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LABORATORY MANUAL EE 202 NETWORK THEORY
AUTUMN 2016 Page 1
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.
3. Tabulate the observation in table 3.
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.
3. Tabulate the observation in table 1.
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:
SL NO NAME OF THE APPARATUS SPECIFICATION QUANTITY
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:
SL NO NAME OF THE APPARATUS SPECIFICATION QUANTITY
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.
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OBSERVATION TABLE:-
Isc= ________ A
Vth = ________ V
Rth = _________ Ω
TABLE 1
Sl
No: Theoretical Experimental
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. Consider the dual supply circuit of Figure 4.2 using E1 = 10 volts, E2 = 15 volts, R1 = 4.7 k, R2
= 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
(2) Digital Multimeter
(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
LABORATORY MANUAL EE 202 NETWORK THEORY
AUTUMN 2016 Page 23
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:
SL NO NAME OF THE APPARATUS SPECIFICATION QUANTITY
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
No: Theoretical Experimental
% 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:
SL NO NAME OF THE APPARATUS SPECIFICATION QUANTITY
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 (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
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.
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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:
SL NO NAME OF THE APPARATUS SPECIFICATION QUANTITY
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:
1. Connect the circuit as shown in figure 7.1 and switch ON the supply.
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).
5. Switch off the supply after taking the readings.
6. Tabulate the theoretical and practical values.
Calculation of ABCD 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. 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).
5. Switch off the supply after taking the readings.
6. Tabulate the theoretical and practical values.
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)
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. Note the readings carefully.
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:
SL NO NAME OF THE APPARATUS SPECIFICATION QUANTITY
1 Circuit Board kit
2 CRO
2 Function Generator
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
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:-
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
(1) Adjustable DC Power Supply
(2) Digital Multimeter
(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
LABORATORY MANUAL EE 202 NETWORK THEORY
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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
(1) Adjustable DC Power Supply
(2) Digital Multimeter
(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
1. Consider the dual supply circuit of Figure 10.1 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, 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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4. Consider the dual supply circuit of Figure 10.2 using E1 = 10 volts, E2 = 15 volts, R1 = 4.7 k, R2
= 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.