department of electronics and ... and density function of sum of two independent random variables....

VNR VIGNANA JYOTHI INSTITUTE OF ENGINEERING AND TECHNOLOGY

(AUTONOMOUS)

DEPARTMENT OF ELECTRONICS AND COMMUNICATIONS ENGINEERING

II B. Tech, Ist Semester

Subject : PROBABILITY THEORY AND STOCHASTIC PROCESS

Subject Code : 5EC02

Academic Year : 2016 – 17

Number of working days : 90

Number of Hours / week : 3 + 1*

Total number of periods planned: 64

Name of the Faculty Member: Shaik Khadar sharif, M. Haritha.

Course Description: The basic aim of this course is to provide a strong background in probability

theory, complete knowledge in statistical methods and stochastic process, with adequate number of

solved problems. The concepts offer clear and concise coverage of the theories of probability,

random variables, and random signals, including the response of linear networks to random signals,

characterization of noise to random signals and noise calculations in communication systems.

Course Objectives:

To describe and interpret the basic concepts of probability and stochastic processes.

To Describe and interpret the discrete time and continuous time stochastic processes.

To learn spectrum of Random process

To learn noise sources and their characteristics

Course Outcomes

After Completion of the course the student is able to

Apply the concepts of probability to experiments that have Random outcomes

Apply the statistical properties to the random variables and processes.

Estimate and Analyze noise characteristics in communication systems

SYLLABUS

UNIT I

Overview of Probability Theory: Definitions, Scope and history, sets, sample space and events,

Axioms of Probability, Discrete, Continuous and Conditional Probabilities, Independence, Total

probability, Bayes’ Rule and Applications.

Random Variables: Definition of Random Variable, classification of Random Variables, Probability

mass function, CDF and PDF of Random Variables and their properties (Single and Multiple

Random variables), Conditional distribution and densities, properties.

Distribution and Density function of sum of two Independent Random variables. Some Special

Random variables: Binomial, Poisson, Uniform, Gaussian, Exponential, Rayleigh, Transformation

of random variables.

UNIT II

Operations on Single and Multiple Random Variables: Mean, Variance, Skew and Moments of

Random Variables- Raw and Central Moments, Joint Moments, Marginal distribution and density

functions. Characteristic Function, Moment Generating Function, Operations on distribution and

density functions of special Random variables, central limit theorem.

UNIT III

Random Processes: Concept and classification of Random Process; Probabilistic structure of a

random process; Concept of Stationary Random Process, Wide Sense Stationary, Time Averages,

Ergodicity, Auto Correlation, Cross Correlation and Covariance of Random Processes.

UNIT IV

Spectral Characteristics of Random Process: Power Spectrum-Properties, Relation between PSD

and Autocorrelation function of a Random Process, Cross spectral Density and its relation with

Cross Correlation function.

Random signal Response of Linear Systems: System Response-Convolution, Mean and Mean-

squared value of system Response, autocorrelation Function of Response, Cross-Correlation

Functions of input and output, Spectral Characteristics of System Response; Power Density

Spectrum of Response, Cross Power Density Spectrums of Input and Output.

UNIT V

System Noise: Mathematical Modeling of Various system Noise sources, White Noise and colored

noise, Effective Noise Temperature, Noise Figure, Average Noise Figure of Cascaded networks.

TEXT BOOKS 1. Probability, Random Variables and Random Signal Principles - Peyton Z Peebles 4th Edidtion,TMH,

2001.

2. Communication Systems – R.P. Singh, SP Sapre, 2nd

Edition,TMH, 2007.

REFERENCES 1. Probability, Random Variables and Random Process – K. Murugeshan, P. Guruswamy, Anuradha

publicatoins.

2. Theory of probability and stochastic Processes – pradip Kumar Gosh University press.

3. Probability and Random processes with application to signal processing – Henry Stark and John W,

Woods, 3rd Edition, PE.

4. Principles of Communication Systems – H.Taub, Donald L. Schiling, Goutham Saha, 3rd

Edition,TMH,2007.

5. Probability, Random Variables and Stochastic Processes- Athanasios Papoulis and S. Unnikrishnan

Pillai,4th

Edition, TMH

Teaching plan

UNIT-I

Learning Objectives:

To understand the definitions of the probability

To illustrate the probability theorems

To define random variable from outcome of probability

To construct density and distribution functions and discuss their properties

Transform random variables from one variable to another variable

To define distribution and density functions of some standard random variables

S.No. Description of Topic No. of Hrs. Method of Teaching

1. Introduction to probability theory 1st Black board

2. Definitions, Sets and events, definition of

probability, Axioms of probability

2nd Black board + PPT

3. Discrete, Continuous and Conditional Probabilities,

Independent events.

3rd Black board + PPT

4. Total probability theorem, Baye’s Rule and

Applications and related problems

4th and 5th Black board + PPT

5. Introduction to Random Variable, Definition,

Discrete, continuous and Mixed random variables

6th Black board + PPT

6. Distribution and Density function of one variable and

its properties, related problems


7. Distribution and Density function of two variables

and its properties, related problems


8. Transformation of Random variables: Functions of a

single Random variables, Functions of two random

variables and Discrete /Random variables.


9. Definitions for distribution and densities of Gaussian,

Exponential, Rayleigh, Binomial, Poisson and

Uniform random variables - their properties and

applications


10. Problems on the above topics 15th and 16th Black board

Assignment/ Tutorial Problems:

1. A Jar contains 52 badges numbered 1 to 52. Suppose that the numbers 1 thro 13 are

considered ‘lucky’. A sample of size 2 is drawn from the jar with replacement. What is the

probability that A. both badges drawn will be ‘lucky’ B. Neither badge will be lucky

C. Exactly one of the badges drawn will be lucky D. At least one of the badges will be lucky

2 .What is the probability of picking an ace and a king from a deck of 52 cards

3. A box contains 4 point contact diodes and 6 alloy junction diodes. What is the probability that

3 diodes picked at random contain at least two point contact diodes

4. Find the probability of three half-rupee coins falling all heads up when tossed simultaneously

5. A letter is known to have come either from LONDON or CLIFTON. On the postmark only the

two consecutive letters ‘ON’ are legible. What is the Chance that it came from London

6. Show that the chances of throwing six with 4,3 or 2 dice respectively are as 1:6:18

7. A jar contains two white and three black balls. A sample of size 4 is made. What is the

Probability that the sample is in the order white, black, white, black

8. A box contains 4 bad and 6 good tubes. The tubes are checked by drawing a tube at random,

testing and repeating the process until all 4 bad tubes are located. What is the probability that

the fourth bad tube will be located (i) on the fifth test (ii) on the tenth test

9. If A and B are any events, not necessarily mutually exclusive events, derive an expression for

probability of A Union B. When A and B are mutually exclusive what happens to the above

expression derived

10. A coin is tossed. If it turns up heads, two balls will be drawn from box A, otherwise, two

balls will be drawn from box B. Box A contains three black and five white balls. Box B

contains seven black and one white balls. In both cases, selections are to be made with

replacement. What is the probability that Box A is used, given that both balls drawn are black.

11. In a single throw of two dice, what is the probability of obtaining a sum of at least 10

12. Three boxes of identical appearance contain two coins each. In one box both are gold; in the

second both are silver and in the third box one is silver and the other is the gold coin.

Suppose that a box is selected at random and further that a coin in that box is selected at

random. If this coin proves to be gold, what is the probability that the other coin is also gold.

13. A shipment of components consists of three identical boxes. One box contains 2000

components of which 25% are defective, the second box has 5000 components of which 20%

are defective and the third box contains 2000 components of which 600 are defective. A box

is selected at random and a component is removed at random from the box. What is the

probability that this component is defective. What is the Probability that it came from the

second box.

14. Consider the experiment of tossing four fair coins. The random variable X is associated with

the number of tails showing. Compute and sketch Cumulative distribution function of X.

15. A fair coin is tossed three times and the faces showing up are observed

i) write the sample description space. ii) If X is the number of heads in each of the outcomes

of this experiment find the probability function iii) Sketch the CDF and PDF

16. The continuous random variable X has a pdf f(x) = X/ 2, 0≤ X ≤ 2. Two independent

determinations of X are made. What is the Probability that both these determinations will be

greater than one. If three independent determinations are made, what is the probability that

exactly two of these are larger than one

17. A pair of dice is tossed. Define a random variable X to be the difference of the face values

turned up. Determine the probability mass function of X

18. An analog signal received at the detector may be modeled as a Gaussian random variable

N(200,256) at a fixed point in time what is the probability that the signal will exceed 240μV.

What is the probability that the signal is larger than 240μV, given that it is larger than 210μV

19. Find the mean value, mean squared value and the cumulative distribution function for the

Rayleigh distribution with parameter α > 0, specified by the pdf f(x) = x/ α2 exp -x / 2 α

20. Consider the probability density f(x) = a e-b| x |

, where x is a random variable whose allowable

values range from x = -∞ to ∞. Find i) the CDF ii) the relationship between a and b.

and iii) the probability that the outcome x lies between 1 and 2

21. The probability distribution function of X is given by the following table:

X 0 1 2 3 4 5 6

P(x) K 3K 5K 7K 9K 11K 13K

Find (i) P(X<4) (ii) P(X ≥ 5) (iii) P (3 < X ≤ 6 )

22. A continuous random variable X has a PDF f(x) = 3X2 , 0 ≤ X ≤ 1. Find a and b such that

P ( X≤ a) = P(x > a) and ii) P( X > b) = 0.05

23. If the probability density of a random variable is given by

f(x) = x for 0 < X < 1

= 2 – x for 1<X< 2

24. Find the probabilities that a random variable having this probability density will take on a

value i) between 0.2 and 0.8 ii) between 0.6 and 1.2

25. Two random variables have the joint probability density

f(x1 , x2) = 2/3 (x1 +2x2) for 0<x1 <1 , 0<x2 <1

= 0 else where Find (i) The marginal density of x2

(ii) Conditional desity of the first given that the second takes on the value x2

26. Let X and Y be jointly continuous random variables with joint density function

f( x,y) = xy exp [- ½ (x

2 + y

2)] x>0 , y> 0

= 0 other wise

Check whether X and Y are independent. Find i) P(X≤1,Y≤1) and ii) P(X+Y ≤1)

27. Two discrete random variables X and Y have joint pmf given by the following table:

X / Y 1 2 3

1 1/ 12 1/6 1/12

2 1/6 1/4 1/12

3 1/12 1/12 0

Compute the probability of each of the following events i) X ≤ 1 ½ ii) XY is even

iii) Y is even given that X is even

28. Let X and Y be jointly continuous random variable with joint pdf

f(x,y) = x2 + xy /3, 0 ≤ x ≤ 1 , 0 ≤ y ≤ 2

= 0 else where

find i) f(x) ii) f(y) iii) are X and Y independent? iv) f(x/y) v) f(y/x)

29. Two independent random variables X and Y have the probability density functions

respectively f(x) = x e –x

, x>0 and f(y) = 1 for 0 ≤ y ≤ 1 and 0 otherwise. Calculate

the probability distribution and density functions of the random variable Z = XY

30. A joint probability density function is f(x,y) = 1/ab for 0 < x < a, 0<y<b and 0 else where.

Find the joint probability distribution function

31. Let X and Y be random variable with the joint density function f(x,y) = 2 for 0 < x < y < 1

Find the marginal and conditional density functions.

32. A random variable X is uniformly distributed on the interval (-5,15) another random variable

Y= exp(-x / 5) is formed. Find E(Y) and f(y)

33. If the function f(x,y) = be – 2x

cos(y / 2) 0 ≤ x ≤ 1 , 0 ≤ y ≤ π and 0 else where. ‘b’ is a

positive constant, is valid joint probability density function, find ‘b’

34. Joint probabilities of two random variables X and Y are given in table

X / Y 1 2 3

1 0.2 0.1 0.2

2 0.15 0.2 0.15

Find out i) Joint and marginal distribution functions and plot Joint and marginal density

functions and plot

UNIT – II


To Define Mean, Variance and Skew of a one and two random variables

To discuss Moments of a random variable and its properties

To Construct Moment Generating Function and Characteristic Function and their Properties

To Perform all the operations discussed above on special random variables


1. Mean, variance and Skew of single random variable -

their properties and applications

1st and 2nd

Black board + PPT

2. Mean, variance and Skew of two random variables -

their properties and applications

3rd and 4th Black board + PPT

3. Raw moments and central moments of one and two

variables–properties and applications

5th and 6th Black board

4. Marginal distribution and density functions and

problems related to these topics.


5. Moment generating function and Characteristics

function-properties and applications

9th and 10th Black board+ PPT

6. Operations on special distribution and density

functions(Gaussian, Rayleigh Poission, Binomial,

Uniform, exponential)


7. Problems on the above topics 13th and 14th Black board

.


1.Let X be a random variable defined by the density function . f(x) = 16

cos(

8

x) -4 ≤ X≤ 4

= 0 else where find E[3X] and E[X2] .

2.Find the expected value of the function g(X) = X2, where X is a random variable defined by the

density f(x) = ae-ax

u(x), where a is a constant

3.For the Rayleigh density function f(x) = b

ax )(2 e

bax /)( for x > a

= 0 for x< a

Show that E[X] = a+ 4/b and σ2 = b(4-π) / 4

4. The characteristic function for a random variable X is given by Φ(ω) = 2/

)21(

1N

j

find mean and second moment of X.

5. The Density function of a random variable X is g(X) = 5 e – 5x

0 ≤x ≤ ∞

= 0 else where

find i) E[X] ii) E[(X – 1 )2] iii) E[3X-1]

6. If the mean and variance of the binomial distribution are 6 and 1.5 respectively.

Find E[X – P(X≥ 3)]

7. Find the density function whose characteristic function is is exp(-|t| )

8. Let X be a continuous random variable with pdf f(x) = 8 / x3 , x> 2. Find E[W] where W= X/3

If the random Variable X has uniform distribution, find its variance

9. Let X is a Gaussian random Variable with zero mean & variance σ2. Let Y = X

2. Find

mean of Random Variable Y.

10. A random variable X is uniformly distributed on the interval ( -5, 15), another random variable

Y = exp(-x/5) is formed. Find E(Y) and f(y).

11. A Gaussian-distributed random variable X of zero mean and variance σ2

is transformed by

rectifier characterized by input-output relations.Y = X, X ≥ 0 and = 0, X < 0 Determine

probability density function of Y

12. Find the rth

moment of the random variable X in terms of its characteristic function x(ω)

13. Prove that σ2

x+y = σ2

x + σ

2y + 2[E[XY]] – E[X]E[Y]] where X and Y are two random variables.

14. If X has the probability density function f(x) = exp(-x), x>0 = 0, other wise

Find the expected value of g(X) = exp(3x / 4).

15. Random variable X has probability function p(x) = 1 / 2x, x = 1,2,3,…. Find the moment

generating function, mean & Variance

16. Find the mean and mean squared value and cumulative distribution function for the Rayleigh

distribution with parameter α > 0, specified by the pdf f(x) = x / α2 exp-1/2 x / α ; x>0

17. Show that E[X-m]3 = E[X]

3 -3m σ

2 – m

3

18. A fair coin is tossed three times. Let X be the number of tails appearing. Find the probability

distribution of X calculate the expected value of X.

19. For Poissions distribution Prove that Variance = λ

21. Let X and Y be independent random variables, prove that Var(XY) = Var(X) Var(Y)

if E[X] = E[Y] = 0

20. The average life of a certain type of electric bulb is 1200 hours. What percentage of this type

of bulbs is expected to fail in the first 800 hours of working? What is percentage is expected

to fail between 800 and 1000 hours? Assume normal distribution with σ = 200 hours

22 Prove that E[x] = E[X/Y], where X and Y are independent random variables

23. Find the moment generating function of the random variable having probability density function

f(x) = x 0 ≤ x ≤ 1

= 2 – x 1 ≤ x ≤ 2

= 0 else where

24. Find the moment generating function of the random variable whose moments are

mr = (r+1)! 2r.

25. Let X be the random variable with probability law P(X=r) = qr-1

p, r=1,2,3…..

Find the moment generating function & hence mean and variance. Assume p+q = 1

26. The random variable X has the characteristic function is given by

Φ(t) = 1 - | t |, | t | ≤ 1

| t | > 1

Find the density function of random variable X.

27. For a function Y=(X-m) / σ, Prove that mean is zero & variance is

28. If X is random variable, show that var(aX+b) = a2 var(X)

29. State and prove Central Limit theorem

30. Let Y = X1 + X2 +X3 + ………+ XN be the sum of N statistically independent random

variables Xi,

31. I = 1,2,3……. N. If Xi are identically distributed then find density of Y, f(y).

32. Consider random variables Y1 and Y2 related to arbitrary random variables X and Y by the

coordinate rotation. Y1 = X Cos θ + Y Sin θ, Y2 = - X Sin θ + Y Cos θ i) Find the covariance of

Y1 and Y2 , C Y1Y2 ii) For what value of θ, the random variables Y1 and Y2 uncorrelated.

33. For two random variables X and Y f(x,y) = 0.5δ(x+1)δ(y) +0.1 δ(x)δ(y)+0.1 δ(x)δ(y - 2)+0.4

δ(x-1)δ(y+2) + 0.2 δ(x-1)δ(y-1) +0.5 δ(x-1)δ(y-3) Find a) the correlation b) the covariance

c) the correlation coefficient of X and Y d) are X and Y either uncorrelated or orthogonal

34. Random variables X and Y have he joint density function

f(x,y) = (x+y)2 / 40 -1<x<1 and -3<y<3, find all the third order moments for X and Y

35. If f(X,Y) = 0.5exp(-| X | - | Y |), where X and Y are two random variables. If Z = X+Y find

f(Z)

36. For the joint distribution of (X,Y) given by f(x,y) given by f(x,y) = a4

12 [(1+xy)(x

2 – y

2)] for

|x|≤a, |y|≤a, a>0 and 0 other wise. Show that the Characteristic function of X+Y is equal to

the product of the characteristic function of X & Y

37. A random variable Z is uniformly distributed having probability density function

38. f(z) = ½ -1 ≤ Z ≤ 1 and 0 otherwise. Show that the random variables X=Z and Y=Z2 are

uncorrelated despite of the fact that they are statistically dependant.

UNIT-III


To define Random Process and to classify it.

To check the Ensemble of a random process

To define the correlation functions of a random process and its properties


1. Introduction to Random Process and Classification of

Random Process

1st Black board + PPT

2. Stationary Random Process, Strict sense stationary

process and Wide Sense stationary of the random process

and problems.

2nd and 3rd Black board + PPT

3. Ergodicity, Time Average and Meam Ergodic process. 4th Black board + PPT

4. Autocorrelation function, Cross correlation, Covariance

function and their properties

5th , 6th and

7th

Black board + PPT

5. Problems on the above topics. 8th and 9th Black board + Video


1. given the auto correlation function for a stationary ergodic process with no periodic

components is R(τ) = 25 + 261

4

. Find the mean and variance of the random process X(t)

2. Consider a random process X(t) = cos(ωt + θ) where ω is a real constant and θ is a uniform

random variable in (0, π/2). Show that X(t) is not a WSS process. Also find the average power

in the process.

4. Find the Auto correlation function for the white noise shown in the figure below:

A

- τ0 / 2 τ0 / 2

5. Consider a random process x(t) = A cos(ωot + θ) where A and ωo are real constants and θ is a

random variable uniformly distributed on the interval (0 , π/2) find the average power P in x(t).

UNIT-IV


To visualize the Power Density Spectrum and its properties (PSD)

To establish the relationship between Power spectrums and Correlation Functions

To study the linear systems response


1. Introduction to power density spectrum, Definition and

its properties

1st and 2nd Black board

2. Relationship between PSD and Autocorrelation function

of a Random Process

3rd Black board

3. Cross spectral Density and its properties & Relationship

between Cross Correlation function and Cross PSD


4. Linear System Response-Convolution, Mean and Mean-

squared value, Autocorrelation Function, Cross-

Correlation Function of Response.

6th ,7th and

8th

Black board + PPT

5. Power Density Spectrum, Cross Power Density

Spectrums of Response.

9th and 10th Black board+ PPT

6. Problems to the above topics 11th Black board

ASSIGNMENT IV:

1. If the auto correlation function of a WSS process is R(τ) = k e -k| τ |

show that its spectral

density is given by S(ω) =

)(1

2

k

2 .

2. Find the auto correlation function of the following PSD’s

a) )9)(16(

1215722

2

b)

22 )9(

8

3. The PSD of a stationary random process is given by S(ω) = A -k < ω < k and 0 otherwise.

Find the auto correlation function.

4. A class of modulation signal is modulated by Xc(t) = AX(t) Cos(ωct + θ), where X(t) is the

message signal and A Cos(ωct + θ) is the carrier. The message signal x(t) is modeled as a zero

mean stationary random process with the autocorrelation function R(τ) and the PSD G(f). The

carrier amplitude A and frequency ωc are assumed to be constants and the initial carrier phase θ

is assumed to be a random variable uniformly distributed in the interval (-π,π). Further more x(t)

and θ are assumed to be independent.

a) Show that Xc(t) is stationary b) Find the PSD of Xc(t)

5. Consider a Random binary wave form that consists of a sequence of pulses with the following

properties:

a) Each pulse is of duration To b) Pulse are equally likely to ±1

c) All pulses are statistically independent

d) The pulses are not synchronized, that is the starting time T of the first pulse is equally

likely to be anywhere between 0 and Tb

Find the Auto correlation and power spectral density function of x(t)

6. Find the PSD of a random process z(t) = x(t) + y(t) where x(t) and y(t) are zero-mean

individual random process.

7. Find the PSD of a random process x(t) if E[x(t)] = 1 and R(τ) = 1+ e – α |τ|

8. The cross power spectrum defined by S(ω) = a + (jbω / β) -W < ω < W and 0 elsewhere

where W>0, a and b are real constants. Find the cross correlation function.

9.Consider a train of rectangular pulses having as amplitude of 2 volts and widths which are

either 1μs or 2 μs with equal probability. The meantime between pulses is 5 μs. Find the PSD

G(f) of the pulse train.

10. Find the Auto correlation function and power spectral density of the random process

x(t) = K Cos (ωot + θ) where θ is a random variable over the ensemble and is uniformly

distributed over the ensemble and is uniformly distributed over the Range ( 0 , 2π)

X(t) is a stationary random process with zero mean and auto correlation R(τ) = e - 2|τ|

is applied

to a system of function H(w) = jw2

1 11. Find mean and PSD of its output.

1. The input voltage to an RLC series circuit is a stationary Random Process X(t) with E[x(t)]=2

and R(τ) = 4 + e - 2|τ|

. Let Y(t) be the voltage across capacitor. Find E[Y(t)] and G(f).

UNIT-V


To Study various noise sources available in receiver and to quantify them

T o construct the mathematical modeling of the communication system.


1. Introduction to system noise and Mathematical

Modeling of Various system Noise sources

1st

Black board + PPT

2. Shot Noise, flicker noise, Thermal noise, White

Noise, colored noise

2nd Black board + PPT

3. Effective Noise Temperature & Available Noise

Temperature

3rd and 4th Black board + PPT

4. Noise Figure of communication system,

Mathematical modeling of Noise temperature.


5. Average Noise Figure of Cascaded networks. 7th Black board + PPT

6. Problems on the above topics 8th Black board

ASSIGNMENT V:

1. low noise receiver for satellite ground station consists of the following stages

Antenna with Ti = 125 oK, Wave guide with a loss of 0.5 dB

Power amplifier with ga = 30dB, Te = 6 oK , BN = 20 MHz

TWT amplifier with ga = 16dB, F = 6 dB , BN = 20 MHz

Calculate the effective noise temperature of the system

2. The Noise figure of an amplifier at room temperature (T=290 oK) is 0.2dB. Find the

equivalent temperature

3. A random process n(t) has a power spectral density g(f) = η/2 for –α ≤f≤α. Random process is

passed thorough a low pass filter which has transfer function H(f) = 2 for –fm ≤ f ≤ fm and H(f) =

0 otherwise. Find the PSD of the waveform at the output of the filter.

4. Bring out the differences between narrowband and broadband noises.

5. A signal x(t) = u(t) e –α t

is applied to a network having an impulse response h(t)=ωu(t)e

–ωt

Here α and ω are real positive constant. Find the network response?

6. Two systems have transfer function H1(w) & H2 (w). Show that transfer function H(w) of the

cascade of the two is H(w) = H1(w) H2 (w).

7. For cascade of N systems with transfer functions Hn(w), n = 1,2,……N. Show that

H(w)=πHn(w).

8. An amplifier with ga = 40dB and BN = 20 KHz is found to have Nao = 10K To when Ti=To.

Find Te and noise figure.

9. In any communication system the first stage must have low noise operation. Justify the reason.

VNR VIGNANA JYOTHI INSTITUTE OF ENGINEERING & TECHNOLOGY

(An Autonomous Institute & Accredited by NBA & NAAC with ‘A’ Grade)

Bachupally, Nizampet (S.O.), Hyderabad – 500 090

Department of ECE

II B. Tech, Semester I (ECE)

Subject : Signals & Systems

Subject Code : 5EI03

Academic Year : 2016– 17


Number of Hours / week : 5

Total number of periods planned : 70

Name of the Faculty Members : Dr.S.Rajendra Prasad, L.V.Rajani Kumari

Pre-requisites

Basics of mathematical concepts

Course Objectives

To understand various fundamental characteristics of signals and systems.

To study the importance of transform domain.

To analyze and design various systems.

To study the effects of sampling.

Course Outcomes

After Completion of the course the student is able to

Classify the signals and systems and determine the response of the systems.

Analyze the spectral characteristics of signals and systems

Design the continuous-time and discrete-time systems

UNIT I

Representation of Signals

Continuous time and Discrete Time signals, Classification of Signals – Periodic and aperiodic,

even and odd, energy and power signals, deterministic and random signals, complex exponential

and sinusoidal signals. Concepts of Impulse function, Unit step function, Signum function. Various

operations on Signals.

Signal Transmission through Linear Systems

Classification of Continuous time and discrete time Systems, impulse response, Response of a

linear system, Transfer function of a LTI system. Filter characteristics of linear systems. Distortion

less transmission through a system, Signal bandwidth, system bandwidth, Ideal LPF, HPF and BPF

characteristics, Causality and Paley -Wiener criterion for physical realization, relationship between

bandwidth and rise time.

UNIT II

Signal Analysis

Analogy between vectors and signals, Orthogonal signal space, Signal approximation using

orthogonal functions, Closed or complete set of orthogonal functions

Fourier Series Representation of Periodic Signals

Representation of Fourier series, Continuous time periodic signals, Dirichlet’s conditions,

Trigonometric Fourier series and Exponential Fourier series, Complex Fourier spectrum, Gibb’s

Phenomenon.

.

UNIT III

Fourier Transforms

Deriving Fourier transform from Fourier series, Fourier transform of arbitrary signals, Fourier

transform of standard signals, Fourier transform of periodic signals, properties of Fourier

transforms

Laplace Transforms

Concept of region of convergence (ROC) for Laplace transforms. Properties of ROC. Relation

between Laplace Transforms and Fourier transform of a signal. Introduction to Hilbert Transform.

UNIT IV

Convolution and Correlation of Signals

Concept of convolution in time domain and frequency domain, Graphical representation of

convolution, Properties of Convolution, Concepts of correlation, properties of correlation. Relation

between convolution and correlation, Detection of periodic signals in the presence of noise by

correlation.

Sampling Theorem

Representation of continuous time signals by its samples - Sampling theorem – Reconstruction of a

Signal from its samples, aliasing – discrete time processing of continuous time signals, sampling of

band pass signals.

UNIT V

Z –Transforms

Basic principles of z-transform, region of convergence, properties of ROC, Properties of z-

transform , Poles and Zeros. Inverse z-transform using Contour integration, Residue Theorem,

Convolution Method and Partial fraction expansion.

TEXT BOOKS

1. Signals, Systems and Communications - B.P. Lathi, BS Publications, 2009.

2. Signals and Systems – Alan V.Oppenheim, Alan S.Willsky and S.Hamid Nawab,2nd

Edition, PHI.

REFERENCES

1. Signals and Systems- A.Anand Kumar, 2nd

Edition, PHI,2012

2. Signals and Systems -Simon Haykin and Barry Van Veen, 2nd

Edition, John Wiley.

3. Signals and Systems- Cengage Learning, Narayana Iyer, 2011.

4. Signals, Systems and Transforms –C.L.Philips,J.M Parr and Eve A. Riskin,3rd

Edition,

Pearson, 2004 .

5. Signals and Systems Schaum’s Outlines - HWEI P. HSU , Tata Mc Graw Hill, 2004.

(5EI03) SIGNALS AND SYSTEMS

UNIT I Representation of Signals: Continuous signals, Classification of Signals – Periodic and aperiodic,

even and odd, energy and power signals, deterministic and random signals, complex exponential

and sinusoidal signals. Concepts of Impulse function, Unit step function, Signum function. Various

operations on Signals.

Signal Transmission through Linear Systems

Classification of Continuous time and discrete time Systems, impulse response, Response of a

linear system, Transfer function of a LTI system. Filter characteristics of linear systems. Distortion

less transmission through a system, Signal bandwidth, system bandwidth, Ideal LPF, HPF and BPF

characteristics, Causality and Paley -Wiener criterion for physical realization, relationship between

bandwidth and rise time.

Learning objectives :

After completion of the unit, students will be able to:

Understand the terminology of signals

Understand various signals & basic operations on signals

Analyze the response of linear systems to different input signals. Describe LTI

Describe Transient and steady state response of systems, response of a system to causal periodic,

non sinusoidal signals.

Analyze the filter characteristics of linear systems, distortionless transmission through a system

Define and derive Signal bandwidth, system bandwidth, Ideal filters- LPF, HPF, BPF, BRF

characteristics.

Describe the causality and physical realizability, Poly- wiener criterion, response of Linear

system to non- causal signals.

Define the relationship between bandwidth and rise time. Describe Energy density spectrum.

Lecture plan :

S.NO Period(

S)

Brief Note of Topic(S) Covered Active

Learning

Technique

used

1 Unit – I

Represent

ation of

Signals

1 Introduction to signals and systems Chalk &

Talk, PPT's

2 1 Continuous signals, discrete time signals Chalk & Talk

3 2 Concepts of Impulse function, Unit step

function, Signum function.

Chalk & Talk

4 1 Properties of Impulse Chalk & Talk

5 2 Various operations on Signals Chalk & Talk

6 1 Classification of Signals Chalk & Talk

7 1 Energy and power signals Chalk & Talk

8 2 Problems Chalk & Talk

9 Signal

Transmis

sion

2 Classification of Continuous time and

discrete time Systems

Chalk & Talk

PPT

10 through

Linear

Systems

2 impulse response, Response of a linear

system, Transfer function of a LTI system

Chalk & Talk

11 1 Filter characteristics of linear systems,

Distortion less transmission through a

system, Signal bandwidth, system

bandwidth

Chalk & Talk

12 1 Ideal LPF, HPF and BPF characteristics,

Causality and Paley -Wiener criterion for

physical realization, relationship between

bandwidth and rise time

Chalk & Talk


Total No. of Periods:19

Assignment :

1. Determine whether the signal is periodic or not, if periodic, find out its

Fundamental period.

i) x(t) = 2 cos (10t+ 1) – sin(4t-1)

ii) x(t) = jej 10 t

2.Obtain the conditions for the distortion less transmission through a system.

What do you understand by the term signal bandwidth?

3.If a signal g(f) is passed through an ideal LPF of bandwidth fc Hz , determine

the energy density of the o/p signal.

4.What do you mean by causality? What is the relationship between bandwidth

and rise time? What is the difference between signal and system bandwidth?

UNIT II

Signal Analysis

Analogy between vectors and signals, Orthogonal signal space, Signal approximation using

orthogonal functions, Closed or complete set of orthogonal functions

Fourier Series Representation of Periodic Signals : Representation of Fourier series, Continuous

time periodic signals, properties of Fourier series, Dirichlet’s conditions, Trigonometric Fourier

series and Exponential Fourier series, Complex Fourier spectrum, Gibb’s Phenomenon.

Learning objectives:

After completion of the unit, the students will be able to:

Describe the analogy between vectors and signals

Describe orthogonal signal space, approximation of function by a set of mutually orthogonal

functions, and evaluate mean square error.

Describe the Fourier series.

Derive properties of Fourier series.

Do problems using properties.

Define and Derive Dirichlet’s conditions, Trigonometric Fourier series and analyze

exponential Fourier series

Do problems on Trigonometric Fourier series & Exponential Fourier series.

Describe complex Fourier Spectrum, Problems.

Lecture plan :

S.NO Perio

d(S)


Learning

Technique

used

1 UNIT II

Fourier

Series

Represent

ation of

Periodic

Signals

1 Analogy between vectors and signals Chalk & Talk

2 1 Orthogonal vector space,Orthogonal signal

space

Chalk & Talk

3 2 Signal approximation using orthogonal

function,Evolution of mean square error

Chalk & Talk

4 1 Representation of a function by complete

set of orthogonal function, 0rthogonality in

complex function

Chalk & Talk

5 1 Representation of Fourier series Chalk & Talk

Video

6 1 Trigonometric Fourier series, Cosine

Fourier series representation

Chalk & Talk

Video

7 1 Dirichlet’s conditions, Gibb’s

Phenomenon

Chalk & Talk

8 2 Properties of Fourier series Chalk & Talk

PPT

9 2 Exponential Fourier series,Complex

Fourier spectrum, Problems

Chalk & Talk


Assignment :

1.Define mean square error and derive the expression for evaluating mean

square error.

2. Explain the concept of orthoganolity of complex functions.

3. A pulse train shown below in fig is fed to an LTI system whose impulse

response is e-2t

u (t). Find the exponential F S of the output.

4. Write a short note on Dirchlet’s conditions.

5. Derive relationship between the trigonometric F S and Exponential F S.

6. State and prove any three properties of F S.

UNIT III

Fourier Transforms

Deriving Fourier transform from Fourier series, Fourier transform of arbitrary signals, Fourier

transform of standard signals, Fourier transform of periodic signals, properties of Fourier

transforms

Laplace Transforms: Concept of region of convergence (ROC) for Laplace transforms. Properties

of ROC. Relation between Laplace Transforms and Fourier transform of a signal. Introduction to

Hilbert Transform.



Understand the concept of time domain & frequency domain representation

Derive Fourier transform from Fourier series and Fourier transform of arbitrary signal.

State and derive the properties of Fourier transforms.

Analyze the Fourier transforms involving impulse function and Signum

function

Define and describe the Laplace Transforms

Describe the Region of Convergence of Laplace Transforms, and constraints on ROC

Find the Laplace Transform of some useful functions.

Compare the Fourier and Laplace Transforms.

Lecture plan :

S.NO Perio

d(S)


Learning

Technique

used

1 UNIT III

Fourier

Transfor

ms

Laplace

Transfor

2 Deriving Fourier transform from Fourier

series, Fourier transform of arbitrary

signals.

Chalk & Talk

Video

2 2 Fourier transform of standard signals,

Fourier transform of periodic signals

Chalk & Talk

3 3 Properties of Fourier transform Chalk & Talk

PPT


5 2 Introduction to Laplace Transforms, Concept

of region of convergence (ROC) for

Laplace transforms

Chalk & Talk

Video

6 2 Properties of ROC Chalk & Talk

7 ms 1 Relation between Laplace Transforms and

Fourier transform of a signal

Chalk & Talk

8 1 Introduction to Hilbert Transform Chalk & Talk


Assignment :

1. Obtain the Fourier transform of the square wave of unit amplitude and periodic time 2T.

2. State and prove the following properties F T.

i) Multiplication in time domain ii) Convolution in time domain

3. Distinguish between Fourier series and Fourier transform.

4. State the conditions for the existence of FT of a signal.

5. State and prove initial and final value theorems of laplace transform.

6. Obtain the LT of the periodic rectified half sine wave. And explain time

differentiation and time integration properties of LT

UNIT IV

Convolution and Correlation of Signals : Concept of convolution in time domain and frequency

domain, Graphical representation of convolution, Properties of Convolution, Concepts of

correlation, properties of correlation. Relation between convolution and correlation, Detection of

periodic signals in the presence of noise by correlation, Extraction of signal from noise by filtering.

Sampling Theorem

Representation of continuous time signals by its samples - Sampling theorem – Reconstruction of a

Signal from its samples, aliasing – discrete time processing of continuous time signals, sampling of

band pass signals.



Define and describe Correlation and Cross correlation.

Describe Autocorrelation of functions, Properties of autocorrelation of functions, correlation

and convolution.

Analyze the relationship between autocorrelation and energy density spectrum.

Describe detection of periodic signals in the presence of noise by correlation and detection by

Autocorrelation

State and derive the sampling theorem-Graphical and analytical proof for Band limited

Signals.

Describe the impulse Sampling, Natural and Flat top Sampling

Describe the reconstruction of signal from its samples effect of under sampling- aliasing

Define band pass sampling

Lecture plan :

S.No Period(

S)


Learning

Technique

used

1 UNIT IV

Convolution

and

Correlation

of Signals

2 Concept of convolution in time domain and

frequency domain, Graphical representation

of convolution, Properties of Convolution

Chalk & Talk

2 2 Concepts of correlation, properties of

correlation, Relation between convolution

and correlation

Chalk & Talk

3 1 Detection of periodic signals in the presence

of noise by correlation

Chalk & Talk

4 1 Extraction of signal from noise by filtering Chalk & Talk

5 Sampling

Theorem

2 Representation of continuous time signals by

its samples - Sampling theorem

6 2 Reconstruction of a Signal from its samples,

aliasing

7 1 discrete time processing of continuous time

signals

8 1 sampling of band pass signals


Assignment :

1. Consider a signal g(t) given by

g(t) = A0 + A1 cos ( π2f1 t + θ ) + A2 cos (2 π f2 t + θ )

i) Determine the auto correlation function R( ) of this signal.

ii) What is the value of R(0).

2. What do you understand by the term autocorrelation function of a signal? What

are its applications? In what way PSD and ACF are related.

3. State and prove the properties of Auto correlation function.

4. Compare convolution and correlation.

5. State and prove low pass sampling theorem in time domain

6. What is the effect of the under sampling a signal .

7. Explain the signal recovery from its sampled signal.

UNIT V

Z –Transforms: Basic principles of z-transform, region of convergence, properties of ROC,

Properties of z-transform ,Poles and Zeros. Inverse z-transform using Contour integration, Residue

Theorem, Power Series expansion and Partial fraction expansion. Distinction among Fourier

transform, Laplace Transform and Z - Transforms.



Describe the concept of Z- transform

Define the Z – plane, and Region of Convergence of various sequences

Describe the Inverse Z – Transform, Long division method, Partial fraction

Expansion method, Residue theorem method, Contour method, Convolution method.

Lecture plan :

S.NO

Period(

S)


Learning

Technique

used

2 UNIT V

Z –

Transfor

ms

2 Basic principles of z-transform, region of

convergence, properties of ROC

Chalk & Talk

Video

8 1 Properties of z-transform ,Poles and Zeros Chalk & Talk

PPT

9 1 Inverse z-transform using Contour

integration

Chalk & Talk

10 1 Residue Theorem, Power Series expansion

and Partial fraction expansion

Chalk & Talk

11 1 Distinction among Fourier transform,

Laplace Transform and Z - Transforms

Chalk & Talk

12 2 problems Chalk & Talk


Assignment :

1. Define Z-transform. State and prove the differentiation and convolution properties

of Z- transforms.

2. Distinguish between one sided & two sided Z-transforms. What are the

applications.

3.What are the methods by which inverse Z-transform can be found out?

VNR VIGNANA JYOTHI INSTITUTE OF ENGINEERING & TECHNOLOGY

(Autonomous)

DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING

II B. Tech, Ist Semester (Electronics and Communication Engineering)

Subject : Electronic Devices and Circuits

Subject Code : 15ECE001

Academic Year : 2016 – 17


Number of Hours / week : 4 + 1

Total number of periods planned: 58

Name of the Faculty Member: Mrs.L.Dharma Teja

Course Objectives:

To learn principle of operation, construction and characteristics of various electronic

devices.

To know about different applications of these devices

To provide the concepts involved in design of Electronic Circuits

Course Outcomes (COs): Upon completion of this course, students should be able to:

CO-1: Use devices in real life applications

CO-2: Design small signal model for BJT, FET.

CO-3: Analyse and Design a few applications using these devices

CO-4: Design and construct a simple DC power supply.

UNIT : I

Syllabus:

P-N Junction Diode and Applications

Review of Semi Conductor Materials, Theory of p-n Junction, p-n Junction as a Diode, Diode

Equation, Volt-Ampere Characteristics, Temperature dependence of VI characteristic, Ideal versus

Practical diode Equivalent circuits, Static and Dynamic Resistance levels, Transition and Diffusion

Capacitances, The p-n Junction diode as a rectifier, Half wave Rectifier, Full wave rectifier, Bridge

Rectifier, Harmonic components in a Rectifier Circuit, Inductor filters, Capacitor filters, LC Section

Filters, - section filters, Comparison of Regulation Characteristics of different Filters, Breakdown

Mechanisms in Semi Conductor Diodes, Zener Diode Characteristics, Shunt Voltage Regulation

using Zener Diode.

Learning Objectives: After completion of the unit, the student must able to:

Draw and explain the energy band diagram of intrinsic semiconductor.

Define drift current and diffusion current

Define mobility of charged particle

Derive an expression for the conductivity of a semiconductor.

Describe extrinsic semiconductor

What is doping and why is it required.

Explain the formation of n type semiconductor

Explain conductivity of n type semiconductor

Explain the formation of p type semiconductor

Explain conductivity of p type semiconductor

Draw and explain the energy band diagram of extrinsic semiconductor

Give an expression for the conductivity of p type and n type semiconductor

State and explain Law of mass action

Explain carrier concentrations in extrinsic semiconductor

Explain pn junction diode

Derive expression for junction potential.

Explain forward bias and reverse bias

Explain the V-I characteristics of forward biased pn junction diode

Explain the V-I characteristics of reverse biased pn junction diode

Explain the effect of temperature on V-I characteristics of pn junction diode

Explain the energy band diagram of open circuited diode.

Define static resistance, dynamic resistance and bulk resistance of a diode.

Define reverse saturation current and reverse breakdown voltage of a diode.

Derive current equation of diode.

Explain the current components of a diode

State and explain continuity equation

Define transition capacitance and diffusion capacitance of a diode.

Distinguish the features of Si and Ge diodes

Explain the function of rectifier

Explain half wave rectifier and full wave rectifier

Explain the advantages of full wave rectifier over half wave rectifier

Explain the advantage of bridge rectifier

Define and derive Ripple factor, % regulation, efficiency of HWR

Define and derive Ripple factor, % regulation, efficiency of FWR

Explain how harmonic components are rectified with L filter, Derive ripple factor.

Explain how harmonic components are rectified with C filter, Derive ripple factor.

Explain how harmonic components are rectified with LC or L section filter, Derive ripple

factor.

Explain how harmonic components are rectified with π section filter, Derive ripple factor.

Explain multiple L section and π section filters

Compare the ripple factors of a rectifier with different filters.

Explain avelanche and zener breakdown mechanisms.

Explain the V-I characteristics of zener diode

Define different zener diode parameters.

Explain Zener diode as a Regulator.

Compare the performances of different types of filters.

Lecture Plan


1. Intrinsic, extrinsic semiconductors, p type and

n type semiconductors

1st hour PPT + Video

2. Drift current, diffusion current, mobility,

conductivity of extrinsic semiconductors

2nd

hour Black board + Video

3. PN-junction diode FB, RB Characteristics &

junction Potential.

3rd

hour Black board

4. Continuity equation, Current components and

diode current equation.

4th


5. Temperature dependency of VI characteristics

5th

hour Black board

6. Diode parameters, specifications, equivalent

circuits, problems on pn diode

6th

hour Black board + PPT

7. Introduction to Rectifiers, Half wave rectifier

circuits, operation.

7th


8. Full wave rectifier, circuits, operation. Bridge

rectifier

8th

hour Black board

9. Performance Parameters (Regulation, Ripple

factor, efficiency etc.) Derivations of HWR

9th


10. Performance Parameters (Regulation, Ripple

factor, efficiency etc.) Derivations of FWR

and bridge rectifier.

10th

hour Black board

11. Problems on Performance Parameters 11th

hour Black board

12. Introduction to filters, Capacitor filters

explanation, Derivations

12th


13. L filter, explanation, derivations 13th


14. L-section filters, ∏- section filters 14th


15. Multiple L-section & ∏- section filters 15th


,Comparison

16. Problems on Rectifiers and Filters 16th


17. Break down mechanism in diodes, Zener

diode characteristics

17th


18. Shunt Voltage Regulators, Regulator using

Zener diode ,Series Voltage Regulator

18th


Assignment – 1

1. What is a rectifier? Define Ripple Factor, PIV, efficiency TuF, form factor of a

Rectifier.

2. Define the value of forward current in case of Si junction diode with I0 = 10µA, Vf =

0.8v at T = 3000k.

3. A Si diode has a reverse saturation current of 7.5µA at room temperature 3000K

.Calculate the reverse saturation current at 4000k.

4. The voltage across a silicon diode at room temperature (300ok) is 0.7 volts when 2mA

current flows through it. If the voltage increases to 0.75V calculate the diode current

5. What is the ratio of current for a forward bias of 0.08V to the current for the same

magnitude of reverse bias for the Germanium diode.

6. The transition capacitance of an abrupt junction diode is 30pf at 8V

Determine the value of Capacitance for an increase in the bias voltage of 2 V.

7. Find the value of dc resistance and ac resistance of a Ge junction diode at 25 0C, I0 =

10μA and applied voltage is 0.1 V.

8. Calculate the Dynamic forward and reverse resistance of a PN junction diode when the

applied voltage is 0.2 V, I0 =2 μA and T= 25 0C. Consider Ge diode.

9. A Half wave rectifier circuit feeds a resistive load of 10KΩ through a power

transformer having a step down turns ratio of 8:1 and operated from 230V, 50Hzs ac

mains supply. Assume the forward resistance of a diode to be 40Ω and transformer

secondary winding resistance as 12Ω. Calculate the maximum, RMS and average values

of current ,DC output voltage and power ,efficiency of rectification and ripple factor.

10. A full wave rectifier circuit is fed from a transformer having centre tapped secondary

winding .The rms voltage from either end of secondary tap to centre is 20V.If the diode

forward resistance is 3Ω and that of secondary is 5Ω,for a load of 1KΩ,calculate

a. power delivered to load

b. % regulation at full load

c. efficiency at full load

d. TUF of secondary.

UNIT : II

Syllabus:

Transistors, Biasing and Stabilization

The Bipolar Junction Transistor, Transistor Current Components, Transistor construction, BJT

operation, Common Base, Common Emitter and Common Collector Configurations, Limits of

operation, transistor as an Amplifier, BJT specifications, Principle of series voltage regulators. The

DC and AC Load lines, Quiescent operating Point, Need for Biasing, Fixed Bias, Collector

Feedback Bias, Emitter Feedback Bias, Collector-Emitter Feedback Bias, Voltage Divider Bias,

Bias Stability, Stabilization Factors, Stabilization against variations in VBE, β1 and ICO. Bias

Compensation using Diodes, Thermistors and sensistors, Thermal Runway, Thermal Stability.


Explain the principle of operation of transistor (pnp and npn)

Explain the basic techniques used for the construction of transistor (grown type, micro

alloy type, electrochemically etched type, diffusion type, epitaxial growth type)

Explain the effect of temperature on transistor characteristics

Draw the symbols and different configurations of transistor

Draw and explain the input and output characteristics of common emitter configuration.

Draw and explain the input and output characteristics of common base configuration

Draw and explain the input and output characteristics of common collector configuration

Identify active ,cutoff and saturation regions on out put characteristics

Derive expression for collector current in CE configuration.

Explain why CE provides large current amplification while CB can not.

Explain why CE configuration is most widely used.

Define current gain, voltage gain, input impedance and output impedance.

Define αdc and βdc .Derive relationship between αdc and βdc

Calculate αdc and βdc, if base current and collector current are given.

Explain Early effect.

Explain Punch through effect

List out the applications of BJT

Explain the significance of Q point

What are the factors that affect the stability of an amplifier.

Define the three stability factors and explain their significance in BJT

List out different techniques used for biasing transistor amplifiers

Define and derive the expressions for stability factors S,S’,S”

Explain the fixed bias circuit and derive expression for stability factor S

Explain the collector feedback bias circuit and derive expression for stability factor S

Explain Collector to base bias circuit and derive expression for stability factor S

Explain the collector-emitter feedback bias circuit and derive expression for stability factor

S

Explain voltage divider bias or emitter bias circuit and derive expression for stability factor

S

Explain why emitter bias circuit provides more stability amongst the five types of biasing

methods

What are the compensation techniques used for V be and I co

Explain diode compensation circuit, thermistor compensation and sensistor compensation

techniques

Explain what is Thermal runaway

State the condition for thermal stability

Lecture Plan


1. Introduction to Bipolar junction transistor

(BJT), Construction of BJT, Transistor

operation (pnp and pnp)

19th

hour PPT + Video

2. Transistor current components, current

amplification Factor, Common base (CB),

common emitter (CE)and common collector

(CC) configurations

20th


3. Common base configuration characteristics,

early effect, punch through.

21st hour Black board

4. Common emitter configuration

characteristics, active, cut-off and saturation

regions.

22nd


5. Common collector configuration

characteristics.

23rd

hour Black board

6. Comparison of CB, CE, CC characteristics,

specifications, problems

24th


7. Transistor biasing, operating point, dc load

line, ac load line.

25th


8. Fixed bias circuit & collector feedback bias

circuit- analysis, derivation of expression for

S.

26th

hour Black board

9. Collector base bias circuit and collector –

emitter feedback bias circuit-, analysis, S,

problems

27th


10. Self bias or emitter bias circuit- analysis, S,

problems

28th

hour Black board

11. Problems on biasing circuits. 29th

hour Black board

12. Compensation techniques using diode,

thermistor and sensistors

30th


13. Thermal run away, Thermal stability, 31st hour Black board + Video

Assignment - 2

1. Calculate the values of collector current and emitter current for a transistor with αdc= 0.99

and ICBO= 5 μA. The base current is measured as 20 μA.

2. The reverse leakage current of a transistor when connected in CB configuration is 0.2 μA

while it is 18 μA when the same transistor is connected in CE configuration. Calculate αdc

and βdc.

3. The collector and base currents are measured as 5.202 ma and 50 μA respectively.ICB0 is

measured as 2 μA. Calculate a) α, β and Ie b)new level of Ib to make Ic=10 mA.

4. An npn transistor, with β = 50 is used in common emitter circuit with

Vcc=10V,Rc=2KΩ.The bias is obtained by connecting 100KΩ resistor from collector to

base. Find quiescent operating point and stability factor.

5. Consider a self bias circuit ,where Vcc=22.5V, Re = 5.6kΩ, R1=90 kΩ, R2 = 10kΩ, and Re

=

1 kΩ. hfe =55 and VBE = 0.6. The transistor operates in active region. Determine operating

point and stability factor S.

UNIT III

Syllabus:

Small signal low frequency BJT Amplifiers

Small signal low frequency transistor amplifier circuits: h-parameter representation of a transistor,

Analysis of single stage transistor amplifiers CE, CC, CB configurations using h-parameters:

voltage gain, current gain, Input impedance and Output impedance. Comparison of CB, CE, CC

configurations in terms of AI, Ri, AV, RO.


Define ‘ h parameters’ for a two port network

Draw the h parameter equivalent circuits for the three transistor configurations CE, CB,

CC.

Explain the operation of CE amplifier as an amplifier

Explain the need of C1, C2 and Ce in a single stage CE amplifier

Derive Ai, Av, Ri, R0 of a single stage CE amplifier

Give the general steps for the analysis of transistor amplifier

Derive Ai, Av, Ri, R0 of a single stage CB amplifier

Derive Ai, Av, Ri, R0 of a single stage CC amplifier

Compare CC, CE and CB with respect to Ri, Ro, Ai, Av.

Lecture Plan


1. Introduction two port network devises,

Hybrid model

32nd

hour PPT + Video

2. H-parameter-hi , hf, hr, ho

33rd


3. Transistor hybrid model of CB, CC, CE

configurations

34th

hour Black board

4. Analysis of transistor amplifier (CE) using h-

parameters Ai , Zi Av, Y ,Avs, Ais.

35th


5. Simplified CE analysis ,problems 36th

hour Black board

6. Analysis of CE amplifier with un bypassed

Re

37th


7. Analysis of CB amplifier. 38th


8. Analysis of CC amplifier, problems.

39th

hour Black board

9. Comparison of CC, CB, CE amplifiers

characteristics

40th


10. RC couple amplifier, frequency response

analysis(low frequency)


Assignment – 3

1. A common base amplifier has the following components: Rc = 5.6KΩ, RE = 5.6KΩ, RL =

39KΩ,RS = 600Ω. The transistor parameters are, hie = 1000Ω, hfe = 85, and hoe =2x10-

6mhos. Calculate Av, Ri, Ro, Avs.

2. Consider a single stage CE amplifier with

Rs=1K,R1=1K,r2=2K,RL=1.2K,hfe=50,hie=1.1K,hoe=24microA/V and hre=2.5*10-4

3. calculate Ri,Ai=Il/Is,Av,Avs=Vo/Vs,Ro.

4. Calculate Ri,Ai=Il/Is,Av,Avs=Vo/Vs,Ro for the CB ckt with

R1=10K,Rs=1K,R2=10K,RL=20K.

For the CB ckt the transistor parameters are hib=22ohms,hfb=-0.98,hob=0.49microA

UNIT : IV

Syllabus:

FET, Biasing and Amplifiers

The Junction Field Effect Transistor (Construction, Principle of operation) –Voltage-Volt-Ampere

characteristics, FET as Voltage variable Resistor, Biasing FET, The JFET Small Signal Model, FET

common source Amplifier, Common Drain Amplifier, MOSFET (Construction, Principle of

operation), MOSFET Characteristics in Enhancement and Depletion modes. Comparison of BJT

and FET amplifiers.


Explain why FET is called unipolar device

Explain why FET is called voltage-operated device

Classify FETs and give their application areas.

Explain construction of n channel JFET with neat diagram.

Explain construction of p channel JFET with neat diagram.

Explain the operation of n channel JFET

Explain the operation of p channel JFET

Draw the Static Characteristics of JFET and explain different portions of the Characteristics.

Define Pinch Off Voltage.

Draw the Transfer Characteristics of JFET and explain different portions of the

Characteristics.

Define Rd, gm and μ of JFET.

Explain how Rd, gm can be calculated from Characteristic curves.

Explain how JFET can be used as Switch.

Explain how JFET can be used as Voltage Variable Resistor.

Explain how MOSFET differs from JFET.

Explain the constructional features of Depletion mode MOSFET and explain its basic

operation.

Explain the significance of Threshold Voltage VT in Depletion mode MOSFET

Draw and explain the drain Characteristics of Depletion mode MOSFET along with

different operating regions.

Explain the constructional features of Enhancement mode MOSFET and explain its basic

operation.

Draw and explain the drain Characteristics of n Channel Enhancement. Mode MOSFET.

Sketch graphical Symbols for n-Channel JFET, p-Channel JFET, n-Channel

Enhancement mode MOSFET, p-Channel Enhancement mode MOSFET, n-Channel

Depletion mode MOSFET, and p-Channel Depletion mode MOSFET

Lecture Plan


1. FET introduction, construction operation

Drain and Transfer characteristics of n-

channel and p-channel FETs.

42nd

hour PPT + Video

2. Pinch off voltage, definitions of Rd, gm and μ

of JFET. Calculation from characteristic

curves.

43rd


3. Small signal model of JFET, analysis of

Common source FET amplifier.

44th

hour Black board

4. Problems on JFET 45th


5. Depletion MOSFET construction, symbol,

operation, characteristics,

46th

hour Black board

6. Enhanced MOSFET construction, symbol,

operation, characteristics

47th


7. Problems on MOSFET. 48th


Assignment - 4

1. Explain the construction and operation of JFET.

2. Define Transconductance gm of a FET. Write the expression for gm.

3. Why a Field Effect Transistor is called so?

4. Draw the small signal model of FET.

5. Draw the diagram for the Basic Structure of Depletion mode and Enhancement mode

MOSFET.

UNIT : V

Syllabus:

Special Purpose Electronic Devices

Principle of Operation and Characteristics of Tunnel Diode (with the help of Energy Band

Diagram) Varactor Diode and Schotky barrier diode. Principle of Operation and Characteristics of

UJT, UJT Relaxation Oscillator. Principle of Operation of SCR, Schockley diode Diac and Triac.

Principle of Operation of Semiconductor Photo Diode, PIN Diode, Photo Transistor, LED and

LCD.


Explain the principle of operation of Tunnel diode

Explain the V-I characteristics of Tunnel diode

Explain the applications of Tunnel diode.

Explain the principle of operation of Varactor diode

Explain the V-I characteristics of Varactor diode

Explain the applications of Varactor diode

Explain the principle of operation of Schotky barrier diode

Explain the V-I characteristics of Schotky diode

Explain the constructional details of UJT

What is intrinsic stand of ratio η

Draw and explain UJT VI characteristics

Draw the symbol and equivalent circuit of UJT

Explain how UJT can be used as negative resistance device with the aid of static

characteristics

List out the applications of UJT and explain UJT relaxation oscillator.

Explain the constructional details and operation of SCR, Diac and Triac.

Draw the characteristics of SCR and explain

Explain a) Holding current and b) Latching current

Explain a) Reverse break down voltage and b) Forward break over voltage

Explain two-transistor analogy of SCR

State the application of SCR

Explain which material is used for LED

Explain is photo emissive effect

Define radiant flux , irradiation , illumination, luminosity curve and light intensity

Explain the basic principle of operation of LED

Explain the constructional details of LED

State advantages and disadvantages of LED

Compare LED with normal PN diode

Sketch output characteristics of LED

Explain why LEDs are preferred in displays

Explain the VI characteristics of photo diode

State any two applications of photo diode and Photo Transistor.

Explain the principle of operation and working of LCD

Lecture Plan


1. Principle of Operation and Characteristics of

Tunnel Diode (with the help of Energy Band

Diagram)

49th

hour PPT + Video

2. Principle of operation of Varactor Diode and

its applications.

50th


3. Principle of operation, characteristics and

applications of Schotky barrier diode


4. Principle of Operation and Characteristics of

UJT, UJT Relaxation Oscillator

52nd


5. Principle of Operation, characteristics and

applications of SCR, Diac and Triac.

53rd

hour Black board

6. Principle of Operation, characteristics and

applications of Diac and Triac

54th


7. Principle of Operation, characteristics

and applications PIN Diode

55th


8. Principle of Operation and applications of

Semiconductor Photo Diode and Photo

56th

hour Black board

Transistor.

9. Principle of Operation and applications of

LED

57th

hour Black board

10. Principle of Operation and applications of and

LCD

58th

hour Black board

Assignment - 5

1. Define Negative resistance region, peak point and valley point in Tunnel diode

characteristics.

2. Describe the two transistor analogy of SCR.

3. Describe the construction and equivalent circuit of UJT.

4. Explain the principle of operation of photo diode and photo transistor.

5. Describe the principle of operation of LCD.

TEXT BOOKS

1. Electronic Devices and Circuits – J.Millman, C.C.Halkias, and Satyabratha Jit, Tata

McGraw Hill, 2nd

Edition, 2007.

2. Electronic Devices and Circuits – R.L. Boylestad and Louis Nashelsky, Pearson/Prentice

Hall, 11th

Edition, 2006.

3. Electronic Devices and Circuits – David A Bell, Oxford University Press,5th

edition (2008)

REFERENCES

1. Integrated Electronics - J.Millman and Christos.C.Halkias, and Satyabratha, Jit Tata

McGraw Hill, 2nd

Edition, 2008.

2. Electronic Devices and Circuits – T.F. Bogart Jr., J.S.Beasley and G.Rico, Pearson

Education, 6th Edition, 2004.

3. Electronic Devices and Circuits- S. S Salivahanan, N. Sursh Kumar, A. Vallava Raju,2nd

Edition., TMH, 2010.

VNR VIGNAN JYOTHI INSTIYUTE OF ENGINEERING AND TECHNOLOGY

BACHUPALLY (VIA), KUKATPALLY, HYDERABAD-72

ACADEMIC PLAN: 2016-17

II Year B. Tech ECE – I Sem L T/P/D C

4 0 4

Subject: PRINCIPLES OF ELECTRICAL ENGINEERING Subject Code: 13EEE077


Number of Hours / week : 5

Total number of periods planned : 60

Name of the Faculty Member : Mr. N.Amarnadh Reddy,Mr. Y.Srikanth Reddy,shivateja

& Ranjit reddy.

PREREQUISITES

13MTH001, 13MTH002, 13MTH005, 13PHY003, 13EEE001.

COURSE OBJECTIVES

1. To analyze transient response of circuits with dc excitation.

2. To understand two port network parameters, filters and attenuators.

3. To know about performance of DC machines.

4. To understand the operation of transformers and AC machines.

COURSE OUTCOMES

Upon completion of the syllabus student will be able to

1. Analyze transient response of circuits Evaluate two port parameters and design simple

filters.

2. Appreciate the working of DC machines.

3. Understand the operation of transformers and AC machines.

MAPPING OF COs WITH POs

PO a PO b PO c PO d PO e PO

f PO g PO h

PO

i

PO

j PO k

PO

l

CO 1 3

2 2

2 2

3

CO 2

3 2 1 2 1

2 2

CO 3

2 2 1 1 2 2 2 2 1 2 3

3-storng 2-moderate 1-Week Blank-Not relevant

DETAILED SYLLABUS

UNIT- I

Transient Analysis (First and Second Order Circuits) :

Transient Response of RL, RC and RLC Circuits for DC excitations, Initial Conditions, Solution

using Differential Equations approach and Laplace Transform Method.

Learning Outcomes

After completion of this unit the student will be able to

1. Define Transient.

2. Describe Initial conditions of Basic R, L, C elements.

3. Derive equations for transient Response of RL circuit.

4. Derive equations for transient Response of RC circuit.

5. Derive equations for transient Response of Series RLC circuit.

6. Solution of above transient Responses using Differential Equations approach and Laplace

Transform Method.

TEACHING PLAN

S. No Description No. of

Periods (16)

Mode of delivery

1 Introduction Transients 01 BBT

2 Transient Response of RL, RC and RLC Circuits

for DC excitations

06 BBT+

https://www.yout

ube.com/watch?v

=oPwsrq29w18

3 Initial Conditions 01 BBT

4 Solution using Differential Equations approach

and Laplace Transform Method.

06 BBT

5 Assignment Questions Discussion 01 Assignment Sheet

6 Tutorial 01 Tutorial sheet

Tutorial

1. (a) what is the impartance of time constant of R-L circuit.what are the different ways of

defing timeconstant.

(b).what is the initial condition of a circuit? Why do you need them?

2. (a) Derive the expression for transient response of R-L-C series circuit with unit step

input?

(b).Explain why the current in a pure inductance can not change in zero time.

Assignment

(1) Find i (t) for t > 0 for the circuit shown in Fig When the switch is opened at t = 0

(2) Determine i (t) for the circuit shown in Fig When the switch is closed at t = 0.Assume

initial current through inductor is zero

UNIT-II

Two Port Networks :

Impedance Parameters, Admittance Parameters, Hybrid Parameters, Transmission (ABCD)

Parameters, Conversion of one Parameter to another, Conditions for Reciprocity and Symmetry,

Interconnection of Two Port networks in Series, Parallel and Cascaded configurations, Image

Parameters, Illustrative problems.

Learning Outcomes


1. Define port, one port network, Two port network.

2. Define various types of parameters of Two port network.

3. Derive expressions for individual Z-parameters of Two port network.

4. Derive expressions for individual Y-parameters of Two port network.

5. Derive expressions for individual ABCD-parameters of Two port network.

6. Derive expressions for individual h-parameters of Two port network.

7. Verify Reciprocity and Symmetry conditions for all the parameters.

8. Convert of one Parameter to another

9. Derive expressions for equivalent parameters when the twp port networks are connected in

Series, Parallel and Cascaded configurations.

10. Derive expressions for Image Parameters

TEACHING PLAN


Periods (16)

Mode of delivery

1 Impedance Parameters, Admittance Parameters 04 BBT+

https://www.yout

ube.com/watch?v

=WVxWesqPto8

2 Hybrid Parameters, Transmission (ABCD)

Parameters

03 BBT+

https://www.yout

ube.com/watch?v

=a2ce5VGQbkk

3 Conversion of one Parameter to another 02 BBT

4 Conditions for Reciprocity and Symmetry 01 BBT+

https://www.yout

ube.com/watch?v

=GasWAlIvvD8

5 Interconnection of Two Port networks in Series,

Parallel and Cascaded configurations, Image

Parameters

02 BBT

6 Illustrative problems.

02 BBT



Tutorial

1. Find The Z Parameters For The Two Port Network In Fig.1

Fig-1: ideal transformer

2. Find the Z Parameters For The Two Port Network In Fig.2

Fig-2.

Assignment

1. Determine the ABCD parameters for the p-network shown at Fig. Is this network Bilateral

or not? Explain.

2. For the two port network shown in Fig the currents I1 and I2 entering at ports 1 and 2

respectively are given by the equations. I1=0.5V1-0.2V2, I2=-0.2V1+V2, where V1 and V2 are

the voltages at port 1 and 2 respectively. Find the Y, Z, ABCD parameters of the network. Also

find its equivalent π network.

3. (a) Determine the transmission parameters and hence determine the short

circuit admittance parameters for the circuit shown in Fig. a

(b) Obtain Z parameters of the circuit shown in Fig.b and hence derive

h – parameters.

Fig.a Fig.b

UNIT-III

Filters and Symmetrical Attenuators :

Classification of Filters, Classification of Pass band and Stop band, Characteristic Impedance in the

Pass and Stop Bands, Constantk and m-derived filters-Low Pass Filter and High Pass Filters (both

qualitative and quantitative treatment); Band Pass filter and Band Elimination filters (qunatitaive

treatment only), Illustrative Problems. Symmetrical Attenuators – T-Type Attenuator, pType

Attenuator, Bridged T-type Attenuator, Lattice Attenuator.

Learning Outcomes


1. Define Filter, Pass band, Stop band, cut-off frequency.

2. Describe types of filters.

3. Derive expressions for Characteristic Impedance in the Pass and Stop Bands.

4. Derive expressions for series and shunt arm impedances of Constant-k Low Pass Filter and

High Pass Filters

5. Describe disadvantages of constant-k type filters.

6. Describe advantages of m-derived filters.

7. Derive expressions for series and shunt arm impedances of m-derived filters-Low Pass Filter

and High Pass Filters.

8. Derive expressions for series and shunt arm impedances of Constant-k Band Pass filter and

Band Elimination filters.

9. Describe the function of attenuator.

10. Describe the types of attenuator.

11. Design T- -Type Attenuator

12. Design Bridged T-type Attenuator and Lattice Attenuator.

TEACHING PLAN


Periods (16)

Mode of delivery

1 Classification of Filters, Classification of Pass

band and Stop band

02 BBT

2 Characteristic Impedance in the Pass and Stop

Bands, Constantk and m-derived filters-Low Pass

Filter and High Pass Filters (both qualitative and

quantitative treatment)

03 BBT

3 Band Pass filter and Band Elimination filters

(qunatitaive treatment only)

02 BBT

4 Illustrative Problems 03 BBT

5 Symmetrical Attenuators – T-Type Attenuator 02 BBT

6 pType Attenuator, Bridged T-type Attenuator,

Lattice Attenuator.

02 BBT



Tutorial

1. What is a constant – K low pass filter, derive its characteristics impedance.

2. A low pass π section filter consists of an inductance of 25mH in series arm and two

capacitors of 0.2μF in shunt arms. Calculate the cut off frequency, design impedance,

attenuation at 5 KHz and phase shift at 2 KHz also find the characteristic impedance at 2

KHz.

3. Design a band elimination filter having a design impedance of 600Ω and cut–off frequencies

f1=2 KHz and f2=6 KHz.

Assignment

1. Design a band pass, constant–K filter with cut off frequency of 4 KHz and nominal

characteristic impedance of 500 Ω.

2. Design a low pass constant–K (i) T–Section and (ii) π–section filter with cut–off frequency

(fc) 6 kHz and nominal characteristic impedance of 500 Ω.

3. (a ) A high pass constant–K filter with cut off frequency 40 kHz is required to procedure a

maximum attenuation at 36 kHz when used with terminated resistance of 500 Ω. Design a

suitable m– derived T–section.

(b) Design a m–derived high pass filter with a cut – off frequency of 10KHz; design

impedance of 5Ω and m=0.4.

4 (a) explains T–type attenuator and also design a T–type attenuator to give an

attenuation of 60dB and to work in a line of 500Ω impedance.

(b) Explain symmetrical π–type attenuator and also design it to give 20db attenuation and to

have characteristic impedance of 100Ω.

UNIT-IV- DC Machines

DC Generators: Principles of Operation of DC Generator, construction, EMF equation, Types of

Generators, Magnetization, Internal and external Characteristics of DC Generators.

DC Motors : DC Motors, Types of Dc Motors, Characteristics of Dc Motors, Losses and

Efficiency, Swinburne’s Test, Speed Control of Dc Shunt Motor- Flux and Armature Voltage

control methods.


At the end of completion of all learning activities the student is able to

1. Describe Faraday’s Laws of electromagnetic Induction.

2. Describe the principle of DC generator.

3. Explain the operation of DC generator.

4. Describe the construction of DC Machine.

5. Derive the EMF equation of DC generator.

6. Describe the types of DC generators.

7. Plot Magnetization, Internal and external Characteristics of DC Generators

8. Determine critical resistance and critical speed of given DC Generator.

9. Explain the Principle of DC motor.

10. Explain the operation of DC motor.

11. Describe the significance of Back EMF in DC motor.

12. Describe the types of DC motors.

13. Plot the Characteristics of DC Motors

14. Calculate Losses and Efficiency by using Swinburne’s Test

15. Describe the advantages and disadvantages of Swinburne’s Test.

16. Describe Speed Control of Dc Shunt Motor by Flux and Armature Voltage control

methods.

TEACHING PLAN


Periods (16)

Mode of delivery

1 DC Generators: Principles of Operation of DC

Generator .

01 BBT+

https://www.yout

ube.com/watch?v

=6dF3LDzb-tE

2 construction, EMF equation 01 BBT+

https://www.yout

ube.com/watch?v

=DmHw9M7Zfw

I

3 Types of Generators, Magnetization, Internal and

external Characteristics of DC Generators.

03 BBT

4 DC Motors : DC Motors, Types of Dc Motors 01 BBT+

https://www.yout

ube.com/watch?v

=1OfLgpFq6Rc

5 Characteristics of Dc Motors, Losses and

Efficiency

03 BBT

6 Swinburne’s Test, 01 BBT

7 Speed Control of Dc Shunt Motor- Flux and

Armature Voltage control methods

04 BBT



Tutorial

1. (a) Explain in detail the construction and the principle of operation of a dc generator

(b) The armature of a 4 – pole lap wound shunt generator has 480 conductors. The flux

perpole is 0.05Wb. The armature and field resistances are 0.05 Ω and 50 Ω. find the speed

of the machine when supplying 450A at a terminal voltage of 250V. Derive the expression

for the emf generated in a DC machine.

2. (a) Derive the expression for the EMF generated in a DC generator.

(b) A 6 – pole dc shunt generator with a wave – wound armature has 960 conductors. It runs

at a speed of 500 rpm. A load of 20Ω is connected to the generator at a terminal voltage of

240V. The armature and field resistances are 0.3Ω and 240Ω respectively. Find the armature

current, the induced emf and flux per pole.

3. (a) What are the different types of dc generators? Draw the connection diagrams and load

characteristics of each type. Also mention the applications of different types.

(b) A 250V DC shunt motor takes 4A when running unloaded. Its armature and field

resistances are 0.3 Ω and 250 Ω respectively. Calculate the efficiency when the dc shunt

motor taking current of 60A.

ASSIGNMENT

1. (a) Draw the speed–load characteristics of a dc shunt, series and compound motors.

(b) A 200V, 14.92kW, dc shunt motor when tested by Swinburne’s method gave the

following test results. Running light: Armature current of 6.5A and field current is 2.2A.

With armature locked: Ia=70A when potential difference of 3V was applied to the brushes.

Estimate efficiency of motor when working under full load.

2. (a) Explain why a dc series motor should never run unloaded.

(b) A 250V, 10kW shunt motor takes 2.5A when running light. The armature and field

resistances are 0.3Ω and 400Ω respectively. Brush contact drop of 2V. Find the

full–load efficiency of motor?

3. (a) Discuss in detail the different methods of speed control of a dc motor.

(b) A 4-pole, 220V dc series motor has a wave connected armature with 1200 conductors.

The flux per role is 20×10-3

wb, when the motor is drawing 46A. Armature and series field

resistances are 0.25 Ω and 0.15 Ω respectively. Find i) The speed ii) Total torque.

4. (a) Derive the torque equation of a dc motor.

(b) A 500V dc shunt motor draws 4A on no load. The field current of the motor is 1A. Its

armature resistance including brushes is 0.2Ω. Find the efficiency, when the input

current is 20A.

Unit –V Transformers and AC Machines

Transformers and Their Performance : Principle of Operation of Single Phase transformer,

Types, Constructional Features, Phasor Diagram on No Load and Load, Equivalent Circuit, Losses,

Efficiency and Regulation of Transformer, OC and SC Tests, Predetermination of Efficiency and

Regulation, Simple Problems.

AC Machines Three Phase Induction Motor : Principle of operation of three phase induction

motors- Slip ring and Squirrel cage motors –Slip_Torque characteristics.

Alternators: Principle of operation –Types - EMF Equation- Predetermination of regulation by

Synchronous Impedance Method- OC and SC tests.


At the end of completion of all learning activities the student is able to

1. Describe Principle of operation of transformer and constructional details.

2. Describe difference between Ideal Transformer and Practical Transformer.

3. Draw Phasor Diagram on No Load and Load for different types of loads.

4. Derive the expressions for equivalent resistance and reactance of Single Phase

transformer.

5. Draw Equivalent Circuit.

6. Define Efficiency and Regulation of Transformer.

7. Describe OC and SC Tests for the Predetermination of Efficiency and Regulation.

8. Learn about three phase induction motor. Principle of operation of three phase induction

motor.

9. Slip and rotor frequency along with torque calculation of three phase induction motor.

10. Learn about three phase alternator.

11. Principle of operation of a alternator.

TEACHING PLAN


Periods (16)

Mode of delivery

1 Transformers and Their Performance :

Principle of Operation of Single Phase

transformer, Types, Constructional Features,

Phasor Diagram on No Load and Load, Equivalent

Circuit, Losses

04 BBT+

https://www.yout

ube.com/watch?v

=oJtY6xn6dkQ

2 Efficiency and Regulation of Transformer, OC and

SC Tests, Predetermination of Efficiency and

Regulation, Simple Problems.

03 BBT+

https://www.yout

ube.com/watch?v

=9TTxUY0vNb8

3 AC Machines Three Phase Induction Motor : Principle of operation of three phase induction

motors- Slip ring and Squirrel cage motors –Slip

Torque characteristics.

04 BBT

4 Alternators: Principle of operation –Types - EMF

Equation- Predetermination of regulation by

Synchronous Impedance Method- OC and SC

tests.

03 BBT+

https://www.yout

ube.com/watch?v

=b24jORRoxEc



Tutorial

1. (a) Single phase induction motors are not self starting. Explain Why?

(b) How is single-phase induction motors made self started? Explain one method.

2. (a) Draw the torque speed characteristics of a 3 phase induction motor.

(b) Derive the expression for the starting torque to Maximum torque

3. (a) why 1-_ induction motor is not self starting and explain the principle of Operation of

shaded pole induction motor with a neat diagram?

(b) A 14 pole, 50Hz induction motor runs at 415 r.p.m. Deduce the frequency of the current in

the Rotor winding and the slip?

Assignment

1.Explain the rotor resistance starter for an induction motor. A 3-phase, 6 pole, 400 V, 50 Hz

induction motor. takes a power input of 35kW at its full-load speed of 890 r.p.m. The total

stator losses are 1 kW and the friction and wind age losses are 1.5 kW.Calculate

i. slip

ii. Rotor ohmic losses

iii. Shaft power

iv. Shaft torque and

v. efficiency.

2.(a) How the torque-speed characteristics of a motor are modified, if rotor resistance is

increased.

(b) ( i) A 3-phase, 6-pole, slip-ring induction machine is directly driven from the shaft by

a 4-pole3-phase synchronous motor. If stator of both the machines is given a

50 Hz supply, what frequencies are available at the rotor slip-rings of the induction

machine?

(ii) A 3-phase, 50 Hz, induction motor has a starting torque which is 1.25times full-

load torque and a maximum torque which is 2.50 times full-load torque.

Neglecting stator resistance and rotational losses and assuming constant rotor

resistance, find

(A). the slip at full-load.

(B). the slip at maximum torque and

(C). the rotor current at starting in per unit of full-load rotor current.

3 .(a) Derive the expressions for induced e.m.f of an alternator for lagging, leading and

unity power factor loads. Draw the relevant phasor diagram.

(b) Derive the relation between speed and frequency.

(c) Explain the two types of rotors used in alternators with neat sketch

TEXT BOOKS:

1. Principles of Electrical Engineering- A.Sudhakar, ShyammohanS.Palli, TMH publications.

2. Introduction to Electrical Engineering – M.S.Naidu and S. Kamakshaiah, TMH publications

3. Network analysis and Synthesis- C L Wadhwa, New Age International Publishers.

REFERENCES :

1. Networks, Lines, and Fields – John.D.Ryder, PHI publications.

2. Engineering Circuit Analysis – W.H.Hayt and J.E Kemmerly and S.M.Durbin, TMH

publications.

3. Circuit Theory by Chakrabarti, DhanpatRai and Co.

4. Network Analysis – N.C.Jagan and C.LakshmiNarayana, BS publications.

5. Network Analysis – A.Sudhakar, ShyammohanS.Palli, TMH publications

COURSE ASSESSMENT METHODS

Mode of

Assessment Assessment Tool Periodicity

Percentage

Weightage Evidences

Direct

Mid Terms

Examinations Twice in a semester 25 Answer Scripts

Assignment, Quiz

etc. At the end of each unit 5

Assignment

Books / Quiz

sheets etc.

End Semester

Examination

At the end of the

Semester 70 Answer Scripts

Indirect Course End

Survey At the end of Semester 100 Feedback forms

VNR VIGNANA JYOTHI INSTITUTE OF ENGINEERING AND TECHNOLOGY

BACHUPALLY, NIZAM PET (SO), HYDERABAD-500090

MODELQUESTION PAPER

Subject: PRINCIPLES OF ELECTRICAL ENGINEERING

Branch: ECE Time: 3

Hr

Max marks: 70

Part-A (compulsory)

(Answer all questions) 5X1=5

1(Answer all questions)

a .The time constant of a series RL Circuit.

b. Which parameters are widely used in transmission line theory.

c An attenuator is used to………

d. In a dc machine, inter poles are used to

e. By open circuit test we measure

2 ( Answer all questions) 5X2=10

1. What do you understand by transient and steady state parts of response? How can they be

identified in a general solution?

2. What is a constant-K low pass filter?

3. Explain about the lattice Attenuator.

4. State the principle of operation of a dc generator?

5. Derive the expression for the induced emf of a transformer?

3 (Answer all questions) 5X3=15

1. For the circuit shown in Fig.1, find the current equation i (t), when the switch‘s’ is opened at

t = 0.

.

Fig.1

2 Find Z and Y parameters of the network shown in Fig. 2.

Fig.2

3. Explain Bridge–T attenuator and also design it with an attenuation of 20dB and

terminated in a load of 500Ω.

4. Discuss in detail the different methods of speed control of a dc motor

5. Derive an expression for the induced e.m.f. of a single phase Transformer.

PART-B

(Answer any four questions) 4X10=40

4 (a) What is a transient. For the circuit shown in Fig.3, find the current in 20Ω resistor

when the switch ‘S’ is opened at t = 0.

Fig.3

(b) For the Series RLC circuit shown in Fig.4, the capacitor is initially charged to 1V, find the

current i(t), when the switch ‘S’ is closed at t=0usingLaplace transform.

Fig. 5

5 (a) Determine the transmission parameters and hence determine the short-circuit

admittance parameters for the circuit shown in Fig. 6

(b) Obtain Z parameters of the circuit shown in Fig.7 and hence derive h –

parameters.

Fig. 6 Fig. 7

6. (a) Design a m-derived high pass filter with cut-off frequency of 10 kHz; design

impedance 0f 5Ω and m=0.4

(b) Explain π – type attenuator and also design it to give 20db attenuation and to

have characteristic impedance of 100Ω.

7. (a) Explain in detail the principle of operation of a dc generator.

(b) The armature of a 4–pole lap wound shunt generator has 480 conductors. The flux per pole

is 0.05Wb. The armature and field resistances are 0.05Ωand50Ω. Find the speed of the machine

when supplying 450A at a terminal voltage of 250V.

8 (a) Explain the constructional details of

i. core type and

ii. shell type transformer.

(b) A 1- φ transformer has 800 turns on the primary and 100 turns on the secondary.

The no load current is 2.5 Amps at a p.f of 0.2 lagging. Calculate the primary current

and power factor when the secondary current is 250A at a p.f of 0.8 lagging..

9 (a) Derive the relation between speed and frequency.

(b) Explain the two types of rotors used in alternators with neat sketch.

department of electronics and ... and density function of sum of two independent random variables....

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