ee 202 network theory laboratory - …agnigarh.tezu.ernet.in/~bjsece/ee 202 network lab...

LABORATORY MANUAL EE 202 NETWORK THEORY

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EE 202 NETWORK THEORY LABORATORY

DEPARTMENT OF ELECTRONICS AND COMMUNICATION

ENGINEERING

SCHOOL OF ENGINEERING

TEZPUR UNIVERSITY

NAPAAM, TEZPUR, ASSAM, INDIA

PIN:784028


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CONTENTS

Introduction

Course Goals and Objectives

Use of Laboratory Instruments

Laboratory Notebooks and Reports

Format of Lab Report

LIST OF EXPERIMENTS

1. Realization of Current Source and Voltage Source.

2. To study the application of Thevenin’s Theorem.

3. To study the application of Norton’s Theorem.

4. To study the application of Superposition Theorem.

5. To study the application of Maximum Power Transfer Theorem.

6. To study the step response of RL, RC & RLC circuits.

7. Calculation and Verification of Z, Y, ABCD Parameters of a Two-port Network.

8. Design and frequency response of Passive Filter circuit.

9. Ladders and Bridges

10. Multi DC Mesh Analysis

APPENDIX


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Introduction

This course is intended to enhance the learning experience of the student in topics encountered in EE

202 Network Theory. In this lab, students are expected to get hands-on experience in using the basic

measuring devices used in electrical engineering and in interpreting the results of measurement

operations in terms of the concepts introduced in the network theory course. How the student

performs in the lab depends on his/her preparation, participation, and teamwork. Each team member

must participate in all aspects of the lab to ensure a thorough understanding of the equipment and

concepts.

Student Responsibilities:

The student is expected to be prepared for each lab. Lab preparation includes reading the lab

experiment and related textbook material. Students are expected to have active participation in the

laboratory activities. The student is expected to ask the teaching assistant any questions he/she may

have. DO NOT MAKE COSTLY MISTAKES BECAUSE YOU DID NOT ASK A SIMPLE

QUESTION. Students should emphasize on understanding the concepts and procedure of each lab

for successful completion of the lab. The student should remain alert and use common sense while

performing a lab experiment. He/she is also responsible for keeping a professional and accurate

record of the lab experiments in a laboratory notebook.

Laboratory Teaching Assistant Responsibilities:

The LTA shall provide the students with a syllabus and safety review during the first class. The

syllabus shall include the LTA's office hours, telephone number, and the name of the faculty

coordinator. The LTA is responsible for insuring that all the necessary equipment and/or preparations

for the lab are available and in working condition. The Laboratory Teaching Assistant (LTA) shall be

completely familiar with each lab prior to class. LAB EXPERIMENTS SHOULD BE CHECKED IN

ADVANCE TO MAKE SURE EVERYTHING IS IN WORKING ORDER. The LTA should

supervise the students performing the lab experiments. The LTA is expected to grade the lab

notebooks and reports in a fair and timely manner. The reports should be returned to the students in

the next lab period following submission. The LTA should report any errors in the lab manual to the

faculty coordinator.

Faculty Coordinator Responsibilities:

The faculty coordinator should insure that the laboratory is properly equipped, i.e., that the teaching

assistants receive any equipment necessary to perform the experiments. The coordinator is

responsible for supervising the teaching assistants and resolving any questions or problems that are

identified by the teaching assistants or the students. The coordinator may supervise the format of the

final exam for the lab. He/she is also responsible for making any necessary corrections to this

manual. The faculty coordinator is responsible for ensuring that the manual is continually updated.


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Lab Policy and Grading:

The student should understand the following policies:

ATTENDANCE:

Attendance is mandatory and any absence must be for a valid excuse and must be documented. In

case of prior knowledge of absence from class by the student, proper approval in due format must be

taken from the Head of the Department. A copy of the approved leave application must be submitted

to the TA/ faculty in charge of the laboratory.

LAB RECORDS:

The student must:

1. Always carry a rough note copy to record the results of the experiments.

2. Keep all work in preparation of and obtained during lab in an approved format of the

department ; and

3. Prepare a lab report on performed experiments.

GRADING POLICY:

The final grade of this course is determined using the following criterion:

Laboratory notebook and in-class work along with attendance: 30%

Lab reports: 30 %

Final exam: 40% (To be decided by the course instructor Practical/Laboratory assignment of mini

project or viva or combination of the above)

In-class work, laboratory notebook and attendance will be determined by the teaching assistant, who,

at his/her discretion may use evaluations to aid in this decision. The final exam should contain a

written part along with practical (physical operations) and followed up by a viva-voce.

Course Goals and Objectives:

The Network Theory Laboratory is designed to provide the student with the knowledge to use

measuring instruments and techniques with proficiency to complement the concepts introduced in

course code EE 202. In addition, the student should learn how to record experimental results

effectively and present these results in a written report. More explicitly, the class objectives are:

1) To gain proficiency in the use of common measuring instruments.

2) To enhance understanding of electrical engineering circuit analysis concepts including:

a) Independent and dependent sources.

b) Passive circuit components (resistors, capacitors, inductors, and switches).

c) Ohm's law, Kirchhoff's voltage law, and Kirchhoff's current law.

d) Power and energy relations.

e) Thévenin's theorem, Norton's theorem, Superposition Theorem and Maximum power

Transfer Theorem.

f) To study the step response of RL, RC & RLC circuits.

g) Calculation and Verification of Z, Y, ABCD Parameters of a Two-port Network.


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h) Design and frequency response of Passive Filter circuit.

i) Ladders and Bridges

j)Multi DC Mesh Analysis

4) To compare theoretical predictions with experimental results and attempt to resolve any apparent

differences.

Use of Laboratory Instruments:

One of the major goals of this lab is to familiarize the student with the proper equipment and

techniques for making electrical measurements. Some understanding of the lab instruments is

necessary to avoid personal or equipment damage. By understanding the device's purpose and

following a few simple rules, costly mistakes can be avoided.

Ammeters and Voltmeters: The most common measurements are those of voltages and currents. Throughout this manual, the

ammeter and voltmeter are represented as shown in Figure 1.

Figure 1 - Ammeter and voltmeter.

Ammeters are used to measure the flow of electrical current in a circuit. Theoretically, measuring

devices should not affect the circuit being studied. Thus, for ammeters, it is important that their

internal resistance be very small (ideally near zero) so they will not constrict the flow of current.

However, if the ammeter is connected across a voltage difference, it will conduct a large current and

damage the ammeter. Therefore, ammeters must always be connected in series in a Circuit,

never in parallel with a voltage source. High currents may also damage the needle on an analog

ammeter. The high currents cause the needle to move too quickly, hitting the pin at the end of the

scale. Always set the ammeter to the highest scale possible, then adjust downward to the

appropriate level.

Voltmeters are used to measure the potential difference between two points. Since the

voltmeter should not affect the circuit, the voltmeters have very high (ideally infinite) impedance.

Thus, the voltmeter should not draw any current, and not affect the circuit. In general, all devices

have physical limits. These limits are specified by the device manufacturer and are referred to as the

device rating. The ratings are usually expressed in terms of voltage limits, current limits, or power

limits. It is up to the engineer to make sure that in device operation, these ratings (limit values) are

not exceeded. The following rules provide a guideline for instrument protection.


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Instrument Protection Rules:

1) Set instrument scales to the highest range before applying power.

2) Be sure instrument grounds are connected properly. Avoid accidental grounding of "hot" leads,

i.e., those that are above ground potential.

3) Check polarity markings and connections of instruments carefully before connecting power.

4) Never connect an ammeter across a voltage source. Only connect ammeters in series with

loads.

5) Do not exceed the voltage and current ratings of instruments or other circuit elements. This

particularly applies to wattmeters since the current or voltage rating may be exceeded with the needle

still on the scale.

6) Be sure the fuse and circuit breakers are of suitable value. When connecting electrical elements to

make up a network in the laboratory, it is easy to lose track of various points in the network and

accidently connect a wire to the wrong place. A procedure to follow that helps to avoid this is to

connect the main series part of the network first, then go back and add the elements in parallel. As an

element is added, place a small check by it on your circuit diagram. Then go back and verify all

connections before turning on the power.

Laboratory Notebooks and Reports

The Laboratory Notebook:

The student must records and interprets his/her experiments via the laboratory notebook and the

laboratory report. The laboratory notebook is essential in recording the methodology and results of

an experiment. Therefore, it is important to learn to keep an accurate notebook. The laboratory

notebook should:

1) Be kept in a sewn and bound or spiral bound notebook.

2) Contain the experiment's title, the date, the equipment and instruments used, any pertinent circuit

diagrams, the procedure used, the data (often in tables when several measurements have been made),

and the analysis of the results/discussions.

3) Contain plots of data and sketches when these are appropriate in the recording and analysis of

observations.

4) Contain an accurate and permanent record of the data obtained during the experiment and the

analysis of the results. You will need this record when you are ready to prepare a lab report.

The Lab Report:

The laboratory report is the primary means of communicating your experience and conclusions to

other professionals. In this course you will use the lab report to inform your LTA what you did

and what you have learned from the experience. Engineering results are meaningless unless they can

be communicated to others.

Your laboratory report should be clear and concise. As a guide, use the format on the next page. Use

tables, diagrams, sketches, and plots, as necessary to show what you did, what was observed, and

what conclusions you draw from this. Even though you will work with one or more lab partners,

your report will be the result of your individual effort in order to provide you with practice in

technical communication.


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Format of Lab Report:

EE 202 NETWORK THEORY LABORATORY AUTUMN 2015

EXPERIMENT NO WITH TITLE- Indicate the lab title and number

DATE - Indicate the date the lab was performed

ENROLLEMENT NUMBER - Give your enrollment no.

.

OBJECTIVE/AIM - Clearly state the objective of performing the lab.

APPARATUS USED - Indicate which equipment was used in performing the experiment. Range of

equipments used must be clearly indicated. The manufacturer and model number should be specified.

CIRCUIT DIAGRAM - Draw the electrical circuit diagram for the experiment performed.

PROCEDURE - Provide a concise summary of the procedure used in the lab. Include any

modifications to the experiment.

DATA - Provide a record of the data obtained during the experiment. Data should be retrieved from

the lab notebook and presented in a clear manner using tables.

OBSERVATIONS - The student should state what conclusions can be drawn from the experiment.

Plots, charts, other graphical medium, and equations should be employed to illustrate the student's

viewpoint. Sources of error and percent error should be noted here.

CONCLUSIONS/REPORT - The student should present conclusions which may be logically

deduced from his/her data and observations.

DISCUSSIONS/QUESTIONS - Questions pertaining to the lab may be answered here. These

questions may be answered after the lab is over and as assignment to help clarify and provide clear

understanding of the experiment and its application.


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EXPERIMENT NO: 1

TITLE:-Realization of Current and Voltage Sources.

AIM : -

i) To draw the characteristics of ideal voltage & current sources.

ii) To draw the characteristics of non- ideal voltage & current sources.

iii) Conversion of Voltage to Current source.

Apparatus Required:

SL NO NAME OF THE APPARATUS SPECIFICATION QUANTITY

1 DC VOLTAGE SOURCE

2 DC VOLTMETER

3 DC AMMETER

4 RHEOSTAT

5 CONNECTING WIRES

CIRCUIT DIAGRAM:-

Fig.1.1 Fig.1.2

FIG.1. 3 FIG.1.4

THEORY:-

An ideal voltage source is energy sources which can supply energy at constant voltage i.e. when the load

current is change from minimum to maximum the terminal voltage remain same. To satisfy this requirement

the internal resistance of the source should be zero. A non ideal voltage source has non zero internal resistance

as a result the terminal voltage decreases with load current

Fig 3


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An ideal current source is an energy source which can supply energy at constant current. To satisfy this

requirement the internal resistance of the source should be zero. A non ideal current source has a finite

internal resistance as a result the load current changes with change in load current.

PROCEDURE:

For Ideal Voltage Source:

1. Connect the circuit as fig1

2. Vary the value of RL (min - max) in five equal steps.

3. Tabulate the observation in table 1

4. Draw the graph between Vs & Is

For Ideal Current Source:

1. Connect the circuit as fig 2

2. Vary the value of RL(min - max) in five equal steps.

3. Tabulate the observation in table 2.

4. Draw the graph between Is &Vs.

For non- Ideal Voltage Source:

1. Connect the circuit as fig3.

2. Vary the value of RL(min - max) in five equal steps.


4. Draw the graph between Vs& Is.

For non- Ideal Current Source:

1. Connect the circuit as fig4.

2. Vary the value of RL (min - max) in five equal steps.


4. Draw the graph between Is &Vs.

OBSERVATION TABLE:-

TABLE 1

SL NO VOLTMETER READING,V

(V)

AMMETER READING,I

(A)


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TABLE 2

SL NO VOLTMETER READING,V

(V)

AMMETER READING,I

(A)

TABLE 3

SL

NO

VOLTMETER

READING,V

(V)

AMMETER

READING,I

(A)

SOURCE

RESISTANCE,Rs

(Ω)

SOURCE

VOLTAGE,Vs

(V)

TABLE 4

SL

NO

VOLTMETER

READING,V

(V)

AMMETER

READING,I

(A)

SOURCE

RESISTANCE,Rs

(Ω)

SOURCE

CURRENT,Is

(A)

PRECAUTION:-

CONCLUSION/RESULT:-

DISCUSSION:-

1. Why it is not possible to have an ideal source in real world?

2. Why voltage remains constant in ideal voltage source?

3. Why current remains constant in ideal current source?


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EXPERIMENT NO: 2

TITLE:-To study the application of Thevenin’s theorem

AIM : -

iv) To find the Thevenin’s equivalent resistance (Rth) for a given circuit

i) To find Thevenin’s equivalent voltage (Vth) for a given circuit

ii) To find the Thevenin’s equivalent of the given network circuit.

iii) To find the Circuit current in the equivalent Thevenin’s Network

Apparatus Required:


1 DC VOLTAGE SOURCE

2 DC CURRENT SOURCE

2 DC VOLTMETER

3 DC AMMETER

4 RHEOSTAT

5 CONNECTING WIRES

CIRCUIT DIAGRAM:-

Fig.2.1 Fig.2.2

FIG.2.3

THEORY:-

Thevenin’s Theorem for DC circuits states that any two port linear network may be replaced by a single

voltage source with an appropriate internal resistance. The Thevenin’s equivalent will produce the same load

Fig 3


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current and voltage as the original circuit to any load. Consequently, if many different loads or sub-circuits are

under consideration, using a Thevenin’s equivalent may prove to be a quicker analysis route than “reinventing

the wheel” each time.

The Thevenin’s voltage is found by determining the open circuit output voltage. The Thevenin’s resistance is

found by replacing any DC sources with their internal resistances and determining the resulting combined

resistance as seen from the two ports using standard series-parallel analysis techniques. In the laboratory, the

Thevenin’s resistance may be found using an ohmmeter (again, replacing the sources with their internal

resistances) or by using the matched load technique. The matched load technique involves replacing the load

with a variable resistance and then adjusting it until the load voltage is precisely one half of the unloaded

voltage. This would imply that the other half of the voltage must be dropped across the equivalent Thevenin’s

resistance, and as the Thevenin’s circuit is a simple series loop then the two resistances must be equal as they

have identical currents and voltages.

PROCEDURE:

1. Connect the circuit as shown in figure 1.

2. Set the voltage source to 4 V and current source to 1mA.

3. Measure the current flowing through the load resistance equal to 1kΩ.

4. Find the Thevenin’s equivalent of the given network by finding the equivalent circuit parameters.

Calculate Rth as shown in figure 2.

5. Calculate Vth for the given network.

6. Construct the Thevenin’s Equivalent circuit for the given network by connecting the Vth and Rth in

series and reconnecting the load resistance 1kΩ. Measure the Current through the equivalent circuit.

7. Compare the current available in both the cases.

OBSERVATION TABLE:-

Voc=Vth = _______ V

Rth = _________ Ω

TABLE 1

Sl

No: Theoretical Experimental

Deviation

(IE1-IE2)

Current for

Circuit 2.1

Ammeter

Reading (A)

IT1

Current for

circuit 2.3

Ammeter

Reading

(A)

IT2

Current for

circuit 2.1

Ammeter

Reading (A)

IE1

Current for

circuit 2.3

Ammeter

Reading (A)

IE2

PRECAUTION TO BE TAKEN IF ANY:-

CONCLUSION/RESULT:-


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DISCUSSION:-

1. Do you note any difference between the theoretical results and experimental results? If yes then why is

it so? Give reasonable explanation.

2. How is the Thevenin’s Theorem applicable in case of AC circuits? Explain giving a suitable example.

3. What is the advantage of network reduction using Thevenin’s Theorem?

4. Where is the application of Thevenin’s Theorem practically in real Electrical engineering?


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EXPERIMENT NO: 3

TITLE:- To study the application of Norton’s theorem

OBJECTIVES : -

i) To find the Nortons’s equivalent resistance (RN) for a given circuit

ii) To find Nortons’s equivalent current source (Isc) for a given circuit

iii) To find the Nortons’s equivalent of the given network circuit.

iv) To find the circuit current in the equivalent Nortons’s Network

v) Using Source Transformation Technique find the Thevenin’s Equivalent of the given Circuit

work

Apparatus Required:


1 DC VOLTAGE SOURCE

2 DC CURRENT SOURCE

2 DC VOLTMETER

3 DC AMMETER

4 RHEOSTAT

5 CONNECTING WIRES

CIRCUIT DIAGRAM:-

Fig.3.1 Fig.3.2

FIG. 3.3

Fig 3


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THEORY:-

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).

This theorem is just alternative of Thevenin theorem. In Norton theorem, we just replace the circuit

connected to a particular branch by equivalent current source . In this theorem, the circuit network is

reduced into a single constant current source in which, the equivalent internal resistance is connected

in parallel with it. Every voltage source can be converted into equivalent current source .

Suppose, in complex network we have to find out the current through a particular branch. If the

network has one of more active sources, then it will supply current through the said branch. As in the

said branch current comes from the network, it can be considered that the network itself is a current

source . So in Norton theorem the network with different active sources is reduced to single current

source that's internal resistance is nothing but the looking back resistance, connected in parallel to the

derived source. The looking back resistance of a network is the equivalent electrical resistance of the

network when someone looks back into the network from the terminals where said branch is

connected. During calculating this equivalent resistance, all sources are removed leaving their

internal resistances in the network. Actually in Norton theorem, the branch of the network through

which we have to find out the current, is removed from the network. After removing the branch, we

short circuit the terminals where the said branch was connected. Then we calculate the short circuit

current that flows between the terminals. This current is nothing but Norton equivalent current IN of

the source. The equivalent resistance between the said terminals with all sources removed leaving

their internal resistances in the circuit is calculated and said it is RN. Now we will form a current

source that's current is IN A and internal shunt resistance is RN Ω.

PROCEDURE:

1. Connect the circuit as shown in figure 1.

2. Set the voltage source to 4 V and current source to 1mA.

3. Measure the current flowing through the load resistance equal to 1kΩ.

4. Find the Nortons’s equivalent of the given network by finding the equivalent circuit

parameters. Calculate Rth=RN as shown in figure 2.

5. Calculate ISC for the given network.

6. Construct the Nortons’s Equivalent circuit for the given network by connecting the ISCand RN

in series and reconnecting the load resistance 1kΩ. Measure the Current through the

equivalent circuit.

7. Compare the current available in both the cases.

8. Construct the Thevenin’s Equivalent Circuit from the Norton’s Circuit using Source

Transformation Technique.

http://www.electrical4u.com/thevenin-theorem-and-thevenin-equivalent-voltage-and-resistance/

http://www.electrical4u.com/ideal-dependent-independent-voltage-current-source/


http://www.electrical4u.com/electrical-resistance-and-laws-of-resistance/



http://www.electrical4u.com/electric-current-and-theory-of-electricity/






















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OBSERVATION TABLE:-

Isc= ________ A

Vth = ________ V

Rth = _________ Ω

TABLE 1

Sl


Deviation

(IE1-IE2)

Current for

Circuit 1

Ammeter

Reading (A)

IT1

Current

for circuit

3

Ammeter

Reading

(A)

IT2

Current for

circuit 1

Ammeter

Reading (A)

IE1

Current for

circuit 3

Ammeter

Reading

(A)

IE2

PRECAUTION TO BE TAKEN IF ANY:-

CONCLUSION/RESULT:-

DISCUSSION:-

1. Do you note any difference between the theoretical results and experimental results? If yes

then why is it so? Give reasonable explanation.

2. How is the Norton’s Theorem applicable in case of AC circuits? Explain giving a suitable

example.

3. Do the equivalent circuits constructed Using Thevenin’s Theorem in Experiment no 2 and

Norton’s Theorem give the same results for current in the circuit? Is there any difference in

the results obtained? If so why? Give reasonable explanation.

4. Suggest one application of Norton’s Theorem practically in real Electrical engineering related

problem?


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Experiment no:4 Superposition Theorem

Aim

The aim of this exercise is to investigate the application of the superposition theorem to multiple DC

source circuits in terms of both voltage and current measurements. Power calculations will also be

examined.

Equipment

(1) Adjustable Dual DC Power Supply

(1) Digital Multimeter

(1) 6.8 kΩ __________________

(1) 10 kΩ __________________

(1) 22 kΩ __________________

(1) 33 kΩ __________________

Circuit Diagram

Figure 4.1


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Figure 4.2

Theory

The superposition theorem states that in a linear bilateral multi-source DC circuit, the current

through or voltage across any particular element may be determined by considering the contribution

of each source independently, with the remaining sources replaced with their internal resistance. The

contributions are then summed, paying attention to polarities, to find the total value. Superposition

cannot in general be applied to non-linear circuits or to non-linear functions such as power.

Procedure

Voltage Application

1. Consider the dual supply circuit of Figure 4.1 using E1 = 10 volts, E2 = 15 volts, R1 = 4.7 k, R2

= 6.8 k and R3 = 10 k. To find the voltage from node A to ground, superposition may be used.

Each source is considered by itself. First consider source E1 by assuming that E2 is replaced with

its internal resistance (a short). Determine the voltage at node A using standard series-parallel

techniques and record it in Table 4.1. Make sure to indicate the polarity. Repeat the process using

E2 while shorting E1. Finally, sum these two voltages and record in Table 4.1.

2. To verify the superposition theorem, the process may be implemented directly by measuring the

contributions. Build the circuit of Figure 4.1 with the values specified in step 1, however, replace

E2 with a short. Do not simply place a shorting wire across source E2! This will overload the

power supply.

3. Measure the voltage at node A and record in Table 4.1. Be sure to note the polarity.

4. Remove the shorting wire and insert source E2. Also, replace source E1 with a short. Measure

the voltage at node A and record in Table 4.1. Be sure to note the polarity.


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5. Remove the shorting wire and re-insert source E1. Both sources should now be in the circuit.

Measure the voltage at node A and record in Table 4.1. Be sure to note the polarity. Determine

and record the deviations between theory and experimental results.

Current and Power Application


= 6.8 k, R3 = 10 k, R4 = 22 k and R5 = 33 k. To find the current through R4 flowing from node

A to B, superposition may be used. Each source is again treated independently with the

remaining sources replaced with their internal resistances. Calculate the current through R4 first

considering E1 and then considering E2. Sum these results and record the three values in Table

4.2.

7. Assemble the circuit of Figure 4.2 using the values specified. Replace source E2 with a short and

measure the current through R4. Be sure to note the direction of flow and record the result in

Table 4.2.

8. Replace the short with source E2 and swap source E1 with a short. Measure the current through

R4. Be sure to note the direction of flow and record the result in Table 4.2.

9. Remove the shorting wire and re-insert source E1. Both sources should now be in the circuit.

Measure the current through R4 and record in Table 4.2. Be sure to note the direction. Determine

and record the deviations between theory and experimental results.

10. Power is not a linear function as it is proportional to the square of either voltage or current.

Consequently, superposition should not yield an accurate result when applied directly to power.

Based on the measured currents in Table 4.2, calculate the power in R4 using E1-only and E2-

only and record the values in Table 4.3. Adding these two powers yields the power as predicted

by superposition. Determine this value and record it in Table 4.3. The true power in R4 may be

determined from the total measured current flowing through it. Using the experimental current

measured when both E1 and E2 were active (Table 4.2), determine the power in R4 and record it

in Table 4.3.


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Observation Tables

Table 4.1

Source VA Theory VA Experimental Deviation

E1 Only

E2 Only

E1 and E2

Table 4.2

Source IR4 Theory IR4 Experimental Deviation

E1 Only

E2 Only

E1 and E2

Table 4.3

Source PR4

E1 Only

E2 Only

E1 + E2

E1 and E2

Conclusion

After analyzing the readings from Table 4.1, Table 4.2, and Table 4.3 we can conclude that for a

linear bilateral multi-source DC circuit, the superposition theorem is verified.

Questions

1. Based on the results of Tables 4.1, 4.2 and 4.3, can superposition be applied successfully to

voltage, current and power levels in a DC circuit?

2. If one of the sources in Figure 4.1 had been inserted with the opposite polarity, would there be a

significant change in the resulting voltage at node A? Could both the magnitude and polarity

change?


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3. If both of the sources in Figure 4.1 had been inserted with the opposite polarity, would there be a

significant change in the resulting voltage at node A? Could both the magnitude and polarity

change?

4. Why is it important to note the polarities of the measured voltages and currents?


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Experiment no: 5: Maximum Power Transfer Theorem

Aim

The objective of this exercise is to determine the conditions under which a load will produce

maximum power. Further, the variance of load power and system efficiency will be examined

graphically.

Equipment

(1) Adjustable DC Power Supply


(3) 3.3 kΩ __________________

(4) Resistance Decade Box

Circuit Diagram

Figure 5.1

Theory

In order to achieve the maximum load power in a DC circuit, the load resistance must equal the

driving resistance, that is, the internal resistance of the source. The internal resistance of the source

can be calculated as the Thevenin’s resistance of the source’s electric circuit. Any load resistance

value above or below this will produce a smaller load power. System efficiency (η) is 50% at the

maximum power case. This is because the load and the internal resistance form a basic series loop,

and as they have the same value, they must exhibit equal currents and voltages, and hence equal

powers. As the load increases in resistance beyond the maximizing value the load voltage will rise,

however, the load current will drop by a greater amount yielding a lower load power. Although this


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is not the maximum load power, this will represent a larger percentage of total power produced, and

thus a greater efficiency (the ratio of load power to total power).

Procedure

1. Consider the simple the series circuit of Figure 5.1 using E = 10 volts and Ri = 3.3 k. Ri forms a

simple voltage divider with RL. The power in the load is VL2/RL and the total circuit power is

E2/(Ri+RL). The larger the value of RL, the greater the load voltage, however, this does not mean

that very large values of RL will produce maximum load power due to the division by RL. That

is, at some point VL2 will grow more slowly than RL itself. This crossover point should occur

when RL is equal to Ri. Further, note that as RL increases, total circuit power decreases due to

increasing total resistance. This should lead to an increase in efficiency. An alternate way of

looking at the efficiency question is to note that as RL increases, circuit current decreases. As

power is directly proportional to the square of current, as RL increases the power in Ri must

decrease leaving a larger percentage of total power going to RL.

2. Using RL = 30, compute the expected values for load voltage, load power, total power and

efficiency, and record them in Table 5.1. Repeat for the remaining RL values in the Table. For

the middle entry labeled Actual, insert the measured value of the 3.3 k used for Ri.

3. Build the circuit of Figure 5.1 using E = 10 volts and Ri = 3.3 k. Use the decade box for RL and

set it to 30 Ohms. Measure the load voltage and record it in Table 12.2. Calculate the load power,

total power and efficiency, and record these values in Table 5.2. Repeat for the remaining resistor

values in the table.

4. Create two plots of the load power versus the load resistance value using the data from the two

tables, one for theoretical, one for experimental. For best results make sure that the horizontal

axis (RL) uses a log scaling instead of linear.

5. Create two plots of the efficiency versus the load resistance value using the data from the two

tables, one for theoretical, one for experimental. For best results make sure that the horizontal

axis (RL) uses a log scaling instead of linear.


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Observation Tables:

Table 5.1

RL VL PL PT η

30

150

500

1 k

2.5 k

Actual=

4 k

10 k

25 k

70 k

300 k

Table 5.2

RL VL PL PT η

30

150

500

1 k

2.5 k

Actual=

4 k

10 k

25 k

70 k

300 k


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Conclusion

After analyzing the readings from Table 5.1 and Table 5.2, it can be concluded that In order to

achieve the maximum load power in a DC circuit, the load resistance must equal the driving

resistance, that is, the internal resistance of the source. System efficiency (η) is 50% at the maximum

power case. This is because the load and the internal resistance form a basic series loop, and as they

have the same value, they must exhibit equal currents and voltages, and hence equal powers.

Questions

1. At what point does maximum load power occur?

2. At what point does maximum total power occur?

3. At what point does maximum efficiency occur?

4. Is it safe to assume that generation of maximum load power is always a desired goal? Why/why

not?


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EXPERIMENT NO: 6 (a)

TITLE:-To study the transient response of a RL and RC circuit for a DC Square wave input

AIM : -

i) To plot the transient response of a RL circuit.

ii) To plot the transient response of a RC circuit.

iii) To calculate the time constant of the RL and RC network circuits

Apparatus Required:


1 AC Power source

2 Circuit Board kit

2 CRO

3 Function Generator

4 Connecting leads

5 Resistor

6 Inductor

7 Capacitor

CIRCUIT DIAGRAM:-

Fig.6.1 Fig 6.2

THEORY:-

For RL Circuit:

On switching the supply on, function generator supplies the input square wave to the RL circuit, the transient

characteristic of the circuit is given by the equation -

L di/dt + Ri = 0

di/i = - (R/L) dt

Integrating both sides of the equation and taking log on both sides – we have

log i = - (R/L) t + log C ; where C is a constant

Fig 3


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or i = C exp(-Rt/L) ---------------- (1)

Equation (1) gives the general solution of a RL circuit. Calculating for the value of C at time t=0, just before

the switching instant we have

i(0) = V/R ; where V is the supply voltage

Substituting for i(0) at t=0 in equation (1), we get C =V/R

We get the particular solution of the problem as

i = V/R exp(-Rt/L) or i = V/R exp(-t/ ); = L/R is the time constant of the RL circuit

For RL Circuit:

On switching the supply on, function generator supplies the input square wave to the RC circuit, the transient

characteristic of the circuit is given by the equation -

1

C idt + Ri = V

Differentiation with respect to ‘t’

1

Ci + Rdi/dt = 0

Rdi/dt = -1/Ci

di/i= -1/RC dt

Integrating both sides of the equation and taking log on both sides – we have

log i = - (1/RC) t + log C2 ; where C2 is a constant

or i = C2 exp(-t/RC) ---------------- (2)

Assuming initial conditions, i.e. i(0) = V/R ; where V is the supply voltage

Substituting for i(0) at time t=0, we get C2 =V/R

We get the particular solution of the problem as

i = V/R exp(-t/RC) or i = V/R exp(-t/ ); 1T = RC is the time constant of the RC circuit

PROCEDURE :

1. Connect the circuit as shown in figure 6.1 and 6.2 switch ON the supply.

2. Feed square wave from the function generator to the I/P terminal of the circuit.

3. Connect the CRO to the output terminal and note down the O/P wave.

4. Calculate the time required by the output to reach 0.632 times the final value (peak).

5. Draw the input and output wave of the CRO monitor on graph paper or tracing paper.

6. Note down the practical time constant. Tabulate the theoretical and practical values.


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GRAPH:

Fig 6.3

PRECAUTIONS TO BE TAKEN:-

1. Make the connections according to the circuit diagram. Power supply should be switched off.

2. Connections should be tight.

3. Handle the CRO carefully.

4. Note the readings carefully.

OBSERVATION TABLE:-

Vp-p = ______ V ; R = _______Ω ; L=______ mH; C = _______ µF


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TABLE 1:

Sl


% Error %Error

Time

constant for

RL circuit

( 1T )

(1)

Time

constant for

RC circuit

( 2T )

(2)

Time

constant for

RL circuit

( 1E )

(3)

Time

constant for

RC circuit

( 2E )

(4)

For RL Circuit

( 1T )-( 1E )

(1)-(3)

For RC circuit

( 2T )-( 2E )

(2)-(4)

CONCLUSION/RESULT:-

DISCUSSION:-

1. Do you note any difference between the theoretical results and experimental results? If yes then why is

it so? Give reasonable explanation.

2. If the value of Vp-p (i.e. supply voltage) is changed do you expect the value for the time constant to

change? Justify your answer with reasonable explanation.

3. What is the function of the inductor in a RL circuit? If in the given circuit the value of inductor is

doubled, what will be the effect in the time constant of the circuit?

4. How is the time constant of the RC circuit affected if the resistance value is doubled and the

capacitance value doubled as well?

5. If the input to the circuit is changed from a square wave to a triangular wave, what change in the

circuit transient response can you expect for the RL and RC circuit?


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EXPERIMENT NO: 6 (b)

TITLE:-To study the frequency response of a RLC series circuit

AIM : -

i) To plot the frequency response of a RLC series circuit at resonance.

ii) To calculate the bandwidth of the RLC circuit at resonance.

iii) To calculate Q-factor of the RLC series circuit at resonance.

Apparatus Required:


1 AC Power source

2 Circuit Board kit

2 CRO


4 Connecting leads

5 Resistor

6 Inductor

7 Capacitor

CIRCUIT DIAGRAM:-

Fig.6 (b).1

THEORY:-

For RLC series circuit:

In an ac circuit, the circuit is said to be in resonance when the current is in phase with the applied voltage.

Thus at resonance, the equivalent complex impedance of the circuit consists of only resistance R. Since V and

I are in phase, the power factor of the resonant circuit is unity.

The total impedance for the series RLC circuit is given by

Z = R + j (XL –XC) = R + j (1

LC

)

Fig 3


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At series resonance condition, we have XL = XC or 1

r

r

LC

;

where r = 2π fr ; fr is the resonant frequency

and fr = 1/(2 π (LC)1/2

);

PROCEDURE :

1. Connect the circuit as shown in figure 6.b.1 and switch ON the supply.

2. Feed the sine wave to the I/P terminal from function generator.

3. Adjust the peak to peak voltage of the sine wave to 2 V and frequency to 1 KHz.

4. Reduce the input frequency to about 100 Hz with the help of function generator and note down the

corresponding reading of peak value of output voltage from the CRO screen.

5. Repeat step 4 by changing the frequency of the supply and take readings well beyond the resonant

frequency.

6. At the cut off frequency the voltage becomes 0.707 Vm.

7. At resonance frequency the output voltage will be maximum.

8. Plot the graph between frequency and output voltage. Calculate the frequency bandwidth and the Q

factor.

GRAPH:

Fig 6.(b).2







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OBSERVATION TABLE:-

For RLC series circuit; Supply voltage Vs =________ V; R = _______Ω ;

L=______ mH; C = _______ µF

TABLE 1:

Sl. No Frequency (Hz) Peak Output Voltage (V)

Bandwidth BW = f2 – f1

Q factor = fr/ BW

CONCLUSION/RESULT:-

DISCUSSION:-

1. In case of series resonance circuits what do you expect the value of current and impedance at

resonance to be? Give reasonable explanation.

2. In the case of parallel resonance circuits what do you expect the value of current and impedance at

resonance to be? Give reasonable explanation.

3. What is the effect of the resistance on the frequency response curve? Explain.

4. Is the condition of resonance valid for DC circuits? If not why?

5. In the case of series resonance circuit, if the operating frequency is less than the resonant frequency

what is the effect on the overall reactance of the network? If the frequency is above the resonant

frequency what is the overall reactance of the network?

6. What do you understand by selectivity? Illustrate with an example.


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EXPERIMENT NO: 7

TITLE:-To determine the two port network parameters for a given circuit.

AIM : -

i) To calculate and verify the Z parameters of a two-port network

ii) To calculate and verify the Y parameters of a two-port network

iii) To calculate and verify the ABCD parameters of a two-port network

Apparatus Required:


1 Regulated Power supply

2 Circuit Board kit/ Breadboard

2 Multimeter (DMM)

3 Connecting leads

4 Resistors

5 Ammeter

6 Voltmeter

CIRCUIT DIAGRAM:-

Fig.7.1

THEORY:-

Z parameters:

In a two port network configuration, the Z parameters relate the input and output voltages V1 and V2

in terms of the input and output currents I1 and I2. Out of the four variables (V1 ,V2 ,I1 and I2), V1 and

V2 are the dependent variables and I1 and I2 are the independent variables. Thus we have

V1 = Z11I1 + Z12 I2------------------------------ (1)

V2 = Z21I1 + Z22 I2 ----------------------------- (2)

Fig 3


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Where Z 11 and Z22 are the input and output driving point impedances while Z12 and Z21 are the

reverse and forward transfer impedances.

Y parameters:

In a two port network configuration, the Y parameters relate the input and output Currents I1 and I2

in terms of the input and output voltages V1 and V2. Out of the four variables (V1 ,V2 ,I1 and I2), in the

Y parameter configuration of a two-port network I1 and I2 are the dependent variables while V1 and

V2 are the independent variables. Thus we have

I1 = Y11V1 + Y12V2------------------------------(3)

I2 = Y21V1 + Y22V2 -----------------------------(4)

Where Y 11 and Y22 are the input and output driving point admittances while Y12 and Y21 are the

reverse and forward transfer admittances.

ABCD parameters:

ABCD parameters are generally used in analysis of power transmission engineering where they are

termed as “Circuit Parameters”. ABDC parameters are also known as “Transmission Parameters”. In these

parameters, the voltage & current at the sending end terminals can be expressed in terms of voltage and

current at the receiving end. Thus we have

V1 = AV2 + B(-I2) ----------------------------------(5)

I1 = CV2 + D (-I2) ----------------------------------(6)

Where A is called the reverse voltage ratio, B is called the transfer impedance, C is called the transfer

admittance and D is called reverse current ratio.

PROCEDURE :

Calculation of Z parameters:

1. Connect the circuit as shown in figure 7.1 and switch ON the supply.

2. Open circuit the output terminals and give a 5V supply to the input terminal. Using ammeter and

voltmeter/ DMM measure the output voltage and input current. Tabulate the readings.

3. Open circuit the input terminals and give a 5V supply to the output terminal. Using ammeter and

voltmeter/ DMM measure the input voltage and output current. Tabulate the readings.

4. Calculate the Z parameters using equations (1) and (2).

5. Switch off the supply after taking the readings.

6. Tabulate the theoretical and practical values.

Calculation of Y parameters:


2. Short circuit the output terminals and give a 5V supply to the input terminal. Using ammeter / DMM

measure the output and input currents. Tabulate the readings.

3. Short circuit the input terminals and give a 5V supply to the output terminal. Using ammeter / DMM

measure the output and input currents. Tabulate the readings.


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4. Calculate the Y parameters using equations (3) and (4).



Calculation of ABCD parameters:


2. Open circuit the output terminals and give a 5V supply to the input terminal. Using ammeter and

voltmeter/ DMM measure the output voltage and input current. Tabulate the readings.

3. Short circuit the input terminals and give a 5V supply to the output terminal. Using ammeter and

voltmeter/ DMM measure the input current and output current. Tabulate the readings.

4. Calculate the ABCD parameters using equations (5) and (6).



SAMPLE CALCULATIONS:

Z parameters:

1. When O/P is open circuited i.e. I2 = 0 ; then

Z11 = V1/I1 and Z21 = V2/I1

2. When I/P is open circuited , i.e. I1 =0 ; then

Z12 = V1/I2 and Z22 = V2/I2

Y parameters:

1. When O/P is short circuited i.e. V2 = 0 ; then

Y11 = I1/VI1 and Y21 = I2/V1

2. When I/P is short circuited , i.e. V1 =0 ; then

Z12 = V1/I2 and Z22 = V2/I2

ABCD parameters:

1. When O/P is open circuited i.e. I2 = 0 ; then

A = V1/V2 and C = I1/V2

2. When O/P is short circuited , i.e.V2 =0 ; then

B = (-V1/I2) and D = (-I1/I2)





OBSERVATION TABLE:-

For Z parameter calculations: R1 = _______Ω ; R2 = _______Ω ; R3 = _______Ω

For Y parameter calculations: R1 = _______Ω ; R2 = _______Ω ; R3 = _______Ω

For ABCD parameter calculations: R1 = _______Ω ; R2 = _______Ω ; R3 = _______Ω


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TABLE 1: Z PARAMETERS

Sl No. When I/P is open circuit When O/P is open circuit V2( V) V1 (V) I2 (A) V2( V) V1(V) I1(A)

TABLE 2: Y PARAMETERS

Sl No. When I/P is short circuit When O/P is short circuit V2( V) I1 (A) I2 (A) V1( V) I1 (A) I1(A)

TABLE 3: ABCD PARAMETERS

Sl No. When O/P is short circuit When I/P is short circuit V1( V) I1 (A) I2 (A) V2( V) V1(V) I2(A)

TABLE 4: VERIFICATION TABLE

Network Parameters Theoretical Experimental Error

Z Parameters Z11

Z12

Z21

Z22

Y Parameters Y11

Y12

Y21

Y22

ABCD Parameters A

B

C

D

CONCLUSION/RESULT:-

REPORT/DISCUSSION:-

1. For the Z parameters when does the network exhibit the conditions of Reciprocity and symmetry? Also

give the conditions for reciprocity and symmetry for Y parameters and ABCD parameters.

2. Given the Z parameters of a two port network, can you derive the equivalent Y parameters? How can

these parameters be determined?

3. For a transmission system network given the availability of information on Z parameters, Y parameters

and ABCD parameters, which one will be best suited to represent the network? Give reasons for your

answer.


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EXPERIMENT NO: 8

TITLE:-To study the frequency responses of a Low pass and high pass filters

AIM : -

i) To design and study the frequency response characteristics of passive low pass and high pass filter.

ii) To plot the gain in (dB) vs the frequency plot for the low pass and high pass filter circuit.

iii) To compare the theoretical and practical cut off frequency.

Apparatus Required:


1 Circuit Board kit

2 CRO


3 Connecting leads

4 Resistor

5 Capacitor

6 Voltmeters (2)

7 DMM

CIRCUIT DIAGRAM:-

Fig.8 .1 Fig.8 .2

THEORY:-

Low pass filter circuit:

A low pass filter is one which passes without attenuation all frequencies upto the cut-off frequency fc while all

other frequencies greater than fc are attenuated. The filter transmits all frequencies from zero to cut-off

frequency. The band is called pass band. The frequency range over which transmission does not take place is

called the stop band. Figure 8.3 shows the frequency response of a LP filter.

Fig 3


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High pass filter circuit:

A high pass filter attenuates all the frequencies below a designated cut off frequency fc and passes all the

frequencies above fc. Thus the pass band of this filter is the frequency range above fc and the stop band is the

frequency range below fc. An attenuation characteristic of a HP filter is shown in figure 8.4.

PROCEDURE :

1. Connect the circuit as shown in figure 8.1 (for low pass filter) and 8.2 (for high pass filter) and switch

ON the supply.

2. Feed the sine wave to the I/P terminal from function generator.

3. Adjust the peak to peak voltage of the sine wave to 2 V and frequency to 1 KHz.

4. Reduce the input frequency to about 100 Hz with the help of function generator and note down the

corresponding reading of peak value of output voltage from the CRO screen.

5. Repeat step 4 by changing the frequency of the supply and take readings well beyond the cut off

frequency.

6. Calculate the gain in dB for each set of reading and tabulate them.

7. Plot the graph between frequency vs gain in dB in a semi log graph paper.

8. Calculate the cut-off frequency obtained from experimental results from the graph and compare it

with the theoretical value.

GRAPH:

Fig 8.3 Fig 8.4






OBSERVATION TABLE:-

For LP filter circuit; Supply voltage Vs =________ V; R = _______Ω; C = _______ µF

For HP filter circuit; Supply voltage Vs =________ V; R = _______Ω; C = _______ µF


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TABLE 1: For Low Pass Filter circuit:

Sl. No Frequency (Hz) Peak Output Voltage

(V0) (V)

Gain (dB)

20log (Vo/Vs)

TABLE 2: For High Pass Filter circuit:

Sl. No Frequency (Hz) Peak Output Voltage

(V0) (V)

Gain (dB)

20log (Vo/Vs)

CONCLUSION/RESULT:-

1. The passive low pass filter and high pass filter have been constructed and their frequency response

has been obtained.

2. The theoretical and practical cut-off frequencies of both filters have been obtained and tabulated

below for comparative assessment.

TABLE 3: Comparison of cut-off frequency:

Type of Filter Cut off Frequency (Hz) % error

Theoretical Practical

Low Pass

High Pass

REPORT/DISCUSSION:-

1. Where are filter circuits applicable in electrical engineering? Give a example and highlight the

importance of filter circuits.

2. What do you understand by frequency scaling?

3. Given a particular cut-off frequency and a capacitance of known value, how can you design a 1st order

RC low pass filter?


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Experiment no. 9

Ladders and Bridges

Objective

The objective of this exercise is to continue the exploration of basic series-parallel DC circuits. The basic

ladder network and bridge are examined. A key element here is the concept of loading, that is, the effect that a

sub-circuit may have on a neighboring sub-circuit.

Equipments



(3) 1 kΩ __________________

(4) 2.2 kΩ __________________

(5) 3.3 kΩ __________________

(6) 6.9kΩ __________________

(7) 10 kΩ __________________

(8) 22 kΩ __________________

Circuit Diagram

Figure 9.1


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Figure 9.2

Theory

Ladder networks are comprised of a series of alternating series and parallel connections. Each

section effectively loads the prior section, meaning that the voltage and current of the prior section

may change considerably if the loading section is removed. One possible technique for the solution

of ladder networks is a series of cascading voltage dividers. Current dividers may also be used. In

contrast, bridge networks typically make use of four elements arranged in dual series and parallel

configuration. These are often used in measurement systems with the voltage of interest derived from

the difference of two series sub-circuit voltages. As in the simpler series-parallel networks; KVL,

KCL, the current divider rule and the voltage divider rule may be used in combination to analyze the

sub-circuits.

Procedure

1. Consider the circuit of Figure 9.1. R5 and R6 form a simple series connection. Together, they are

in parallel with R4. Therefore the voltage across R4 must be the same as the sum of the voltages

across R5 and R6. Similarly, the current entering node C from R3 must equal the sum of the

currents flowing through R4 and R5. This three resistor combination is in series with R3 in much

the same manner than R6 is in series with R5. These four resistors are in parallel with R2, and

finally, these five resistors are in series with R1. Note that to find the voltage at node B the

voltage divider rule may be used, however, it is important to note that VDR cannot be used in

terms of R1 versus R2. Instead, R1 reacts against the entire series-parallel combination of R2

through R6. Similarly, R3 reacts against the combination of R4, R5 and R6. That is to say R5 and

R6 load R4, and R3 through R6 load R2. Because of this process note that VD must be less than

VC, which must be less than VB, which must be less than VA. Thus the circuit may be viewed as a

sequence of loaded voltage dividers.

2. Construct the circuit of Figure 9.1 using R1 = 1 k, R2 = 2.2 k, R3 = 3.3 k, R4 = 6.9 k, R5 = 10 k,

R6 = 22 k, and E = 20 volts. Based on the observations of Step 1, determine the theoretical


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voltages at nodes A, B, C and D, and record them in Table 9.1. Measure the potentials with a

DMM, compute the deviations and record the results in Table 9.1.

3. Based on the theoretical voltages found in Table 9.1, determine the currents through R1, R2, R4

and R6. Record these values in Table 9.2. Measure the currents with a DMM, compute the

deviations and record the results in Table 9.2.

4. Consider the circuit of Figure 9.2. In this bridge network, the voltage of interest is VAB. This may

be directly computed from VA - VB. Assemble the circuit using R1 = 1 k, R2 = 2.2 k, R3 = 10 k,

R4 = 6.9 k and E = 10 volts. Determine the theoretical values for VA, VB and VAB and record

them in Table 9.3. Note that the voltage divider rule is very effective here as the R1 R2 branch

and the R3 R4 branch are in parallel and therefore both “see” the source voltage.

5. Use the DMM to measure the potentials at A and B with respect to ground, the red lead going to

the point of interest and the black lead going to ground. To measure the voltage from A to B, the

red lead is connected to point A while the black is connected to point B. Record these potentials

in Table 9.3. Determine the deviations and record these in Table 9.3.

Observation Tables

Table 9.1

Voltage Theory Measured Deviation

VA

VB

VC

VD

Table 9.2

Current Theory Measured Deviation

R1

R2

R4

R6


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Table 9.3

Voltage Theory Measured Deviation

VA

VB

VAB

Questions

1. In Figure 9.1, if another pair of resistors was added across R6, would VD go up, down, or stay the

same? Why?

2. In Figure 9.1, if R4 was accidentally opened would this change the potentials at B, C and D?

Why or why not?

3. If the DMM leads are reversed in Step 5, what happens to the measurements in Table 9.3?

4. Suppose that R3 and R4 are accidentally swapped in Figure 9.2. What is the new VAB?


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Experiment no. 10

Multi-source DC Circuit Mesh Analysis

Objective

The study of mesh analysis is the objective of this exercise, specifically its usage in multi-source DC

circuits. Its application to finding circuit currents and voltages will be investigated.

Equipments



(3) 4.7 kΩ __________________

(4) 6.8 kΩ __________________

(5) 10 kΩ __________________

(6) 22 kΩ __________________

(7) 33 kΩ __________________

Circuit Diagram

Figure 10.1


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Figure 10.2

Theory

Multi-source DC circuits may be analyzed using a mesh current technique. The process involves

identifying a minimum number of small loops such that every component exists in at least one loop.

Kirchhoff’s Voltage Law is then applied to each loop. The loop currents are referred to as mesh

currents as each current interlocks or meshes with the surrounding loop currents. As a result there

will be a set of simultaneous equations created, an unknown mesh current for each loop. Once the

mesh currents are determined, various branch currents and component voltages may be derived.

Procedure


= 6.8 k and R3 = 10 k. To find the voltage from node A to ground, mesh analysis may be used.

This circuit may be described via two mesh currents, loop one formed with E1, R1, R2 and E2,

and loop two formed with E2, R2 and R3. Note that these mesh currents are the currents flowing

through R1 and R3 respectively.

2. Using KVL, write the loop expressions for these two loops and then solve to find the mesh

currents. Note that the third branch current (that of R2) is the combination of the mesh currents

and that the voltage at node A can be determined using the second mesh current and Ohm’s Law.

Compute these values and record them in Table 10.1.

3. Build the circuit of Figure 10.1 using the values specified in step one. Measure the three branch

currents and the voltage at node A and record in Table 10.1. Be sure to note the directions and

polarities. Finally, determine and record the deviations in Table 10.1.


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= 6.8 k, R3 = 10 k, R4 = 22 k and R5 = 33 k. This circuit will require three loops to describe

fully. This means that there will be three mesh currents in spite of the fact that there are five

branch currents. The three mesh currents correspond to the currents through R1, R2, and R4.

5. Using KVL, write the loop expressions for these loops and then solve to find the mesh currents.

Note that the voltages at nodes A and B can be determined using the mesh currents and Ohm’s

Law. Compute these values and record them in Table 10.2.

6. Build the circuit of Figure 10.2 using the values specified in step four. Measure the three mesh

currents and the voltages at node A, node B, and from node A to B, and record in Table 10.2. Be

sure to note the directions and polarities. Finally, determine and record the deviations in Table

10.2.

Observation Tables

Table 10.1

Parameter Theory Experimental Deviation

IR1

IR2

IR3

VA

Table 10.2

Parameter Theory Experimental Deviation

IR1

IR2

IR4

VA

VB

VAB


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Questions

1. Do the polarities of the sources in Figure 10.1 matter as to the resulting currents? Will the

magnitudes of the currents be the same if one or both sources have an inverted polarity?

2. In both circuits of this exercise the negative terminals of the sources are connected to ground. Is

this a requirement for mesh analysis? What would happen to the mesh currents if the positions of

E1 and R1 in Figure 10.1 were swapped?

3. If branch current analysis (BCA) was applied to the circuit of Figure 10.2, how many unknown

currents would have to be analyzed and how many equations would be needed? How does this

compare to mesh analysis?

4. If the circuits of Figures 10.1 and 10.2 had been analyzed previously in the Superposition

Theorem exercise. How do the results of this exercise compare to the earlier results? Should the

resulting currents and voltages be identical? If not, what sort of things might affect the outcome?


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Appendix

(LABORATORY REGULATIONS AND SAFETY RULES)

The following Regulations and Safety Rules must be observed in all concerned laboratory

Location:

1. It is the duty of all concerned who use any electrical laboratory to take all reasonable steps

to safeguard the HEALTH and SAFETY of themselves and all other users and visitors.

2. Be sure that all equipment is properly working before using them for laboratory exercises.

Any defective equipment must be reported immediately to the Lab. Instructors or Lab.

Technical Staff.

3. Students are allowed to use only the equipment provided in the experiment manual or

equipment used for senior project laboratory.

4. Power supply terminals connected to any circuit are only energized with the presence of the

Instructor or Lab. Staff.

5. Students should keep a safety distance from the circuit breakers, electric circuits or any

moving parts during the experiment.

6. Avoid any part of your body to be connected to the energized circuit and ground.

7. Switch off the equipment and disconnect the power supplies from the circuit before leaving

the laboratory.

8. Observe cleanliness and proper laboratory house keeping of the equipment and other related

accessories.

9. Wear the proper clothes and safety gloves or goggles required in working areas that involves

fabrications of printed circuit boards, chemicals process control system, antenna

communication equipment and laser facility laboratories.

10. Double check your circuit connections specifically in handling electrical power machines,

AC motors and generators before switching “ON” the power supply.

11. Make sure that the last connection to be made in your circuit is the power supply and first

thing to be disconnected is also the power supply.

12. Equipment should not be removed, transferred to any location without permission from the

laboratory staff.

13. Software installation in any computer laboratory is not allowed without the permission

from the Laboratory Staff.

14. Computer games are strictly prohibited in the computer laboratory.

15. Students are not allowed to use any equipment without proper orientation and actual hands

on equipment operation.

16. Consumption of cooked food, packaged food and drinks in the laboratory are not

permitted.

All these rules and regulations are necessary precaution in Electrical Laboratory to safeguard

the students, laboratory staff, the equipment and other laboratory users.

ee 202 network theory laboratory - …agnigarh.tezu.ernet.in/~bjsece/ee 202 network lab...

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