Ie(meas) (A)

Ie(calc) (A)

DiffI (%)

3V

N/A

N/A

5V

N/A

N/A

- 47 - 

 

Pe (W)

5.

Network N5. Agilent E3620A V1 1

R1

R2

2

10KΩ V1

10V

N5

V2

3

30KΩ R3

3KΩ

15V

V2

1

2

R1

4

R2

3

R3 4

(a)

(b)

Figure 5 (a) Network N5 (b) Component connections Table 5 N5 measured and calculated variables Element

Specified value

R1

10KΩ

R2

30KΩ

R3

3KΩ

V1 V2

Measure value

Ve(meas) (V)

Ie(meas) (A)

Ie(calc) (A)

DiffI (%)

10V

N/A

N/A

15V

N/A

N/A

- 48 - 

 

Pe (W)

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.

- 49 - 

 

IV.

Resistor Networks Network N1 v1

1

Agilent E3620A V1

V1

R1

10V

1KΩ

eV1

eR1

G1 N1 (a)

2

R1 v2

1KΩ 1

(b)

2 (c)

Figure 1.1 (a) Network N1 (b) Graph G1 of N1 (c) Component connections

Figure 1.2 Breadboard layout of N1

- 50 - 

 

V2

Table 1.1 Voltage, current, and power map for N1 Element voltage Nodes Element

Specified value

R1

1KΩ

V1

10V

Measured value

+



1

2

Element current Nodes

Measured value (V)

+



Calculated value (A)

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)

V1, R1

- 51 - 

 

KVL (Vcw – Vccw) (V)

Element power (W)

Network N2 R1

1

2

v1

eR1

Agilent E3620A

v2

V1

1KΩ V1

R2

9V

2KΩ

eV1

eR2 1

R3 N2

4

3KΩ

(a)

V2

3

v4

eR3

4

v3

G2

R1 (b)

R3

2

3 R2 (c)

Figure 2.1 (a) Network N2 (b) Graph G2 of N2 (c) Component connections

Figure 2.2 Breadboard layout of N2

- 52 - 

 

Table 2.1 Voltage, current, and power map for N2 Element voltage Nodes Element

Specified value

R1

1KΩ

R2

2KΩ

R3

3KΩ

V1

9V

Measured value

+



1

4

Element current Nodes

Measured value (V)

+



Calculated value (A)

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)

V1, R1, R2, R3

- 53 - 

 

KVL (Vcw – Vccw) (V)

Element power (W)

Network N3 1

R1

R2

2

3 v1

3.9KΩ R5

15V

V1

eV1

9.1KΩ

R3

12KΩ R4

R6 6 4.7KΩ

eR1

v2

5

eR5

v6

2.2KΩ

eR6 v 5 G3

4

N3 (a)

(b)

Agilent E3620A V1

V2

1

6

R1

R6

R5

2

R2

3

5

R4

R3

4 (c)

Figure 3.1 (a) Network N3 (b) Graph G3 of N3 (c) Component connections

Figure 3.2 Breadboard layout of N3 - 54 - 

 

eR2

v3

1.2KΩ eR3

eR4

v4

Table 3.1 Voltage, current, and power map for N3 Element voltage Nodes Element

Specified value

R1

3.9KΩ

R2

1.2KΩ

R3

9.1KΩ

R4

2.2KΩ

R5

12KΩ

R6

4.7KΩ

V1

15V

Measured value

+



1

6

Element current Nodes

Measured value (V)

+



Calculated value (A)

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)

V1, R1, R5, R6 R5, R2, R3, R4 V1, R1, R2, R3, R4, R6

- 55 - 

 

KVL (Vcw – Vccw) (V)

Element power (W)

Network N4 V1 R2

1

R3

2

82KΩ R1

220KΩ

3.3KΩ

N4

3

V2

10V

R4

R7

150KΩ

12KΩ

4

G4

eR7 (b)

Agilent E3620A V2

3 1

R3

2

R2 R1

6

R4

R7

R5 4 R6 (c)

Figure 4.1 (a) Network N4 (b) Graph G4 of N4 (c) Component connections

- 56 - 

5

v3

eR5 v5

4.7KΩ

V1

eR3

eR4

eR6 v6

(a)

 

v2

eV2

eR1

R5

5

eR2

v1

47KΩ

R6

6

eV1

5V

v4

Figure 4.2 Breadboard layout of N4 Table 4.1 Voltage, current, and power map for N4 Element voltage Nodes Element

Specified value

R1

220KΩ

R2

82KΩ

R3

47KΩ

R4

150KΩ

R5

12KΩ

R6

3.3KΩ

R7

4.7KΩ

V1 V2

Measured value

+



5V

1

3

10V

2

5

Nodes Measured value (V)

- 57 - 

 

Element current

+



Calculated value (A)

Element power (W)

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)

R1, R2, V2, R6 V2, R3, R4, R5 R2, V1, R3 R6, R5, R7

- 58 - 

 

KVL (Vcw – Vccw) (V)

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. - 59 - 

Network N1 R1

1

R2

2

33KΩ

47KΩ 56KΩ

R5 R7

3

22KΩ

12KΩ

R3 5 Eps R6

6

N1

10V R4

0

68KΩ

4

18KΩ

Figure 1 Resistive network N1 Table 1(a) Variable map for network N1 from direct measurements Component

Spec value

R1

33KΩ

R2

47KΩ

R3

12KΩ

R4

18KΩ

R5

56KΩ

R6

68KΩ

R7

22KΩ

Eps

10V

Measured value

VRi (V)

Table 1(b) Node-to-ground voltages Node i

Vni (V)

1 2 3 4 5 6

- 60 - 

 

IRi (A)

PRi (W)

Table 1(c) Variable map for N1 from node measurements Component

KVL

VRi (V)

R1 R2 R3 R4 R5 R6 R7 Eps

- 61 - 

 

IRi (A)

PRi (W)

Network N2 R7 10KΩ

R1

1

R2

2

47KΩ

33KΩ

R8

Eps

R9

15V

82KΩ

R6 5 N2

3

R5

20KΩ

R3

8.2KΩ

68KΩ

R4

0

13KΩ

4

39KΩ

Figure 2 Resistive network N2 Table 2(a) Variable map for network N2 from direct measurements Component

Spec value

R1

47KΩ

R2

33KΩ

R3

68KΩ

R4

39KΩ

R5

20KΩ

R6

13KΩ

R7

10KΩ

R8

82KΩ

R9

8.2KΩ

Eps

15V

Measured value

VRi (V)

Table 2(b) Node-to-ground voltages Node i

Vni (V)

1 2 3 4 5

- 62 - 

 

IRi (A)

PRi (W)

Table 2(c) Variable map for N2 from node measurements Component

KVL

VRi (V)

R1 R2 R3 R4 R5 R6 R7 R8 R9 Eps

- 63 - 

 

IRi (A)

PRi (W)

Network N3 R1

1

4

100Ω

Eps1

R4

12V

1.2KΩ R2

0

R8

2.4KΩ

R7

3

6

R5

1.8KΩ

2.7KΩ

120Ω

2.4KΩ Eps2

1.2KΩ

12V

R9

R6 R3 2

5

100Ω

Figure 3 Resistive network N3 Table 3(a) Variable map for network N3 from direct measurements Component

Spec value

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

Measured value

VRi (V)

Table 3(b) Node-to-ground voltages Node i

Vni (V)

1 2 3 4 5 6

- 64 - 

 

IRi (A)

PRi (W)

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

KVL

VRi (V)

R1 R2 R3 R4 R5 R6 R7 R8 R9 Eps

- 65 - 

 

IRi (A)

PRi (W)

Example Network R1

R2

A

1

4

10KΩ

3.3KΩ

Vps

56KΩ

680Ω

R5

R3

10V R6

R4

B 2

56KΩ

3

51KΩ

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

- 66 - 

 

Table 4(c) Variable map for example network from node measurements Component

KVL

VRi (V)

IRi (A)

PRi (W)

R1

V A – V1

1.09

110.86µ

120.84µ

R2

V 1 – V4

0.17948

55.27µ

9.919µ

R3

V 4 – V3

37.316m

55.32µ

2.064µ

R4

V 3 – V2

2.7577

55.22µ

152.29µ

R5

V 1 – V2

2.9745

53.55µ

159.3µ

R6

V2

6.0255

108.75µ

655.29µ

Eps

VA

10.09

(-IR1) -108.97µ

-1.0985m

- 67 - 

 

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?

- 68 - 

 

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

30KΩ

Eg1

12V

R3

15KΩ

10KΩ

R5

R4 30KΩ

15KΩ

R6

15KΩ

V1

V2

V3

N1

Figure 1 Network N1 Table 1(a) N1 component values Component

Specified value

Eg1

12V

R1

30KΩ

R2

15KΩ

R3

10KΩ

R4

30KΩ

R5

15KΩ

R6

15KΩ

- 69 - 

 

Measured value

Table 1(b) N1 voltage values

Voltage

Calculated from specified R values (V)

Calculated from measured R values (V)

V1 V2 V3

- 70 - 

 

Measured from N1 (V)

Difference (%)

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. R1

A

R3

1

15KΩ R2

RAB R9 B

30KΩ R8

10KΩ 5

2

2KΩ 30KΩ R5

R4

4

7.5KΩ

2KΩ

N2 (a)

RG

EG

10V

A

VAB

B (b)

Figure 2 (a) Network N2 (b) Voltage divider with N2

- 71 - 

 

24KΩ R6 R7

N2

10KΩ

3

Table 2(a) N2 component values Component

Specified value

R1

15KΩ

R2

30KΩ

R3

2KΩ

R4

30KΩ

R5

24KΩ

R6

10KΩ

R7

2KΩ

R8

7.5KΩ

R9

10KΩ

Measured value

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)

- 72 - 

 

RAB calculated (Ω)

Difference (%)

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. RG1 1KΩ IG I1

RG2 1KΩ 24V

EG

R2

R1

2KΩ

R4 I3

1KΩ R3

R6 I5

1KΩ

2KΩ

R5

I7

1KΩ

2KΩ

R7

2KΩ

I8 R8 2KΩ

N3

Figure 3 R-2R network N3 Table 3 N3 currents Current

Calculated from current division (A)

Measured from N3 (A)

IG I1 I3 I5 I7 I8

- 73 - 

 

Difference (%)

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. R1

R2

A

30KΩ

EG1

14V

15KΩ R3

VAB

7.5KΩ N4 B

Figure 4 Network N4

- 74 - 

 

EG2

14V

Table 4(a) N4 component values Component

Specified value

EG1

14V

EG2

14V

R1

30KΩ

R2

15KΩ

Measured value

Table 4(b) N4 voltages

Voltage

Calculated from specified R values (V)

Calculated from measured R values (V)

VAB (EG2 = 0) VAB (EG1 = 0) VAB (total)

- 75 - 

 

Measured from N4 (V)

Difference (%)

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. R1 1KΩ EG1

R2

A N5

R3

D 8.2KΩ

15V

5.1KΩ

R5

6.8KΩ

R4

4.7KΩ

EG2

R6 C 3.9KΩ

B 12V R7 2.7KΩ

Figure 5 Network N5 Table 5 N5 voltages

Voltage

Measured with EG2 = 0 (V)

Measured with EG1 = 0 (V)

Total from superposition (V)

VAB VCD

- 76 - 

 

Total measurement (V)

Difference (%)

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. R2

R1 30KΩ

EG1

15KΩ

A RL

20V

10V

7.5KΩ 15KΩ

N6

R3

B

30KΩ R4

(a)

RTH A RL

ETH

7.5KΩ B

N6TH (b)

Figure 6 (a) Network N6 (b) Thevenin’s equivalent network

- 77 - 

 

EG2

Table 6(a) N6 component values Component

Specified value

EG1

20V

EG2

10V

R1

30KΩ

R2

15KΩ

R3

15KΩ

R4

30KΩ

RL

7.5KΩ

Measured value

Table 6(b) N6 Thevenin’s equivalent Component

Calculated from specified R values

Calculated from measured R values

ETH RTH IL

- 78 - 

 

Measured from N6

Difference (%)

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] Rt (T ) = Rt (To ) e

⎛1 1 ⎞ B ⎜⎜ − ⎟⎟ ⎝ T To ⎠

(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 ⎡ TCR Rt (T ) = Rt (To ) ⎢1 + (T − To )⎤⎥ ⎣ 100 ⎦

(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 Vin =

Rt (T )

Rt (T ) + R1

(3)

VCC

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. - 79 - 

 

The schematic for the second version (Ckt. 2) of the control circuit is shown in Figure 4. In this circuit, the pchannel 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 Red LED

NPN BJT: 2N3904 (2) PJFET: J271

Instruments: Power supply Agilent E3620A

Multimeter Agilent 34401A

Additional: 12V cooling fan Tool box

Breadboard 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.

- 80 - 

 

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 McGrawHill Companies, Inc., New York, NY, 2002. (ISBN 0-07-232084-2) 1 .10

3

Resistance (Kohms)

100

10

1

0.1

50

25

0

25

50 Temperature (C)

75

100

125

150

B = 3900K B = 4100K

Figure 1 RT curve for a typical thermistor Agilent power supply +VCC red C1

10μF 25V R1

black

10KΩ trimpot

C2

8 2

Vps

555 timer

Vin

3

R2 1KΩ

Rt(T)

5KΩ NTC thermistor

Q1

0.01μF

R3 1KΩ

1

Q1, Q2 - 2N3904

Figure 2 Fan control circuit Ckt. 1 with a thermistor in a voltage divider

- 81 - 

 

100Ω

R4 C3

0.01μF

Vo

6

12V RT

D1 red LED

fan

Q2

Vo

12V fan on

hysteresis band

fan off

0V

VTH 8V

VTL 4V

0V

12V

Vin

increasing decreasing

Figure 3 Control circuit VTC Agilent power supply +VCC red C1

10KΩ trimpot

R1

10μF 25V

D1 red LED

fan black C2

8

J1 2

Vps

555 timer

Vin

3

Vo R2 1KΩ

6

12V

Q1

0.01μF

R3 1KΩ

1 RT Rt(T)

5KΩ NTC thermistor

J1 - J271

Q1, Q2 - 2N3904

Figure 4 Fan control circuit Ckt. 2with a thermistor driven by a current source

- 82 - 

 

100Ω

R4 C3

0.01μF

Q2

Figure 5 Breadboard layout Ckt. 1

- 83 - 

 

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 30KΩ 39KΩ 51KΩ 10KΩ single-turn potentiometer Instruments: Function generator Agilent 33120A 15MHz Power supply Agilent E3620A

20KΩ

Oscilloscope Agilent 54621A 60MHz dual-channel Multimeter 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.

- 84 - 

 

R1L

R3L

5KΩ

10KΩ

R2L

20KΩ

+5V

VoL

OAL

left channel -5V RP 10KΩ Vin

+5V right channel VoR

OAR

5KΩ

10KΩ

R1R

R3R

-5V

R2R 20KΩ

 

Figure 1 Audio panpot amplifier R1a

R2a

10KΩ

+5V Vo1

OA1

-5V

Vin

RL

ΔVo

510Ω R2b

R1b

Vo2

10KΩ

+5V

OA2

-5V

  Figure 2 Bridge amplifier (aka Boomer Amplifier)

- 85 - 

 

Appendix 1

Breadboard Layout Examples EE 1205 Bread board layout techniques September 13, 2008 HTR, Jr.

binding post (black)

binding post (red)

R3

R1

1KΩ

R2 33KΩ Figure 1 Resistor network schematic

Figu re 2 Wrong way – off the board with loops

- 86 - 

 

200KΩ

Figure 3 Right way - low to the board and tight

Figure 4 Right way – low to the board and even tighter

- 87 - 

 

Breadboard layout examples HTR, Jr. February, 25, 2009

- 88 - 

 

- 89 - 

 

Appendix 2

Lab Measurement Example Lab Measurement Example 1 R1

R2

A

1

4

10KΩ Vps

3.3KΩ

56KΩ

680Ω

R5

R3

10V R6 B

56KΩ

R4 2

Figure 1 Network schematic

Figure 2 Breadboard layout

- 90 - 

 

51KΩ

3

Table 1 Voltage, current, and power map Element voltage Nodes Element

Specified value

Measured value

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

Element current Nodes

Measured value (V)

+



Calculated value (A)

Table 2 Kirchhoff current law Node

Total current into (Iin) (A)

Total current out of (Iout) (A)

1 2 3 4 A B

- 91 - 

 

KCL (Iin – Iout) (A)

Element power (W)

Table 3 Kirchhoff voltage law Circuit

Total cw voltage drop (Vcw) (V)

Total ccw voltage drop (Vccw) (V)

Vps, R1, R5, R6 R5, R2, R3, R4 Vps, R1, R2, R3, R4, R6

- 92 - 

 

KVL (Vcw – Vccw) (V)

Lab Measurement Example 1

Solutions R1

R2

A

1

4

10KΩ Vps

3.3KΩ

56KΩ

680Ω

R5

R3

10V R6 B

56KΩ

R4 2

Figure 1 Network schematic

Figure 2 Breadboard layout

- 93 - 

 

51KΩ

3

Table 1 Voltage, current, and power map Element voltage Nodes

Element current Nodes

Measured value

+



Measured value (V)

+



Calculated value (A)

Element power (W)

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

Element

Specified value

R1

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%)

- 94 - 

 

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%)

R1

R2

A

1

4

10KΩ Vps

3.3KΩ

R5

56KΩ

R3

680Ω

10V R6 B

56KΩ

R4 2

51KΩ

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%)

- 95 - 

 

3

Appendix 3

Bills of Material Lab 2 BOM

Lab 2 bill of materials (BOM) – resistor values 12Ω 15Ω 27Ω 30Ω 56Ω 62Ω 75Ω 82Ω 91Ω

200Ω 300Ω

1KΩ (3) 1.2KΩ (4) 1.3KΩ (2) 1.5KΩ (2) 1.8KΩ 2KΩ (2) 2.2KΩ (3) 2.7KΩ 3KΩ (2) 3.3KΩ 3.6KΩ 3.9KΩ 5.1KΩ 5.6KΩ 6.2KΩ 7.5KΩ (2) 8.2KΩ (2) 9.1KΩ

10KΩ (2) 15KΩ (4) 20KΩ 22KΩ 30KΩ (3) 47KΩ 75KΩ

Other – 47Ω 4.7KΩ

- 96 - 

 

100KΩ (2) 120KΩ 150KΩ 300KΩ

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

- 97 - 

 

Lab 4 BOM Lab 4 bill of materials (BOM) – resistor values Lab experiment No. 4 resistor list Network N1 1K

Network N2 1K 2K 3K

Network N3 1.2K 2.2K 3.9K 4.7K 9.1K 12K

- 98 - 

 

Network N4 3.3K 4.7K 12K 47K 82K 150K 220K

Lab 5 BOM Lab 5 bill of materials (BOM) – resistor values Lab experiment No. 5 resistor list Network N1 12K 18K 22K 33K 47K 56K 68K

Network N2 8.2K 10K 13K 20K 33K 39K 47K 68K 82K

Network N3 100 (2) 120 1.2K (2) 1.8K 2.4K (2) 2.7K

- 99 - 

 

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 7.5K 15K 30K

Network N5 1K 2.7K 3.9K 4.7K 5.1K 6.8K 8.2K

Thevenin’s equivalent networks: (Same as N4 and N5)

- 100 - 

 

Lab 7 BOM Lab 7 bill of materials (BOM) – component and resistor values Resistors: 100Ω 1KΩ (2) Capacitors: 0.01µF (2)

10KΩ trim pot

NTC thermistor

10µF

Active devices: IC: 555 timer Red LED

NPN BJT: 2N3904 (2) PJFET: J271

Additional: 12V cooling fan

- 101 - 

 

Lab 8 BOM Lab 8 bill of materials (BOM) – component and resistor values Lab 8 Bill of Materials Part

Description

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

- 102 - 

 

Count

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