Manual Circuito 1 Lab

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University of Turabo

Jos Domingo Prez School of Engineering

ELEN 302 Electrical Networks I Laboratory Manual

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Table of Contents

Syllabus

Safety Rules and Operating Procedures

Laboratory Rules and Policies Laboratory Safety Precautions Introduction

Trouble Shooting Hints

Report Evaluation Method and Evaluation Criteria

Experiments

Appendix

Laboratory Topics:

Ohms and Kirchoffs laws; series/parallel circuits 1 session Nodal voltage and mesh current techniques 1 session Function generators and oscilloscopes 1 session Thevenin and Norton equivalent circuits, and the Superposition Principle

1 session

Midterm exam 1 session AC Circuits 1 session RC Circuits 1 session RL Circuits 1 session Desgin and circuit analysis 1 session Maximum Power Transfer 1 session Presentation of project 1 session

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Department of Electrical and Computer Engineering

ELEN 302 Electrical Networks I Laboratory (Required)

Catalog description:

One credit-hour. One three-hour laboratory session per week. Application of the theory learned

in ELEN 301 Electrical Networks I. Characteristics of electrical components and circuits; use of

electronic test equipment.

Co-requisite:

ELEN 301 Electrical Networks I.

Prerequisites: PHSC 206 Physics II with Lab.

Textbook:

Laboratory manual.

Course objectives:

After successful completion of this course the student shall be able to:

Course Objectives

(Performance Criteria)

Applicable

Program

Outcomes*

Material

to be

Assessed

1. Construct basic electrical circuits to measure AC and DC voltages and currents.

A Exam (practical)

2. Compare theoretical with experimental results. B Laboratory Report

3. Use an oscilloscope to measure and compare voltages, period, and phase shift.

K Exam (practical)

4. Use a signal generator to produce input signals for testing electrical circuits.

K Exam (practical)

5. Measure resistance, capacitance, inductance, and frequency.

B Laboratory Report

6. Work as a laboratory team of three students per setup. D Project Presentation

7. Produce written laboratory reports and give oral presentations.

G Project Report

*Relationship of course to program outcomes: A. An Ability to apply knowledge of mathematics, science, and engineering.

B. An ability to design and conduct experiments, as well as to analyze and interpret data.

D. An ability to function on a multidisciplinary team.

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G. An ability to communicate effectively.

K. An ability to use the techniques, skills, and modern engineering tools necessary for engineering

practice.

Topics covered:

1. Resistances, multimeter, and Ohms law. 2. Kirchhoff laws; series/parallel circuits. 3. Nodal voltage and mesh current techniques. 4. Function generators and oscilloscopes. 5. Power measurements in DC and AC circuits. 6. Thevenin and Norton equivalent circuits.

Class schedule:

1 x 3 hr session per week.

Contribution of course to meeting curriculum requirements:

Engineering design: 10%

Engineering science: 90%

Person(s) who prepared this document and date of preparation:

Ms. Jennifer Jimnez, March 2008 and revised by Dr. Jorge Vargas, June 2010

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Safety Rules and Operating Procedures

1. Note the location of the Emergency Disconnect to shut off power in an emergency.

2. Students are allowed in the laboratory only when the Instructor is present.

3. Open drinks and food are not allowed near the working benches.

4. Report any broken or defective parts to the lab Instructor. Do not open, remove the

cover, or attempt to repair any equipment.

5. When the lab is over all the equipment must be turned off. Return everything to its

place of origin. Your lab grade will be affected if your station is not neat when you leave.

6. University property must not be taken from the laboratory.

7. Do not move instruments from one station to another lab station.

8. Do not tamper with or remove security straps, locks or other security devices.

9. ANYONE VIOLATING ANY RULES OR REGULATIONS MAY BE DENIED ACCES TO THESE

FACILITIES.

I have read and understand these procedures. I agree to abide these rules and procedures at all

times while using these facilities. I understand that failure to follow these rules and procedures

will result in my immediate dismissal from the laboratory and additional disciplinary action may

be taken.

_________________________________ __________________

Signature Date Lab section and date

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Laboratory Rules and Policies

1. You will work as a lab team of two per setup. You can share lab results with your partner but not with other groups. Do not copy other groups lab report. Doing so will be considered academic dishonesty.

2. You may submit an individual report or a joint report with your partner. If you decide to submit an individual work, do not include your partners name.

3. Attendance to lab sessions is mandatory. If you miss the lab you must bring a written excuse. Excuses are valid only on medical or emergency cases. In such cases you must make arrangements with the lab instructor to reschedule the missed laboratory session within the next three working days. Otherwise you will be awarded with a zero on the report for the missed experiment. More than three absences will ensure your failure in the course. Arriving thirty minutes late is considered an absence. Arriving five to fifteen minutes late in three different occasions will be considered an absence.

4. Lab reports are due the next lab session. Each day of delay will be punished by subtracting 50 % out of 100%.

5. Students are required to attend all examinations. If a student is absent from an examination for a justifiable reason acceptable to the professor, he or she will be given a special examination. Such excuse must be one of the following:

Medical certificate indicating illness. Legal certificate indicating an appointment to attend a Court of Law. Otherwise, he or she will receive a grade of zero of F in the examination missed. 6. Disabilities: All the reasonable accommodations according to the Americans with

Disability Act (ADA) Law will be coordinated with the Dean of Students and in accordance with the particular needs of the student.

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Laboratory Safety Precautions

1. Do not perform any experiment without the supervision of the lab instructor. Do not deviate from the stated procedure on the lab manual.

2. Check your circuit before energizing (your instructor must check the connections after you).

3. If any device or instrumentation equipment is burning or smells like it, turn off the power supply and DO NOT touch anything, some cables or equipment could be burning. Call the instructor and check the equipment again.

4. Dont be a clown in the lab and dont ever allow yourself to be distracted while performing an experiment.

5. Be careful when moving around your experiment workbench. Always think first what is it you want to do.

6. Prior and after the circuit is energized work always with one hand at a time. A current between two hands crosses your heart and can be more lethal than any other electric shock your body may be subjected to.

7. If you dont know or forget a procedure ASK YOUR INSTRUCTOR. 8. Always check that the power is off while making connections in the circuit. 9. The power should be turned off after completing each individual measurement. 10. Avoid wearing open shoes (such as sandals) that expose your feet to potential

accidents. You will not be allowed to perform the lab if you wear open shoes. 11. Be cautious of rings, watches, and necklaces. Skin beneath a watch or a ring is damp,

lowering the skin resistance. 12. Never touch electrically live equipment without prior knowledge of the voltage

level. Do not work with wet hands. It is imperative that you avoid electrical shock. Never increase the voltage level of the power supply above the level stated on the lab manual. The severity of an electrical shock is a function of the amount of current that flows through the human body. The effects of such levels are illustrated on the following table for a 60Hz (AC voltage) shock.

Current Intensity, 1 sec. Contact Effect

1 milliAmperes Threshold of perception. 5 milliAmperes Accepted as maximum harmless current

intensity

10-20 milliAmperes Let-go current before sustained muscular contraction occurs.

50 milliAmperes Pain. Possible fainting, exhaustion, mechanical injury. Respiratory function continuous.

100-300 milliAmperes Ventricular fibrillation will start, but respiratory center remains intact.

6 Amperes Sustained myocardial contraction. Temporary respiratory paralysis.

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13. If the victim isnt breathing, find someone certified in CPR. Be quick! If the victim is unconscious or needs an ambulance, contact the Department Office for help or call 911. If able, the victim should go to the Students Health Services for examination and treatment.

14. Do not smoke, eat or drink in the vicinity of the lab equipment. 15. Treat the lab equipment kindly. Turn knob and pushbuttons slowly and gently. 16. Return the used equipment to its original place. Work in an orderly manner.

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Introduction

The Electrical Networks I laboratory has the objectives to familiarize the student with the

operation of electronic test equipment such as oscilloscopes, function generators, multimeters,

and also with computer simulators such as Multisim. Another important goal is to apply the

theory learned in ELEN301 Electrical Networks I, re-enforcing theoretical knowledge with

practice, and vice-versa. This is accomplished by building, testing and comparing theoretical

with experimental results on basic AC and DC circuits.

The experiments are organized as follows:

It is crucial that all students come to the lab prepared. The Preparation Part or pre-lab is

mandatory. Most experiments have a computer simulation part. This provides the opportunity

of verifying the experiments without coming to the lab. This will confirm that the theoretical

calculations are correct. However, no simulator can substitute the actual experiment. In the

experimental part the students performs the actual experiments, where he/she obtains hands

on experience on how to correctly connect circuits, and use the various laboratory equipment.

The design part gives the student the opportunity to create a circuit, or freely select

components values to meet some specifications. No experiment is complete with a report. In

the report the student confirms the knowledge gained during the experiment.

Experiments were designed to be one week experiences, but extra time can be allowed if

needed.

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Trouble Shooting Hints

1. Be sure that the power is turned on.

2. Be sure the ground connections are common.

3. Verify that the circuit you built is identical to that in the diagram.

4. Check that the supply voltages are correct.

5. Be sure that the equipment is set up correctly and that you are measuring the correct

parameters.

6. Make sure that the components of your experiment are making contact with the

protoboard and are not loose.

7. If steps 1 through 6 are correct, then you probably have used a component with the

wrong value or one that doesnt work, or the protoboard may have some unwanted

paths between nodes. Check the voltages node by node and make sure you have the

correct signal. If there are differences use your engineering judgment or ask the

Instructor.

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Report Evaluation Method

1. Presentation Clarity and neatness are observed. Use a computer to write the report.

2. Objectives 3. Table of Contents (Should include the name of the student working each part) 4. Summary

Brief description of the contents of the report. It should be a compilation of significant information. Do not write the procedure in this section or theory.

5. Circuit Diagrams and/or Instrument Block Diagram Use black ink or a computer. Do not cut-and- paste from the manual. If no diagram is available, you should draw a block diagram of the instruments used in the experiment.

6. Data/Results Present them in the provided table. If no table is present you should prepare your own tables.

7. Example of Calculations Include only one example of each different type of computation.

8. Discussion of Results Thorough of the analysis of the results obtain in the experiment.

9. Conclusion Use the Discussion of Results to answer what was demonstrated with the experiment.

10. References Books, notes, and other sources. Use the format: Author, Title, (Section), (Place of publishing), Year, Pages.

11. Original data with the Instructors signatures 12. All laboratory reports must be handed in on time. 13. Copy paste from the Internet will be awarded with a zero. 14. Utilize Spelling & Grammar at the end of each work. Grammar errors will affect your

grades.

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Evaluation Criteria:

Lab. Reports (1-9) 40 %

Midterm Exam 25 %

Final Project 25 %

Participation/Attendance 10%

Grading Scale: 90-100 A 80-89 B 70-79 C 60-69 D 0-59 F

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Experiment #1-Ohms and Kirchhoffs laws; series/parallel circuits

Objectives:

1. To investigate Ohm's Law and Kirchhoff's rules using resistors in DC circuits connected in

series and parallel.

2. Use the resistor color code to determine the values of the resistors R1, R2, R3, R4, Rn.

3. To learn how to use a DC Power Supply and a Multimeter.

4. To compare theoretical with experimental values.

Background & Theory:

The Ohm's law states that the current through a conductor between two points is directly

proportional to the potential difference or voltage across the two points, and inversely

proportional to the resistance between them.

The mathematical equation that describes this relationship is:

I=V/R

where V is the potential difference measured across the resistance in units of volts; I is the

current through the resistance in units of amperes and R is the resistance of the conductor in

units of ohms. More specifically, Ohm's law states that the R in this relation is constant,

independent of the current.

Electrical resistance is the capacity of material to impede the flow of current. The circuit

element used to model this behavior is the resistor. The most common resistors are made of

carbon film and a color code exists to identify the resistors values.

The electronic symbol for the resistor is:

Figure 1. The Resistor

R Resistor

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Resistor Color Code

band A is first significant figure of component value

band B is the second significant figure

band C is the decimal multiplier

band D if present, indicates tolerance of value in percent (no color means 20%)

Gold signifies that the tolerance is 5%, so the real resistance could lie anywhere between

4,465 and 4,935 ohms.

Table 1. Resistor Color Code

Color 1st Band 2nd Band Multiplier Tolerance

Black 0 0 1

Brown 1 1 10

Red 2 2 100

Orange 3 3 1K

Yellow 4 4 10K

Green 5 5 100K

Blue 6 6 1M

Violet 7 7 10M

Grey 8 8 1

White 9 9 1

Gold 5%

Silver 10%

Variable Resistors

Variable resistors are elements that change their resistance value due to a physical or

mechanical phenomenon such as thermistors and photoresistors. Variable resistors are

adjustable by changing the position of a contact on the resistive element, such as with a

movable sliding contact, known as a potentiometer.

Symbols of variable resistors:

Figure 2. Variable Resistors

Variable Resistors

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Kirchhoffs Laws

Most of the circuit problems we encounter can be solved by repeatedly applying the rules for

adding resistors in series or parallel, until the problem has been reduced to one of a battery

connected to a single resistor. Sometimes it is to necessary to write equations based on

Kirchhoff's Laws, which are formal mathematical statements of two physical facts:

Kirchhoff's law #1 states that the voltage changes around a closed path in a circuit add up to

zero,

This law is based on the conservation of energy whereby voltage is defined as the energy per

unit charge. The total amount of energy gained per unit charge must equal the amount of

energy lost per unit charge. This seems to be true as the conservation of energy states that

energy cannot be created or destroyed; it can only be transformed from one form to another.

Kirchhoff's law #2 states that the sum of the currents entering any node (i.e., any junction of

wires) equals the sum of the currents leaving that node.

i1 = i2 + i3.

The Multimeter

A typical multimeter may include features such as the ability to measure voltage, current and

resistance. There are two categories of multimeters, analog multimeters and digital

multimeters (often abbreviated DMM or DVOM.). They can be used to troubleshoot electrical

problems in a wide array of industrial and household devices such as batteries, motor controls,

appliances, power supplies, and wiring systems.

To measure voltage two different points from one element should be connected. The polarity

will indicate the current flow direction.

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The most common way to measure current in a circuit is to break the circuit open and insert an

"ammeter" in series (in-line) with the circuit so that all electrons flowing through the circuit also

have to go through the meter. Because measuring current in this manner requires the meter be

made part of the circuit, it is a more difficult type of measurement to make than either voltage

or resistance:

Figure 3. Proper connections for measuring voltage and current.

Series and parallel resistors

Resistors in a parallel configuration each have the same potential difference (voltage). To find

their total equivalent resistance (Req):

The current through resistors in series stays the same, but the voltage across each resistor can

be different. The sum of the potential differences (voltage) is equal to the total voltage. To find

their total resistance:

Preparation(Pre-lab)

1. For the entire experiment resistor values fill out the first three columns of the following

table using the resistor color code discussed in the background and theory. Assume a

tolerance of 5 % for your calculations (gold band). Please remember to include this table

in the lab report.

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Table 1. The Resistor Color Code

Nominal Value ()

Max. value Min. value Measured Value

tolerance % difference

For determining the percent of difference use the following formula:

%difference=

2. Use Ohms and Kirchhoffs laws to calculate the voltage drops in each of the resistors in

circuits 1 through 4. Provide your results in the appropriate table of the Report Sheet.

Equipment and Parts List

DC Power Supply

Digital Multimeter

Resistor values: 560(2), 5.1k (2), 10K(2), 5.6K(2)

Protoboard

Connecting wires

Experiment

1. Construct the following circuit and use the digital multimeter to measure the DC

voltages in R1 and R2, and the DC current. Adjust the DC Power Supply to V= 1V.

R1=R2=560. Please fill out the table provided in the Report Sheet.

Circuit 1. Resistors in series

v

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2. For the following circuit use the digital multimeter to measure the DC voltages in R1 and

R2, and the DC current. Adjust the DC Power Supply to V= 1V. R1=R2=560. Please fill

out the table provided in the Report Sheet.

Circuit 2. Resistors in parallel

3. For the circuit 3. use the digital multimeter to measure the DC voltages in R1, R2,R3, and

R4. Measure the DC current through all the resistors. Adjust the DC Power Supply to V=

1V. R1=R2=5.1k, R3=R4=10k. Please include these values in the appropriate table.

Circuit 3. Resistors in parallel

4. Construct the following circuit and use the digital multimeter to measure the DC

voltages in R1, R2, R3, and R4. Measure the DC current through all the resistors. Adjust

the DC Power Supply to Vs= 10V. R1=R2=5.1k, R3=R4=10k, R5=R6=5.6k. Please

include these values in the appropriate table.

Circuit 4. Series and parallel resistors combination

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Report Sheet: Experiment #1- Ohms and Kirchhoffs laws; series/parallel circuits

Students Names: ____________________,__________________

ID:______________,_______________Instructor:__________________Date:_______________

Instructors Signature:__________________

Table I. Results of calculated values for voltages and currents using ohms and Kirchhoffs laws

Voltages and currents

Circuit 1 Calculated Values




V1

V2

V3

V4

V5

V6

I1

I2

I3

I4

I5

I6

Table II. Results of experimental values for voltages and currents of circuit 1 through 4.


Circuit 1 Measured Values



Circut4 Measured Values

V1

V2

V3

V4

V5

V6

I1

I2

I3

I4

I5

I6

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Table III. Percent Difference of voltages and currents of circuits 1 through 4.


%Difference Circuit 1




V1

V2

V3

V4

V5

V6

I1

I2

I3

I4

I5

I6

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Experiment #2-Nodal Voltage and Mesh Current Techniques

Objectives:

1. To construct a planar circuit having two voltage sources and five resistors. 2. To study node voltages and mesh currents. 3. To compare calculated and measured results using both nodal and mesh analyses.

Background & Theory:

In this laboratory we work with two powerful techniques of circuit analysis that aid in the

analysis of complex circuit structures: the Node Voltage Method (N-V) and the Mesh Current

Method (M-C). These techniques give us two systematic methods of describing circuits with the

minimum number of simultaneous equations.

We must define several basic terms for describing circuits:

Name Definition

Node A point where two or more circuit elements join

Essential Node A node where three or more circuit elements join

Path A trace of adjoining circuit elements with no elements included more than once

Branch A path that connects two nodes

Essential Branch A path which connects two essential nodes without passing through an essential node

Loop A path whose last node is the same as the starting node

Mesh A loop that does not enclose any other loops

Planar Circuit A circuit that can be drawn in a plane with no crossing branches

SUMMARY OF NODE VOLTAGE (N-V) METHOD

1. Number of equations needed is one less than the number of essential nodes, except as noted

in item 7 below.

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2. Select one of the essential nodes as a reference node (the node with the most branches

usually is a good choice).

3. Then assign node voltages at the other essential nodes. By definition, node voltages are a

"rise" above ref. node.

4. Next, generate N-V equations by summing currents at each non-reference node (using KCL).

Currents are to be considered leaving the node, unless a current source exists in the branch

(then you use the direction of the arrow for determining the sign).

5. If a voltage source exists in the branch, subtract or add its voltage (depending on polarity) to

the node voltage before dividing by the resistance in the branch.

6. When a dependent source exists, you must express the controlling voltage or current in

terms of the assigned node voltages.

7. If a voltage source is connected directly between an essential node and the ref. node, that

reduces the number of equations needed.

8. If a voltage source (independent or dependent) exists between two non-reference nodes,

then you can use the supernode concept, and proceed as in 4. above to write the equations.

Note that the voltage existing in the supernode must be expressed as a function of the node

voltages to obtain one equation.

SUMMARY OF MESH CURRENT (M-C) METHOD

1. Number of equations needed is equal to the number of meshes (windows) in the network,

except as noted in 7 below.

2. The M-C method is used for planar networks only, where the network is drawn with no

crossing branches.

3. Assign clockwise mesh current in each mesh. A mesh current exists only in the perimeter of a

mesh. In some parts of the mesh, the mesh current may be the same as the branch current.

4. Next, generate M-C equations by summing voltages around each mesh (using KVL). Voltages

are to be considered positive unless a voltage source exists in the mesh (then you use the

polarity of the voltage to determine the sign). Where two meshes have a common branch, a net

current (one mesh current minus the other) must be used to express voltage in that branch.

5. When a dependent source exists, you must express the controlling voltage or current in

terms of the assigned mesh currents.

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6. If a current source (independent or dependent) is common to two meshes, then you can use

the supermesh concept, and proceed as in 4. above to write the equations.

Note that the "common" current source must be expressed as a function of the mesh currents

to obtain one equation.

7. If a current source exists in the outer perimeter of the circuit, KVL need not be applied to that

mesh (because that mesh current has to be equal to the current in that source).

NOTE: The primary advantage of both the N-V and M-C methods is that you can analyze a

circuit (which has many unknowns) with a fewer number of simultaneous equations.

However - WHEN IS N-V METHOD USED INSTEAD OF M-C METHOD? - AND VICE VERSA

1. One approach: Use the one which requires the fewest number of simultaneous equations.

2. Look at location of v-sources and i-sources. The analysis may be simplified if v-sources exist

between essential nodes and reference you might select, or if i-sources exist in the outer

perimeter of meshes.

3. If a certain voltage is of primary interest, then the N-V method will probably be the best, or if

your primary interest in a certain current, then the M-C method will probably be the best

choice.

4. The N-V method can be applied to any circuit, whereas the M-C method requires that the

circuit have a planar network.

5. When you have more v-sources than i-sources, the best selection will probably be the N-V

method.

6. When you have more i-sources, the best selection will probably be the M-C method.

Equipment and Parts List:

DC Power Supply.

Digital Multimeter

Resistors one each: 1.5 k, 2.2 k, 4.7 k, 5.6 k, and 6.8 k.

Connecting wires

Protoboard

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Experiment

1.Construct the circuit shown in Figure 1 using available power supply, resistors, breadboard, and

connecting wires provided. R1 = 2.2 k, R2 = 4.7 k, R3 = 6.8 k, R4 = 5.6 k, R5 = 1.5 k.

Figure 1

2. Set VS1 = 18 V and VS2 = -18 V. Note that while VS1 and VS2 have the same magnitude, VS1

is positive and is connected to Node 1 and VS2 is negative and connected to Node 4.

3. Note that the reference node, nodal voltages (V1, V2, V3, & V4) and mesh currents (I1, I2, &

I3) have already been designated.

4. Measure all nodal voltages (not Branch voltages) and the mesh not branch (ia & ib) currents.

5. Don't forget to measure all the resistor values.

COMPARISONS AND QUESTIONS:

1. From your measured mesh currents, calculate the value of the branch currents ia and ib

shown in Figure 1.

2. By observation, what are the values of V1 and V4? With the given values of VS1 and VS2.

3. Node Equations:

a. Set up the nodal equations for the circuit, and solve for V2 and V3, using nominal values of

resistances and nominal voltage sources. Show all your calculations in your laboratory

notebook.

b. Compare all measured node voltages with the calculated values.

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c. Repeat a & b using the measured values of resistances and measured values of the source

voltages. You may use a computer or calculator to solve the equations.

4. Mesh Equations:

a. Set up the mesh equations for the circuit, and solve for the three mesh currents, using

nominal values of resistances and the nominal voltage sources. Show your calculations in your

laboratory notebook.

b. Compare all measured mesh currents with the calculated values.

c. Repeat a & b using the measured values of resistance and measured values of the source

voltages. You may use a computer or calculator to solve the equations.

5. Calculate the percent difference between calculated and measured values. Please include the

results in the appropriate table.

6. Calculate the power absorbed by resistors R2 and R4. For each resistor calculate power by

using three different methods: P=VI, P=I2R, P=V2/R. Use measured resistances, measured node

voltages, and the branch currents calculated from the measured mesh currents. Fill out the

provided table below. Explain any differences in the power obtained by the three methods. Are

the differences small enough to be explained by the specified meter errors? Justify your

answers.

CONCLUSIONS:

Based on your experimental observations. (What laws and principles have been verified by this

experiment?)

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Report Sheet: Experiment #2- Nodal Voltage and Mesh Current Techniques

Students Names:____________________,__________________

ID:______________,_______________Instructor:_________________Date:________________


Table I. Results

Voltages and Currents

Calculated Values Experimental Values

V1

V2

V3

V4

I1

I2

I3

ia

ib Table II. Percent Difference between calculated and experimental values.

Voltages and Currents

% difference

V1

V2

V3

V4

I1

I2

I3

ia

ib Table III. Power Calculations

Resistors Power (P=VI)

R1

R2

R3

R4

R5

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Experiment #3-Function Generators and Oscilloscopes

Objectives

1. To learn how to use a Function Generator.

2. To learn how to use an oscilloscope.

3. The student will also verify the concept of voltage division through measurements.

Background and Theory

Function Generators

A function generator is a type of electronic test equipment or software used to generate

electrical repetitive waveforms. A signal generator delivers a choice of a number of different

waveforms, with provisions for varying the frequency over a wide range.

Sine, square, triangle, and sawtooth waveforms Function Generator Control Buttons Some of the most common used buttons in the lab experiments are described below:

1. SWEEP Button. Activates the internal sweep generator, which produces a signal that traverses a range of frequencies. This button enables the SWEEP RATE and SWEEP WIDTH knobs.

2. SWEEP RATE Knob. Adjusts how often the frequency sweep reiterates-the rate at which the signal traverses the frequencies. If you pull this button out, the sweep will stop and you can adjust the sweep stop frequency with the SWEEP WIDTH knob.

3. GATE SEL Button. Selects the gate time. If the gate time is too slow for the incoming signal, the OVERRANGE LED lights.

4. ATTN Button. Selects between two levels of input signals for the EXT COUNTER INPUT. When you push the button in, the CFG280 Function Generator attenuates the incoming signal by a factor of ten (the Peak-to-peak input level must be between 3 V and 42V).

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When you push the button out, the function generator does not attenuate the input signal (the peak-to-peak input level must be between 50 mV and 5 V).

5. SOURCE Button. Selects between internal and external counter input. When you push the button in, the counter readout displays the signal frequency count from the EXT COUNTER INPUT. When you push the button out the counter readout displays the frequency count of the signal being generated by the CFG280 Function Generator.

6. AMPLITUDE Knob. Adjusts the voltage within the presently selected range. This control is used with the MAIN control to set the voltage level of the MAIN OUT signal.

7. DC OFFSET Knob. Sets the DC level (and therefore the polarity) of the MAIN OUT signal. This knob has no effect until you pull it out.

8. SWEEP WIDTH Knob. Adjusts the range of frequencies that are traversed by each sweep.

9. SWEEP OUT BNC. This connector sends sweep signals that you can adjust with the sweep controls. You can use a sweep signal to synchronize an external device such as an oscilloscope.

10. MAIN OUT BNC. This connector sends sine, triangle, square, and positive and negative pulse/ramp signals.

11. SYNC OUT BNC. This connector sends TTL trigger signals. Amplitude and DC offset adjustments do not affect TTL trigger output.

12. EXT COUNTER INPUT BNC. This connector can accept external signals with frequencies between 1 Hz and 100 MHz.

13. FREQ FINE ADJ knob. Allows small adjustments in output frequency. 14. FREQUENCY Dial. Determines the frequency of the function generator output, within

the range set by the MULTIPLIER buttons. 15. POWER switch. Toggles instrument power on and off.

Oscillospes An oscilloscope is a type of electronic test instrument that allows signal voltages to be viewed, usually as a two-dimensional graph of one or more electrical potential differences (vertical axis) plotted as a function of time or of some other voltage (horizontal axis). In most instances, oscilloscopes show events that repeat with either no change, or slow changes. The oscilloscope is one of the most versatile and widely-used electronic instruments. The Oscilloscope control buttons and how the instrument works is described in the Appendix.


Function Generator

Oscilloscope

DC Power supply

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Digital Multimeter

Connecting wires

Resistors: 10K(2), 5K(2)

Experiment

I-Function Verification with the Oscilloscope

1. Connect the function generator output directly to one of the inputs of the oscilloscope.

2. Select a 10 Hz square wave as output on the function generator with a 2 Volt Peak-to-

Peak amplitude.

3. Use your cursors to display the period and peak-to-peak voltage on the oscilloscope.

Save a screenshot (a picture, e.g. jpg is recommended) showing these measurements

and include it in your lab report.

Figure 1: Voltage Division Circuit

II- Verification of Voltage Division with a DC Voltage Source

The circuit that will be used to verify voltage division is shown in Figure 1.

1. Turn on the DC power supply and measure the output with the Digital Multimeter

(DMM).

2. Adjust the output until the DMM reads 5 Voltsthis will correspond to VS in Figure 1.

3. Select 10 k resistors for R1 and R2 and measure them each using the DMM. Record

these values in Tables 1 and 2.

30

4. Use the equation for voltage division to calculate the theoretical voltages across the two

resistors and record these values in Table 1.

5. Next, use the DMM to measure the actual voltages across R1 and R2 and record these

values in Table 2. Replace R2 with a 5 k resistor, repeat the process and record your

values in the bottom row of Tables 1 and 2.

III-Voltage Division with a Waveform Voltage Source

1. Set the function generator to output a 20 Hz sine wave with a 10 Volt Peak-to-Peak

amplitude. Verify these characteristics on the oscilloscope.

2. Using the same resistor values as before, replace the DC power supply with the function

generator in Figure 1 (VS).

3. Use a set of clamps to measure the VS waveform on Channel 1 of the oscilloscope. Use

another set of clamps to measure the VR2 voltage waveform on Channel 2. In addition to

these two channels, use the math function to display the VR1 voltage waveform.

4. For each of the two same resistor combinations, measure the frequency and peak-to-

peak amplitudes of each waveform, display them on the oscilloscope, and take a

screenshot of them, draw in graph paper or take a picture. Include these screenshots in

your lab report and record the measurements in Table 3.

Conclusions

This concludes Lab 3. If time permits, you are encouraged to explore other settings on the

oscilloscope and function generator. Please return all components to their appropriate places.

1. Explain any functions of the oscilloscope that were found easy or difficult.

2. Explain whether the voltage division equation was verified by your results. Did the equation

hold true with a DC voltage source? With a waveform voltage source? What are some reasons

for any differences between the theoretical and measured values?

3. How do the equations for voltage division and current division differ?

4. Why is it useful to know the voltage division equation when we already have the other

equations necessary to determine each of the voltages? (i.e. Ohms law, Kirchhoffs Voltage

Law, and the fact that elements in series have the same current)

31

Report Sheet: Experiment #3- Function Generator and Oscilloscopes

Students Names:____________________,__________________



Table 1: Theoretical Calculations DC Voltage Source

VS (Volts) R1 (k ) R2 (k ) VR1 (Volts) VR2 (Volts)

5.00

5.00

Table 2: Measured Values (DC Voltage Source)

VS (Volts) R1 (k ) R2 (k ) VR1 (Volts) VR2 (Volts)

5.00

5.00

Table 3: Measured Values (Waveform Voltage Source)

VS (Vpp) R1 (k ) R2 (k ) VR1 (Vpp) VR2 (Vpp)

10.00

10.00

32

Experiment #4- Thevenin and Norton Equivalent Circuits

Objectives

1. Experimentally determine the Thevenin and Norton equivalent circuits by measuring the

open circuit voltage and short circuit currents of the test circuits.

2. Use the principle of superposition along with Thenvenin's and Norton's theorems to

reduce complex circuits to simple voltage and current source models.

3. Compute the theoretical equivalents and compare them to the experimental

equivalents.

4. Develop circuit construction skills. Develop dc circuit voltage and current measurement

skills.

5. Experimentally apply the principle of superposition in the laboratory.


Thevenins Theorem

Thevenin's Theorem states that it is possible to simplify any linear circuit, no matter how

complex, to an equivalent circuit with just a single voltage source and series resistance

connected to a load. The qualification of linear is identical to that found in the Superposition

Theorem, where all the underlying equations must be linear (no exponents or roots). If we're

dealing with passive components (such as resistors, and later, inductors and capacitors), this is

true.

Thevenin's Theorem is especially useful in analyzing power systems and other circuits where

one particular resistor in the circuit (called the load resistor) is subject to change, and re-

calculation of the circuit is necessary with each trial value of load resistance, to determine

voltage across it and current through it.

Any linear one-port network can be replaced with a single voltage source in series with a

single resistor (see Fig. 1 below). The voltage source is called the Thevenin equivalent voltage,

and the resistor is called the Thevenin equivalent resistance. This means that the single voltage

source and series resistor must behave identically to the actual network it is replacing.

You can use Thevenins theorem to solve a complex DC circuit.

33

Figure 1- A network replaced with its Thevenin equivalent circuit

The steps used for implementing Thevenins Theorem are listed below:

Step 1

Remove the resistor, R through which you wish to calculate the current or across which you

want to know the voltage. Label these terminals (where the resistor was removed) a and b.

Calculate the voltage that appears across these open terminals. This is called the open circuit

voltage or the Thevenin equivalent voltage, VTH.

Figure 2

Consider the example shown in Fig. 2. Use the voltage source, V1, and the voltage dividing

network made up of R4, R3 and R2. Here resistor R2 does not influence the voltage that

appears across the a and b terminals. This is because no current is drawn through R2 when

measuring the voltage across the a and b terminals. This leaves only R3 and R4. What is left

looks remarkably like a series circuit. From Kirchhoffs laws we know that the series circuit will

divide V1 as given in Eq. 1.

34

(1)

Step 2

From the open terminals, (a and b) calculate the resistance looking back from the open

terminals into the network. Each voltage source must be replaced by a resistor equal to the

internal resistance of the voltage source before the Thevenin resistance is evaluated. If RInternal =

0, then replace the voltage source with a zero ohm resistor (short). This resistance is RTH.

Figure 3

Let us consider the example shown in Fig. 3. After the sources are removed we can find the

resistance looking back from the open terminals of the network by measuring the resistance

with an ohmmeter connected to terminals a and b. This is just like an equivalent resistance as

we saw in the Kirchhoff lab. We can also calculate this resistance. It is easiest to calculate the

equivalent resistance starting from the left side of the network shown in Fig. 3. We can see that

R3 is in parallel with R4. Remember that the resistance of 2 resistors in parallel is:

(2)

This parallel resistance is in series with R2. This gives us a Thevenin resistance of:

(3)

Now we have the components we need to create the Thevenin equivalent circuit shown in Fig.

1. Next the load resistor is replaced and we can write the equations for the current and voltage

this resistor is exposed to. Fig. 4 shows the Thevenin equivalent circuit with the load resistor, R,

replaced.

35

Figure 4

Step 3

From the Kirchhoff lab we know the current through R is:

(4)

and the voltage across R is:

(5)

VTH is the Thevenin equivalent voltage obtained in Step 1, RTH is the Thevenin

equivalent resistance obtained in Step 2, and R is the load resistor removed in Step 1.

Nortons Theorem

Norton's Theorem states that it is possible to simplify any linear circuit, no matter how

complex, to an equivalent circuit with just a single current source and parallel resistance

connected to a load. Just as with Thevenin's Theorem, the qualification of linear is identical to

that found in the Superposition Theorem: all underlying equations must be linear (no

exponents or roots).The Norton equivalent is used to represent any network of linear sources

and impedances, at a given frequency.

Norton's theorem is an extension of Thvenin's theorem. To find RN follow the steps as for

Thevenins resistance. The current source value is found by Then, to find the Norton current

(for the current source in the Norton equivalent circuit), place a direct wire (short) connection

between the load points and determine the resultant current. Note that this step is exactly

opposite the respective step in Thevenin's Theorem, where we replaced the load resistor with a

break (open circuit).

RTH= RN

36

Figure 5- Norton Equivalent Circuit


DC Power Supply

Digital Multimeter

Resistors: 10K, 4.7K, 6.8K, 8.2K, 15K

Experiment

1. Construct the circuit shown in Figure 1 and measure the voltage, Vab, across the 10

k resistor. Record the value of Vab for future use in Table 1. Use a dc power supply

for the battery

Figure 1. Test Circuit for Part 1 of the Experiment.

2. Remove the 10 k resistor from the circuit in Figure 1 and measure the Thevenin's

open circuit voltage, Voc, for the remaining circuit. Figure 2 shows the circuit used to

make the open circuit voltage measurements.

37

Figure 2. Circuit Connections for Measuring Thevenin's Open Circuit Voltage.

3. Connect an ammeter between the points a and b as shown in Figure 3 and measure

the short circuit current, Isc. Record the value in Table 1 for future use. Note the

positive direction of current flow.

Figure 3. Short Circuit Current Measurement.

4. From the measurements made in parts 2 and 3, calculate the Thevenin's equivalent

resistance for the circuit. This is numerically equal to the Norton's equivalent

resistance. Use the formula below to find these values. RTH=RN=Voc/Isc

where: RTH = the Thevenin's equivalent resistance

RN = the Norton's equivalent resistance.

Record these values in Table 1.

38

5. Calculate the theoretical values of RTH, RN, Voc, and Isc for the circuit above. Record

the computed values in Table 1.

6. Using the Thevenin's equivalent circuit, compute the value of Vab with the 10 k

resistor attached to points a-b.

7. Using the Norton's equivalent circuit, compute the value of Vab with the 10 k


8. Construct the circuit show in Figure 4 and measure the voltage across points a and b.

Record this value in Table 2 for later use. Use dc power supplies for the batteries.

Figure 4. Circuit 2 Showing the Voltage Vab.

9. Use the principle of superposition to find the value of Vab in Figure 4. To practically

use superposition in the lab, sequentially disconnect each dc power supply from the

circuit and replace them with short circuits in turn. DO NOT SHORT ACROSS THE

TERMINALS OF THE POWER SUPPLY. Find the value of Vab due solely to the 5 Vdc

source and record the value in Table 2. Find the value of Vab due solely to the 15

Vdc source and record the value in Table 2. Add these two measurements to find the

total response and record it in Table 2.

10. Remove the 8.2 K resistor and measure the Thevenin's open circuit voltage

11. Add a 10 ohm resistor and an ammeter between points a-b to measure, Isc. Figure 5

shows this circuit. Record this reading in Table 2.

39

Figure 5. Circuit 2 Short Circuit Measurement Setup.

12. Repeat steps 4 and 5 above for this circuit. Record the values in Table 2.

13. Using the Thevenin's equivalent circuit, compute the value of Vab with the 8.2 k


14. Using the Norton's equivalent circuit, compute the value of Vab with the 8.2 k


Report:

1. Follow the standard laboratory report procedures and format.

2. Compute the theoretical values for all of the measured superposition values. Include

drawings of the Thevenin and Norton equivalent circuits with all values labeled.

3. Compare the theoretical values to the measured values by computing the percentage error

between the theoretical and measured values. Use the formula below to compute the

percentage error.

%error=

40

Report Sheet: Experiment #4- Thevenin and Norton Equivalent Circuits

Students Names:____________________,__________________


Instructors signature:__________________

Table 1- Figure 1

Quantity Measured Value Theoretical Value

Vab(V)

Voc(V)

Isc(mA)

RTH(K)

Vab(Thevenin)

Vab(Norton)

Table 2-Figure 4

Quantity Measured Value Theoretical Value V

ab (V)

Vab

(V) 5Vdc Source

Vab

(V) 15Vdc Source

Vab

(V) +15Vdc Source

Voc

(V)

Isc

(mA)

RTH

(k)

RN

(k)

Vab

(Thevenin)

Vab

(Norton)

*Create table 3 for percentage error in figure 1 and table 4 for percentage error in figure 4

41

Experiment#5-AC Circuits

Objectives

1. To study the measurements that can be done on signals with specific waveforms such as

sinusoidal and square waves.


Properties of electrical signals

An electrical signal is a voltage or current which conveys information. The voltage-time graph

below shows various properties of an electrical signal.

In addition to the properties labeled on the graph, there is frequency (f) which is the number of

cycles per second.

The frequency is measured in hertz Hz and the relationship with period is as follows:

f=1/T Hz=1/sec.

Figure 1-Sine wave

The diagram shows a sine wave but these properties apply to any signal with a constant shape.

Amplitude is the maximum voltage reached by the signal. It is measured in volts, V.

Peak voltage is another name for amplitude.

Peak-peak voltage is twice the peak voltage (amplitude). When reading an oscilloscope trace it

is usual to measure peak-peak voltage.

Time period is the time taken for the signal to complete one cycle.

It is measured in seconds (s), but time periods tend to be short so milliseconds (ms) and

microseconds (s) are often used. 1ms = 0.001s and 1s = 0.000001s.

Frequency is the number of cycles per second.

42

It is measured in hertz (Hz), but frequencies tend to be high so kilohertz (kHz) and megahertz

(MHz) are often used. 1kHz = 1000Hz and 1MHz = 1000000Hz.

Root Mean Square (RMS) Values

The value of an AC voltage is continually changing from zero up to the positive peak, through

zero to the negative peak and back to zero again. Clearly for most of the time it is less than the

peak voltage, so this is not a good measure of its real effect.

Instead we use the root mean square voltage (VRMS) which is 0.7 of the peak voltage (Vpeak):

VRMS = 0.7 Vpeak and Vpeak = 1.4 VRMS

These equations also apply to current.

Figure 2- Peak and RMS Voltages

They are only true for sine waves (the most common type of AC) because the 0.7 and 1.4 are

different values for other shapes.

The RMS value is the effective value of a varying voltage or current. It is the equivalent steady

DC (constant) value which gives the same effect.

For example a lamp connected to a 6V RMS AC supply will light with the same brightness when

connected to a steady 6V DC supply. However, the lamp will be dimmer if connected to a 6V

peak AC supply because the RMS value of this is only 4.2V (it is equivalent to a steady 4.2V DC).

Phase

The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an

offset in the displacement from a specified reference point at time t = 0. is sometimes

referred to as a phase-shift, because it represents a "shift" from zero phase. But a change in is

also referred to as a phase-shift.

For infinitely long sinusoids, a change in is the same as a shift in time, such as a time-delay.

Two waves that have the same frequency and different phases have a phase difference, and the

oscillators are said to be out of phase with each other. The amount by which such oscillators

43

are out of step with each other can be expressed in degrees from 0 to 360, or in radians from

0 to 2.

The horizontal control section may have an XY mode that lets you display an input signal rather

than the time base on the horizontal axis. (On some digital oscilloscopes this is a display mode

setting.) This mode of operation opens up a whole new area of phase shift measurement

techniques.

The phase of a wave is the amount of time that passes from the beginning of a cycle to the

beginning of the next cycle, measured in degrees. Phase shift describes the difference in timing

between two otherwise identical periodic signals.

Figure 3- Phase Shift

Preparation (Pre-lab)

1. What do AC meters show, is it the RMS or peak voltage?


Power Supply

Function Generator

Digital Multimeter

Oscilloscope

Protoboard

Resistor: 100

Capacitor: 1F

44

Experiment

I-Peak and RMS Voltages

1. Adjust the Function Generator to provide a sinusoidal signal of 1 volts and a frequency

of 1KHz.

2. With the digital multimeter measure the function generator output voltage. Include the

result in Table 1.

3. Connect the oscilloscope and graph the signal.

4. Measure the peak voltage from the oscilloscope image. Include this value in the

appropriate table.

5. Compare the multimeter vs. oscilloscope values. Divide the peak value of the peak

value(oscilloscope value) are they the same?

6. Repeat the process for a square waveform.

II-Time

1. Adjust the function generator to provide a sinusoidal signal of 5Vp and a frequency of

10kHz.

2. Adjust the oscilloscope to obtain one period in the screen. Include the value of the

period in Table 2.

3. From the period value determine the frequency and compare it to the expected value of

10 KHz.

4. Adjust the function generator to provide a sinusoidal signal of 5Vp and a frequency of

5kHz.

5. Connect the oscilloscope and adjust the TIME/DIV button in the 0.2ms scale.

6. Determine the number of signals in one second (5 divisions). This is the frequency value.

Include the result in the appropriate table.

III-Phase

1. Construct the following circuit with C=1F and R=100.

45

2. Adjust the function generator to provide a sinusoidal signal of 5 Vp and 1KHz.

3. Connect the input to channel A and the output to channel B of the oscilloscope.

4. Make the proper adjustments to measure the phase shift. Include the results in your

report.

Report Sheet: Experiment #5- AC Circuits

Students Names:____________________,__________________



Graph 1 :Sinusoidal wave

Part I-Peak and RMS Voltages

Table1

VRMS(multimeter value)

VPEAK(oscilloscope value)

VPEAK/ (VRMS)

46

Graph 2 : Square wave

Part II-Time

Table 2

Period

Calculated frequency

Number of signal in five divisions

47

Experiment #6- RC Circuits

Objectives

1. In this lab you will determine the input-output characteristics of an RC filter

2. Use Multisim to simulate the RC filter behavior.


Resistance-Capacitance Circuits

Theory (see textbook) shows that for a capacitor, C, charging through a resistor, R, the voltage

across the capacitor, V, varies with time according to:

V(t) = Vo (1 et/RC), (1)

where Vo is the final, equilibrium voltage.

When the same capacitor discharges through the same resistor,

V(t) = Voet/RC (2)

The product of the resistance and capacitance, RC, governs the time scale with which the

changes take place. For this reason it is called the time constant, which we call (tau). It can be

found indirectly by measuring the time required for the voltage to fall to Vo /2 (see Figure 1

below). This time interval is called the half-life, T1/2, and is given by the equation T1/2 = (ln2), so

= T1/2 /ln2 = T1/2 /(0.693) (3)

Figure 1-Discharge of a Capacitor

RC Filter Characteristics

Figure 1 below shows an RC filter connected to a sinusoidal voltage source. This circuit is

termed a two-port circuit (Fig. 2) where the voltage source produces the input voltage Vin and

the output voltage Vout appears across resistor R.

48

Recall that we customarily represent an AC voltage as a periodic function of time, such as

V(t) = V0cos(t)

where V0 is the amplitude of the voltage, t is time, and is the angular frequency, whose units are radians per second. The angular frequency is related to frequency, f, measured in Hertz, by = 2f. For example, if the frequency, f, of the ordinary power line voltage in the U.S. is 60 Hz, then the associated angular frequency, , is 377 radians/s (260).

Transfer Function

A two-port circuit is characterized by its transfer function, whose magnitude is defined as |Vout/Vin|, where Vout and Vin are phasor voltages. The variation of the transfer function with frequency characterizes the circuit, whether the circuit is an amplifier (does it amplify high frequencies more than low frequencies?) or a filter (does the filter pass the low frequencies or the high frequencies better?). If you analyze the RC circuit of

Fig. 1 Using Kirchhoffs voltage law, the phasor voltages Vout and Vin, the resistance R and the impedance of the capacitor ZC = 1/jC, you can show that the magnitude of the transfer function is

An approximate log-log plot of transfer function magnitude vs. frequency is shown in Figure 3.

The filter characteristic has been simplified to appear as two lines that intersect at the angular

frequency for which RC = 1, or = 1, where is the time constant RC for this circuit. If

plotted precisely, the characteristic would transition smoothly from the upward sloping line to

the horizontal line, but for many purposes the two-straight-line approximation is adequate. This

circuit is called a high-pass filter, since for frequencies above = 1/RC the output voltage

equals the input voltage.

49

Figure 3: Log-log plot of transfer function magnitude vs. angular frequency times RC, for the

circuit of Fig. 1.

If we reverse the positions of R and C in the filter circuit (Figure 4), we obtain the transfer

function:

This transfer function results in a low-pass filter, as frequencies below = 1/RC yield an output

voltage that has an amplitude equal to the input voltage (Fig. 5).

Figure 4: Circuit with a series resistor R and the capacitor C as the output element.

Figure 5: Log-log plot of transfer function magnitude vs. angular frequency times RC for the

circuit of Fig. 4.


1. Use Multisim to simulate the RC filter behavior. For the filter values use the same as

part 1 of the experiment.

50

2. Plot the amplitude of the voltage across the resistor.

3. Plot the phase of the voltage across the resistor. Use the input signal as a reference (Vin

has a phase of zero degrees).

4. Repeat Step 1 using a square wave input. Vary the frequency and observe the effects of

the filter circuit on the output at f = 100 Hz, 1 kHz, and 10 kHz of the square wave input

and the output.


Function Generator

Oscilloscope

Connecting Wires

Capacitor: 0.1F

Resistor: 10k

Experiment

Determining RC Filter Characteristics

In this part of the experiment, you will make measurements to observe the filtering effects of

an RC circuit.

1. Connect a 10-k resistor and a (non-polarized) 0.1 F capacitor in series with the signal

generator, making sure that your oscilloscope ground and the signal generator ground are

connected together (see Fig. 1 for the circuit configuration). Set the signal generator to output a

2 V peak to peak sine wave. Frequency varies at f = 100 Hz, 1 kHz, and 10 kHz

2. Determine the time constant . Include this value in the lab report.

3. Repeat Step 1 using a square wave input. Vary the frequency and observe the effects of the

filter circuit on the output.

51

Report Sheet: Experiment #6- RC Circuits

Students Names:____________________,__________________



Please include your plots from Multisim.

Table 1:

Time constant Experimental Theoretical

52

Experiment #7-RL Circuits

Objectives


Resistance-Inductance Circuits

In this part we conduct a similar study of a circuit containing a resistor and an inductor, L. First

consider the circuit shown in Figure 1, below. If we start with the battery connected to the LR

circuit, after a long time the current reaches a steady-state value, io = Vo/R .

Figure 1. A model circuit with an inductor and resistor

If we call t = 0 the time when we suddenly throw the switch to remove the battery, allowing

current to flow to ground. The current changes with time according to the equation:

i(t) = ioe(R/L)t (1)

If at a new t = 0 we throw the switch so the battery is connected, the current increases

according to the equation:

i(t) = io(1 e(R/L)t) (2)

The time constant for both equations is L/R and

LR= =T1/2/0.693 (3)

We can find the current by measuring the voltage across the resistor and using

the relationship i= V/R.


An ideal inductor has no DC resistance. A practical inductor is made of a wire wrapped around a

ferromagnetic core. The resistance of this wire may have to be taken into account in some

applications. A practical inductor can be modeled as an ideal inductor in series with a resistor.

Consider the low-pass RL filter shown below (infinite load resistance) with Ri denoting the

resistance of the practical inductor.

53

Circuit Analysis: a) Derive the expression for H(j) and calculate the magnitude and phase of the transfer function and the cut-off frequency. b) Show that for Ri R, this circuit acts like a RL filter with an ideal inductor? Multisim: Use Multisim to simulate this circuit and obtain the frequency response of the filter for L = 10 mH, Ri = 10 , and R = 1 k (Hint: You can ignore Ri based on the circuit analysis results above). Attach the Bode plots (both magnitude and phase) to your report. From the Bode plots, find the cut-off frequency of the filter and compare with your circuit analysis results.


Function Generator

Oscilloscope

Connecting Wires

Resistor: 10, 1k

Inductor: 10mH

Experiment

1. First measure and record the inductance and the resistance of the 10-mH inductor. Does the measurement of inductor inductance match its spec (10 mH 20%)?

2. Build the circuit. Attach the function generator to the input. Attach Scope channel A to input and Scope channel B to the output. Set the input to a sinusoidal wave with an amplitude of 5 V (and no DC offset).

3. Vary the frequency and at the each frequency measure the output voltage and the phase shift between input and output.

4. Determine the value of the time constant experimentally and theoretically. Include these values in your lab report.

54

5. Find the cut-off frequency of the filter and compare with your simulation and calculations. Write down your observations from this set of experiments and calculations.

Report Sheet: Experiment #7- RL Circuits

Students Names:____________________,__________________



Please include your plots from Multisim.

Table 1:

Time constant Experimental Theoretical

Cutoff frequency

55

Experiment #8- Design and Circuit Analysis

Objectives

1. Design and Circuit Analysis: In this exercise, we will design, built and experiment with a band-pass filter made of a high-pass and a low-pass RC filter (See circuit below).


A band-pass filter is a device that passes frequencies within a certain range and attenuates

frequencies outside that range. The bandwidth of the filter is simply the difference between the

upper and lower cutoff frequencies. An ideal bandpass filter would have a completely flat

passband (e.g. with no gain/attenuation throughout) and would completely attenuate all

frequencies outside the passband. Additionally, the transition out of the passband would be

instantaneous in frequency. In practice, no bandpass filter is ideal. The filter does not attenuate

all frequencies outside the desired frequency range. (See the graph below)

Figure 1- Band Pass Filter


Band pass filter

1. Design parameters: This circuit should drive a load 100 k, and have lower and upper cut-off frequencies of 250 Hz and 25 kHz, respectively. We also want this filter to have the highest input impedance that we can manage. Find the appropriate values of

56

resistors and capacitors. Use commercially available resistor and capacitors. Please check the capacitors that are available in the Lab. Commerical resistor values are 1, 1.1, 1.2, 1.3, 1.5, 1.6, 1.8, 2, 2.2, 2.4, 2.7, 3., 3.3, 3.6, 3.9, 4.3, 4.7, 5.1, 5.6, 6.2, 6.8, 7.5, 8.2, 9.1 (x 10n where n is an integer).

2. Multisim Simulation: Use Multisim to simulate the frequency response of the circuit you have designed. Attach the Bode Plots to your report. From the Bode plots find the center and lower and upper cut-off frequencies. How close are you to the design values?


Function Generator

Oscilloscope

Connecting Wires

Experiment

1. Build the circuit you have designed in the Laboratory. Obtain frequency response of the filter both amplitude and phase shift.

2. Report the data in tabular form and plot the Bode plots. Compare the Bode plots and center and cutoff frequencies with design values and Multisim simulations. What is the bandwidth, B, of this filter? Write down your observations from this experiment and calculations.

Report Sheet: Experiment #8- Design and Circuit Analysis

Students Names:____________________,__________________



Please include your simulations and your graphed papers.

57

Experiment #9- Maximum Power Transfer

Objectives

1. To demonstrate that maximum power will be delivered to the load in resistive circuits

when the load resistor is equal to the Thevenin Equivalent Resistance of the rest of the

circuit.


Power in DC Circuits

Electric power is defined as the rate at which electrical energy is transferred by an electric

circuit. The SI unit of power is the watt. The product of voltage and current as the following

equation describes power in a DC circuit:

P=VI

Where V is the voltage applied to a given element and I is the current flowing through it. From

the Ohms law the previous equation can be expressed as:

P=V2/R or P=I2R

Maximum Power Transfer in DC Circuits


1. Come up with an equation for PL as a function of RL. Show this equation in your lab

report.

2. Calculate RL for maximum power transfer to the load.


DC Power Supply

Digital Multimeter

Function Generator

Oscilloscope

Protoboard

Resistors: 1K, 1.5 K, 2 K, 2.7 K, 3 K, 4.7K, 5.6 K

58

Experiment

Maximum Power Transfer

1. Given the following circuit with RTH =2K, RTH = 4.7K and VTH = 5 volts with load resistor

RL shown connected to the Thevenin Equivalent of the rest of a given circuit:

a. Measure the value of your RTH. Compare with its nominal value.

b. PreLab - Come up with an equation for PL as a function of RL. Show this equation in your lab

report.

c. PreLab - Use Matlab to graph your PL as a function of RL.

d. Measure VL for the following different values of RL:

RL= 1K, 3 K and 5.6 K. Show these values in the Table 1.

e. Then make use of your results to calculate corresponding values of the power PL.

f. Put your data points on your Matlab graph.

g. Make use the data on your graph to find the value of RL when the most power is delivered to

the load. What is this power?

h. PreLab - Calculate RL for maximum power transfer to the load

i. Compare your calculated and measured values of RL for maximum power transfer. Include

these values in your lab report.

2. Given the following circuit with R=2K , R = 4.7K and VS = 5 volts:

a. Measure the values of your resistors. Compare with nominal values.

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b. Take measurements to find the value of RL for maximum power transfer. Include a sketch of

PL versus RL to show what's going on.

c. Calculate the value of RL for maximum power transfer.

d. Compare your theoretical and measured values of RL for maximum power transfer.

Report Sheet: Experiment #9- Power Measurements

Students Names:____________________,__________________



Table 1

RL 1K 3 K 5.6 K

VL

*Create another Table (Table 2) to show your data for part 2.

Sketch of PL vs. RL

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APPENDIX: REFERENCE MATERIAL How does an oscilloscope works?

An outline explanation of how an oscilloscope works can be given using the block diagram shown below:

http://www.doctronics.co.uk/scope.htm#other

Like a television screen, the screen of an oscilloscope consists of a cathode ray tube. Although the size and shape

are different, the operating principle is the same. Inside the tube is a vacuum. The electron beam emitted by the

heated cathode at the rear end of the tube is accelerated and focused by one or more anodes, and strikes the front of

the tube, producing a bright spot on the phosphorescent screen.

The electron beam is bent, or deflected, by voltages applied to two sets of plates fixed in the tube. The horizontal

deflection plates, or X-plates produce side to side movement. As you can see, they are linked to a system block

called the time base. This produces a sawtooth waveform. During the rising phase of the sawtooth, the spot is driven

at a uniform rate from left to right across the front of the screen. During the falling phase, the electron beam returns

rapidly from right to left, but the spot is 'blanked out' so that nothing appears on the screen.

In this way, the time base generates the X-axis of the V/t graph.

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The slope of the rising phase varies with the frequency of the sawtooth and can be adjusted, using the TIME/DIV

control, to change the scale of the X-axis. Dividing the oscilloscope screen into squares allows the horizontal scale to

be expressed in seconds, milliseconds or microseconds per division (s/DIV, ms/DIV, s/DIV). Alternatively, if the

squares are 1 cm apart, the scale may be given as s/cm, ms/cm or s/cm.

The signal to be displayed is connected to the input. The AC/DC switch is usually kept in the DC position (switch

closed) so that there is a direct connection to the Y-amplifier. In the AC position (switch open) a capacitor is placed in

the signal path. As will be explained in Chapter 5, the capacitor blocks DC signals but allows AC signals to pass.

The Y-amplifier is linked in turn to a pair of Y-plates so that it provides the Y-axis of the the V/t graph. The overall gain

of the Y-amplifier can be adjusted, using the VOLTS/DIV control, so that the resulting display is neither too small or

too large, but fits the screen and can be seen clearly. The vertical scale is usually given in V/DIV or mV/DIV.

The trigger circuit is used to delay the time base waveform so that the same section of the input signal is displayed on

the screen each time the spot moves across. The effect of this is to give a stable picture on the oscilloscope screen,

making it easier to measure and interpret the signal.

Changing the scales of the X-axis and Y-axis allows many different signals to be displayed. Sometimes, it is also

useful to be able to change the positions of the axes. This is possible using the X-POS and Y-POS controls. For

example, with no signal applied, the normal trace is a straight line across the center of the screen. Adjusting Y-POS

allows the zero level on the Y-axis to be changed, moving the whole trace up or down on the screen to give an

effective display of signals like pulse waveforms which do not alternate between positive and negative values.

Other oscilloscope controls

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http://www.wisc-online.com/objects/index_tj.asp?objID=ACE3803

.screen: usually displays a V/t graph, with voltage V on the vertical axis and time t on the horizontal axis. The scales

of both axes can be changed to display a huge variety of signals.

on/off switch: pushed in to switch the oscilloscope on. The green LED illuminates.

X-Y control: normally in the OUT position.

When the X-Y button is pressed IN, the oscilloscope does not display a V/t graph. Instead, the vertical axis is

controlled by the input signal to CH II. This allows the oscilloscope to be used to display a V/V voltage/voltage graph.

The X-Y control is used when you want to display component characteristic curves, or Lissajous figures.

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TV-separation: Oscilloscopes are often used to investigate waveforms inside television systems. This control allows

the display to be synchronized with the television system so that the signals from different points can be compared.

You must not try to investigate television systems because of the dangerously high voltages inside. The correct

position for this control is OFF.

TIME / DIV: Allows the horizontal scale of the V/t graph to be changed.

trigger controls: This group of controls allows the oscilloscope display to be synchronized with the signal you want to

investigate.

When the AT/NORM button is in the OUT position, triggering is automatic. This works for most signals.

If you change the AT/NORM button to its IN position, the most likely result is that the signal will disappear and the

oscilloscope screen will be blank. However, if you now adjust the LEVEL control, the display will be reinstated. As you

adjust the LEVEL control, the display starts from a different point on the signal waveform. This makes it possible for

you to look in detail at any particular part of the waveform.

The EXT button should normally be in its OUT position. When it is pushed IN, triggering occurs from a signal

connected to the trigger input, TRIG INP, socket.

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The slide switch to the left of TIME/DIV gives additional triggering options. AC is the normal position and is suitable

for most waveforms.

In the DC position, you use the LEVEL control to select a particular DC voltage on the signal waveform where

triggering will occur.

The +/- button gives triggering on the upward slope of the signal waveform in the OUT position, and triggering on the

downward slope in the IN position.

The green TRIG LED illuminates when a trigger point is detected.

HF gives triggering in response to high frequency parts of the signal, LF gives triggering for low frequency

components and indicates that triggering will occur at 50 Hz, You are not likely to need any of these slide switch

positions.

The HOLD OFF control allows you to introduce a delay relative to the trigger point so that a different part of the signal

can be seen.

Normally, you will want to leave the HOLD OFF control in its minimum position, as illustrated.

With more experience of using the oscilloscope, you will develop a clear understanding of the functions of the

important trigger controls and be able to use them effectively.

intensity and focus: Adjusting the INTENSITY control changes the brightness of the oscilloscope display. The FOCUS

should be set to produce a bright clear trace.

If required, TR can be adjusted using a small screwdriver so that the oscilloscope trace is exactly horizontal when no

signal is connected.

X-POS: Allows the whole V/t graph to be moved from side to side on the oscilloscope screen.

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This is useful when you want to use the grid in front of the screen to make measurements, for example, to measure

the period of a waveform.

X-MAG: In the IN position, the horizontal scale of the V/t graph is increased by 10 times. For example, if TIME/DIV is

set for 1 ms per division and X-MAG is pushed IN, the scale is changed to 0.1 ms per division.

CAL outputs: The top terminal gives a 0.2 V peak to peak square wave, while the lower terminal gives a 2 V peak to

peak square wave, both at 50 Hz.

The signals from these outputs are used to confirm that the oscilloscope is correctly calibrated.

component tester: The output socket provides a changing voltage which allows component characteristic curves to be

displayed on the oscilloscope screen.

When the button is IN, the oscilloscope displays a V/V graph, with the component tester voltage connected internally

to provide the horizontal axis.

To get normal V/t graph operation the component tester button must be in the OUT position.

Y-POS I and Y-POS II: These controls allow the corresponding trace to be moved up or down, changing the position

representing 0 V on the oscilloscope screen.

To investigate an alternating signal, you adjust Y-POS so that the 0 V level is close to the centre of the screen. For a

pulse waveform, it is more useful to have 0 V close to the bottom of the screen.

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Y-POS I and Y-POS II allow the 0 V levels of the two traces to be adjusted independently.

invert: When the INVERT button is pressed IN, the corresponding signal is turned upside down, or inverted, on the

oscilloscope screen.

This feature is sometimes useful when comparing signals.

CH I and CH II inputs: Signals are connected to the BNC input sockets using BNC plugs.

The smaller socket next to the BNC input socket provides an additional 0 V, GROUND or EARTH connection.

VOLTS / DIV: Adjust the vertical scale of the V/t graph. The vertical scales for CH I and CH II can be adjusted

independently.

DC/AC/GND slide switches: In the DC position, the signal input is connected directly to the Y-amplifier of the

corresponding channel, CH I or CH II. In the AC position, a capacitor is connected into the signal pathway so that DC

voltages are blocked and only changing AC signals are displayed.

In the GND position, the input of the Y-amplifier is connected to 0 V. This allows you to check the position of 0 V on

the oscilloscope screen.

The DC position of these switches is correct for most signals.

trace selection switches: The settings of these switches control which traces appear on the oscilloscope screen.

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The effects of different settings are summarized in the table:

CH

I/II DUAL ADD effect of setting

OUT OUT OUT normal operation:

only CH I displayed, triggering from CH I

IN OUT OUT only CH II displayed, triggering from CH II

OUT IN OUT CH I and CH II displayed on alternate sweeps, triggering

from CH I

IN IN OUT CH I and CH II displayed on alternate sweeps, triggering

from CH II

OUT OUT IN CH I and CH II signals added together to produce a single

trace, triggering from CH I

IN OUT IN CH I and CH II signals added together to produce a single

trace, triggering from CH II

OUT IN IN CH I and CH II displayed simultaneously, triggering from

CH I

IN IN IN CH I and CH II displayed simultaneously, triggering from

CH II

Settings highlighted in yellow are used frequently. Experience with the oscilloscope will help you to decide which

setting is best for a particular application.

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For normal operation, all three buttons are in the OUT position.

Lissajous Method

Switch the display mode from Voltage-time mode to X-Y mode. The display on the

oscilloscope will show an elliptical pattern similar to the following. Always adjust the

oscilloscope horizontal scale so that the ellipse, X total, is the full width of the screen.

this will maximize the accuracy of the measurements. Before measuring the, X zero,

distance increase the vertical gain to make the zero crossings steep for more accurate

measurements. Having the top and bottom of the figure off the screen will not effect the

measurement since the distance measured is along the horizontal axis. The horizontal

scale does not matter since both measurements are measured with the same scale.

Therefore the scale factor cancels out when the two values are divided. Also check to

make sure the vertical zero is exactly in the center of the screen.

Documents

Manual Circuito 1 Lab