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5th Sem Consolidate Lesson Plan
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DEPARTMENT OF EEECourse Information
Dept. of EEE Sess: Aug-Dec 2013 Sem: V Sem Page 1
V SEM LESSON PLAN
INDEX
SL.NO.
SUBJECTS CODE STAFF PAGE NO
1. INDEX -- -- 01
2. GENERAL GUIDELINES -- -- 02
3. Field Theory 11EE301 SV 3 5
4. Electric machinery - I 11EE302 MNV 6-12
5. Power Electronics 11EE303 VN 13-17
6. Digital Signal ProcessingSystems 11EE304 ASP 18-21
7. Control Theory 11EE305 SD 22-29
8. Electric machinery I Lab 11EE306 MNV 30
9. Power Electronics Lab 11EE307 VN 31
10. Digital Signal Processing Lab 11EE308 ASP 32
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DEPARTMENT OF EEECourse Information
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GENERAL GUIDELINES
1. Students are not permitted to attend the class without the identity card.2. Students should be well on time right from the first class.3. Students should keep the classrooms, laboratories and library clean.4. Writing on the desks and walls is strictly prohibited, failing which the students will be fined
heavily. If the identity of the individual is not established the entire class/students in the blockwill be fined.
5. Students are advised to show due respect to all faculty regardless of their department andmaintain an affable personality.
6. Students are to maintain absolute discipline and decorum, so as to promote the fair name ofthe college in all its activity.
7. Students securing less than 85% attendance in any individual subject will not be allowed totake up the University exams.
8. Students are informed that they may clarify their doubts in the respective subjects with thefaculty by taking prior appointment.
9. Students are to inform their parents to follow up the progress of their wards by being in touchwith the college authorities at regular intervals.
10. Ragging is punishable under Karnataka Education Act and is strictly prohibited. Any studentinvolved in ragging will be severely punished.
11. Students who secure less than 60% in the University Examination and / or who secure lessthan 60% in the internal test are to go through the Student Academic Support Programme(SASP) compulsorily. The guidelines will be issued separately by the concerned Department.
12. Students should come prepared for all the experiments before attending the laboratorysession.
13. Students should bring the component packet and completed observation book and laboratoryrecords to the laboratory & return the components issued in good condition at the end of thesemester, failing which double the component cost will be charged as fine.
14. Students have to score a minimum of 50% in internal assessment in the Lab & theory, failingwhich he/she will be denied the university exam under the clause not satisfying sessionalrequirements(NSSR).Sessional marks are given averaging best two of three tests conducted.No fourth test will be given. No appeals will be entertained regarding shortage of attendance.
15. The sessional marks will be displayed on the notice board at the end of the semester. It is theresponsibility of the students to verify the correctness and report discrepancies, if any, to theconcerned faculty / class incharge.
16. If a student is found guilty of any malpractices in the test, his/her sessional marks in all thesubjects of that test will be treated as zero. In addition, the parents have to personally comeand discuss the issue with the HoD to avoid rusticating the student from the college.
17. Students are informed to make adequate use of the locker facilities provided by the
department. The department will not be responsible for any loss of students belongings. 18. Mobile phone strictly prohibited on campus.
SMILE AND BE PROUD OF BEING A PART OF THE P.E.S.I.T FAMILY
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DEPARTMENT OF EEECourse Information
Dept. of EEE Sess: Aug-Dec 2013 Sem: V Sem Page 3
SUB: Fi eld TheorySUB CODE: 11EE301 NO. OF H OURS: 52 FA CULTY: S VENKAT ESH
UNIT
NO.
CHAPTERTITLE/REFERE
NCE
LITERATURE
CLASS TOPICS TO BE COVERED
% OF PORTIONSCOVERED
Test / Ref
CUMU
LLATIVE
1. Vector analysis& Electrostatics
1 - 2 Introduction Cartesian coordinates, cylindricalcoordinates, spherical coordinate systems
1/1/2
22
3 4 charge distributions, Coulombs Law, Field intensity,electric flux density
5 6 Relationship between Electric field and electric potential, Gradient
1/1/2
7 - 8 Gausss Law, Applications of Gausss Law,9 10 Divergence & divergence theorem11- 12 Electric dipole; Energy density in electrostatic fields. 1/1/2
2ELECTRICFIELDS IN
MATERIALSPACE
13 -14 properties of materials, convection and conductioncurrents
1/1/2
42
15 16 polarization in dielectrics, dielectric constant andstrength, continuity equation and relaxation time,
17 18 boundary conditions perfect dielectric, dielectric conductor, & with free space.
19 21 Poissons and Laplaces equation, solving Laplacesequation. to find C
1/1/2
22 - 23 Solution of Poissons equation; finding resistance,R
3. MAGNETOSTATICS
24 25 Introduction, Biot- Savarts Law, magnetic fluxdensity
1/1/2
60
26 27 Amperes law ; curl Stokes theorem28 29 magnetic scalar and vector potentials,
30 -31 Derivation of Biot- Savarts Law and Amperes Law. 1/1/232 33 Maxwells equation for static fields
4
MAGNETICFORCES,
MATERIALSAND DEVICESMAXWELLS
EQUATIONS
34 35 Introduction, forces due to magnetic fields, 1,1
82
36 37 magnetic torque and moment, a magnetic dipole,magnetization in materials
11
38 39 magnetic boundary conditions, inductors andinductances, magnetic energy
1,1
40 41 Faradays Law, transformer and motionalelectromotive forces
1,1
41- 42 dis placement current, Maxwells equations in finalforms, time varying Time harmonic fields
1,1
5
ELECTROMAGNETIC WAVEPROPAGATIO
N
43 - 44 Wave equation & solution, , plane waves in freespace
1,1
100
45 - 46 wave propagation in lossy dielectrics, plane waves inlossless dielectrics,
1,1
47 - 48 plane waves in good conductors, Poynting vector 1,1
51 52 reflection of a plane wave at normal incidence &oblique incidence
1,1
Reference literature:
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DEPARTMENT OF EEECourse Information
Dept. of EEE Sess: Aug-Dec 2013 Sem: V Sem Page 4
Reference books Title & Author
Publication Info
Edition Year
1 Engineering Electromagnetics- William H Hayt Jr., 7th 2007
2 Electromagnetics J.A. Edminister, Schaums outlines, 2n 2006
Text Books:
Test Books Title & AuthorPublication Info
Edition Year
1 Principles of Electromagnetics - Matthew N.O.Sadiku, Oxford University press
4TH 2011
Sample Question bank:Three point charges q1 = 10 6 coulomb, q2 = - 10 6 coulomb and q3 = 0.5x10 -6
coulomb are located in air at the corners of an equilateral triangle of 50 cm side. Determine the magnitudeand direction force on q3.
Four point charges, each 10 uC , are on the x and y axes at + 5 m . Find the force on a 400 uC point
charge at ( 0,0 , +7) m
Four point charges each 20 u C are placed on the X and Y axes at a distance of + 4 cm. Calculate theforce on a 100 uC point charge placed at (0, 0, 3) m
. A point charge is located at each corner of an equilaeral triangle, If the charges are 3Q, 2Q and 1Q , locatethe position ( not at infinity) at which the total force on a test charge is zero.
3 charges 2c, 2c and 3c lie on the vertices of an equilateral triangle side length d meters, find themagnitude and direction of the force on 3c charge.
Three negative charges Q, -2Q, -3Q are placed at the corners of an equilateral triangle. If thelength of each side is d find the magnitude and direction of the electric field at the point bisecting the line
joining Q and 3Q.Four point charges of +Q, -2Q, +3Q and 4Q coulombs are located at the corners of a square of side d.Find the intensity of electric field at , i) center of the square. ii) at the mid poit of line joining the charges+3Q and 4Q coulomb.
. Find E at ( 0, 0, 5) m due to Q1 = 0.35 C at ( 0, 4, 0 ) m and q2 =-0.55 uC at ( 3, 0, 0,)
. It is required to hold three point charges of +q coulomb each in equilibrium at the corners of an equilateraltriangle of side d. Find the magnitude of the point charge which will do this, if place at the centroid of thetriangle.
.It is required to hold four equal point charges, +q each in equilibrium at the corners of a square. Find the point charge which will do this if placed at the center of the square.
Two small identical conducting spheres having charges of 2x10 9 and 0.5x10 9 coulomb respectively,when they are placed 4 cm apart what is the force between them. If they are brought into contact and thenseparated by 4 cm , what is the force between them?
Two point charges of 10 9 coulomb and +10 9 coulomb are located at points P(-3 , 1, 5) m and Q ( 6, -5 ,2) m respectively find the value of electric scalar potential and electric field strength at the point R ( 3, -6, -9) m
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DEPARTMENT OF EEECourse Information
Dept. of EEE Sess: Aug-Dec 2013 Sem: V Sem Page 6
SUB: Electrical Machinery ISUB CODE: 11 EE 302 NO. OF HOURS: 52 FACULTY: M.N.Viswanath
UNITNO.
CHAPTER
TITLE/REFER ENCE
LITERATURE
CLASS TOPICS TO BE COVERED
% OF PORTIONS
COVEREDREFERENCE
CHAPTER
CUMULLATI
VE
1.
DC Generators
1-2
3
4-5
6
7
8-9
10-11
12
Introduction, Construction, Principle ofoperation, Types of armature winding. Lap andwave winding, characteristic features,
Generating modes and Motoring modes,
Armature Reaction in generators, Methods ofreducing these effects,
Problems
Commutation, Ideal Commutation,
Resistance Commutation, Voltage Commutation
Methods of excitation, MagnetizationCharacteristic ,Problems
Self excitation, Characteristics of generators,
Compound generators, Comparison of
V- I characteristic of dc generators
6.3,
7.1,
7.3-7.5,
7.7,
7.8 7.11
23 %
23%
2. D C Motors
13-19
(i) Principle of operation, Torque Equation
Problems
Characteristics of a shunt motor, Compoundmotor and Series Motor,
Torque and efficiency, Problems
Speed Control of shunt motors Armature andfield control, Ward Leonard method
7.12,
7.16
23%
46%
20-24
(ii) Testing of D C Machines, Testing of motors,Swinburnes Test, Hopkinsons Test, Advantagesand disadvantages of Hopkinsons test,Retardation test,Field test on dc series motor
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DEPARTMENT OF EEECourse Information
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3 Single PhaseTransformers
25-27
28-2930-32
33-35
Use of transformer, Construction Core type andShell typeEmf equation, ProblemsConcept of leakage flux and leakage reactance,operation of transformer under no load and onload with phasor diagramsEquivalent Circuit, Efficiency and Regulation,
problems
3.1-3.6
19.2%
65.2%
4
Testing ofTransformers
36- 38
39-40
41-42
Objective of testing, phasing out, polarity test,D.C resistance testOC and SC test, Sumpners test, Problems Parallel operation of two single phasetransformers- different cases, problems
3.7-3.9,3.14,
15.38%
80.58%
5Three PhaseTrnsformer
43-44
45-48
49-51
52
Connections of transformer:- Y- Y, -, Y- , -Y, ProblemsOpen , Three phase to two phase connections, Scott Connection, ProblemsAuto transformers , Principle, equivalent
Circuit, ProblemsAdvantages and disadvantages, No load and onload tap changers
3.11,3.13,3.15,3.16,3.17
19.42%
100%
Reference literature:
Reference books Title & Author
Publication Info
Edition Year
1.
Electrical MachineryBy
A.E.FitzgeraldCarles Kingsley,Jr.Stephen D Umans
Mc Graw-Hill
4th Edition1985
2Problems In Electrical Engineering
BYParker Smith
CBS Publishers
3
Theory and problems of ElectricalMachines
ByI..J.Nagrath and Kothari
TMH outline series 4 th print 1997 edition
4Electrical Technology
ByH.Cotton
CBS Publishers7th Edition 2005
Text Books:
Test Books Title & AuthorPublication Info
Edition Year
1.Electrical Machines by
I.J.Nagarath and Kothari 3rd edition
TMH Publishers 13th reprint 2009
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DEPARTMENT OF EEECourse Information
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QUESTION BANK:
1. What are the different types of DC Generators ?
DC Generators are characterized by the method in which the flux is produced in the magnetizing circuit (
Field Winding ) of the DC generator. The flux required for the DC Generator is produced by
1. A Permanent magnet
2. Field Coils excited by the external source
3. Field Coils excited by the same source.
Based on the method of excitation flux produced DC Generators are Characterized by
Separately Excited DC Generator:
In Separately excited DC Generator the field winding excitation current (which produces the flux) of the DC
Generator is controlled by the External source such as battery or current from a small DC machine.
Series Wound Generator:
In Series Wound Generator the field winding of the DC Generator is connected in series of the armature
winding of the DC machine. The current which flows out from the DC Generator through the armature
winding the same current flow through the series field winding of the DC Generator. Series field winding
consists of thick coils of lesser turns.
Shunt Wound Generator:
In Shunt wound Generator the field winding of the DC Generator is connected in parallel to the armature
winding of the DC Generator. In Shunt type of construction the current produced at the armature is divided
between the load and field winding. Some part of the current flow through the field winding and remaining
through the load. Shunt field winding consists of high resistance winding with thin coils of more turns
Compound Wound Generator:Compound wound generators contain both series and shunt type of field windings. They are connected aslong shunt and short shunt. In long shunt the shunt field winding is connected parallel to the series windingand armature winding. In Short shunt type of arrangement the shunt field winding will be placed just parallelto the armature winding alone. This type of machines has the both the characteristics of series woundmachine and shunt wound machine.
2 What are the Characteristics of DC Generator?
Magnetic or Open circuit characteristics:
This is also called no load characteristics. It gives the relation between the generated emf in the armature on
load and field current at constant speed.
Internal or total Characteristics:
This gives the relation between the emf generated in the armature and the armature current
External Characteristics:This curve gives the relation between the terminal voltage and armature current under constant speed andexcitation.
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3. Why Saturation Curve for the DC Generator does not start with zero?
Saturation curve or Magnetization curve in a DC Generator gives the relation between the Field Ampereturns (X axis) required to produce the flux per pole ( Y axis ). This curve starts from a point which is slightlyhigher than the origin representing that there is some flux produced by the field poles even no current is
passed through the field windings. This flux produced is because of the property called residual magnetism
which always exists in the DC Generator with out which DC Generator cannot be started. 4 What is Open Circuit Characteristics of DC Generator ?
Magnetic or Open Circuit Characteristics of a DC Generator is the plot between the Field Current in Amps (
X axis) required to produce or build up emf in the generator terminals ( Y axis) of a DC Generator.
EMF generated E=KN.
Where K is the constant
is the flux and
N is the speed of the DC Generator
Under constant speed the emf generated o f the dc generator proportional to the flux .Which is producwith the amount of field current.
Therefore it is a curve drawn between the generating emf produced under no load and field current when themachine is running at constant speed. It is the curve drawn under no load,so it is called open circuitcharacteristics of the machine.
5 Given the OCC curve and what happen when the field resistance of the generator increases?
When the field resistance of the DC generator increases then the slope of the OCC characteristics of the dcgenerator increases, i.e., the line will move to the left towards the vertical position. This can be explained
with the help of Ohms law. 6 What is Critical Field Resistance?
Critical Resistance of a DC Generator is defined as the maximum field resistance required to start the dcgenerator. Beyond this resistance the generator will not able to build up the voltage (EMF) and the motorfails to start. So care should be taken that field resistance of the dc generators should be less than the criticalresistance.
7 What are the causes of failure to build up voltage in DC Generator?
In a DC Generator voltage will be build up in a step wise manner.
Some of the reasons for the generator failure to build up the voltage are
1. No Residual magnetism
2. Reversal of Field connections ( destroys the residual magnetism when connections reversed)
3. Resistance of the field winding is more than the Critical Resistance
8 Explain the applications of the DC Generators?
1. Separately excited Generators are used in Ward Leonard Systems of speed control because self
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excitation at lower voltage would be unstable.
2. Series Wound generators are used in regenerative braking operation of the electrical dc
locomotives. They are used in series lighting.
3. Shunt wound generators with field regulators are used in the light and power supply requirements.
They have the property of providing constant voltage at any load.4. Cumulative compound generators are used in lighting and power supply requirements
5. Differential compound generators are used in applications where generators are required related to
the arc welding.
9 Explain the Importance of the Commutator in DC Machine?Answer: Commutator in the DC machine is the component which converts the ac induced current in thearmature to the uni directional current or dc current to the load circuit.In the DC Generator the due to theElectro-magnetic Induction principle the current induced in the armature coils are alternative current innature.Commutator of the DC machine contains segments separated by the insulation medium.It happens that when the alternating current in the armature varies from one half cycle ( say positive halfcycle) and enters in to other half cycle ( say negative half cycle), at the same time the polarity of the
commutator segments changes i.e, initially the commutator segment which is in contact with the positive polarity of the brush when the induced currents in the armature changes at that instant the segment of thecommutator which is earlier in contact with the positive polarity brush will now will be in contact with thenegative polarity brush results in the same direction of current flow in the external circuit.
10 Commutator in a DC machine converts AC to DC or DC to AC quantity of the current?Answer: In DC Generator the commutator converts from AC induced current produced in the armaturewindings is converted to DC and gives to the external load connected.On the Other hand, in case of DC Motor when the supply given is DC it is converted from DC to AC and
provided to the armature windings so that in order to produce the rotational torque.Thus Commutator in a DC machine converts both AC to DC and DC to AC.
11 What are Eddy currents and where they are present in DC machine and how they are minimized?Answer: Eddy currents are the circulating currents produced in the iron because of the alternating magneticfield. This eddy currents will cause local circulating currents which produces flux and magnetic field which
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apposes the main magnetic field. This results in the loss to the machine.Eddy currents are produced in the field poles and armature of the DC machineEddy Currents are minimized by providing thin laminations separated by the insulating coating Thislaminations reduces the area for producing the circulating currents. Hence eddy current losses are minimized.
12 What happen when the poles of the DC Generator increases?Answer: When the poles of the DC Generator increases the rate at which the coils cut the magnetic fluxincreases ( For two pole machine the rate at which the flux cut by the conductor is less compared to four polemachine), at constant speed this results in the increase in the production of the output voltage.More number of poles in DC Machine have some advantages such as Overall diameter and length of themachine reduces, reduction in weight of the core and the yoke. Reduction in the copper usage for the fieldand armature windings, and reduction in the length of the commutator.It also have some disadvantages such as Frequency of flux reversals increases results in increase of the ironloss, labor charges increases and sparking at the brushes takes place and commutation failure occurs.
13 Explain the relation between torque and speed of dc motorSpeed of DC motor N is proportional to (E b/) Torque of DC machine T is proportional to Ia Eb is the back emf of the motor is the flux Ia is the armature current of the DC motor
From the above two equations it can be derived that with increase in the flux () can increase the and decrease the speed of the machine (N). But with increase in torque which is cause of the rotation of themotor will also have to increase the speed of the machine. The above two equations contradict with eachother.When the motor is running with constant speed, when the field strength is made weak which can be possible
by providing an additional resistance in the field circuit in a dc shunt motor. The immediate effect will bemomentary reduction in the back emf (Eb). Back emf in a dc machine limits the flow of armature currentduring normal operation. As the back emf is reduced armature current (Ia) increases. With the increase in thearmature current, torque (T) increases momentarily. The increased torque accelerates and motor ( speedincreases ) and back emf increases. The motor will attain steady speed when the back emf attains steady
value. Thus the decreased flux results in decrease in back emf which increases the armature current. Thisarmature current increase the torque. Excess torque generated increases the speed of the machine.
14 Can I connect a single-phase transformer to a three-phase source?
Yes, and the transformer output will be single-phase. Simply connect any two wires from a 3- or 4-wiresource to the transformer's two primary leads. Three single-phase transformers can be used for three-phaseapplications. They can be used in delta-connected primary and wye or delta-connected secondary. To avoidan unstable secondary voltage, NEVER connect wye primary to delta secondary.
15 Can I use a transformer to change three-phase to single-phase?
It is not possible for a transformer to present a balanced load to the supply and deliver a single-phase output.
Changing three-phase to two-phase, and vice-versa, can be done using special circuitry with standard dual-wound transformers.
16 Can Transformers be used in parallel?
It is very common for transformers to be placed in parallel service. To provide maximum efficiency andvoltage, impedance values must match closely for each transformer involved. A failure to match voltage andimpedances will cause unbalanced loading for the transformers and may lead to "overheating" or premature
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failure.17 What is a non-linear (K-factor) transformer?
A transformer that is designed to handle the odd harmonic current loads caused by much of today's modernoffice equipment. A non-linear transformer has a K-factor rating that is an index of its ability to supplyharmonic content in its load current while remaining within its operating temperature limit.
18 How can we minimize eddy current loss in transformersBy laminating the core we can minimize eddy current loss in transformers19 A 5 kVA transformer has 35 W core loss and 40 W copper loss at full load. It operates at rated kVA and 0.8
power factor lagging for 6 hours, one half rated kVA and 0.5 power factor lagging for 12 hours and no loadfor 6 hours. Find its all day efficency?
Copper loss at full load for 6 hours = 40 * 6 = 240 WhCopper loss at full load for 12 hours = 40 * (1/2) 2 * 12 = 120 WhTotal copper loss for 24 hours = 360 Wh = 0.360 WhIron loss for 24 hours = 35 * 24 = 840 Wh = 0.84 kWhTotal loss in one day of 24 hours = 0.36 + 0.84 = 1.2 kWhTransformer energy output in 24 hours = 6* full load output + 12 * full load output
= 6 * (5 * 0.8) + 12 * (2.5* 0.5) = 39 kWh
Therefore all day efficiency = 39/(39 + 1.2) = 0.97 = 97 %20 The primary of a 1000/250 V step-down transformer has a resistance of 0.15 and leakage reactance of 0.
. Find the primary induced emf when the primary current is 60 Amperes at 0.8 power factor lagg
The primary impedance is Z 1 =0.15 + j 0.8 = 0.814 79.6 Cos =0.8, =-36.9
I1 = 60 -36.9 = 60 * ( 0.8 j 0.6) = 48 j 36 AThe leakage impedance drop isI1Z 1 = (0.814 79.6 ) * (60 -36.9) = 48.8 42.7 = 30 + j 27.5 V
Therefore primary induced emf is given byE 1 = V 1 I 1 Z 1 = 970.5 -1.6
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SUB: POWER EL ECTRONI CS
SUB CODE: 10EE303 NO.OF H OURS: 52 FACULTY: VASUDHA N.
UNIT
NO.
CHAPTERTITLE/REFERENCE
LITERATURE
CLASS TOPICS TO BE COVERED
% OF PORTIONSCOVERED
REFERENCE
CHAPTER
CUMULATIVE
1.POWER DEVICES
1. Power semiconductor Devices
24 24
2. Control characteristics of power devices
3. Types of power electronic circuits
4. Thyristor characteristics
5. Two transistor model of thyristor
6. Thyristor turn-on di/dt protection , dv/dt protection
7. Thyristor turn-off
8. Thyristor types- phase-controlledthyristors
9. fast-switching thyristors
10. GTOs, TRIACs,RCTs,SITHs and LASCR
11. Series operation of thyristors
12. Parallel operation of thyristors.
2.
THYRISTORCOMMUTATION
TECHNIQUES:&
DC CHOPPERS
13. Natural Commutation, ForcedCommutation- Self commutation
20 44
14. Impulse commutation
15. Resonant pulse commutation
16. Complementary commutation.
17. Principle of step-down operation
18. Step-Down chopper with RL load
19. Principle of step-up operation
20. Switch mode regulators- buck regulator
21. Buck regulator
22. Boost regulator, buck-boost regulators
3. PULSE-WIDTH- 23. Principle of operation 20 64
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MODULATEDINVERTERS
24. Three-phase inverters-180-degree and120-degree conduction
25. Three-phase inverters 120-degreeconduction
26. Problems on above topic
27. Single-phase bridge inverters
28. Voltage control of single-phase inverters
29. Single-pulse-width modulation
30. Multiple pulse-width modulation
31. Sinusoidal-pulse-width modulation
32. Phase-displacement control
4. CONTROLLEDRECTIFIERS
33. Principle of phase-Controlled converteroperation
20 84
34. Single-phase semi converters
35. Problems
36. Single-phase full converters
37. Problems
38. Single phase dual converters
39. Problems
40. Three-phase full converters with RL load
41. Problems
42. Power factor improvements- extinction
angle control
5.
AC VOLTAGECONTROLLERS
43. Principle of on-off control
20 10044. Problems
45. Principle of phase control
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46. Problems
47. Single-phase bidirectional controllers withresistive loads
48. Problems
49. Problems
50. Single-Phase Controllers with inductiveloads
51. Problems
52. Problems
Reference literature:
Reference books Title & Author
Publication Info
Edition Year
1.
Power Electronics,
by
M.D.Singh & Khanchandani K.B
2nd edition TMH
Text Books:
Test Books Title & Author Publication InfoEdition Year
1.
Power Electronics devices
by
M. H Rashid
Pearson education
( 2nd edition)
QUESTION BANK:
1. Define latching and holding current.
2. What are the factors that influence the turn off time of a thyristor?
3. Explain snubber circuit protection.
4. Give the applications of BJT?
5. Differentiate MOSFET and IGBT.
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6. Discuss the different modes of operation of thyristor with the help of static
VI characteristics.
7. Draw the switching characteristics of SCR and explain it.
8.
Discuss the different modes of operation of TRIAC with the help of VI
characteristics.
9. Draw the basic structure of an IGBT and explain the operation.
10. Draw the transient characteristics of IGBT and explain it.
11. Explain the construction and operation of power MOSFET.
12. Explain the switching characteristics of MOSFET.
13. Explain the driver circuit and protection circuits for MOSFET.
14.
Explain the switching characteristics of GTO. Indicate clearly the various
intervals into which turn-on and turn-off times can be subdivided. Discuss briefly
the nature of these curves.
15. Draw complete protection scheme for a SCR and explain the use of each and
every component.
16. Explain the operation of LASCR.
17. What do you mean by commutation?
18. Describe Snubber circuit?
19. Describe the di/dt rating?
20. Discuss various methods of forced commutation in brief.
21. Differentiate between constant frequency and variable frequency control
strategies of varying duty cycle of dc choppers.
22. Distinguish step down and step up converters.
23. Explain the buck-boost converter
24.
Discuss the principle of operation of DC-DC step down chopper with suitable waveforms. Derive the
expression for its average dc voltage
25. Describe various types of PWM inverters with their working?
26. Enumerate the various methods by which thyristors be triggered into conduction
27. Describe the sinusoidal pulse modulator?
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28. Describe the Multiple Pulse modulations?
29. What is PWM? Explain the various techniques involved in it.
30. What is full converter? Mention its uses.
31. What is a delay angle of converters?
32. Write the expression for 3_ full converter with RL load.
33. Differentiate unidirectional and bi-directional ac voltage controllers
34. What are the difference between Freewheeling Diode and feedback diode?
35. Draw and explain the circuit for Extinction Angle Control, with various waveforms.
36. What are the advantages and disadvantages of AC voltage controllers?
37. Differentiate unidirectional and bi-directional ac voltage controllers
38. Write the e xpression for 3 full converter with RL load.
39. Write the expression for 3 full converter with R load.
40. What are the advantages and disadvantages of on-off control?
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DEPARTMENT OF EEECourse Information
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DIGITAL SIGNAL PROCESSING
Sub Code : EE 304 SEM: 5 th Sem
Faculty : Asha.S.Patil No of Classes :52
Class No.
Chapter title/Referenceliterature
Topics to be covered % of Portions to becoveredReferencechapter
Cumulativ
1-4 Review of signals andsystems
Convolution, Impulse response, Fourier representation.
5-14
Chapter1- DiscreteFourier Transform
(Properties andApplications)
Text 1: chapter 7
The DFT Frequency domain sampling and reconstruction of discrete timesignals, DFT as a linear transformation, relationship with other transforms,
properties periodicity, linearity and symmetry, multiplication of DFTsand circular convolution, use of DFT in linear filtering.
19 19
15-25
Chapter 2 - EfficientComputation of DFT:
Fast Fourier TransformAlgorithms
Text 1: chapter 8
Direct computation of DFT, FFT Algorithms- Radix-2, Decimation inTime FFT Algorithm, Decimation in Frequency FFT Algorithm and in-
place computations.19 38
90I26-33
Chapter 3 Analog filters Text 1: chapter 10
Characteristics of commonly used analog filters Butterworth andChebyshev filters, Analog to analog frequency transformations.
19 57
34-43
Chapter 4- Design of IIRfilters from analog filters
Text 1 chapter 10
IIR Filter design using approximation of derivatives, Impulse Invariancetechnique,
bilinear transformation, Matched z-transform, Verification for stability andlinearity during mapping.
23 80
44-52CHAPTER 5- FIR filter
design Text 1 chapters 9 and 10
Introduction to FIR filters, design of FIR filters using Rectangular,Hamming, Bartlet and Kaiser windows, FIR filter design using frequencysampling technique. Implementation of discrete-time systems: Structuresfor IIR and FIR systems-direct form I and direct form II systems, cascade,lattice and parallel realization.
20 100
Book type Code Title and author Publication informationEdition Publisher Year
Text book Digital Signal Processing Principle, algorithms and applications.Proakis and Manolakis
4e Pearson/PHI, 2007
Reference Digital Signal Processing Sanjit K. Mitra, 2e TMH 2001Understanding Digital Signal Processing Richard Lyons 2e Pearson 2005
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QUESTION BANK:
1. Define DFT and IDFT. Explain why DFT is basically applicable for aperiodic signals. Also explain the necessity ofcomputing DFT of a given signal.
2. Substantiate the following statements:I. DFT of aperiodic and periodic extended signals of length L are same.II. Periodic extended signal and its shifted version can be represented on a circle with modulo operation.
III. Response computed by N-point circular convolution and Linear convolution are not same for the given N length sequences
IV. It is unnecessary to compute all points of X (k), if x (n) is real.V. Inverse of twiddle matrix can be computed using the conjugate of twiddle matrix.
3. Show that DFT can be computed for periodic as well as aperiodic signals. Under what condition x(n) is recoveredfrom periodic extension signal xp(n). Is the same true for computing IDFT?
4. What is twiddle factor? Explain how DFT and IDFT are expressed as a linear transformation and establish therelationship between W N and W N
-1.5. Compute the DFT of x (n) = {0, 1, 2, 3} by a) direct computation and b) Linear transformation.6. Obtain N-point DFT of
i) x (n) = 1 for n even and x (n) = 0 for n odd.ii) x (n) = cos ( )
20
nk N
.
7. State and prove i) Periodicity and ii) Linearity properties of DFT or IDFT.8. Show that circular shift of an N point sequence is equivalent to a linear shift of its periodic extension.9. Show that for real sequences: X (N-k) = X * (k) = X (-k). For any sequence show that x ((-n)) N = X (N k).10. Given x1 (n) = {0,1,0,1} & x2 (n) = {1,1,0,0}. Prove that Y (k) = 2X1(k) +X2 (k), where Y (k) is the DFT {2 x1 (n)
+ x2 (n)}.11. Compute the DFT of the sequence x (n) = {2, 1, 1, 2}. Use appropriate property to compute the DFT of I) x ((-n))
and ii) x ((n-2)) 412. Show that DFT of W N
n l x (n) is X ((k l)) N.If g (n) = { 3.1, 2.4, 4.5, 6, 1, 3, 7} and H (k) = G ((k 4)) 7, compute h (n) without computing the DFT.13. Obtain simpler DFT or IDFT formulas when the sequence is i) real and even ii) real & odd iii) purely imaginary.14. Show that multiplication of two DFTs is the circular convolution of the two sequences given.15. Perform circular convolution on x (n) = {2, 1, 2, 1} and h (n) = {1, 2, 3, 4} using i) concentric circles method II)
tabular method.16. Explain how circular convolution is different from linear convolution. Given the impulse response of a system, what
adjustments are carried out in order to compute the response of a system due to a given excitation by the twoconvolutions?
17. Obtain the circular convolution of the sequences x (n) = (2, 1, 2, 1} and h (n) = {1, 2, 3, 4} using DFT and IDFT ofthe sequences.
18. Use direct evaluation and appropriate property to find DFTs of real sequences I) x1 (n) = {0, 1, 2, 3, {0, 1, 0, 0, 0}. Compute a sequence y (n) so that Y (k) = X1 (k) X2 (k).
19. Use DFT and IDFT to compute the response of a FIR filter, given its impulse response h( n) = { 1,2,3), to the inputsequence x (n) = { 1,2,2,1}.
20. State and prove i) circular time shift and ii) circular frequency shift properties of N point DFT.21. State and prove the DFT property: multiplication of two sequences.22. Show that DFT of W N
n l x (n) is X ((k l)) N.If g (n) = { 3.1, 2.4, 4.5, 6, 1, 3, 7} and H (k) = G ((k 4)) 7, compute h (n) without computing the DFT.23. State and prove Parsevals theorem in DFT for two complex valued sequences x (n) and y (n).24. Discuss the problems associated with filtering of long data sequences using DFT and IDFT and suggest methods by
which such filtering can be done efficiently.25. Explain i) overlap-save and overlap-add methods of filtering long duration sequences.26. Given the input sequence x (n) = {1, 1, 2, 2, 0, 1, 1, -2, 1, 0, 1, 2) and impulse response of the system h (n) = {1, -
1}. Use overlap save method to compute the response of the system.
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27. Given the input sequence x (n) = {1, 1, 2, 2, 0, 1, 1, -2, 1, 0, 1, 2) and impulse response of the system h (n) = {1,-1}.Use overlap add method to compute the response of the system.
28. The first 10 samples of a long duration sequence isx (n) = {1, 0, 2, 0, 0, 2, 1, 0, 0, 1}. The impulse response of the system is h (n) = {0, 1}. Use overlap add or overlap save method to compute the response up to the first 10 samples by evaluating 4-point DFT and IDFT.29. What is FFT? Explain the need for an FFT algorithm. Tabulate the number of various computations required by
FFT algorithm with the direct computation of DFT for an N point sequence. .30. Develop a DIT FFT algorithm to compute N point DFT X (k) of an N point sequence.31. Develop a DIF FFT algorithm to compute N point DFT X (k) of an N point sequence.32. Develop a decimation in - time 2 radix FFT algorithm to compute N - point DFT X (k) of an N - point sequence x
(n). Also explain butterfly configuration for implementation.33. Given x (n) = {1, 2, 3, 4, 4, 3, 2, 1} find X (k) using DIT radix 2 algorithm.34. Given x (n) = {1, 2, 3, 4, 4, 3, 2, 1} find X (k) using DIF radix 2 algorithm.35. A 50 Hz sinusoidal signal of 1 V peak value is sampled 8 times in a cycle. Compute its frequency samples using
suitable DFT algorithm.36. Given x (n) = n + 1, find 8 - point DFT using DIF FFT algorithm.37. Compute the 4 point DFTs using radix -2 algorithm of the sequences
i) x (n) = 1 for n even and x (n) = 0 for n odd.
ii) x (n) = cos ( )2
0nk
N
. Assume k 0 =1.38. The DFT X (k) of sequence is given as X (k) = {0, 2 2(1- j), 0,0,0,0,0, 2 2(1+j)}. Determine the correspondi
sequence x (n) and write its signal flow graph.39. First five points of 8 point DFT of a real sequence is given by X (0) =0, X (1) = 2+j2, X (2) = - j4, x (3)=2 - j2, x
(4) =0. Determine the remaining points. Hence find the original sequence x(n) using DIF FFT algorithm.40. Develop DIT FFT algorithm for N =3 X 3 and draw the complete signal flow graph.41. Develop DIF FFT algorithm for N =3 X 2 and draw the complete signal flow graph.42. Discuss the FIR and IIR systems and also discuss the need for different structures of realization.43. Realize a linear phase FIR filter with the following impulse response. Give the necessary equations. h
1 ) - (n-2)+ (n-4) + (n-3).
44. Realize the following system function by linear phase FIR structure: H (z) =3
2z + 1 +
3
2 1 z .
45. Realize the following system function in i) direct from and ii) cascade form: H (z) = 1+4
3 1 z +8
17 2 z
4
3 3 z + 4 z
46. Obtain he direct and cascade realization of the following FIR filter transfer function: H (z) = (1 -4
1 1 z +8
3 2 z
(1 -8
1 1 z +2
1 2 z ).
47. Obtain the direct form 1, direct form 2, cascade and parallel form realizations for the system: y (n) = 0.75 y (n-1) 0.125 y (n-2) +6 x (n) +7 x (n-1) + x (n-2).
48. A system is represented by a transfer function given by H (z) =i) Does H (z) represent a FIR or IIR system?ii) Give a difference equation realization of this system using direct form 1.iii) Draw the block diagram for the direct form 2 canonic realization and give the governing equation
for implementation.
49. The transfer function of a discrete causal system is given by
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H (z) = 21
1
15.02.011
z z
z
i) Find the difference equation.ii) Draw cascade and parallel realization.iii) Calculate the impulse response of the system.
50. Obtain the direct from 2 and cascade realization of H (z) = 3 +
2
14
z
z -
4
12
z
The cascade section should consist
of two bi-quadratic sections.
51. Obtain ladder form realization using Routh array technique for the system function H (z) = 21
21
1281682
z z
z z
52. Obtain ladder form realization using continued fraction expansion technique for the system function H (z) =
21
21
1231 z z
z z
53. What are analog and digital filters? Give the differences and also list advantages and disadvantages of the twofilters.
54. Explain the following methods of designing digital filters from analog: i) impulse invariance method ii) Bilineartransformation.
55. List the properties of i) Butterworth filter ii) Chebyshev filter with reference to low pass filters.56. Derive equation for the order of filter and cutoff frequency of low pass Butterworth filter in terms of given
specifications.57. Derive equation for the order of filter and cutoff frequency of low pass Chebyshev type 1 filter in terms of given
specifications58. What do you understand by warping effect? What is its effect on the magnitude and phase response? What is pre-
warping?59. Compare Chebyshev type 1 and Chebyshev type 2 filters and derive an expression for the order of Chebyshev type
2 filter.60. Design a low pass Butterworth filter to satisfy the constraints:
0.8 | H () | 1 0 0.2 | H () | 0.2 0.6 using impulse invariant technique.
61. Design a low pass Butterworth filter to satisfy the constraints:0.8 | H () | 1 0 0.2
| H () | 0.2 0.6 using bilinear transformation technique.
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CONTROL THEORY
LESSON PLAN
Subject Code:11 EE 305 Faculty: Prof. Susmita Deb No. of Hours: 52
Unit(Class#)
Chapter Title/Reference Literature Portions to be Covered
% Portions CoveredReferenceChapter
Cumulative
1
(1-12)
Chapter:2
Mathematical Models of Systems
T: 2.1 to 2.7
Introduction, Differential Equations ofPhysical Systems, Linear Approximationsof Physical Systems, The LaplaceTransform, The Transfer Function ofLinear Systems, Block Diagram Models,Signal Flow Graph Models.
24 24Chapter:4
Feedback Control SystemCharacteristics
T: 4.1 to 4.6
Open and Closed Loop Control Systems,Sensitivity of Control Systems to ParameterVariations, Control of the TransientResponse of Control Systems, DisturbanceSignals in a Feedback Control System, costof feedback.
2
(13-22)
Chapter:3
State Variable Models
T: 3.1 to 3.4,3.6 & 3.7
Introduction, The State Variables of aDynamic System, The State DifferentialEquation, Signal Flow Graph StateModels, Transfer function from the stateequation, The time Response and theState Transition Matrix.
19 43Chapter:5
The Performance of FeedbackControl Systems
T: 5.1 to 5.8
Introduction, Test Input Signals,Performance of a Second Order System,Effects of a Third Pole and a Zero on theSecond Order System Response,Estimation of the Damping Ratio, The s Plane Root Location and the TransientResponse. Steady State Errors of unityand non-unity feedback systems
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Unit(Class#)
Chapter Title/Reference Literature Portions to be Covered
% Portions CoveredReferenceChapter
Cumulative
3(23-32)
Chapter: 6
The Stability of LinearFeedback SystemsT: 6.1 to 6.4
The Concept of Stability, The Routh HurwitzStability Criterion, The Relative Stability ofFeedback Control Systems, The Stability ofState Variable Systems.
19 62Chapter: 7
The Root Locus Method
T: 7.1 to 7.4
Introduction, The Root Locus Concept, TheRoot Locus Procedure, an Example of a ControlSystem Analysis and Design utilizing by RootLocus method.
4(33-42)
Chapter: 8
Frequency Responsemethods
T: 8.1 to 8.5
Introduction, Frequency Response Plots, theBode Diagram, Frequency ResponseMeasurements, Performance Specifications inthe Frequency Domain.
19 81Chapter: 9
Stability in the FrequencyDomain
T: 9.1 to 9.6
Introduction, Mapping Contours in the s Plane, The Nyquist Criterion, Relative Stabilityand the Nyquist Criterion, Time DomainPerformance Criteria Specified in the frequencyDomain, System Bandwidth.
5(43-52)
Chapter: 10
The Design of FeedbackControl Systems
T: 10.1-10.4, 10.8, 9.9
Introduction, Approaches to System Design,Cascade Compensation Networks, Phase Leadand Phase-Lag design using Bode Diagram. P,
PI, PID controllers.19 100
Chapter: 11
The Design of StateVariable Feed Back
SystemsT: 11.1-11.3,11.5,11.6
Introduction,Controllability, Observability, pole-placement using state-variable feedback.Ackermanns formula.
Literature:
Text book: Modern ControlSsystems, R.C. Dorf and R.H. Bishop, Addison-Wesley, 8 th edition,1999.
Reference Books:1. Control Systems Engineering, I.J.Nagrath and M.Gopal, New Age International Publications, 5th edition,2007.2. Modern Control Engineering, K.Ogata, Pearson Education Asia, 4 th edition, 2002.3. B.C.Kuo, Automatic Control Systems, PHI, 5 th Edition, 1989.
Portions for T1: Unit 1 & Unit 2 (1 st half) Portions for T2: Unit 2 (2 nd half) & Unit 3Quiz : Unit 1 to 5
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Question Bank
1. Compare closed loop control systems with open-loop control systems on the basis of(i) gain or transfer function(ii) sensitivity to parameter variations(iii) rejection to disturbance input2. Determine the overall transfer function (C/R) of the system shown in figure by block diagram reductiontechnique.
3. Draw the Signal flow graph of the above system & verify the result by using Masons gain formula.
4. Obtain block diagram representation for an armature-controlled DC Servomotor. Find overall transferfunction of this system.Comment on order & type of this system.
5. Consider the following field-controlled position control system. The motor e.m.f e m is 100V. The motortorque constant K T = 0.5 Nm/ ampere and the inertia of load is 10
-4 kg-m 2. Assuming negligible viscousfriction, determine the transfer function (s) / VF(s).
6. Define transfer function.
Name two different kind of modeling of a system.
7. Find the transfer function E o(s)/E i(s) of the electrical system as shown below.
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8. Using Masons gain formula find C/R of the following signal flow graph.
9.What are the two major types of control system? Explain the difference between them.
10. Determine the overall transfer function (C/R) of the system shown in figure by block diagram reductiontechnique.
11. A system is described by its transfer function
Obtain a state-space model in phase variable canonical form. Also draw signal flow graph.12. For a unity feedback system whose open loop transfer function is
G(s) ) , find the position, velocity & acceleration error constants.
13. How a second order system is classified depending on the value of damping ratio?
14. Deduce expression for output response of a second order system for critically damped condition, when subjected to unit step input .
15. The closed loop transfer function of a unity feedback control system is given by-
=
Determine(i) Undamped natural frequency(ii) Damping ratio
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16. Obtain state-equation & output-equation of the mechanical system shown below.
Take state variables as x 1=x, x 2= , x 3 =y, x 4=17. List the properties of state transition matrix.
18. The unity feedback system is characterized by an open loop transfer function is G(S) = .
Determine the gain K ,so that the system will have a damping ratio of 0.5.For this value of K, determine
settling time, Peak overshoot and time to Peak overshoot for a unit-step input.19. Define(i) Delay time (ii) Rise time (iii) Peak overshoot (iv) settling time 20. Write state equation & output equation for the given electrical system.
21. What are the conditions for a system to be stable? 22. The closed loop transfer function of an antenna control system is given
by-
,
Determine the range in which K must lie for the system to be stable, unstable &limitedly stable.23. The matrix differential equation for a magnetic bearing system is
x
Where x T= [y, dy/dt,i], y= bearing gap, and I is the electromagnetic current. Determine whether the systemis stable.24. The open loop transfer function of a unity gain feedback is given by-
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(i) Determine all the poles & zeros of G(s).(ii) Draw the root locus.(iii) Comment on the stability of the system.
25. Deduce & draw the output response of a system whose transfer function is as given ,
when subjected to unit impulse response.26. Utilize the Routh table to determine the number of roots of the following polynomials in the right halfof the s-plane. Comment the stability of the system.s5+6s 4+15s 3+30s 2+44s+2427. For the characteristic equation of feedback control system given, determine the range of k for stability.Determine the value of k so that the system is marginally stable and find the frequency of sustainedoscillations.s4+25s 3+15s 2+20s+k=028. The open loop transfer function of a unity gain feedback is given by-
(i) Draw the root locus when K varies from 0 to infinity .(ii) Comment on the stability of the system.29. Write the rules for constructing the root locus.
30. Characteristic equation of a closed-loop system is given asF(S) =S 4 +5S 3 +5S 2+4S+10 =0.Find the number of roots falling in the RHS plane and LHS plane.31. A system has open-loop transfer function as
Draw root locus when K varies from 0 to & comment on the stability of the system. Now add a zero at s=-2, so that new open-loop transfer function is
Draw root locus when K varies from 0 to & comment on the effect of addition of zero regarding thestability of the system.32. Sketch the bode plot of the following open loop transfer function and from the
plot determine the phase margin and gain margin.
A.G(s) =100(1+0.1s)/s(1+0.2s)(1+0.5s)
33. A system has open-loop transfer function as
Draw Bodes plot & find gain cross-over frequency, phase cross-over frequency, Gain margin, and phasemargin from the plot.
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34. Check the stability of a system whose Nyquist plot is as given below.Given that there is no pole on the right half of s-plane.
35. What is polar plot ?
36. What is minimum phase system ?
37. What is All-Pass systems ?
38. Derive the expression for the frequency domain specifications of a
Second order system.
. Gain Margin
. Phase margin
. Gain cross over frequency
. Phase crossover frequency
39. Write the step by step procedure for plotting the magnitude plot andphase plot of a open loop systemrepresented by the transfer function G(s).
40. A system has open-loop transfer function as
Find the transfer function of the compensator circuit required to attain damping factor =0.5 & steady-stateerror for unit-ramp input, E ss= 0.16 unit.41.
A PID controller is implemented by the above electronic circuit, find the proportional gain K p, integral gainK I& derivative gain K D.42. What is compensation?
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43. What is compensator? What are the different types of compensator?
44. When lag /lead/lag-lead compensation is employed?
45. Why compensation is necessary in feedback control system?
46. What is lag-compensation?
47. What are the characteristics of lead compensation? When lead compensation is employed?
48. Write the transfer function of a typical lag-lead compensation49. Write the procedure to design a lead compensator
50. A unity feed back system has an open loop transfer function
G(s) = k /(s(s+1)). Design a suitable phase lag compensator to achieve the with usual notations. followingspecifications: kV =8 and phase margin= 40
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SUB: Electrical Machinery Lab I
SUB CODE: 11 EE 306Faculty: BKK/MNV/USV
Cycle 1:1 Open circuit and short circuit test on a 1 phase transformer and pre determination of efficiency &
regulation2 Speed control of D.C Shunt Motor by armature voltage control and flux control3 Load test on D.C Shunt Motor determination of speed torque and
B.H.P efficiency characteristics.4 Ward Leonard method of speed control of D.C Motor5 Load characteristics of a D.C shunt and compound generator6 Swinburnes Test
Cycle 2:1 Hopkinsons test
2 Retardation test- electrical braking method3 Sumpners Test 4 Parallel operation of two dissimilar 1 phase transformers5 Polarity test & connection of 3 single phase transformers in Y - and determination of efficiency &
regulation under balanced UPF load6 Scott connection for balanced and unbalanced two phase UPF loads
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POWER ELECTRONICS LAB
Cycle 1:
Cycle 2:
1. Static characteristics of SCR
2. Static characteristics of IGBT
3. Analysis of a self commutation circuit for commutating a SCR operating on a dcsupply
4. Analysis of an impulse commutation circuit for commutating a SCR operating on adc supply
5. Analysis of single quadrant MOSFET based chopper supplying R/ RL load
6. Testing a digital firing circuit for a line commutated SCR circuit
7. Analysis of a full bridge converter supplying R/RL load
8. Analysis of boost converter
9. Analysis of a single phase full bridge inverter with R/RL load
10. Study of stepper motor operation with control circuit
11. Speed control of PMDC motor using single quadrant chopper
12. Speed control of an universal motor using ac voltage controller
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DEPARTMENT OF EEECourse Information
DSP LABORATORY
Sub Code: 11EE308
Cycle 1:1 Computation of N point DFT of a given sequence and to plot magnitude
and phase spectrum.2 Linear convolution & Circular convolution of two given sequences 3 Circular convolution of two given sequences without using built in functionCycle 2:1 Autocorrelation & cross correlation of a given sequence and verification of its
properties. 2 Linear filtering of long sequence data by Overlap save & add techniques 3 Verification of sampling theorem.
Cycle 3:1 Design and implementation of IIR analog filter to meet given specifications. 2 Design and implementation of IIR digital filter to meet given specifications 3 Design and implementation of FIR digital filter using non- adjustable windows
to meet given specificationsCycle 41 Linear convolution & circular convolution of two given sequences using CCS2 Computation of N- Point DFT of a given sequence using CCS 3 Impulse response of first order and second order system using CCS