Ece - Ilyr - Ivsem - Qb

RVS FACULTY OF ENGINEERING

Coimbatore- 402

Department of Electronics and Communication Engineering

II Year – IV Semester

Question Bank

Student Name :

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PROBABILITY AND RANDOM PROCESSPROBABILITY AND RANDOM PROCESS

UNIT I- RANDOM VARIABLES

Part A -2 Mark Questions & Answers

UNIT - I

PART - A

1. Show that the function f(x) = is a P.D.F

Ans :

Hence f(x) is a P.D.F.

2. Is the function defined as follows a density function ?

f(x) =

Ans : f(x) is a P.D.F.

3. A random variable X has the following probability function

X 0 1 2 3 4

P(x) k 3k 5k 7k 9k

(a) Find K (b) Find mean (c) Find P(X<3) , P(X ) (d) F(X)

Ans :

(a) Total Probability = 1

Hence k + 3k + 5k + 7k + 9k = 1

1

PROBABILITY AND RANDOM PROCESS 25k = 1

K = 1/25

(b) Mean = E(X) = 0(k) + 1(3k) + 2(5k) + 3(7k) + 4(9k)

= 0(1/25) + 1(3/25) + 2(5/25) + 3(7/25) + 4(9/25)

(c) P(x<3) = P(0) + P(1) + P(2)

= k + 3k + 5k

= 9/25

P(x 3) = 16/25

P(0<x<4) = 15/25

(d) X 0 1 2 3 4

P(x) 1/25 3/25 5/25 7/25 9/25

F(x)1/25 4/25 9/25 16/25 1

4. A random variable X has the following probability function.

X 1 2 3 4 5 total

P(x) 0.1 0.2 k 2k 0.1 1

(a) Find K (b) Find mean

5. If X is a continuous random variable whose P.D.F is given by

f(x) = find (a) c (b) P(x>1)

Ans :

(a)

c(16/6) = 1

2

PROBABILITY AND RANDOM PROCESS c = 3/8

(b) P(x>1) =

=

= ½

6. If X is a continuous random variable whose P.D.F is given by

f(x) = find (a) P(x<1) (b) P(x>1)

7. If a random variable X has a P.D.F f(x) = find mean and

var(X).

Sol :

Mean =

=

= ½

Mean = 1/3

3

PROBABILITY AND RANDOM PROCESS Hence E(x2) = 1/3

Var(X) = E(X2) – [E(X)]2

= 2/9

8. Find mean and variance if f(x) = e-x , 0 to ∞ .

Ans : mean = 1 , variance = 1.

9. A random variable has the P.D.F given by f(x) =

Find (a) moment generating function

(b) The first 4 moments about origin.

Ans : (a) MX(t) = 2(2-t)-1

(b) (i) MXi(0) = 1/2

(ii) MXii(0) = 1/2

(iii) MXiii(0) =3/4

(iv) MXiv(0) = 3/2

10. A random variable has the P.D.F given by f(x) = find M.D.F

Ans : 1/3[e2t – e-t / t]

11. The mean and S.D of a Binomial distribution are 5 and 2 . Deternine the

distribution.

Ans : 25Cx (1/5)x (4/5)25-x

12. The mean and var of a binomial distribution are 4 and 4/3 find P(X 1) .

Ans :P(X 1) = 0.998

4

PROBABILITY AND RANDOM PROCESS13. The mean and variance of a binomial variable are 8 and 6. Find P(X 2).

Ans : P(X 2) = .9988

14. Suppose P(X=0) = 1-P(X=1). If E(X) = 3 varX , find P(X=0)

Sol: P(X=0) = 1/3

15. 6 dice are thrown 729 times. How many times do you expect atleast three dice to

show a five or six ?

Ans :233

16. In 256 sets of twelve tosses of a coin, how many cases may one expect eight

heads and four tails ?

Ans :31

17. State and prove additive property of independent poisson variable .

18. Six coins are tossed 6400 times. Using the poisson distribution what is the

approximate probability of getting six heads 10 times.

19. The number of monthly breakdoen of a computer is a random variable having a

poisson distribution with mean equal to 1.8. find the probability that this computer will

function for a month with only one breakson.

20. Let one copy of a magazine out of 10 copies bears a special prize following

geometric random distribution. Determine its mean and variance.

21. Sharon and ann play a series of back gammon games until one of them units five

games. Suppose that the games are independent and the probability that Sharon win a

game is 0.58.

(a) Find the probability that the series ends in 7 games.

(b) If the series ends in 7 games, what is the probability that Sharon wins ?

22. State and prove additive property of independent poisson variables.

23. The number of monthly breakdown of a computer is a random variable having a

poisson distribution with mean is 1.8. find the probability that this computer will function

for a month with only one breakson.

5

PROBABILITY AND RANDOM PROCESS

24. Let one copy of a magazine out of 10 copies bears a special price following a

geometric random distribution. Determine its mean and variance.

25. If the probability that a target is destroyed on any one short is 0.5, what is the

probability that it would be destroyed on 6 th attempt.

26. Sharon and ann play a series of back gammon games until one of them wins 5

games. Suppose that the games are independent and the probability that sharon win a

game is 0.58 .

(a) Find the probability that the series ends in 7 games.

(b) If the series ends in 7 games , what is the probability that Sharon wins.

27. If X is uniformly distributed random variable with mean 1 and variance 4/3, find

P(X<0) .

28. The time required to repair a machine is exponentially distribution with parameter

λ = ½.

(a) What is the probability that the repair exceeds 2h ?

(b) What is the conditional probability that a repair takes at 11h given that its direction

exceeds 8h ?.

Part- B

1. Let X be the length in minutes of a long distance telephone conversation.

The PDF of X is given by f(x)= .

2. The life time X in hours of a component is modeled by Weilbull distribution

with = 2 starting with a large number of components . It is observed that 15% of the

components that have lasted 90 hours fail before 100 hours. Find the parameter .

3. State central limit theorem in Lindberg – Levy form. A random sample of

size 100 is taken from a population whose mean is 60 and variance is 400. Using CLT with

what probability can we assert that the mean of the sample will not differ from = 60 by

more than 4? Area under the standard normal curve from z =0 to z=2 is 0.4772.

6

PROBABILITY AND RANDOM PROCESS4. If the life X [in years] of a certain type of car has a Weibull distribution with

parameter = 2. Find the value of given that the probability that the life of the car

exceeds 5 is e-0.25 for these values of and find the mean and variance of X.

5. It is known that the probability of an item produced by a certain machine

will be defective is 0.05. If the produced items are sent to the market in packets of 20, find

the number of packets containing at least exactly and at most 2 defective items in a

consignment of 100 0 packets using Poisson approximation to Binomial distribution.

6. State and prove the memoryless property of the exponential distribution

and geometric distribution.

7. The daily consumption of milk in a city in excess of 20,000 litres is

approximately distributed as an gamma variate with the parameters k=2 and

/10,000).the city has a daily stock of 30,000 litres. What is the probability that the stock is

insufficient on a particular day?

8. Derive the mgf of negative binomial distribution. Also obtain its mean and

SD.

9. Prove that poisson distribution is the limiting case of binomial distribution.

10. Find the MGF of a poisson distribution and hence find its mean and

variance.

11. A coin is tossed until the first head occurs, assuming that the tosses are

independent and the probability of a head occurring is p, find the value of p so that the

probability that an odd no of tosses is required is equal to 0.6. can you find a value of p so

that the probability is 0.05 that an odd no of tosses is required.

12. The number of PC sold daily at a computer world is uniformly distributed

with the minimum of 2000 PC and a maximum of 5000 PC . find i)the probality that daily

sales will fall between 2500 and 3000 PC.ii)what is the probability that the computer world

will sell atleast 4000 PC s ? iii) what is the probability that the computer world will sell

exactly 2500 PC s?

13. Define the pdf of normal distribution and standard normal distribution.

Write down the important properties of its distribution.

7


UNIT-II TWO DIMENTIONAL RANDOM VARIABLES


1. If X and Y are random variables having density function f(x,y) =

,

0 < x < 2, 2 < y < 4, Find P( X + Y < 3 ).

Ans :5/24

2. State the equation of two regression lines.what is the angle between them?

Ans :The regression equation of y on x is [y-y¯/σy]=r[x-x¯/ σx]

The regression equation of x on y is [x-x¯/σx]=r[y-y¯/ σy]

The angle between the lines is tan θ=1-r2/r[σx σy/ σx2+ σy

2].

3. The following table gives the joint probability distribution of X and Y. Find (i)

marginal density function of X. (ii) marginal density function of Y.

Y X 1 2 3

1 0.1 0.1 0.2

2 0.2 0.3 0.1

Ans :

Y X 1 2 3 P(y)

1 0.1 0.1 0.2 0.4

2 0.2 0.3 0.1 0.6

P(x) 0.3 0.4 0.3 1

8

PROBABILITY AND RANDOM PROCESS4. If the joint pdf of the random variable is given by f(x,y) = kxy , x > 0 , y > 0 ,

find the value of k.

Ans :The value of K is 4.

5. The tangent of the angle between the lines of regression y on x and x on y is 0,6 and

x = y , find the correlation coefficient between X and Y.

Ans :tan θ=1-r2/r[σx σy/ σx2+ σy

2]

3/5=(1-r2/r )(2/5)

2 r2+3r-2=0

R=1/2

6. If the joint pdf of (X,Y) is f(x,y) = .

Find P(x+y 1)

Ans : P(x+y 1)=1/8

7. If X and Y have joint pdf f(x,y) = ,check whether X and Y

are independent.

Ans :The marginal probability function of X is f(x)=x+(1/2)

The marginal probability function of Y is f(y)=y+(1/2)

Then f(x).f(y)= [x+(1/2) ][y+(1/2)]≠f(x,y)

Hence X and Y are not independent.

8. Find the marginal density functions of X and Y if

f(x,y) = .

Ans :The marginal density function of X is fX(x)=6/5(x+(1/3))

The marginal density function of Y is fy(y)=6/5(y2+(1/2))

9. Find the marginal density functions of X and Y from the joint density function

9


f(x,y) = .

Ans :The marginal density function of X is fX(x)=(4x+3)/5

The marginal density function of Y is fY(y)=(2+6Y)/5

10. X and Y are two random variables having the joint density function

f(x,y) = , where x and y assumes the integer values 0,1 and 2. Find the

marginal probability distribution of X.

Y X 0 1 2 P(y)

0 0 1/27 2/27 3/27

1 2/27 3/27 4/27 9/27

2 4/27 5/27 6/27 15/27

P(x) 6/27 9/27 12/27 1

11. Find the value of k if f(x,y) = kxye-(x2+y2) for 0 > x,y >0is to be a joint density

function.

Ans : k=4

12. Find k if the joint probability density function of a bivariate random variable (X,Y)

is

given by f(x,y) = k(1-x)(1-y) if 0 < x < 4, 1 < y < 5 and 0 otherwise.

Ans :The value of k is 4.

13. State central limit theorem.

Ans : If X1,X2,…Xn be a sequence of independent RVs with E(Xi) = μi and

var(Xi) = σi2 , i= 1,2,…n and if Sn = X1 + X2 + X3 …. + Xn then under

certain general conditions, Sn follows a normal distribution with mean

10

PROBABILITY AND RANDOM PROCESS μ = as n .

14. State central limit theorem .

Ans : If X1,X2,….Xn be a sequence of independent RVs with E(Xi) = μ and

var(Xi) = σi2 , i= 1,2,…n and if Sn = X1 + X2 + X3 …. + Xn then under

certain general conditions, Sn follows a normal distribution with mean nμ

and variance n σ2 as n tends to infinity.

15. state any one firm of central limit theorem.

Ans : let X1,X2,….Xn be independent, identically distributed bernoullis variates

with common probability of success and let X = X1 + X2 + X3 …. + Xn then

.

Part- B

1. The joint density finction of a random variable X and Y is f(x,y) = 2, 0 < x < Y < .

Find marginal and conditional probability density functions. Are X and y

independent?

2. Two independent random variables X and Y are defined by f(x) = and

f(y) = . Show that U = X + Y and V = X +Y are uncorrelated.

3. (X,Y) is a two dimensional random variable uniformly distributed over the triangular

region R bounded by y = 0, x = 3 and y = . Find the correlation coefficient rxy.

11

PROBABILITY AND RANDOM PROCESS4. X and Y are two random variables having density function f(x,y) =

,

0 < x < 2, 2 < y < 4. Find (i) P ( X < 1 Y < 3 ) (ii) P( X + Y < 3 )

(iii) P( X < 1 / Y < 3 ).

5. Given the joint distribution of X and Y.

Y/X 0 1 2

0 0.02 0.08 0.10

1 0.05 0.20 0.25

2 0.03 0.12 0.15

Obtain (i) marginal distribution and (ii) the conditional distribution of X given Y = 0 .

6. A statistical investigation obtains the following regression equations in a survey.

X – Y – 6 = 0 and 0.64X + 4.08 = 0. Here X = age of husband and Y = age of wife.

Find (i) Mean of X and Y (ii) Correlation coefficient between X and Y and

(iii) y = S.D. of Y if x = S.D. of X = 4.

7. Given the joint density function f(x,y) = cx(x-y), 0 < x <2, -x < y < x, Evaluate c .

Find the marginal densities of X and Y. Find the conditional density of Y given X = x.

8. Calculate the correlation coefficient for the following heights (in inches ) of fathers (x)

And their sons (Y).

X 65 66 67 67 68 69 70 72

Y 67 68 65 68 72 75 69 71

9. If the joint density function of ( X, Y ) is given by f(x,y) = x + y , 0 x , y 1, find

the correlation coefficient between X and Y.

10. The joint pdf of two random variables X and Y is given by

12


f(x,y) = , 0 x , 0 y . Find the marginal distribution of X

and Y and the conditional distribution of Y for X = x.

11.Two random variables X and Y are related as Y = 4X + 9. Find the coefficient of

correlation between X and Y.

12. Marks obtained by 10 students in Mathematics(X) and Statistics (Y) are given below.

Find the two regression lines, Also find Y when X = 55.

X 60 34 40 50 45 40 22 43 42 64

Y 75 32 33 40 45 33 12 30 34 51

13.If two random variables X and Y have pdf f(x,y) = k for x , y > 0 , evaluate k.

14. The joint pmf of the random variables X and Y is p(x,y) = ,

y = 0,1,2, … x, x = 0,1,2, .. where > 0 , 0 P 1, p+q = 1 are constants.Find the

marginal and conditional distributions.

15. Two dimentional random variables aX and y have joint pdf f(x,y) = 8xy,

0 < x < y < 1: 0 otherwise. Find (i) marginal and conditional distributions

(ii) Whether X and Y are independent?

16. The joint pdf of the random variable (X,Y) is given by

f(x,y) = where

k is a constant. (i) Find the value of k. (ii) Find P(X+Y<1) (iii) Are X and Y

independent random variables?

17. If the joint pdf of the random variable (X,Y) is given by

f(x,y) = , find f(y/x) and f(Y/X = x).

18. If y = 2x -3 and y = 5x + 7 are the two regression lines, find the values of x and y .

13

PROBABILITY AND RANDOM PROCESS Find the correlation coefficient between x and y. Find an estimate of x when y = 1.

19. If the independent random variables X and Y have the variances 36 and 16

respectively , find the correlation coefficient between ( X + Y ) and ( X – Y ).

20. From the following data , find

(i) the two regression equations

(ii) the coefficient of correlation between the marks in Economics and Statistics

(iii)the most likely marks in statistics when marks in Economics are 30

21. Two random variables X and Y have joint density function

f(x,y) = .Find E(X) , E(Y), E(XY), E( 2X + 3Y ), V(X),

V(Y), Cov(X,Y).What can you infer from Cov(X,Y).

22. The joint probability density function of the two dimentional random variable is

f(x,y) =

(i)Find the marginal density functions of X and Y.

(ii)Find the conditional density function of Y given X = x.

23. X is a continuous random variable with pdf given by f(x) =

Find the value of k and also the cdf 0f f(x).

24. If the joint pdf of a random variable (X,Y) is given by

f(x,y) = , find the conditional densities of X given Y and

14

Marks in

Economics

25 28 35 32 31 36 29 38 34 32

Marks in

Statistics

43 46 49 41 36 32 31 30 33 39

PROBABILITY AND RANDOM PROCESS Y given X.

25. Let X and Y be random variables having joint density functions

f(x,y) = .Find the correlation coefficient rxy.

UNIT-III CLASSIFICATION OF RANDOM PROCESS


1. Define Stochastic process.

Ans : A random process is acollection of random variables{X(s,t)} that are functions of a real

variable,namely time t where sЄS and t Є T .

2. Classify Random Process.

Ans : A random process is classified into two types:

(i)Continuous random process (ii)Discrete random process

3. What is a continuous random sequence? Give an example.

Ans : Let X is a random variable and t is time.If both X and t are continuous the random

process is called as continuous random process .

Example:If X(t) represents the maximum temperature at a place in the interval (0,t), {X(t)}

is a continuous random process.

4. Give an example of stationary random process and justify your claim.

Ans : Consider the random processs X(t)= cos(0t + ) where x(t) is distributed uniformly in (-

,) and 0 is a constant.X(t) is stationary In this example.

5. Distinguish between wide sense stationary and strict sense stationary processes.

(i)A random process is said to be WSS if it satisfies the following condition:

(a)E(X(t))=constant

(b)R[t1,t2]=afunction of (t1-t2)

(ii)A random process X(t) is SSS if it statistical characteristic do not change with time.

6. Prove that the first order stationary process has a constant mean.

15

PROBABILITY AND RANDOM PROCESSAns : A random process is called stationary to order one if its first order density function does

not change with a shit in time origin.

7. What is a Markov processes.

Ans : If for t1<t2<t3….. <tn<t,p{X(t)≤x/X(t1)=x1,…..X(tn)=xn}=P{x(t) ≤x/X(tn)=xn}

Then the process called as Markov process.

8. Define Markov chain and one – step transition probability.

Ans : Let X(t) be a Markov process which possess markov property and which takes only

discrete values whether t is discrete or continuous. Then {X(t)} is called as markov chain.

The conditional probability p{Xn=aj/Xn-1=ai} is called the one step transition probability from

state ai to state aj at the nth step and is denoted by pij{n-1,n}.

9. Give an example of Markov Processes.

Ans : The probability of raining today depends only on previous weather conditions existed fo

the last two days and not on past weather conditions.

10. Define irreducible Markov chain and state Chapman – Kolmorgow theorem.

Ans : If Pij(n)>0for some n and for all I and j ,then every state can be reached from every other

state .Whe n this condition is satisfied the markov chain is a said to be irreducible.The TPM of

an irreducible chain is an irreducible matrix.

Chapman – Kolmorgow:If P is the TPM of a homogeneous Markov chain then the nth step

TPM p(n) =pn (i.e) [Pij(n)]=[ Pij]n

11. What is meant by Steady state distribution of Markov chain?

Ans : If a homogeneous markov chain is regular ,then every sequence of state probability

distribution approaches a unique fixed probability distribution called the stationary distribution

or a steady state distribution of the markov chain

12. State the Postulates of Poisson process.

Ans : Let X(t)= number of times an event A say ,occurred upto time t so that the

sequence{X(t),tЄ[0,∞]}forms a poission process with parameter λ.

(i)Events occurring in non-over lapping intervals are independent of each other .

(ii)P[X(t)=1 for t in (x,x+h)]=λh+0(h)

(iii) P[X(t)=1 0 for t in (x,x+h)]=1-λh+0(h)

16

PROBABILITY AND RANDOM PROCESS(iv) P[X(t)=2 or move for t in (x,x+h)]= 0(h).

13. State any two properties of Poisson process.

Ans : (i)The poisson process is a markov process

(ii)The sum of two independent poisson process is again a poisson process.

14. What will be the super position of n independent Poisson processes with respective

average rates 1,2, …n ?

Ans : The super position of n independent Poisson processes with respective average rates

1,2, …n is another piosson process with average rate1+2+ …+n.

15.Define Ergodic random process with ex.

Ans : A random process X(t) is called Ergodic if its ensemble averages are equal

to appropriate.Time averages. Ex:A markov chain finite state space,astocastic process X(t)

is Ergodic if its time average tends to ensemble averages as T>∞.

Part-B

1. Define a random (stochastic) processes. Explain the classification of random process.

Give an example to each class.

2. Consider a random process y(t) = x(t) cos(0t + ) where x(t) is distributed uniformly in

(-,) and 0 is a constant. Prove that y(t) is wide – sense stationary.

3. Two random processes X(t) and Y(t) are defined by X(t) = Acost + Bsint and Y(t) =

Bcost - Asint. Show that X(t) and Y(t) are jointly Wide-Sense stationary if a and B are

uncorrelated random variables with zero means and same variances and is constant.

4. Show that the process X(t) = A cost + B sint where A and B are random variables is

wide sense stationary if (i) E(A) = E(B) = 0 (ii) E(A2) = E(B2) and (iii) E(AB) = 0.

5. Show that the random process X(t) = A sin(t+) where is a random variable

uniformly distributed in (0,2) is (i) first order stationary (ii) stationary in the wide

sense.

6. For a random process X(t) = Y sint, Y is an uniform random variable in ( -1, 1 ). Check

whether the process is wide sense stationary or not.

17

PROBABILITY AND RANDOM PROCESS7. If X(t) is a wide sense stationary process with autocorrelation function RXX() and if Y(t)

= X(t+) – X(t-) , show that RYY() = 2RXX(T+2) - RXX( T-2).

8. If X(t) = 5 sin(t+) and Y(t) = 2cos(t+) where is a constant + = /2 and is a

random variable uniformly distributed in (0,2), find RXX() , RYY() , RXY() and RYX().

Verify two properties of autocorrelation function and cross correlation function.

9. If the process is a Poisson process with parameter t, obtain

and .

10. Find the mean and autocorrelation of of Poisson process.

11. State the Postulates of Poisson process. Discuss any two properties of Poisson

processes.

12. Prove that the sum of two independent Poisson process is also a Poisson Process.

13. Let X be a random variable which gives the interval between two successive

occurrences of a Poisson process with parameter . Find out the distribution of X.

14. Given a random variable Y with characteristic function () = E(eiy) and a random

process defined by X(t) = cos(t + y). Show that is stationary in the wide sense

if (1) = (2) = 0.

15. A man either drives a car or catches a train to go to office each day. He never goes 2

days in a row by train but if he drives one day, then the next day he is likely to drive

again he is to travel by train. Now suppose that on the first day of the week, the man

tossed a fair die and drove to work if and only if a ‘6’ appeared. Find (i)the probability

that he takes train on the third day (ii) the probability that he drives to work in the long

run.

16. Three boys A, B and C are throwing a ball to each other. ‘A’ always throws the ball to

‘B’ and ‘B’ always throws the ball to ‘C’ but ‘C’ is just as likely to throw the ball to B as

to A. Show that the process is Markovian. Find the transition matrix and classify the

states.

17. The transition probability matrix of a Markov Chain , n = 1, 2, 3, … having 3 states

1, 2 and 3 is and the initial distribution is

18

PROBABILITY AND RANDOM PROCESS P(0) = ( 0.7, 0.2, 0.1 ) . Find (i) P(X2 = 3) (ii) P(X3 = 2, X2 = 3, X1 = 3, X0 = 2).

18. The one step TPM of a Markov chain having state space S =

is and the initial distribution is P(0) = ( 0.7, 0.2, 0.1 ) . Find (i)

P(X2 = 3) (ii) P(X3 = 2, X2 = 3, X1 = 3, X0 = 0) P(X2 = 3/ X0 = 1) .

19. Let , n = 1, 2, 3, … be a Markov chain with state space S = 0,1,2 and one step

Transition Probability Matrix

(i) Is the chain ergodic? (ii) Find the invariant probabilities.

20. Show that random process X(t) = A cos(t+) is wide sense stationary if a and are

constants and is uniformly distributed random variable in ( 0,2).

21. For a random process X(t) = Y , Y is uniformly distributed random variable in ( -1, 1 ).

Check whether the process is wide sense stationary or not.

22. The process

Show that X(t) is stationary.

23. If X(t) = A cosy + B sint ; t 0 is a random process where A abd B are independent

N(0, 2) random variables, examine the stationary of X(t).

24. Let X(t) = A cos(t+Y) be a random process where Y and are independent random

variables. Further the characteristic function of Y satisfies (1) = 0 and (2) = 0 ,

while the density function f() of satisfies f() = f(-). Show that X(t) is wide sense

stationary .

25. The autocorrelation function of a stationary random process is

19


RXX() = . Find the variance of the process.

26. Let be a random process where

X(t) = total number of points in the interval (0,t) = k , say

= Find the autocorrelation function of X(t).

UNIT – IV

CORRELATION AND SPECTRAL DENSITY


1. Define auto correlation function and state any two of its properties.

Ans : If the process {X(t)} is either wide sense stationary or strict

sense stationary then E{X(t) X(t+)} is a function of , denoted by RXX() or

R() or RX(). This function RXX() is called the Auto correlation function of

the process {X(t)}.

Properties ;

(i) The cross correlation function is not generally an even function of , but it has a

symmetry relationship of RXX() = RXX(-)

(ii) The cross correlation function of two random processes X(t) and Y(t) does not

have a maximum value at the origine. i.e., - = 0.

2. Define autocorrelation function and prove that for a WSS process RXX (-) = RXX ().

Ans : If the process {X(t)} is either wide sense stationary or strict

sense stationary then E{X(t) X(t+)} is a function of , denoted by RXX() or

R() or RX(). This function RXX() is called the Auto correlation function of

the process {X(t)}.

To prove RXX() = RXX(-)

We know that RXX(t , t+) = RXX()

i.e., RXX() = E[X(t). X[(t+)]

Replacing by - , we get

RXX(-) = E[X(t). X[(t- RXX(-) = E[X(t). E[(t-)])]

20

PROBABILITY AND RANDOM PROCESS Putting t- = k then

RXX(-) = E[X(k+). X(k)]

= E[X(k) X(k+)]

= RXX()

RXX(-) = RXX().

3. Define cross correlation function and state any two of its properties.

Ans : The cross correlation of the two random processes X(t) and Y(t) at t1,t2

is defined by RXY(t1 , t2) = E[X(t1). Y(t2)]

Where X(t1) and Y(t2) are random variables.

4. Given the autocorrelation function for a stationary ergodic process with no

periodic components is R() = . Find the mean and variance of the process.

5. If the autocorrelation function of a stationary process is RXX() = , find

the mean and variance of the process.

6 . Define power density spectrum.

Ans : If Rxx( ) is the ACF of a WSS process {X(t)} then the PSD Sxx(ω) of

the process {X(t) } is defined by Sxx(ω) = .

7. Express each of ACF and PSD of a stationary R.P in terms of each other.

Ans: Rxx( ) and Sxx(ω) are Fourier transform pairs (i.e) Sxx(ω) = and R( =

.

7.Write down the Wiener –Khinchine relations .

Ans: Sxx(ω) = or Rxx( ) = .

8. Define cross power spectral density of two random process {X(t)} and {Y(t)}.

If {X(t)} and {Y(t)} are two jointly stationary random process with

cross correlation .

21

PROBABILITY AND RANDOM PROCESS Ans : function Rxy( ), then cross power spectral density of {X(t)} and

{Y(t)} is defined by Sxy( ) = .

9. State any two properties of power spectral density.

Ans:(i)S( ) =S(- )

(ii)S( )>0.

10. If R( ) = is the ACF of a R.P. {X(t)} , obtain the spectral density of X(t).

Ans: Sxx(ω) = Sxx(ω) = = 4λ/4 λ2+ω2.

11. State wiener-khinchin theorem .

Ans : XT( ) : fourier transform of the truncated R.P XT(

where{X(t)} is real WSS with PSD Sxx(ω). Then S (ω) = .

12. Defione power spectral density function of a stationary random process X(t).

Ans : Sxx(ω) =

13. If R( ) = is the auto correlation fu nction of a random process X(t). obtain

the spectral density of X(t).

Ans: S(ω) = 4λ/ (4λ2 +ω2 ).

14. Write the cross correlation coefficient.

Ans : Let {X(t)} and {Y(t)}be any two random process. Then the cross correlation coefficient is

given by (t1,t2)=Cxy(t1,t2)/(√Var(X(t1)) Var(Y(t2)).

Part-B

1.A WSS process has an auto correlation function R(r) = p.e-3\t\, where p is

22

PROBABILITY AND RANDOM PROCESSconstant. Find its PSD of the process.

2. Find the power spectral density of a stationary random process for which the auto

correlation function is Rxx(r) = A2e-αlr│

3. The auto correlation of an aperiodic power signal is Rxx(r) = e-r2 (α2 /2.) Find

the power spectral density of the signal

4. Find the autocorrelation function ofthe random process X(t) for which the power

spectral density is given by S( w) =2α / α2+w2

5. Find the power spectral density of the random process whose autocorrelation

function is R(t) = e-α │r│cos{βr).

6. For the process {x(t)} where x(t) = acos(bt + y), where y is uniformly distributed

over (-pi, ∏). Find the auto correlation function and the spectral density.

7. The impulse response of a low pass filter is ae-atu(t) where a = ie• If a zero mean

white Gaussian process {N(t)} is an input into this filter, find the auto correlation function

and mean square value of the output process.

. 8. Find the auto correlation function corresponding to the PSD Sxx(w) = 4/, 1+.(w 2│4)

-α< W < α

9.Given the power spectral density S x x (w) = 4+1w2' find the average power of the

process.

10. A WSS random process X(t) with auto correlation Rxx(r) = Ae-alTI where 'A' and 'a' are

real positive constants, is applied to the input of an linear . invariant system with

impulse response h(t) = e-btu(t) where b is a real positive constant. Find the auto

correlation of the output Y (t) of the system.

11. X(t) is the input and Y(t) is the output of a system. Also {X(t); t €T} is a stationary

random process with μx = 0 and Rxx(r) = e-α1T1• Find μ y, Syy(w) and Ryy (t), if the power

transfer function is H (w) = R/( R+iL( w) ).

12. A system has a transfer function as1/( l+j(f/l00) if the input to the system is a zero-

mean stationary random process with power density spectrum as 10-9. Find the power of

the output.

23

PROBABILITY AND RANDOM PROCESS13. X(t), a stationary random process with zero mean is given as input to a system with

transfer function H(f) = R/(R+i(2∏)L'The auto correlation of the input is e-βItI. Find the mean

and power of output process. Check whether output process is stationary.

14. Given the power spectral of a continuous process as Sxx(w) =1/ (w4+5w+4 )

Find the mean square of the process.

UNIT – V

LINEAR SYSTEMS WITH RANDOM INPUTS


1. Describe a linear system.

Ans : Given two stochastic processes {Xj(t)i} (j = 1,2) . then we say that L is

a linear transformation if L[a1X1(t) + a2X2(t)] = a1 L[X1(t)] + a2 L[X2(t)].

2. Define a System. When is it called linear system ?

Ans : Mathematically a system is a functional relationship between the input X(t0) and

output Y(t).

The input and output relationship can be written as

Y(t0) = f[x(t) : -∞ < t <∞] ; -∞ < t0 <∞

A system is said to be linear is superposition applies that is if

Y1(t) = f[x1(t)]

Y2(t) = f[x2(t)]

Then for a linear system

f[a1x1(t) + a2x2(t)] = a1Y1(t) + a2Y2(t).

3. Define Spectral density.

Ans; Let{X(t) , t≥0} be a stationary time series with E[X(t)] = 0 and

covariance function R(t-s) = E[X(t)X(s)] and let F(x) be a real , never

decreasing and bounded function of x with dF(x) = f(x)dx

R(t) is non negative definite then

f(w) = 1/2п

which is called spectral density.

24

PROBABILITY AND RANDOM PROCESS4. Define cross spectral density.

Ans: cross spectral density of two jointly WSS continuous time process

{X(t), Y(t)} is defined as the Fourier transform of the cross correlation

function Rxy(z) given by

Sxy(t) = .

5. State the properties of linear filter.

Ans : Let {X1(t)} and {X2(t)} be any two processes and a and b be

two constants.

If L is a linear filter then

L[aX1(t) + bX2(t)] = a L[X1(t)] + b L[X2(t)].

6. What is meant by spectral analysis ?

Ans : Let R() the correlation function of a stationary process {X(t)}.

Then R() = E[X(ξ + )] X(t) and the spectrum S(w) is modestly defined as the Fourier

transform of R().

i.e., S(w) = analysis of this spectrum is called spectral analysis.

7. Define cross spectral density.

Cross spectral density of the two joinly WSS continuous-time process

{X(t), Y(t)} is defined as the fourier transform of the cross-correlation

function Rxy(z) given by

Sxy(t) = .

8. Describe a linear system with an random input.

Ans : Let x(t) represents a sample function a random process {X(t)}, the system

produces an output or response y(t) and the ensemble of the output functions forms a

random process {Y(t)}. The process function {Y(t)} can be considered as output of the

system or transformation f with {X(t)} as the system is completely specified by the

operator f.

9. Define Spectrum of x(t)

Ans : Let x(t) be a deterministic signal. The fourier transform of x(t) is defined as

25


F[x(t)] = X(ω) = here X(ω) is called Spectrum of x(t).

10. Define causality

Ans : Causality is defined as a property of linear systems that the system

response at time t depents only on the past values of the input.

11. Write down the classification of systems:

Ans : There are two types,

(i) Linear system

(ii) Time-invariant system

(iii) Causal system

(iv) Memoryless system

(v) Stable system.

12. Define stable system.

Ans : A linear time invariant system is said to be stable if its response to any bounded

input is bounded.

13. Define memory system.

Ans : If the output Y(t) at agiven time t = t0 depents only on X(t0) and not on any other

past or future values of X(t) , then the system f is called memoryless system.

Part-B

1. If the input to a time-invarient stable linear system is a WSS process,then the out put

will also be a WSS process .Thay is to show that if {X(t)} is aWSS process then the

output {Y(t)} is a WSS process.

2. Consider the white Gaussian noice of zero mean and power spectral density N0/2

apply to a low pass RC filter where transfer function is H(f)=1/(1+2Пj fRC ).Find the

output spectral density and auto correlation function of the output process .

3. If X(t) is the input voltage to a circuit and Y(t) is the output voltage,

{X(t)} is a stationary random process with x=0 and RXX( )= .Find y,Sxx(ω) and

Syy(ω), if the system function is given by H(ω)=1/(ω2+22).

26

PROBABILITY AND RANDOM PROCESS4. If the input X(t) and the output Y(t) are connected by the differential equation T (

dy(t)/dt ) +y(t) =x(t), prove that they can be related by means of a convolution type

integral .Assume X(t) and Y(t) are zero for t 0.

5. Find the input autocorrelation function output autocorrelation function and output

spectral density of the RC – low pass filter shown in the fig,, when the filter is

subjected to a white noise of spectral density N0/2 .

6. A circuit has an impulse response given by h(t) = Evaluate Syy(ω) in

terms of Sxx(ω).

7. Obtain the transfer function of the system whose input is

Sni(ω0) = N0(ω2 + 2/ ω2 + 4) and the output is Sn0(ω0) = N0.

8. consider the bridge circuit with white noise of spectral density N0 as input. Find the

spectral density of the output.

9. Estimate the resultant Φ(ω) if a white noise of spectral density unity is passed through

an RC – low pass filter with transfer function H(ω).

10. A random voltage signal in the form of pisson distributed unit impulses figure (a) is

applied at the input terminals of an RC circuit shown in figure b .Determine the power

spectral density function ,auto correlation function of the output voltage.Also

determine the mean value and mean square value of the output voltage.

11. The occurrence of a pulse is supposed to follow the poisson law (poisson

process).Calculate the auto correlation of such a random telegraph signal.

12. If {X(t)} is a band limited process such that Sxx (ω)=0, > ,prove that 2[Rxx(0)-Rxx(

)] Rxx(0).

27

PROBABILITY AND RANDOM PROCESS13. Let Y(t)=Acos(ω0t+ ) + N(t) where A is a constant is a RV with a uniform distribution

in (-П,П) and {N(t)} is band limited Gaussian white Noise with a power spectral density .

SNN(ω)= .

Find the specrtral density function of {Y(t)} assuming that N(t) and

are independent.

28

ELECTRONIC CIRCUITS IIELECTRONIC CIRCUITS II

UNIT I - FEEDBACK AMPLIFIERS


1. Define positive feedback?

If the feedback signal is in phase with input signal, then the net effect of the

feedback will increase the input signal given to the amplifier. This type of feedback is said

to be positive or regenerative feedback.

2. Define negative feedback?

If the feedback signal is out of phase with the input signal then the input voltage

applied to the basic amplifier is decreased and correspondingly the output is decreased.

This type of feedback is known as negative or degenerative feedback.

3. Define sensitivity?

Sensitivity is defined as the ratio of percentage change in voltage gain with

feedback to the percentage change in voltage gain without feedback.

4. What are the types of feedback?

i. Voltage-series feedback ii. Voltage-shunt feedback iii. Current-series feedback

iv. Current-shunt feedback.

5. Define feedback?

A portion of the output signal is taken from the output of the amplifier and is

combined with the normal input signal. This is known as feedback.

6. Give an example for voltage-series feedback.

The Common collector or Emitter follower amplifier is an example for voltage

series feedback.

7. Give the properties of negative feedback.

i. Negative feedback reduces the gain ii. Distortion is very much reduced.

. 8. Write the expression for input and output resistance of voltage series feedback

amplifier.

Rif=Ri(1+βAv)

Rof=Ro/(1+βAv)

9. Write the expression for input and output resistance of current shunt feedback

amplifier.

Rif=Ri/(1+βA1)

Rof=Ro(1+βAi)

28

ELECTRONIC CIRCUITS II 10. Give the effect of negative feedback on amplifier characteristics.

Type of

feedback

Voltage gain Bandwidth Input

resistance

Output

resistance

Current-series Decreases Increases Increases Increases

Voltage-series Decreases Increases Increases Decreases

Voltage-shunt Decreases Increases Decreases Decreases

Current-shunt Decreases Increases Decreases Increases

11. Write the expression for input and output resistance of voltage shunt feedback

amplifier.

Ri=Rhie/(R+hie)

Rof=Ro’/D

12. Write the expression for input and output resistance of current series feedback

amplifier.

Rif=RiD :Rof=RoD

Part-B

1. Explain bistable Multivibrator and its types?

2. Explain about speedup capacitors or commutating capacitors

3. Explain about Monostable Multivibrator

4. Pulse width of collector coupled Monostable Multivibrator

5. Explain emitter coupled astable Multivibrator

6. Write in detail about Schmitt Trigger circuit?

UNIT 2-OSCILLATORS


1. What is Oscillator circuit?

A circuit with an active device is used to produce an alternating current is called

an oscillator circuit.

2. What are the classifications of Oscillators?

RC Oscillators-RC Phase shift and wienbridge oscillators.

29

ELECTRONIC CIRCUITS IILC Oscillators-Hartley and Collpitts oscillators.

3. Define Barhausen Criterion

The product of Amplifier gain and feedback factor is unity. This is known as

Barhausen Criterion |Aβ|=1

4. What are the types of feedback oscillators?

* RC-Phase shift Oscillator, * LC-Oscillators i. Tuned collector Oscillator ii.

Tuned emitter Oscillator iii. Tuned collector base Oscillator iv. Hartley Oscillator v.

Colpits Oscillator vi. Clap Oscillator.

5. What are the conditions for oscillation?

The total phase shift of an oscillator should be 360 degrees.

For feedback oscillator it should satisfies Barhausen criterion.

6. Define piezoelectric effect.

When applying mechanical energy to some type of crystals called piezoelectric

crystals the mechanical energy is converted into electrical energy is called piezoelectric

effect.

7. What is Miller crystal oscillator?

. It is nothing but a Hartley oscillator its feedback Network is replaced by a crystal.

Crystal normally generate higher frequency reactance due to the miller capacitance are in

effect between the transistor terminal.

8. State the frequency for RC phase shift oscillator.

The frequency of oscillation of RC-phase shift oscillator is

F=1/2piRC√6 Hz

9. State the frequency for RC phase shift oscillator.

The frequency of oscillation of RC-phase shift oscillator is

F=1/2pi√(R1R2C1C2)Hz

10. State the frequency for Hartley oscillator.

The frequency of oscillation of Hartley oscillator is

F=1/2pi√(LCeq) Hz

11. State the frequency for Colpitts oscillator.

The frequency of oscillation of Colpitts oscillator is

F=1/2pi√(LC3) Hz

12. What is the condition for Resonance?

The Resonance condition is given by

F=1/2pi(√LC) Hz.

13. What is the feedback factor of Armstrong oscillator?

The Expression is given as Β=M/L.

30

ELECTRONIC CIRCUITS IIPart-B

1. Explain about pulse transformer?

2. Explain Monostable blocking oscillator using emitter timing?

3. Write about the core saturation method

4. Write about astable blocking oscillator.

5. Write about UJT sawtooth generator

6. What will happen when a step input voltage is applied to the high pass RC Circuit?

UNIT 3 TUNED AMPLIFIERS


1. What is a tuned amplifier?

The amplifier with a circuit that is capable of amplifying a signal over a narrow

band of frequencies are called tuned amplifiers.

2. What happens to the circuit above and below resonance?

Above resonance the circuit acts as capacitive and below resonance the circuit

acts as inductive.

3. What are the different coil losses?

Hysteresis loss

Copper loss

Eddy current loss

4. What is Q factor?

It is the ratio of reactance to resistance.

5. What is dissipation factor?

It is referred as the total loss within a component i.e1/Q

6. What is the classification of tuned amplifiers?

Single tuned

Double tuned

Stagger tuned

7. What is a single tuned amplifier?

An amplifier circuit that uses a single parallel tuned circuit as a load is called

single tuned amplifier.

8. What are the advantages of tuned amplifiers?

They amplify defined frequencies.

Signal to noise ratio at output is good

They are suited for radio transmitters and receivers

31

ELECTRONIC CIRCUITS II 9. What are the disadvantages of tuned amplifiers?

The circuit is bulky and costly

The design is complex.

They are not suited to amplify audio frequencies.

10. What is neutralization?

The effect of collector to base capacitance of the transistor is neutralized by

introducing a signal that cancels the signal coupled through collector base capacitance.

This process is called neutralization.

11. What are double tuned amplifiers?

The amplifiers having two parallel resonant circuit in its load are called double tuned

amplifiers.

12. What is a stagger tuned amplifier?

` It is a circuit in which two single tuned cascaded amplifiers having certain

bandwidth are taken and their resonant frequencies are adjusted that they are separated

by an amount equal to the bandwidth of each stage. Since resonant frequencies are

displaced it is called stagger tuned amplifier.

13. What are the advantages of stagger tuned amplifier?

The advantage of stagger tuned amplifier is to have better flat, wideband

characteristics.

14. What are the advantages of double tuned over single tuned?

1. Possess flatter response having steeper sides

2. Provides larger 3 db bandwidth

3. Provides large gain-bandwidth product.

15. What are the different types of neutralization?

1. Hazeltine neutralization

2. Rice neutralization

3. Neutrodyne neutralization.

16. What is rice neutralization?

It uses center tapped coil in the base circuit. The signal voltages at the end of

tuned base coil are equal and out of phase.

17. What is unloaded Q?

It is the ratio of stored energy to the dissipated energy in a reactor or resonator.

18. What are the applications of mixer circuits?

Used in radio receivers.

Used to translate signal frequency to some lower frequency

19. What is up converter?

When the mixer circuit is used to translate signal to high frequency, then it is

32

ELECTRONIC CIRCUITS IIcalled up converter.

20. What is an amplifier?

An amplifier is a device which produces a large electrical output of similar

characteristics to that of the input parameters.

21. How are amplifiers classified according to the input?

1. Small signal amplifier

2. Large signal amplifier

22. How are amplifiers classified according to the transistor configuration?

1. Common emitter amplifier

2. Common base amplifier

3. Common collector amplifier

23. What is the different analysis available to analyze a transistor?

1. AC analysis

2. DC analysis

24. How can a DC equivalent circuit of an amplifier be obtained?

By open circuiting the capacitor.

25. How can a AC equivalent circuit of a amplifier be obtained?

By replacing dc supply by a ground and short- circuiting capacitors.

26. What is the disadvantage of negative feed back?

It reduces amplifier gain.

27. Define sensitivity.

It is the ratio of percentage change in voltage gain with feedback to the percentage

change in voltage gain without feed back.

28. Define Desensitivity.

It is the ratio of percentage change in voltage gain without feedback to the percentage

change in voltage gain with feed back. the reciprocal of sensitivity.

Part- B

1.Explain the relevant information ,how the negative feed back improves stability

reduce noise and increase input impedance?

2. Explain voltage shunt feed back amplifiers?

3 .Explain current series feed back amplifiers?

4. Explain the classification of amplifiers? Explain the following in detail.

5. Explain current shunt and voltage shunt feed back amplifiers?

6. With simple diagrams explain the operation of negative resistance oscillator using

tunnel diode?

33

ELECTRONIC CIRCUITS II

UNIT 4


1. What is a Multivibrator?

The electronic circuits which are used to generate nonsinusoidal waveforms are called

Multivibrators.

2. Name the types of Multivibrators?

Bistable Multivibrator

Monostable Multivibrator

Astable Multivibrator

3. How many stable states do bistable Multivibrator have?

Two stable states.

4. When will the circuit change from stable state in bistable Multivibrator?

when an external trigger pulse is applied, the circuit changes from one stable state to

another.

5. What are the different names of bistable Multivibrator?

Eccles Jordan circuit, trigger circuit, scale-of-2 toggle circuit, flip-flop and binary.

6. What are the other names of monostable Multivibrator?

One-shot, Single-shot, a single-cycle, a single swing, a single step Multivibrator,

Univibrator.

7. Why is monostable Multivibrator called gating circuit?

This circuit is used to generate the rectangular waveform and hence can be used to gate

other Circuits hence called gating circuit.

8. Why is monostable Multivibrator called delay circuit?

The time between the transition from quasi-stable state to stable state can be

predetermined and hence it can be used to introduce time delays with the help of fast transition.

Due to this application is Called delay circuit.

9. What are the main characteristics of Astable Multivibrator?

The Astable Multivibrator automatically makes the successive transitions from one quasi-

stable State to other without any external triggering pulse.

10. What is the other name of Astable Multivibrator- why is it called so?

As it does not require any external pulse for transition, it is called free running

Multivibrator.

11. What are the two types of transistor bistable Multivibrator?

i. Fixed bias transistor circuit

ii. Self bias transistor circuit.

34

ELECTRONIC CIRCUITS II12. Why does one of the transistors start conducting ahead of other?

The characteristic of both the transistors are never identical hence after giving supply one

of the Transistors start conducting ahead of the other.

13. What are the two stable states of bistable Multivibrator?

i. Q1 OFF (cut off) and Q2 ON (Saturation)

ii. Q2 OFF (Cut off) and Q1 On (Saturation)

14. What finally decides the shape of the waveform for bistable multivibrator?

The spacing of the triggering pulses

15. How are the values R1, R2 and VBB chosen in bistable Multivibrator?

It is chosen in such a way that in one state the base current is large enough to drive the

transistor into saturation while in other state the emitter junctions is well below off.

16. What is the self biased Multivibrator?

The need for the negative power supply in fixed bias bistable Multivibrator can be

eliminated by rising a common emitter resistance Re. The resistance provides the necessary bias

to keep one transistor or and the other OFF in the stable state such type of biasing is called self

biasing and the circuit is called self biased bistable Multivibrator.

17. What are the other names of speed up capacitors?

i. Commutating Capacitors

ii. Transpose capacitors

18. Define transition time?

It is defined as the time interval during which conduction transfers from one transistor to

other.

19. What is the value of commutating capacitor.

It lies in the range of tens to some hundreds of Pico farads.

20. Define resolving time.

The smallest allowable interval between triggers is called resolving time.

21. Give the expression of fmax with respect to resolving time

Fmax = 1/resolving time

22. Define gate width

The pulse width is the time for which the circuit remains in the quasi stable state. It is

also called gate width.

23. What are the advantages of monostable Multivibrator?

-.used to introduce time delays as gate width is adjustable - used to produce rectangular

waveform and hence can be used as gating circuit.

24. What are the applications of astable Multivibtrator?

- used as a clock for binary login signals - used as a square wave generator, voltage to

frequency converter.

35

ELECTRONIC CIRCUITS II

25. What is a complementary Multivibrator?

It is turning half the circuit upside down. So one transistor is n-p-n while the other is p-n-

p. The circuit is called complementary Multivibrator circuit.

26. What is UTP of the Schmitt Trigger?

When Vi reaches to VBE1 +VE the Q1 gets driven to active region. This input voltage

level is called upper threshold point.

27. What is the other name for UTP

It is also called input turn on threshold level

28. What is LTP Schmitt trigger?

The level of Vi at which Q1 becomes OFF and Q2 on is called lower threshold point.

29. Define transfer Characteristics

The graph of output voltage against input voltage is called transfer characteristics of

Schmitt trigger.

30. What is the important application of Schmitt trigger?

It is used as an amplitude comparator

It is used as a squaring circuit.

Part- B

01. Explain RC phase shift oscillator?.

02. Explain Clapp’s oscillator and derive the expression for frequency of oscillation. Also

explain how

frequency stability can be improved Clapp’s oscillator.?

03. Explain Hartly oscillator and derive the equation for oscillation?

04. Explain pierce crystal oscillator and derive the equation for oscillation? Derive the

frequency of

oscillation.

05. Explain in detail about single tuned amplifier

06. Explain in detail about double tuned amplifier

UNIT 5


1. Define Blocking Oscillator?

A special type of wave generator which is used to produce a single narrow pulse or train

of pulses.

2. What are the two important elements of Blocking Oscillator?

Transistor and pulse transformer

36

ELECTRONIC CIRCUITS II 3. What are the applications of blocking Oscillator?

It is used in frequency dividers, counter circuits and for switching the other circuits.

4. Give the formula for transformation ratio

n= Ns/Np = transformation ratio Ns= Secondary Turns; Np= Primary turns

5. Define rise time

It is defined by the time required by the pulse to rise from 10% of its amplitude to 90% of

its amplitude.

6. Define overshoot.

It is the amount by which the output exceeds its amplitude during first attempt.

7. Define flat top response.

The position of the response between the trailing edge and the leading edge.

8. Define droop or a tilt

The displacement of the pulse amplitude during its flat response is called droop or a tilt.

9. What are the applications of pulse transformer?

i. to invert the polarity of the pulse

ii. to differentiate pulse

10. When does the core saturates?

When L≥o as B≥ Bm, the core saturates

11. What is the other name of astable Blocking Oscillator?

Free running blocking Oscillator

12. What are the two types of astable Blocking Oscillator?

1. Diode controlled Astable Blocking Oscillator.

2. Resistor controlled Astable Blocking Oscillator

13. Define Sweep time in sawtooth generator

The period during which voltage increases linearly is called sweep time.

14. What is the other name of sawtooth generator?

Ramp generator

15. Define Displacement error in the sawtooth generator?

It is defined as the maximum difference between the actual sweep voltage and linear

sweep which passes through the beginning and end points of the actual sweep.

16. What is the miller circuit?

Integrator is used to convert a step waveform into ramp waveform.

Part- B

1. Explain in detail about stagger-tuned amplifier

37

ELECTRONIC CIRCUITS II2. Compare single tuned and double tuned amplifier

3. Explain the different types of neutralization?

4. Explain Hazeltine neutralization

5. Explain Rice neutralization.

6. Explain Neutrodyne neutralization

38

COMMUNICATION THEORYCommunication Theory

UNIT I AMPLITUDE MODULATION SYSTEMS


1. Define modulation?

Modulation is a process by which some characteristics of high frequency carrier signal is

varied in accordance with the instantaneous value of the modulating signal.

2. What are the types of analog modulation?

Amplitude modulation

Angle Modulation

1. Frequency modulation

2. Phase modulation.

3. Define depth of modulation.

It is defined as the ratio between message amplitude to that of carrier amplitude.

m=Em/Ec

4. What are the degrees of modulation?

Under modulation m<1

Critical modulation m=1

Over modulation m>1

5. What is the need for modulation?

Needs for modulation:

Ease of transmission

Multiplexing

Reduced noise

39

COMMUNICATION THEORYNarrow bandwidth

Frequency assignment

Reduce the equipments limitations.

6. What are the types of AM modulators?

There are two types of AM modulators. They are

Linear modulators

Non-linear modulators

Linear modulators are classified as follows

Transistor modulator

There are three types of transistor modulator.

Collector modulator

Emitter modulator

Base modulator

Switching modulators

Non-linear modulators are classified as follows

Square law modulator

Product modulator

Balanced modulator

7. Give the classification of modulation.

There are two types of modulation. They are

Analog modulation

Digital modulation

Analog modulation is classified as follows

Continuous wave modulation

Pulse modulation

40

COMMUNICATION THEORY Continuous wave modulation is classified as follows

Amplitude modulation

Double side band suppressed carrier

Single side band suppressed carrier

Vestigial side band suppressed carrier

Angle modulation

Frequency modulation

Phase modulation

Pulse modulation is classified as follows

Pulse amplitude modulation

Pulse position modulation

Pulse duration modulation

Pulse code modulation

Digital modulation is classified as follows

Amplitude shift keying

Phase shift keying

Frequency shift keying

8. What is single tone and multi tone modulation?

If modulation is performed f or a message signal with more than one frequency component

then the modulation is called multi tone modulation.

If modulation is performed for a message signal with one frequency component then the

modulation is called single tone modulation.

9 .The antenna current of an AM transmitter is 8A when only carrier is sent. It increases to

8.93A when the carrier is modulated by a single sine wave. Find the percentage modulation.

Solution:

Given: Ic =8A It=8.93A m=0.8

41

COMMUNICATION THEORY Formula: It=Ic (1+m2/2) ½

8.93=8(1+m2/2) ½

m=0.701

It=8 (1+0.82/2) ½ It=9.1A

10. Compare AM with DSB-SC and SSB-SC.

AM signal DSB-SC SSB-SC

Contains USB, LSB, carrier Contains USB,LSB Contains LSB or USB

More power is required for

transmission

Power required is less than

that of AM

Power required is less than

AM &DSB-SC

11 What are the advantages of VSB-AM?

1. It has bandwidth greater than SSB but less than DSB system.

2. Power transmission greater than DSB but less than SSB system.

3. No low frequency component lost. Hence it avoids phase distortion.

12 Compare linear and non-linear modulators.

Linear modulators Non-linear modulators

1. Heavy filtering is not required. 1. Heavy filtering is required

2. These modulators are used in 2.These modulators are used in low level

high level modulation. Modulation.

3. The carrier voltage is very much 3.The modulating signal voltage is very

much

greater than modulating signal greater than the carrier signal voltage.

voltage.

42

COMMUNICATION THEORY 13. How will you generating DSBSC-AM?

There are two ways of generating DSBSC-AM such as

1. balanced modulator 2.ring modulators

14. What are advantages of ring modulator?

1. Its output is stable.

2. It requires no external power source to activate the diodes.

3. Virtually no maintenance.

4. Long life.

15. Define demodulation.

Demodulation or detection is the process by which modulating voltage is recovered from the

modulated signal. It is the reverse process of modulation.

16. What are the types of AM detectors?

1. Nonlinear detectors

2. Linear detectors

17. What are the types of linear detectors?

1. Synchronous or coherent detector.

2. Envelope or non coherent detector.

18. Draw the block diagram of coherent detector.

19. Define multiplexing.

43

COMMUNICATION THEORYMultiplexing is defined as the process of transmitting several message signals

simultaneously over a single channel.

20. Define sensitivity.

It is defined as a measure o f its ability to receive weak signals.

21. Define selectivity.

Selectivity of a receiver is defined as its ability to select the desired signals among the

various signals.

22. Define stability.

It is the ability of the receiver to deliver a constant amount of output for a given a given

period of time.

Part - B

1. Derive the expression for AM & its Power and Efficiency calculation

2. Describe the generation of AM wave by Non-Linear modulators: Square law modulator:

3. Write short notes on De Modulation of AM wave:

4. Compare the Synchronous Detector and the Costas PLL Detector.

5. Compare Phase shift method and modified Phase shift method

UNIT: II - ANGLE MODULATION SYSTEMS


1.Define super heterodyne principle.

It can be defined as the process of operation of modulated waves to obtain similarly

modulated waves of different frequency. This process uses a locally generated carrier wave,

which determines the change of frequency.

2. A transmitter supplies 8 Kw to the antenna when modulated. Determine the total power

radiated when modulated to 30%.

m=0.3; Pc=8 kw

44

COMMUNICATION THEORYPt = Pc (1+m2/2)

=8.36 kw

3. What are the drawbacks of emitter modulator?

1. The amplifier is operated in class A mode, thus the efficiency is low.

2. The output power is very small. Thus it is not suitable for generating high level

modulation.

4. Define frequency modulation.

Frequency modulation is defined as the process by which the frequency of the carrier

wave is varied in accordance with the instantaneous amplitude of the modulating or message

signal.

5. Define modulation index of frequency modulation.

It is defined as the ratio of maximum frequency deviation to the modulating frequency.

ß = df /fm

6. What do you meant by multi tone modulation?

Modulation done for the message signal with more than one frequency component is

called multi tone modulation.

7. Define phase modulation.

Phase modulation is defined as the process of changing the phase of the carrier signal in

accordance with the instantaneous amplitude of the message signal.

8. How FM wave can be converted to PM wave?

9. How PM wave can be converted to FM wave?

45

COMMUNICATION THEORY

Carrier

10. What are the types of Frequency Modulation?

Based on the modulation index FM can be divided into types. They are Narrow b and FM

and Wide band FM. If the modulation index is greater than one then it is wide band FM and if the

modulation index is less than one then it is Narrow band FM

11. What is the basic difference between an AM signal and a narrowband FM signal?

In the case of sinusoidal modulation, the basic difference between an AM signal and a

narrowband FM signal is that the algebraic sign of the lower side frequency in the narrow band

FM is reversed.

12. What are the two methods of producing an FM wave?

Basically there are two methods of producing an FM wave. They are,

i) Direct method

In this method the transmitter originates a wav e whose frequency varies as function of

the modulating source. It is used for the generation of NBFM

ii) Indirect method

In this method the transmitter originates a wav e whose phase is a function of the

modulation. Normally it is used for the generation of WBFM where WBFM is generated from

NBFM

13. Compare WBFM and NBFM.

WBFM NBFM

Modulation index is greater than 1 Modulation index less than 1

Frequency deviation 75 KHz Frequency deviation 5 KHz

Bandwidth 15 times NBFM Bandwidth 2fm

46

COMMUNICATION THEORYNoise is more suppressed Less suppressing of noise

14. List the properties of the Bessel function.

The properties o f the Bessel function is given by,

i) Jn (ß)=(-1)nJ-n(ß) for all n, both positive and negative.

ii) For small values of the modulation index ß ,we have

J0 (ß) =1

J1 (ß) =ß/2

Jn (ß) =0, n>2.

8

iii) S J2n (ß) =1

n = -8

15. Give the average power of an FM signal.

The amplitude of the frequency modulated signal is constant .The power of the FM

signal is same as that of the carrier power. P=1/2 Ec2.

16. Define phase deviation.

The maximum phase deviation of the total angle from the carrier angle is called phase

deviation.

17. Define frequency Deviation.

The maximum departure of the instantaneous frequency from the carrier frequency is

called frequency deviation.

18. State the Carson’s rule.

An approximate rule for the transmission bandwidth of an FM Signal generated by a

single tone-modulating signal of frequency fm is defined as B =2 f (1+1/ ß)

19. Define the deviation ratio D for non-sinusoidal modulation.

47

COMMUNICATION THEORYThe deviation ratio D is defined as the ratio of the frequency deviation f, which

corresponds to the max imum possible amplitude of the modulation signal m(t),to the highest

modulation frequency .

D = f / fm

20. What is the use of crystal controlled oscillator?

The crystal-controlled oscillator always produces a constant carrier frequency there by

enhancing frequency stability.

21.what are the disadvantages of FM system?

1. A much wider channel is required by FM.

2. FM transmitting and receiving equipments tend to be more complex and hence it is

expensive

22. How will you generate message from frequency-modulated signals?

First the frequency-modulated signals are converted into corresponding amplitude-

modulated signal using frequency dependent circuits. Then the original signal is recovered from

this AM signal.

Part -B

1. Explain the Narrow Band Frequency Modulation

2. Explain the Wide Band Frequency Modulation

3. Explain the method of Generation of FM signal.

4. Write short notes on Foster seeley Discriminator.

5. What do you meant by Noise? Give the different types of noise – explain.

UNIT: III NOISE THEORY


1. What are the types of FM detectors?

Slope detector and phase discriminator.

2. What are the types of phase discriminator?

48

COMMUNICATION THEORYFoster seely discriminator and ratio detector.

3. What are the disadvantages of balanced slope detector?

1. Amplitude limiting cannot be provided

2. Linearity is not sufficient

3. It is difficult to align because of three different frequencies to which various tuned

circuits to be tuned.

4. The tuned circuit is not purely band limited.

4. Define probability.

The probability of occurrence of an event A is defined as,

P (A) = number of possible favorable outcomes

Total number of equal likely outcomes

5. What are mutually exclusive events?

Two possible outcomes of an experiment are defined as being mutually exclusive if the

occurrence of on e outcome precludes the occurrence of the other.

6. Define probability density function.

Probability density function is defined as fx(x) is defined in terms of cumulative

distribution function Fx (x) as

fx(x) = d Fx (x) dx

7. Define noise.

Noise is defined as any unwanted form of energy, which tends to interfere with proper

reception and reproduction of wanted signal.

8. Give the classification of noise.

Noise is broadly classified into two types. They are External noise and internal noise.

9. What are the types of External noise?

External noise can be classified into

1. Atmospheric noise

49

COMMUNICATION THEORY 2. Extraterrestrial noises

3. Man –made noises or industrial noises

10. What are types of internal noise?

Internal noise can be classified into

1. Thermal noise

2. Shot noise

3. Transit time noise

4. Miscellaneous internal noise

11. What are the types of extraterrestrial noise and write their origin?

The two type of ex traterrestrial noise are solar noise and cosmic noise solar noise is the

electrical noise emanating from the sun. Cosmic noise is the noise received from the center part

of our galaxy, other distant galaxies and other virtual point sources.

12. Define transit time of a transistor.

Transit time is defined as the time taken by the electron to travel from emitter to the

collector.

13. Define flicker noise.

Flicker noise is the one appearing in transistors operating at low audio frequencies.

Flicker noise is proportional to the emitter current and junction temperature and inversely

proportional to the frequency.

14. State the reasons for higher noise in mixers.

1. Conversion transconductance o f mixers is much lower than the transconductance of

amplifiers.

2. If image frequency rejection is inadequate, the noise associated with the image

frequency also gets accepted.

15. Define signal to noise ratio.

Signal to noise ratio is the ratio of signal power to the noise power at the same point in a

system.

50

COMMUNICATION THEORY16. Define noise figure.

S/ N at the input

Nose figure F =

S/ N at the output

S/N = Signal power / Noise Power

17. Explain thermal noise.

Thermal noise is the name given to the electrical noise arising from the random Motion of

electrons in a conductor.

18. Give the expression for noise voltage in a resistor.

The mean –square value of thermal noise voltage is given by

Vn2 = 4 K T B R

K – Boltz man constant

R – Resistance

T – Obsolute temperature

B - Bandwidth

19. Explain White Noise.

Many types of noise sources are Gaussian and have flat spectral density over a wide

frequency range. Such spectrum has all frequency components in equal portion, and is therefore

called white noise. The power spectral density of white noise is independent of the operating

frequency.

20. What is narrowband noise?

The receiver of a communication system usually includes some provision for

preprocessing the received signal. The preprocessing may take the form of a narrowband filter

whose bandwidth is large enough to pass modulated component of the received signal essentially

51

COMMUNICATION THEORYundistorted but not so large as to admit excessive noise through the receiver. The noise process

appearing at the output of such filter is called narrow band noise.

21. Give the representation of narrowband noise in terms of envelope and phase

components.

Narrowband noise in terms of envelope and phase components as

n (t) = r(t) cos (2pfct + F (t) )

r (t) = (nI 2(t) + nQ 2(t))½

F (t) = tan -1(nQ(t) / n I (t ))

The function r (t) and F (t) are called envelope and phase of n(t).

22. Give the expression for equivalent noise temperature in terms of hypothetical

temperature.

The expression for equivalent noise temperature in terms of hypothetical temperature is

Te = (F- 1) T0

Where, F is the noise figure and T0 absolute temperature.

23. Give the Friss formula in terms of noise temperature.

The Friss formula in terms of noise temperature is

Te = T1 + T2 / G1 + T3 / G1 G2 + ………

G1, G2… Gain of amplifiers

24. What is called image frequency?

Image frequency is defined as the signal frequency plus twice the intermediate

frequency. This has the effect of two stations being received simultaneously and hence it is

undesirable.

fsi = fs + 2 fi

fsi - image frequency

It can be eliminated by providing adequate image signal selectivity between antenna

and mixer input.

52

COMMUNICATION THEORY 24. What is intermediate frequency?

Intermediate frequency (IF) is defined as the difference between the signal frequency

and the oscillator frequency.

IF = fs – fo when fs > fo (or)

IF = fo –fs when fo > fs

25. Define Partition noise.

In an electron tube having one o r more positive grids, this noise is caused by irratic

partition of the cathode current among the positive electrodes. In a transistor, the partition noise is

created from the random fluctuation in the division of current between the collector and base.

26. Give the expression for noise voltage when several sources are cascaded.

Enr = Sqrt (4 KTB (R1 + R2 + …..) )

Where R1 , R2 --- are the resistances of the noise resistors.

K – Boltz man constant

T – Absolute temperature

B – Bandwidth

Part- B

11. Explain in detail about Noise temperature:

12. Explain the effect of Noise when amplifiers are connected in cascade

13. Describe the effect of noise in reactive circuits

14. Define Noise figure and obtain an expression for Noise figure of an amplifier

15. Obtain an expression for Noise Figure in Terms of Equivalent Noise Resistance

UNIT: IV PERFORMANCE OF CW MODULATION SYSTEMS


53

COMMUNICATION THEORY 1. Define random variable

Random variable is defined as a rule or mapping from the original sample space to a

numerical sample space subjected to certain constraints. Random variable is also defined as a

function where domain is the set of outcomeses and whose range is R, is the real line.

2. Define Random process.

A Random process X (s,t) is a function that maps each element of a samples space into

a time function called sample function. Random process is a collection of time functions.

3. Give the Laws of probability.

Additive law of probability

Case i

When events are mutually exclusive, P (AnB) =F

P (A B) = P (A) + P (B)

Case ii

When events are not mutually exclusive

P (A B) = P (A) + P(B) - P (AnB)

Multiplication law of probability:

Case i when events are independent

P (AnB) = P (A) P (B/A

= P (B) P (A/B)

4. What is frequency translation?

Suppose that a signal is band limited to the frequency range extending from a frequency

f1 to a frequency f2. The process of frequency translation is one in which the original signal is

replaced with a new signal whose spectral range extends from f1’ to f2’ and which new signal

bears, in recoverable form the same information as was borne by the original signal.

5. What are two situations identified in frequency translations?

The two situations identified in frequency translation are

i Up conversion

54

COMMUNICATION THEORY In this case the translated carrier frequency is greater than the incoming carrier

frequency

ii Down conversion

In this case the translated carrier frequency is smaller than the incomin g carrier

frequency.

Thus, a narrowband FM signal requires essentially the same transmission bandwidth as the AM

signal.

6. Define Tracking.

Tracking is the process of correctly tuning a number of tunable circuits in a receiver.

7. What is TRF receiver?

Tuned Radio Frequency is also called straight receiver. Here the receiver operates in

straight forward manner without frequency conversion.

55

COMMUNICATION THEORY 8. What are the advantages of super heterodyne receiver over TRF?

The advantages of super heterodyne receiver over TRF are high selectivity; improved

sensitivity throughout the carrier frequency band.It eliminates image frequency.

9. What is the figure of merit of DSBSC system?

The figure of merit of DSBSC signal is unity

10. Compare the noise performance of an AM and FM system?

The figure of merit of AM system is 1/3 when the modulation is 100 percent and over AM

when (3/2) mf2 > 1/3.mf –modulation index in FM.

11. What is Capture effect?

When the interference signal and FM input are of equal strength, the receiver fluctuates

back and froth between them .This phenomenon is known as the capture effect.

12. What is threshold effect?

As the input noise power is increased the carrier to noise ratio is decreased the receiver

breaks and as the carrier to noise ratio is reduced further crackling sound is heard and the output

SNR cannot be predicted by the equation. This phenomenon is known as threshold effect.

13. How is threshold reduction achieved in FM system?

Threshold reduction is achieved in FM system b y using an FM demodulator with negative

feedback or by using a phase locked loop demodulator.

14. What is Pre-emphasis?

The premodulation filtering in the transistor, to raise the power spectral density of the

base band signal in its upper-frequency range is called pre emphasis (or pre distortion). Pre

emphasis is particularly effective in FM systems which are used for transmission of audio signals.

15. Define de-emphasis.

The filtering at the receiver to undo the signal pre-emphasis and to suppress noise is called de-

emphasis.

16. Define Sampling theorem.

A band limited signal of finite energy, which has no frequency components higher than fm

Hertz may be completely recovered from a knowledge o f its samples taken at the rate of 2fm

samples per second.

56

COMMUNICATION THEORY 17. What do you infer from the receiver output of a coherent detector?

The output equation y( t)=1/2Cacm(t) +1/2n I(t) indicates that the message signal and in-

phase noise component of the filtered noise appear additively at the receiver output. The

quardrature component of the narrow band noise is completely rejected b y the coherent detector.

18. When is the figure of merit of SSBSC system 1?

For the same average transmitted signal power and the same average noise power in the

message bandwidth, an SSB receiver will have exactly the same output signal to noise ratio as a

DSB-SC receiver when both receivers use coherent detection for the recovery of the message

signal.

19. Compare the noise performance of AM receiver with that of DSB-SC receiver.

The figure of merit of DSB-SC or SSB-SC receiver using coherent detection is always

unity, the figure of merit of AM receiver u sing envelop e detection is always less than unity.

Therefore noise performance of AM receiver is always inferior to that of DSB-SC due to the

wastage of power for transmitting the carrier.

20. What is the figure of merit of an AM system with 100 percent modulation?

The figure of merit of an AM system with 100 percent modulation is 1/3.This means that

other factors being equal an AM system must transmit three times as much average power as a

suppressed system in order to achieve the same quality of noise performance.

21. What are the characteristics of a receiver?

The characteristics of a receiver are sensitivity, selectivity, fidelity, signal to noise ratio.

22. Why is equivalent noise temperature used for noise measurement?

For low noise devices the noise figure is close to unity, which makes the comparison

difficult and hence it is preferable to use equivalent noise temperature.

23. What is the function of amplitude limiter in FM system?

The function of amplitude limiter in FM system is used to remove the amplitude variations

by clipping the modulated wave at the filter output almost to the zero ax is .The resultant wave is

rounded off by another BPF that is an integral part of the limiter thereby suppressing the

harmonics of the carrier frequency.

57

COMMUNICATION THEORYPart- B

1. Explain in detail how noise figure is measured?

2. Super heterodyne receiver - Explanation

3. Prove that the figure of merit of DSB – SC system is unity.

4. Noise in AM receivers - AM system using envelope detection

5. Noise in angle modulation System

UNIT: V INFORMATION THEORY


1. What are components in a frequency discriminator?

Frequency discriminator has got two components .Slope detector or differentiator with a

purely imaginary frequency response that varies linearly with frequency. It produces output where

the amplitude and frequency vary with the message signal. An envelope detector that recover the

amplitude variations and produces message signal.

2. What is a post detection filter?

The post detection filter named as “base-b and low pass filter” has a bandwidth that is

just large enough to accommodate the highest frequency component of the message signal.

3. Define lossless channel.

The channel described by a channel matrix with only one nonzero element in each

column is called a lossless channel. In the lossless channel no sources information is lost in

transmission.

4. Define Deterministic channel

A channel described by a channel matrix with only one nonzero element in each row is

called a deterministic channel and this element must be unity.

5. Define noiseless channel.

A channel is called noiseless if it is both lossless and deterministic. The channel matrix

has only one element in each row and in each column and this element is unity. The input and

output alphabets are of the same size.

6. Prove that I (xi xj) = I(xi) + I(xj) if xi and xj are independent.

58

COMMUNICATION THEORY If xi and xj are independent.

P (xi xj) = P(xi) P(x j)

I (xi xj) = log1/P(xi xj)

= log 1/ P(xi) P(xj)

= I(xi) + I(xj)

7. Explain Shannon-Fano coding.

An efficient code can be obtained by the following simple procedure, known as Shannon-

Fano algorithm.

1. List the source symbols in order of decreasing probability.

2. Partition the set into two sets that are as close to equiprobable as possible, and sign 0

to the upper set and 1 to the lower set.

3. Continue this process, each time partitioning the sets with as nearly equal probabilities

as possible until further partitioning is not possible.

8. What are the types of Correlation?

The types of Correlation are Cross Correlation and Auto Correlation

9. What is the difference between Correlation and Convolution?

1. In Correlation physical time‘t’ is dummy variable and it disappears after solution of an

integral. But in convolution‘t’ is a dummy variable.

2. Convolution is a function of delay parameter‘t‘but convolution is a function of‘t’.

3. Convolution is commutative but correlation is noncom mutative.

10. Define Signal.

A signal is defined as any physical quantity carrying information that varies with time. The

value of signal may be real or complex. The types of signal are continuous signal and discrete

time signal.

11. Define entropy.

59

COMMUNICATION THEORY Entropy is the measure of the average information content per second. It is given by the

expression

H(X)= I P(xi)log2P(xi) bits/sample.

12. Define mutual information.

Mutual information I(X,Y) of a channel is defined by

I(X,Y)=H(X)-H(X/Y) bits/symbol

H(X)- entropy of the source

H(X/Y)- conditional entropy of Y.

13. State the properties of mutual information.

1. I(X,Y)=I(Y,X)

2. I(X,Y)>=0

3. I(X,Y)=H(Y)-H(Y/X)

4. I(X,Y)=H(X)+H(Y)-H(X,Y).

14. Give the relation between the different entropies.

H(X,Y)=H(X)+H(Y/X)

=H(Y)+H(X/Y)

H(X)- entropy of the source(Y/X),H(X/Y) -conditional entropy

H(Y)-entropy of destination

H(X,Y)- Joint entropy of the source and destination

15. Define information rate.

If the time rate at which source X emits symbols is r symbols per second. The information

rate R of the source is given by

R=r H(X) bits/second

H(X)- entropy of the source

16. What is data compaction?

60

COMMUNICATION THEORYFor efficient signal transmission the redundant information must be removed from the

signal prior to transmission .This information with no loss of information is ordinarily performed on

a signal in digital form and is referred to as data compaction or lossless data compression.

17. State the property of entropy.

1.0< H(X) < log2K, is the radix of the alphabet X of the source.

18. What is differential entropy?

The average amount of information per sample value of x(t) is measured by

8

H(X)= - 8 fx(x)log fx(x)dx bit/sample

H(X) –differential entropy of X.

19. What is the channel capacity of a discrete signal?

The channel capacity of a discrete signal C= max I(X,Y)

P(xi)

I(X,Y)-mutual information.

20. What is source coding and entropy coding?

` A conversion of the output of a DMS into a sequence of binary symbols is called source

coding. he design of a variable length code such that its average cod word length approaches the

entropy of the DMS is often referred to as entropy coding.

21. State Shannon Hartley theorem.

The capacity ‘C’ of a additive Gaussian noise channel is C=B log2 (1+S/N) B= channel

bandwidth, S/N=signal to noise ratio.

22. What is the entropy of a binary memory-less source?

The entropy of a binary memory-less source H(X)=-p0 log2p0-(1-p0)log2(1-p0) p0-

probability of symbol ‘0’,p1=(1- p0 ) =probability of transmitting symbol ‘1’

23. How is the efficiency of the coding technique measured?

Efficiency of the code =H(X) /L

L= p(xi)li average code word length .li=length of the code word.

61

COMMUNICATION THEORY24. What happens when the number of coding alphabet increases?

When the number of coding alphabet increases the efficiency of the coding technique

decreases.

25. What is channel diagram and channel matrix?

The transition probability diagram of the channel is called the channel diagram and its

matrix representation is called the channel matrix.

26. What is information theory?

Information theory deals with the mathematical modeling and analysis of a

Communication system rather than with physical sources and physical channels

27. What is the channel capacity of a BSC and BEC?

For BSC the channel capacity C=1+plog2 p +(1-p)log2(1-p).

For BEC the channel capacity C= (1-p)

Part – B

1. Explain FM threshold reduction.

Coding algorithm

2. Explain the procedure of Shannon Fano Coding Algorithm and Huffman

3. .State and prove the properties of mutual information.

4. Explain the different types of channel.

5. Calculate the capacity of a Gaussian channel.

6. Find the channel capacity of binary erasure chann

62

LINEAR INTEGRATED CIRCUITSLinear Intergrated Circits

UNIT-I CIRCUIT CONFIGURATION FOR LINEAR ICs


1.Mention the advantages of integrated circuits.

*Miniaturisation and hence increased equipment density.

*Cost reduction due to batch processing.

*Increased system reliability due to the elimination of soldered joints.

*Improved functional performance.

*Matched devices.

*Increased operating speeds.

*Reduction in power consumption.

2.Write down the various processes used to fabricate IC’s using silicon planar

technology.

*Silicon wafer preparation.

* Epitaxial growth

*Oxidation.

*Photolithography.

*Diffusion.

*Ion implantation.

*Isolation.

*Metallisation.

*Assembly processing and packaging.

3.What is the purpose of oxidation?

*SiO2 is an extremely hard protective coating and is unaffected by almost all

reagents.

*By selective etching of SiO2, diffusion of impurities through carefully defined

windows can be accomplished to fabricate various components.

4.Why aluminium is preferred for metallization?

63

LINEAR INTEGRATED CIRCUITS*It is a good conductor.

*it is easy to deposit aluminium films using vacuum deposition.

*It makes good mechanical bonds with silicon.

*It forms a low resistance contact.

5. What are the popular IC packages available?

Metal can package.

Dual-in-line package.

Ceramic flat package.

6. Define an operational amplifier.

An operational amplifier is a direct-coupled, high gain amplifier consisting of

one or more differential amplifier. By properly selecting the external components, it can

be used to perform a variety of mathematical operations.

7.Mention the characteristics of an ideal op-amp.

* Open loop voltage gain is infinity.

*Input impedance is infinity.

*Output impedance is zero.

*Bandwidth is infinity.

*Zero offset.

8.What happens when the common terminal of V+ and V- sources is not grounded?

If the common point of the two supplies is not grounded, twice the supply voltage

will get applied and it may damage the op-amp.

9.Define input offset voltage.

A small voltage applied to the input terminals to make the output voltage as zero

when the two input terminals are grounded is called input offset voltage.

10. Define input offset current. State the reasons for the offset currents at the input

of the op-amp.

The difference between the bias currents at the input terminals of the op-amp is

called as input offset current. The input terminals conduct a small value of dc current

to bias the input transistors.Since the input transistors cannot be made identical,there

exists a difference in bias currents.

11. Define CMRR of an op-amp.

64

LINEAR INTEGRATED CIRCUITSThe relative sensitivity of an op-amp to a difference signal as compared to a

common –mode signal is called the common –mode rejection ratio. It is expressed

in decibels.

CMRR= Ad/Ac

12.What are the applications of current sources?

Transistor current sources are widely used in analog ICs both as biasing

elements and as load devices for amplifier stages.

13. Justify the reasons for using current sources in integrated circuits.

*superior insensitivity of circuit performance to power supply variations and

temperature.

*more economical than resistors in terms of die area required to provide bias

currents of small value.

*When used as load element, the high incremental resistance of current source

results in high voltage gain at low supply voltages.

14. What is the advantage of widlar current source over constant current source?

Using constant current source output current of small magnitude(microamp

range) is not attainable due to the limitations in chip area. Widlar current source

is useful for obtaining small output currents.Sensitivity of widlar current source is

less compared to constant current source.

15.Mention the advantages of Wilson current source.

*provides high output resistance.

*offers low sensitivity to transistor base currents.

16.Define sensitivity.

Sensitivity is defined as the percentage or fractional change in output current

per percentage or fractional change in power-supply voltage.

17.What are the limitations in a temperature compensated zener-reference source?

A power supply voltage of atleast 7 to 10 V is required to place the diode in the

breakdown region and that substantial noise is introduced in the circuit by the

avalanching diode.

18.What do you mean by a band-gap referenced biasing circuit?

65

LINEAR INTEGRATED CIRCUITSThe biasing sources referenced to VBE has a negative temperature co-efficient

and VT has a positive temperature co-efficient. Band gap reference circuit is one in

which the output current is referenced to a composite voltage that is a weighted sum

of VBE and VT so that by proper weighting, zero temperature co-efficient can be

achieved.

19.In practical op-amps, what is the effect of high frequency on its performance?

The open-loop gain of op-amp decreases at higher frequencies due to the

presence of parasitic capacitance. The closed-loop gain increases at higher frequencies

and leads to instability.

20. What is the need for frequency compensation in practical op-amps?

Frequency compensation is needed when large bandwidth and lower closed loop

gain is desired. Compensating networks are used to control the phase shift and hence

to improve the stability.

21.Mention the frequency compensation methods.

*Dominant-pole compensation

*Pole-zero compensation.

22.What are the merits and demerits of Dominant-pole compensation?

*noise immunity of the system is improved.

*Open-loop bandwidth is reduced.

23.Define slew rate.

The slew rate is defined as the maximum rate of change of output voltage caused

by a step input voltage.An ideal slew rate is infinite which means that op-amp’s output

voltage should change instantaneously in response to input step voltage.

24.Why IC 741 is not used for high frequency applications?

IC741 has a low slew rate because of the predominance of capacitance present

in the circuit at higher frequencies. As frequency increases the output gets distorted

due to limited slew rate.

66

LINEAR INTEGRATED CIRCUITS

25.What causes slew rate?

There is a capacitor with-in or outside of an op-amp to prevent oscillation.It is

this capacitor which prevents the output voltage from responding immediately to a

fast changing input.

Part -B

1.Explain in detail the fabrication of ICs using silicon planar technology.

Ans:

*Silicon wafer preparation.

* Epitaxial growth

*Oxidation.

*Photolithography.

*Diffusion.

*Ion implantation.

*Isolation.

*Metallisation.

*Assembly processing and packaging.

2.Design an active load for an emitter-coupled pair(differential amplifier) and

perform a detailed analysis to find its differential mode gain and the output

resistance.

Ans:

Output voltage, Vo=Vcc –VBE(on) + 2VA(eff) tanh(Vid / 2VT)

Gain , Avd = 1 / ( VT/VAN + VT/VAP )

Output resistance,Ro = ronpn || ropnp

3.Design a Widlar current source and obtain the expression for output current.Also

prove that widlar current source has better sensitivity than constant current

source.

Ans:

For Widlar current source, VT ln( Ic1/ Ic2 ) = Ic2 R2

Sensitivity is defined as the percentage or fractional change in output current

per percentage or fractional change in power-supply voltage.

For constant current source sensitivity is unity because the output current is directly

67

LINEAR INTEGRATED CIRCUITSproportional to supply voltage. The sensitivity of a widlar current source is better

compared to constant current source because the output current has a logarithmic

dependence on power supply voltage.

4. Explain the supply independent biasing technique using VBE as the reference

voltage.Also, find the dependence of its output current on temperature.

Ans:

The output current is given by, Iout = VBE1 / R2 = (VT /R2) ln ( Iref / Is1 )

(Circuit diagram, self-biasing VBE reference circuit, start-up circuit to avoid zerocurrent

state)

Temperature co-efficient,

5.Explain supply independent biasing using zener-referenced bias circuit.

Also,design a temperature compensated zener-reference source.

Ans:

The output current is given by, Iout = VZ / R2

(Circuit diagram, self-biasing zener bias reference circuit, temperature compensated

zener reference source )

6.Obtain the frequency response of an open-loop op-amp and discuss about the

methods of frequency compensation .

Ans:

The open-loop gain of op-amp decreases at higher frequencies due to the presence of

parasitic capacitance. The closed-loop gain increases at higher frequencies and leads

to instability. Frequency compensation is needed when large bandwidth and lower

closed loop gain is desired. Compensating networks are used to control the phase shift

and hence to improve the stability.

Frequency compensation methods:

*Dominant-pole compensation

*Pole-zero compensation.

UNIT -II : APPLICATIONS OF OP – AMPS


1.Mention some of the linear applications of op – amps :

Adder, subtractor, voltage –to- current converter, current –to- voltage converters,

68

LINEAR INTEGRATED CIRCUITSinstrumentation amplifier, analog computation ,power amplifier, etc are some of the

linear op-amp circuits.

2.Mention some of the non – linear applications of op-amps:-

Rectifier, peak detector, clipper, clamper, sample and hold circuit, log amplifier,

anti –log amplifier, multiplier are some of the non – linear op-amp circuits.

3.What are the areas of application of non-linear op- amp circuits?

. industrial instrumentation

. Communication

. Signal processing

4.What is the need for an instrumentation amplifier?

In a number of industrial and consumer applications, the measurement of

physical quantities is usually done with the help of transducers. The output of transducer

has to be amplified So that it can drive the indicator or display system. This function is

performed by an instrumentation amplifier.

5.List the features of instrumentation amplifier:

.

high gain accuracy

. high CMRR

. high gain stability with low temperature co-efficient

. low dc offset

._ low output impedance

6.What are the applications of V-I converter?

. Low voltage dc and ac voltmeter

. L E D

. Zener diode tester

7.What do you mean by a precision diode?

The major limitation of ordinary diode is that it cannot rectify voltages

below the cut – in voltage of the diode. A circuit designed by placing a diode in the

feedback loop of an op – amp is called the precision diode and it is capable of rectifying

69

LINEAR INTEGRATED CIRCUITSinput signals of the order of millivolt.

8.Write down the applications of precision diode.

. Half - wave rectifier

. Full - Wave rectifier

. Peak – value detector

. Clipper

. Clamper

9.List the applications of Log amplifiers:

. Analog computation may require functions such as lnx, log x, sin hx

etc. These functions can be performed by log amplifiers

. Log amplifier can perform direct dB display on digital voltmeter and

spectrum analyzer

. Log amplifier can be used to compress the dynamic range of a signal

10.What are the limitations of the basic differentiator circuit?

. At high frequency, a differentiator may become unstable and break

into oscillations

. The input impedance decreases with increase in frequency , thereby

making the circuit sensitive to high frequency noise.

11.Write down the condition for good differentiation :-

For good differentiation, the time period of the input signal must be

greater than or equal to Rf C1

T > R f C1

Where, Rf is the feedback resistance

Cf is the input capacitance

12.What is a comparator?

A comparator is a circuit which compares a signal voltage applied at one

input of an op-amp with a known reference voltage at the other input. It is an open loop

op - amp with output + Vsat .

1

70

LINEAR INTEGRATED CIRCUITS3.What are the applications of comparator?

. Zero crossing detector

. Window detector

. Time marker generator

._ Phase detector

14.What is a Schmitt trigger?

Schmitt trigger is a regenerative comparator. It converts sinusoidal input

into a square wave output. The output of Schmitt trigger swings between upper and lower

threshold voltages, which are the reference voltages of the input waveform.

15.What is a multivibrator?

Multivibrators are a group of regenerative circuits that are used

extensively in timing applications. It is a wave shaping circuit which gives symmetric or

asymmetric square output. It has two states either stable or quasi- stable depending on

the type of multivibrator.

16.What do you mean by monostable multivibrator?

Monostable multivibrator is one which generates a single pulse of

specified duration in response to each external trigger signal. It has only one

stable state. Application of a trigger causes a change to the quasi-stable state.An external

trigger signal generated due to charging and discharging of the capacitor produces the

transition to the original stable state.

17.What is an astable multivibrator?

Astable multivibrator is a free running oscillator having two quasi-stable

states. Thus, there is oscillations between these two states and no external signal are

required to produce the change in state.

18.What is a bistable multivibrator?

Bistable multivibrator is one that maintains a given output voltage level

unless an external trigger is applied . Application of an external trigger signal causes a

change of state, and this output level is maintained indefinitely until an second trigger is

applied . Thus, it requires two external triggers before it returns to its initial state

19.What are the requirements for producing sustained oscillations in feedback

71

LINEAR INTEGRATED CIRCUITScircuits?

For sustained oscillations,

. The total phase shift around the loop must be zero at the desired

frequency of oscillation, fo. ie, $%_ ____RU______

. At fo, the magnitude of the loop gain A should be equal to unity

20.Mention any two audio frequency oscillators :

. RC phase shift oscillator

. Wein bridge oscillator

21.What are the characteristics of a comparator?

. Speed of operation

. Accuracy

. Compatibility of the output

22.What is a filter?

Filter is a frequency selective circuit that passes signal of specified band

of frequencies and attenuates the signals of frequencies outside the band

23.What are the demerits of passive filters?

Passive filters works well for high frequencies. But at audio frequencies,

the inductors become problematic, as they become large, heavy and expensive.For low

frequency applications, more number of turns of wire must be used which in turn

adds to the series resistance degrading inductor’s performance ie, low Q, resulting in high

power dissipation.

24.What are the advantages of active filters?

Active filters used op- amp as the active element and resistors and

capacitors as passive elements.

. By enclosing a capacitor in the feed back loop , inductor less active

fulters can be obtained

. Op-amp used in non – inverting configuration offers high input

impedance and low output impedance, thus improving the load drive

capacity.

25.Mention some commonly used active filters :

.

Low pass filter

72

LINEAR INTEGRATED CIRCUITS. High pass filter

. Band pass filter

. Band reject filter.

Part-B

1.Discuss the need for an instrumentation amplifier? Give a detailed analysis for the

same.

Ans:

In a number of industrial and consumer applications, the measurement of

physical quantities is usually done with the help of transducers. The output of transducer

has to be amplified So that it can drive the indicator or display system. This function is

performed by an instrumentation amplifier.

Circuit diagram, instrumentation amplifier with transducer bridge,

Analysis, Expression for out put voltage.

2.Explain the operation of the Schmitt trigger.

Ans:

Schmitt trigger is a regenerative comparator. It converts sinusoidal input into a

square wave output. The output of Schmitt trigger swings between upper and lower

threshold voltages, which are the reference voltages of the input waveform.

Circuit diagram, Analysis.

Expression for upper and lower threshold voltages with and without Vref.

Hysterisis width.

Waveforms.

3.Discuss in detail the operation of Astable multivibrator.

Ans:

Astable multivibrator is a free running oscillator having two quasi-stable states.

Thus, there is oscillations between these two states and no external signal are required to

produce the change in state.


Expression for time period ,

Waveforms.

Circuit for asymmetric square wave generator.

4. Discuss in detail the operation of Monostable multivibrator.

73


Ans:

Monostable multivibrator is one which generates a single pulse of specified

duration in response to each external trigger signal. It has only one stable state.

Application of a trigger causes a change to the quasi-stable state.An external trigger

signal generated due to charging and discharging of the capacitor produces the transition

to the original stable state.


Expression for time period , , Waveforms.

5. What are the requirements for producing sustained oscillations in feedback

circuits?Discuss any two audio frequency oscillators.

Ans:

For sustained oscillations,

. The total phase shift around the loop must be zero at the desired

frequency of oscillation, fo. ie,

. At fo, the magnitude of the loop gain should be equal to unity.

RC phase shift oscillator: Circuit diagram,Derive the condition for frequency of

oscillation.

Gain,Av >= - 29

Wein bridge oscillator : Circuit diagram,Derive the condition for frequency of

oscillation.

Gain, Av = 3

UNIT – III :ANALOG MULTIPLIER AND PLL


1.Mention some areas where PLL is widely used:

*Radar synchronisation

*satellite communication systems

*air borne navigational systems

*FM communication systems

*Computers.

2.List the basic building blocks of PLL:

74


*Phase detector/comparator

*Low pass filter

*Error amplifier

*Voltage controlled oscillator

3.What are the three stages through which PLL operates?

*Free running

*Capture

*Locked/ tracking

4.Define lock-in range of a PLL:

The range of frequencies over which the PLL can maintain lock with the incoming

signal is called the lock-in range or tracking range.It is expressed as a percentage of the

VCO free running frequency.

5.Define capture range of PLL:

The range of frequencies over which the PLL can acquire lock with an input signal

is called the capture range. It is expressed as a percentage of the VCO free running

frequency.

6.Define Pull-in time.

The total time taken by the PLL to establish lok is called pull-in time.It depends

on the initial phase and frequency difference between the two signals as well as on the

overall loop gain and loop filter characteristics.

7.For perfect lock, what should be the phase relation between the incoming signal and

VCO output signal?

The VCO output should be 90 degrees out of phase with respect to the input

signal.

8.Give the classification of phase detector:

*Analog phase detector

75

LINEAR INTEGRATED CIRCUITS*Digital phase detector

9.What is a switch type phase detector?

An electronic switch is opened and closed by signal coming from VCO and the

input signal is chopped at a repetition rate determined by the VCO frequency.This type of

phase detector is called a half wave detector since the phase information for only one half

of the input signal is detected and averaged.

10.What are the problems associated with switch type phase detector?

*The output voltage Ve is proportional to the input signal amplitude.This is

undesirable because it makes phase detector gain and loop gain dependent on the input

signal amplitude.

11.What is a voltage controlled oscillator?

Voltage controlled oscillator is a free running multivibrator operating at a set

frequency called the free running frequency.This frequency can be shifted to either side

by applying a dc control voltage and the frequency deviation is proportional to the dc

control voltage.

12.On what parameters does the free running frequency of VCO depend on?

*External timing resistor,RT

*External timing capacitor,CT

*The dc control voltage Vc.

13.Give the expression for the VCO free running frequency.

fo = 0.25 / RT CT

14.Define Voltage to Frequency conversion factor.

Voltage to Frequency conversion factor is defined as,

is the modulation voltage required to produce the frequency shift _Io

76

LINEAR INTEGRATED CIRCUITS15.What is the purpose of having a low pass filter in PLL?

*It removes the high frequency components and noise.

*Controls the dynamic characteristics of the PLL such as capture range, lock-in

range,band-width and transient response.

*The charge on the filter capacitor gives a short- time memory to the PLL.

16.Discuss the effect of having large capture range.

The PLL cannot acquire a signal outside the capture range, but once captured, it

will hold on till the frequency goes beyond the lock-in range.Thus , to increase the ability

of lock range,large capture range is required.But, a large capture range will make the PLL

more susceptible to noise and undesirable signal.

17.Mention some typical applications of PLL:

Frequency multiplication/division

Frequency translation

AM detection

FM demodulation

FSK demodulation.

18.What is a compander IC? Give some examples.

The term companding means compressing and expanding.In a communication

system, the audio signal is compressed in the transmitter and expanded in the receiver.

Examples : LM 2704- LM 2707 ; NE 570/571.

19.What are the merits of companding?

*The compression process reduces the dynamic range of the signal before it is

transmitted.

*Companding preserves the signal to noise ratio of the original signal and avoids

non linear distortion of the signal when the input amplitude is large.

*It also reduces buzz,bias and low level audio tones caused by mild interference.

20.List the applications of OTA:

77


OTA can be used in

programmable gain voltage amplifier

sample and hold circuits

voltage controlled state variable filter

current controlled relaxation oscillator.

Part-B

1. Briefly explain the block diagram of PLL and derive the expression for Lock

range and capture range.

Block diagram of PLL

Explanation for each block.

Derivation for capture range and lock range.

2. With a neat functional diagram, explain the operation of VCO. Also derive

an expression for fo.

Internal diagram for VCO IC.

Explanation

Derivation for fo.

3. Analyse the Gilbert’s four quadrant multiplier cell with a neat circuit

diagram.Discuss its applications.

Circuit diagram

Analysis

Expression for output current

Applications.

4. In detail dicuss the applications of PLL:

AM detection

FM demodulation

FSK demodulation

Frequency multiplication/division.

UNIT IV – A/D AND D/A CONVERTERS


78


1. List the broad classification of ADCs.

1. Direct type ADC.

2. Integrating type ADC.

2. List out the direct type ADCs.

1. Flash (comparator) type converter

2. Counter type converter

3. Tracking or servo converter

4. Successive approximation type converter

3. List out some integrating type converters.

1. Charge balancing ADC

2. Dual slope ADC

4. What is integrating type converter?

An ADC converter that perform conversion in an indirect manner by first

changing the analog I/P signal to a linear function of time or frequency and then

to a digital code is known as integrating type A/D converter.

5. Explain in brief the principle of operation of successive Approximation ADC.

The circuit of successive approximation ADC consists of a successive

approximation register (SAR), to find the required value of each bit by trial &

error.With the arrival of START command, SAR sets the MSB bit to 1. The O/P

is converted into an analog signal & it is compared with I/P signal. This O/P is

low or High. This process continues until all bits are checked.

6. What are the main advantages of integrating type ADCs?

i. The integrating type of ADC’s do not need a sample/Hold circuit at the

input.

ii. It is possible to transmit frequency even in noisy environment or in an

isolated form.

79


7. Where are the successive approximation type ADC’s used?

The Successive approximation ADCs are used in applications such as data

loggers & instrumentation where conversion speed is important.

8. What is the main drawback of a dual-slop ADC?

The dual slope ADC has long conversion time. This is the main drawback

of dual slope ADC.

9. State the advantages of dual slope ADC:

It provides excellent noise rejection of ac signals whose periods are integral multiples of the

integration time T.

10. Define conversion time.

It is defined as the total time required to convert an analog signal into its

digital output. It depends on the conversion technique used & the propagation

delay of circuit components.

The conversion time of a successive approximation type ADC is given by

T(n+1)

where T---clock period

Tc---conversion time

n----no. of bits

11. Define resolution of a data converter.

The resolution of a converter is the smallest change in voltage which may

be produced at the output or input of the converter.

Resolution (in volts)= VFS/2n-1=1 LSB increment. The resolution of an

ADC is defined as the smallest change in analog input for a one bit change at the

output.

12. Define accuracy of converter.

Absolute accuracy:

It is the maximum deviation between the actual converter output & the ideal

converter output.

80

LINEAR INTEGRATED CIRCUITSRelative accuracy:

It is the maximum deviation after gain & offset errors have been removed.

The accuracy of a converter is also specified in form of LSB increments or % of

full scale voltage.

13. What is settling time?

It represents the time it takes for the output to settle within a specified

band ±½LSB of its final value following a code change at the input (usually a full

scale change). It depends upon the switching time of the logic circuitry due to

internal parasitic capacitance & inductances. Settling time ranges from 100ns.

10μs depending on word length & type circuit used.

14. Explain in brief stability of a converter:

The performance of converter changes with temperature age & power

supply variation . So all the relevant parameters such as offset, gain, linearity

error & monotonicity must be specified over the full temperature & power supply

ranges to have better stability performances.

15. What is meant by linearity?

The linearity of an ADC/DAC is an important measure of its accuracy &

tells us how close the converter output is to its ideal transfer characteristics. The

linearity error is usually expressed as a fraction of LSB increment or percentage

of full-scale voltage. A good converter exhibits a linearity error of less than

±½LSB.

16. What is monotonic DAC?

A monotonic DAC is one whose analog output increases for an increase in

digital input.

17. What is multiplying DAC?

A digital to analog converter which uses a varying reference voltage VR is

called a multiplying DAC(MDAC). If the reference voltage of a DAC, VR is a

sine wave give by

V(t)=Vin_&RV__ IW

Then, Vo(t)=Vom&RV__ IW______º)

81


18.What is a sample and hold circuit? Where it is used?

A sample and hold circuit is one which samples an input signal and holds

on to its last sampled value until the input is sampled again. This circuit is mainly

used in digital interfacing, analog to digital systems, and pulse code modulation

systems.

19.Define sample period and hold period.

The time during which the voltage across the capacitor in sample and hold

circuit is equal to the input voltage is called sample period.The time period during

which the voltage across the capacitor is held constant is called hold period.

20.What is meant by delta modulation?

Delta modulation is a technique capable of performing analog signal

quantisation with smaller bandwidth requirements. Here, the binary output

representing the most recent sampled amplitude will be determined on the basis of

previous sampled amplitude levels.

Part-B

1. What is integrating type converter?Explain the operation of dual slope ADC:

An ADC converter that perform conversion in an indirect manner by first

changing the analog I/P signal to a linear function of time or frequency and then

to a digital code is known as integrating type A/D converter.

Functional diagram of Dual slope ADC.

Explanation, Derivation.

2. Explain the principle of operation of successive Approximation ADC.

The circuit of successive approximation ADC consists of a successive

approximation register (SAR), to find the required value of each bit by trial &

error.With the arrival of START command, SAR sets the MSB bit to 1. The O/P

is converted into an analog signal & it is compared with I/P signal. This O/P is

82

LINEAR INTEGRATED CIRCUITSlow or High. This process continues until all bits are checked.

Functional diagram

Operation

Truth table, Output graph.

3 . Explain the operation of sample and hold circuit .

Circuit diagram

Operation ,Output waveforms.

4. Explain the various types of digital to analog converters:

Weighted resistor DAC

R-2R ladder DAC

Inverted R-2R ladder DAC

Circuit diagram & operation for each

5.What is delta sigma modulation?Explain the A/D conversion using Delta

modulator.

Delta modulation is a technique capable of performing analog signal

quantisation with smaller bandwidth requirements. Here, the binary output

representing the most recent sampled amplitude will be determined on the basis of

previous sampled amplitude levels.

Functional diagram

Operation.

UNIT V – SPECIAL FUNCTION ICs


1.Mention some applications of 555 timer:

*Oscillator

*pulse generator

*ramp and square wave generator

*mono-shot multivibrator

*burglar alarm

*traffic light control.

83


2.List the applications of 555 timer in monostable mode of operation:

*missing pulse detector

*Linear ramp generator

*Frequency divider

*Pulse width modulation.

3. List the applications of 555 timer in Astable mode of operation:

*FSK generator

*Pulse-position modulator

4.What is a voltage regulator?

A voltage regulator is an electronic circuit that provides a stable dc voltage

independent of the load current, temperature, and ac line voltage variations.

5.Give the classification of voltage regulators:

*Series / Linear regulators

*Switching regulators.

6.What is a linear voltage regulator?

Series or linear regulator uses a power transistor connected in series between the

unregulated dc input and the load and it conducts in the linear region .The output voltage

is controlled by the continous voltage drop taking place across the series pass transistor.

7.What is a switching regulator?

Switching regulators are those which operate the power transistor as a high

frequency on/off switch, so that the power transistor does not conduct current

continously.This gives improved efficiency over series regulators.

8.What are the advantages of IC voltage regulators?

84

LINEAR INTEGRATED CIRCUITS*low cost

*high reliability

*reduction in size

*excellent performance

9.Give some examples of monolithic IC voltage regulators:

78XX series fixed output, positive voltage regulators

79XX series fixed output, negative voltage regulators

723 general purpose regulator.

10.What is the purpose of having input and output capacitors in three terminal IC

regulators?

A capacitor connected between the input terminal and ground cancels the

inductive effects due to long distribution leads. The output capacitor improves the

transient response.

11. Define line regulation.

Line regulation is defined as the percentage change in the output voltage for a

change in the input voltage.It is expressed in millivolts or as a percentage of the output

voltage.

12.Define load regulation.

Load regulation is defined as the change in output voltage for a change in load

current. It is expressed in millivolts or as a percentage of the output voltage.

13.What is meant by current limiting?

Current limiting refers to the ability of a regulator to prevent the load current from

increasing above a preset value.

14.Give the drawbacks of linear regulators:

*The input step down transformer is bulky and expensive because of low line

frequency.

*Because of low line frequency,large values of filter capacitors are required to

85

LINEAR INTEGRATED CIRCUITSdecrease the ripple.

*Efficiency is reduced due to the continous power dissipation by the transistor

as it operates in the linear region.

15.What is the advantage of switching regulators?

*

Greater efficiency is achieved as the power transistor is made to operate as low

impedance switch.Power transmitted across the transistor is in discrete pulses

rather than as a steady current flow.

*By using suitable switching loss reduction technique, the switching frequency

can be increased so as to reduce the size and weight of the inductors and

capacitors.

16.What is an opto-coupler IC? Give examples.

Opto-coupler IC is a combined package of a photo-emitting device and a photosensing

device.Examples for opto-coupler circuit : LED and a photo diode,

LED and photo transistor,

LED and Darlington.

Examples for opto-coupler IC : MCT 2F , MCT 2E .

17. Mention the advantages of opto-couplers:

*Better isolation between the two stages.

*Impedance problem between the stages is eliminated.

*Wide frequency response.

*Easily interfaced with digital circuit.

*Compact and light weight.

*Problems such as noise, transients, contact bounce,.. are eliminated.

18.What is an isolation amplifier?

An isolation amplifier is an amplifier that offers electrical isolation between its

input and output terminals.

19.What is the need for a tuned amplifier?

In radio or TV receivers , it is necessary to select a particular channel among all

other available channels.Hence some sort of frequency selective circuit is needed that

will allow us to amplify the frequency band required and reject all the other unwanted

signals and this function is provided by a tuned amplifier.

86


20.Give the classification of tuned amplifier:

(i) Small signal tuned amplifier

*Single tuned

*Double tuned

*Stagger tuned

(ii) Large signal tuned amplifier.

Part-B

1.What is 555 timer? What are the features of 555 timer? Explain the monostable mode in

detail?

Features of 555

Description about 555

Circuit diagram

Derivation for frequency.

2.Explain the Astable mode of operation using 555 timer.

Description about 555

Circuit diagram

Derivation for frequency.

3.In detail dicuss the 723 IC general purpose voltage regulator.

Functional diagram

Low and high voltage regulation using 723

Features of 723.

4.Explain the operation of switching regulators.Give its advantages.

Functional diagram

Operation

Output waveforms.

Advantages.

5.Explain the functional diagram of LM 380 power amplifier.

Introduction ,Internal diagram ,Operation ,Features.

87

ELECTROMAGNETIC THEORYElecromagnetic Theory

UNIT I- STATIC ELECTRIC FIELDS


1. State stokes theorem.

The line integral of a vector around a closed path is equal to the surface integral

of the normal component of its curl over any surface bounded by the path.

2. State coulombs law.

Coulombs law states that the force between any two point charges is directly

proportional to the product of their magnitudes and inversely proportional to the

square of the distance between them. It is directed along the line joining the two

charges.

3. State Gauss law for electric fields

The total electric flux passing through any closed surface is equal to the total

charge enclosed by that surface.

4. Define electric flux.

The lines of electric force are electric flux.

5. Define electric flux density.

Electric flux density is defined as electric flux per unit area.

6. Define electric field intensity.

Electric field intensity is defined as the electric force per unit positive

charge.

E =F/ Q

7. Name few applications of Gauss law in electrostatics.

Gauss law is applied to find the electric field intensity from a closed surface.

e.g.) Electric field can be determined for shell, two concentric shell or

cylinders etc.

8. What is a point charge?

Point charge is one whose maximum dimension is very small in comparison with

any other length.

9. Define linear charge density.

I t is the charge per unit length.

88

ELECTROMAGNETIC THEORY10. Define potential difference.

Potential difference is defined as the work done in moving a unit positive charge

from one point to another point in an electric field .

11. Define potential.

Potential at any point is defined as the work done in moving a unit positive

charge from infinity to that point in an electric field.

12. Give the relationship between potential gradient and electric field.

E= - V

Define current density.

Current density is defined as the current per unit area.

J= I/A Amp/m2

13. What is meant by displacement current?

Displacement current is nothing but the current flowing through capacitor.

J= D / t

14. State point form of ohms law.

Point form of ohms law states that the field strength within a conductor is

proportional to the current density.

J =óE

15. State electric displacement.

The electric flux or electric displacement through a closed surface is equal to the

charge enclosed by the surface.

16. State Divergence Theorem.

The integral of the divergence of a vector over a volume v is equal to the surface

integral of the normal component of the vector over the surface bounded by the

volume.

17. Define divergence.

The divergence of a vector F at any point is defined as the limit of its surface

integral per unit volume as the volume enclosed by the surface around the point

shrinks to zero.

Part-B

1. Explain the Co-ordinate System.

2. Explain and Derive the Stokes theorem.

3. Explain and Derive the Divergence theorem.

4. Explain and derive the Electric Field due to charges distributed uniformly on an

infinite and finite line.

5. Explain and derive the Electric Field on the axis of a uniformly charged circular disc.

6. Explain and derive the Electric Field due to an infinite uniformly charged sheet.

7. Explain and derive the Potential due to infinite uniformly charged line and Potential

due to electrical dipole.

89

ELECTROMAGNETIC THEORY

UNIT II STATIC MAGNETIC FIELD


1. State Biot –Savarts law.

It states that the magnetic flux density at any point due to current element is

proportional to the current element and sine of the angle between the elemental

lengths and inversely proportional to the square of the distance between them.

2. Define magnetic vector potential.

It is defined as that quantity whose curl gives the magnetic flux

density.

3. Write down the expression for magnetic field at the centre of the circular coil.

H = I/2a.

4. Give the relation between magnetic flux density and magnetic field intensity.

B =μ H

5. Define magnetic moment.

Magnetic moment is defined as the maximum torque per magnetic

induction of flux density.

m =IA

6. State Gauss law for magnetic field.

The total magnetic flux passing through any closed surface is equal to

zero.

B.ds =0

7. State the principle of superposition of fields.

The total electric field at a point is the algebraic sum of the individual electric field

at that point.

8. Define ohms law at a point

Ohms law at appoint states that the field strength within a conductor is

proportional to current density.

9. Give the formula to find potential at a point which is surrounded by four

orthogonal points in FDM.

V 0= ¼(V1+V2+V3+V4)

10. Give the formula to find potential at a point which is surrounded by six

orthogonal points in FDM.

V 0= ¼(V1+V2+V3+V4 +V5+V6)

11. State Lenz law.

90

ELECTROMAGNETIC THEORYLenz’s law states that the induced emf in a circuit produces a current which

opposes the change in magnetic flux producing it.

12. What is the effect of permittivity on the force between two charges?

Increase in permittivity of the medium tends to decrease the force between two

charges and decrease in permittivity of the medium tends to increase the force

between two charges.

13. What is displacement flux density?

The electric displacement per unit area is known as electric displacement

density or electric flux density.

14. What is the significance of displacement current?

The concept of displacement current was introduced to justify the production of

magnetic field in empty space. It signifies that a changing electric field induces a

magnetic field .In empty space the conduction current is zero and the magnetic

fields are entirely due to displacement current.

15. Distinguish between conduction and displacement currents.

The current through a resistive element is termed as conduction current whereas

the current through a capacitive element is termed as displacement current.

16. Define magnetic field strength.

The magnetic field strength (H) is a vector having the same direction as

magnetic flux density.

H =B/μ

17. Define electric dipole.

Electric dipole is nothing but two equal and opposite point charges separated by

a finite distance.

18. What is electrostatic force?

The force between any two particles due to existing charges is known as

electrostatic force, repulsive for like and attractive for unlike.

Part-B

1. Explain and derive the Magnetic Field intensity due to a finite and infinite

wire carrying a current I.

2. Explain and derive the Magnetic field intensity on the axis of a circular and

rectangular loop carrying a current I.

3. Explain and derive the Force on a wire carrying a current I placed in a magnetic

field and also derive the Torque on a loop carrying a current I.

4. Explain the Magnetic moment and Magnetic Vector Potential.

UNIT III ELECTRIC AND MAGNETIC FIELDS IN MATERIALS


91

ELECTROMAGNETIC THEORY

1. Write the boundary conditions at the interface between two perfect dielectrics.

i) The tangential component of electric field is continuous i.e.) Et1=Et2

ii) The normal component of electric flux density is continuous i.e.)

Dn1=Dn2

2. What is meant by displacement current?

Displacement current is nothing but the current flowing through capacitor.

J= D / t

3. Write down the magnetic boundary conditions.

i. The normal components of flux density B are continuous across the

boundary.

ii. The tangential component of field intensity is continuous across the

boundary.

4. Give the force on a current element.

dF = BIdlsinè

5. Define self inductance.

Self inductance is defined as the rate of total magnetic flux linkage to the

current through the coil.

6. Give the expression for torque experienced by a current carrying loop situated in a

magnetic field.

T = IABsinè

7. What is torque on a solenoid?

T = NIABsinè

8. Explain the conservative property of electric field.

The work done in moving a point charge around a closed path in a electric field is

zero. Such a field is said to be conservative.

9. Write he expression for field intensity due to a toroid carrying a filamentary

current I

H =NI / 2ïR

10. What are equipotential surfaces?

An equipotential surface is a surface in which the potential energy at every point

is of the same vale.

11. Define loss tangent.

Loss tangent is the ratio of the magnitude of conduction current density to

displacement current density of the medium.

92

ELECTROMAGNETIC THEORY12. What is the expression for energy stored in a magnetic field?

W = ½ LI2

13. What is energy density in magnetic field?

W = ½ μH2

14. Distinguish between solenoid and toroid.

Solenoid is a cylindrically shaped coil consisting of a large number of closely

spaced turns of insulated wire wound usually on a non magnetic frame. If a long

slender solenoid is bent into the form of a ring and thereby closed on itself it

becomes a toroid. 75. Describe what are the sources of electric field and

magnetic field? Stationary charges produce electric field that are constant in

time, hence the term electrostatics. Moving charges produce magnetic fields

hence the term magnetostatics.

15. How is electric energy stored in a capacitor?

In a capacitor, the work done in charging a capacitor is stored in the form of

electric energy.

16. What are dielectrics?

Dielectrics are materials that may not conduct electricity through it but on

applying electric field induced charges are produced on its faces .The valence

electron in atoms of a dielectric are tightly bound to their nucleus.

17. What is a capacitor?

A capacitor is an electrical device composed of two conductors which are

separated through a dielectric medium and which can store equal and opposite

charges, independent of whether other conductors in the system are charged or

not

18. Define dielectric strength.

The dielectric strength of a dielectric is defined as the maximum value of electric

field that can b applied to the dielectric without its electric breakdown.

19. What meaning would you give to the capacitance of a single conductor?

A single conductor also possesses capacitance. It is a capacitor whose one plate

is at infinity.

20. Why water has much greater dielectric constant than mica.?

Water has a much greater dielectric constant than mica .because water ha a

permanent dipole moment, while mica does not have.

21. Define inductance.

The inductance of a conductor is defined as the ratio of the linking magnetic flux

to the current producing the flux.

93

ELECTROMAGNETIC THEORYPart-B

1. Derive the Poisson’s and Laplace’s equation and also explain the Electric

Polarization.

2. Define the Capacitance and also derive the Capacitance of various geometries

using Laplace’s equation.

3. Explain and derive the Boundary conditions for electric fields.

4. Derive the point form of ohm’s law and continuity equation for current.

5. Define the Inductance and derive the Inductance of loops and solenoids.

6. Explain the Energy density in magnetic fields, Electrostatic energy and energy

density, magnetization and permeability.

7. Explain and derive the magnetic boundary conditions.

UNIT IV TIME VARYING ELECTRIC AND MAGNETIC FIELDS


1. Define Poynting vector.

The pointing vector is defined as rate of flow of energy of a wave as it

propagates.

P =E X H

2. State Poyntings Theorem.

The net power flowing out of a given volume is equal to the time rate of

decrease of the energy stored within the volume- conduction losses.

3. Give significant physical difference between poisons and Laplaces equations.

When the region contains charges poisons equation is used and

when there is no charges laplaces equation is applied.

4. Give the difficulties in FDM.

FDM is difficult to apply for problems involving irregular boundaries

and non homogeneous material properties.

5. Explain the steps in finite element method.

i) Discrimination of the solution region into elements.

ii) Generation of equations for fields at each element

iii) Assembly of all elements

iv) Solution of the resulting system

6. State Maxwell’s fourth equation.

The net magnetic flux emerging through any closed surface is zero.

7. State Maxwell’s Third equation

94

ELECTROMAGNETIC THEORYThe total electric displacement through the surface enclosing a volume is equal

to the total charge within the volume.

8. Define pointing vector.

The vector product of electric field intensity and magnetic field intensity at a point

is a measure of the rate of energy flow per unit area at that point.

9. What are the significant physical differences between Poisson‘s and laplace‘s

equations.

Poisson‘s and laplace‘s equations are useful for determining the electrostatic

potential V in regions whose boundaries are known.

When the region of interest contains charges poisons equation can be used to

find the potential.

W hen the region is free from charge Laplace equation is used to find the

potential.

10. What is Lorentz force?

Lorentz force is the force experienced by the test charge .It is maximum if the

direction of movement of charge is perpendicular to the orientation of field lines.

11. Define magnetic moment.

Magnetic moment is defined as the maximum torque on the loop per unit

magnetic induction.

Part-B

1. Derive the Displacement current

2. Explain and derive the Maxwell’s four equations in integral form and differential

form.

3. Explain and derive the Poynting Vector and the flow of power.

4. Derive the Power flow in a co-axial cable and also derive the Instantaneous Average and

Complex Poynting Vector.

UNIT V ELECTROMAGNETIC WAVES


1. Define a wave.

If a physical phenomenon that occurs at one place at a given time is reproduced

at other places at later times , the time delay being proportional to the space

separation from the first location then the group of phenomena constitutes a

wave.

95

ELECTROMAGNETIC THEORY2. Mention the properties of uniform plane wave.

i. At every point in space ,the electric field E and magnetic field H are

Perpendicular to each other.

ii. The fields vary harmonically with time and at the same frequency

everywhere in space.

3. Define intrinsic impedance or characteristic impedance.

It is the ratio of electric field to magnetic field. or It is the ratio of square

root of permeability to permittivity of medium.

4. Define propagation constant.

Propagation constant is a complex number

5. Define skin depth

It is defined as that depth in which the wave has been attenuated to

1/e or approximately 37% of its original value.

6. Define reflection and transmission coefficients.

Reflection coefficient is defined as the ratio of the magnitude of the reflected field

to that of the incident field.

7. Define transmission coefficients.

Transmission coefficient is defined as the ratio of the magnitude

of the transmitted field to that of incident field.

8. What will happen when the wave is incident obliquely over dielectric –dielectric

boundary?

When a plane wave is incident obliquely on the surface of a perfect dielectric part

of the energy is transmitted and part of it is reflected .But in this case the

transmitted wave will be refracted, that is the direction of propagation is altered.

9. What is main cause of eddy current?

The main cause of eddy current is that it produces ohmic power loss and causes

local heating.

10. How can the eddy current losses be eliminated?

The eddy current losses can be eliminated by providing laminations. It can be

proved that the total eddy current power loss decreases as the number of

laminations increases.

11. What is the fundamental difference between static electric and magnetic field

Lines?

There is a fundamental difference between static electric and magnetic field lines

The tubes of electric flux originate and terminates on charges, whereas magnetic

flux tubes are continuous.

12. What are uniform plane waves?

96

ELECTROMAGNETIC THEORYElectromagnetic waves which consist of electric and magnetic fields that are

Perpendicular to each other and to the direction of propagation and are uniform

in plane perpendicular to the direction of propagation are known as uniform plane

waves.

13. What is the significant feature of wave propagation in an imperfect dielectric?

The only significant feature of wave propagation in an imperfect dielectric

compared to that in a perfect dielectric is the attenuation undergone by the wave.

14. What is the major drawback of finite difference method?

The major drawback of finite difference method is its inability to handle

curved boundaries accurately.

15. What is method of images?

The replacement of the actual problem with boundaries by an enlarged region or

with image charges but no boundaries is called the method of images.

16. When is method of images used?

Method of images is used in solving problems of one or more point charges in

the presence of boundary surfaces.

Part-B

1. Derive the Wave Equations for Uniform Plane Waves.

2. Derive the Plane waves in free space and in a homogenous material.

3. Derive the Wave equation for a conducting medium.

4. Derive the Plane waves in lossy dielectric medium.

5. Derive the Reflection of Plane Waves by a conductor –normal and oblique

incidence. Derive the Reflection of Plane Waves by a perfect dielectric – normal

and oblique incidence.

97

CONTROL SYSTEMControl System

UNIT I


1.What is control system?

A system consists of a number of components connected together to perform a specific function

. In a system when the output quantity is controlled by varying the input quantity then the system

is called control system.

2.What are the two major types of control system?

The two major types of control system are open loop and closed loop

3. Define open loop control system.

The control system in which the output quantity has no effect upon the input quantity are called

open loop control system. This means that the output is not feedback to the input for correction.

4. Define closed loop control system.

The control system in which the output has an effect upon the input quantity so as to maintain

the desired output value are called closed loop control system.

5. What are the components of feedback control system?

the components of feedback control system are plant , feedback path elements, error detector

and controller.

6. Define transfer function.

The T.F of a system is defined as the ratio of the laplace transform of output to laplace transform

of input with zero initial conditions.

7. What are the basic elements used for modeling mechanical translational system.

Mass, spring and dashpot

8. What are the basic elements used for modeling mechanical rotational system?

Moment of inertia J,fdashpo with rotational frictional coefficient B and torsional spring with

stiffness K

9. Name two types of electrical analogous for mechanical system.

98

CONTROL SYSTEMThe two types of analogies for the mechanical system are

Force voltage and force current analogy

10. What is block diagram?

A block diagram of a system is a pictorial representation of the functions performed by each

component of the system and shows the flow of signals.The basic elements of block diagram

arew block, branch point and summing point.

11. What is the basis for framing the rules of block diagram reduction technique?

The rules for block diagram reduction technique are framed such that any modification made

on the diagram does not alter the input output relation.

12. What is a signal flow graph?

A signal flow graph is a diagram that represents a set of simultaneous algebraic equations .By

taking L.T the time domain differential equations governing a control system can be transferred to

a set of algebraic equations in s-domain.

13. What is transmittance?

The transmittance is the gain acquired bythe signal when it travels from one node to another

node in signal flow graph.

14. What is sink and source?

Source is the input node in the signal fow graph and it has only outgoing branches. Sink is a

output node in the signal flow graph and it has only incoming branches.

15. Define nontouching loop.

The loops are said to be non touching if they do not have common nodes.

16. Write Masons Gain formula.

Masons Gain formula states that the overall gain of the systm is

T = 1/ ΔΣk Pk Δk

k-o.of forward paqths in the signal flow graph.

Pk- Forward path gain of kth forward path

Δ = 1-[sum of individual loop gains ] +[sum of gain products of allpossible combinations of two

non touching loops]-[sum of gain products of allpossible combinations of three non touching

loops]+…

Δk - Δ for that part of the graph which is not touching kth forward path.

99

CONTROL SYSTEM17.Write the analogous electrical elements in force voltage analogy for the elements of

mechanical translational system.

Force-voltage e

Velocity v-current i

Displacement x-charge q

Frictional coeff B-Resistance R

Mass M- Inductance L

Stiffness K-Inverse of capacitance 1/C

18.Write the analogous electrical elements in force current analogy for the elements of

mechanical translational system.

Force-current i

Velocity v-voltage v

Displacement x-fluxφ

Frictional coeff B-conductance 1/R

Mass M- capacitance C

Stiffness K-Inverse of inductance 1/L

19.Write the force balance equation of an ideal mass element .

F = M d2x /dt2

20. Write the force balance equation of ideal dashpot element .

F = B dx /dt

21. Write the force balance equation of ideal spring element .

F = Kx

22.Distinguish between open loop and closed loop system

Open loop Closed loop

1.Innaccurate Accurate

100

CONTROL SYSTEM2.Simple and economical

3.The changes in output due to external

disturbance are not corrected

4.They are generally stable

Complex and costlier

The changes in output due to external

disturbances are corrected automatically

Great efforts are needed to design a stable

system

23. What is servomechanism?

The servomechanism is a feedback control system in which th output is mechanical position (or

time derivatives of position velocity and acceleration,)

Part B

1. Determine the transfer function X1(S) / F(S) and X2(S) / F(S) of the mechanical system

shown in figure.

2. Write the governing differential equations of the mechanical system shown in figure.

101

CONTROL SYSTEM

3. Write the governing differential equations of the mechanical system shown in figure.

4. Obtain the closed loop transfer function C(S) / R(S) of the system whose block

diagram is shown in figure. Use Block diagram reduction technique and verify the

transfer function with signal flow graph technique.

102

CONTROL SYSTEM

5. Derive the transfer function of

i. Armature controlled d.c. motor

ii. Field control d.c. motor with necessary block diagram

6. Explain the rules for block diagram reduction.

UNIT-II


1. What is transient response

The transient response is the response of the system when the system changes from one state to

another.

2. What is steady state response.

The steady state response is the response of the system when it approaches infinity.

3.What is an order of a system.

The order of asystem is the order of the differential equation governing the system.The order of

the system can be obtained from the transfer function of the given system.

4. Define Damping ratio.

Damping ratio is defined as the ratio of actual damping to critical damping.

103

CONTROL SYSTEM63.List the time domain specifications.

The time domain specifications are

i.Delay time

ii.Rise time

iii.Peak time

iv.Peak overshoot

5. Define Delay time.

The time taken for response to reach 50% of final value for the very first time is delay time.

6. Define Rise time.

The time taken for response to raise from 0% to 100% for the very first time is rise time.

7. Define peak time.

The time taken for the response to reach the peak value for the first time is peak time.

8. Define peak overshoot.

Peak overshoot is defined as the ratio of maximum peak value measured from the Maxmium

value to final value

9. Define Settling time.

Settling time is defined as the time taken by the response to reach and stay within specified error

10.What is the need for a controller?

The controller is provided to modify the error signal for better control action

11.What are the different types of controllers.

Proportional controller

PI controller

PD controller

PID controller

12. What is proportional controller?

It is device that produces a control signal which is proportional to the input error signal.

104

CONTROL SYSTEM13. What is PI controller?

It is device that produces a control signal consisting of two terms –one proportional to

error signal and the other proportional to the integral of error signal.

14. What is PD controller

PD controller is a proportional plus derivative controller which produces an output signal

consisting of two time -one proportional to error singal and other proportional to the derivative of

the signal.

15 What is the significance of integral controller and derivative

controller in aPID controller.

The proportional controller stabilizes the gain but produces a steady state error. The

integral control reduces or eliminates the steady state error.

15. Why derivative controller is not used in control systems.

The derivative controller produces a control action based on the rate of change of error

signal and it does not produce corrective measures for any constant error.

16. Define Steady state error.

The steady state error is defined as the value of error as time tends to infinity.

17. What is the drawback of static coefficients.

The main draw back of static coefficient is that it does not show the variation of error with time

and input should be standard input.

18. What is step signal.

The step signal is a signal whose value changes from zero to A at t= 0 and remains

constant at A for t>0.

19. What is ramp signal

The ramp signal is a signal whose value increases linearly with time from an initial value f

zero at t=0.the ramp signal resembles a constant velocity.

20.What is a parabolic signal.

The parabolic signal is a signal whose value varies as a square of time from an initial

value of zero at t=0.This parabolic signal represents constant acceleration input to the

signal.

21. What are the three constants associated with a steady state error.

Positional error constant

105

CONTROL SYSTEMVelocity error constant

Acceleration error constant

22. What are the main advantages of generalized error co-efficients.

i) Steady state is function of time.

ii) Steady state can be determined from any type of input

23. What are the effects of adding a zero to a system.

Adding a zero to a system results in pronounced early peak to system response

thereby the peak overshoot increases appreciably.

24. State-Magnitude criterion.

The magnitude criterion states that s=sa will be a point on root locus if for that

value of s , | D(s) | = |G(s)H(s) | =1

84.State – Angle criterion.

The Angle criterion states that s=sa will be a point on root locus for that value of s, ,

∟D(s) = ∟G(s)H(s) =odd multiple of 180°

25. What is a dominant pole

The dominant pole is a pair of complex conjucate pair which decides the

transient response of the system.

26.What is stepper motor?

A stepper motor is a device which transforms electrical pulses into equal increments of

rotary shaft motion called steps.

27.What is servomotor?

The motors used in automatic control systems or in servomechanism are called

servomotors. They are used to convert electrical signal into angular motion.

28.Name the test signals used in control system

the commonly used test input signals in control system are impulse step ramp acceleration

and sinusoidal signals.

Part B

106

CONTROL SYSTEM1. Measurements are conducted on a servomechanism show the system response to

be

C(t) = 1 + 0.2 e- 60t – 1.2 e- 10t when subjected to unit step input.

i. Obtain the expression for the closed loop transfer function.

ii. Determine the undamped natural frequency and damping ratio of the

system.

2. The open loop transfer function of a servo system with unity feedback is

G(s). Evaluate the dynamic error using dynamic error coefficients. Obtain the steady

state

UNIT-III


1.What is frequency response

A frequency responses the steady state response of a system when the input to the

system is a sinusoidal signal.

2. List out the different frequency domain specifications?

The frequency domain specification are

i)Resonant peak. ii)Resonant frequency.

3. Define –resonant Peak (r)?

The maximum value of the magnitude of closed loop transfer function is called resonant

peak.

4. Define –Resonant frequency(f)?

The frequency at which resonant peak occurs is called resonant frequency.

5. What is bandwidth?

The bandwidth is the range of frequencies for which the system gain Is more than 3

dbB.The bandwidth is a measure of the ability of a feedback system to reproduce the input signal

,noise rejection characteristics and rise time.

6. Define Cut-off rate?

107

CONTROL SYSTEMThe slope of the log-magnitude curve near the cut-off is called cut-off rate. The cut-off

rate indicates the ability to distinguish the signal from noise.

7. Define –Gain Margin?

The gain margin,kg is defined as the reciprocal of the magnitude of the open loop

transfer function at phase cross over frequency.

Gain margin kg = 1 / G(j pc) .

8. Define Phase cross over?

The frequency at which, the phase of open loop transfer functions is called phase cross

over frequency pc.

9. What is phase margin?

The phase margin , is the amount of phase lag at the gain cross over frequency

required to bring system to the verge of instability.

10. Define Gain cross over?

The gain cross over frequency gc is the frequency at which the magnitude of the open

loop transfer function is unity..

11. What is Bode plot?

The Bode plot is the frequency response plot of the transfer function of a system. A Bode

plot consists of two graphs. One is the plot of magnitude of sinusoidal transfer function versus

log .The other is a plot of the phase angle of a sinusoidal function versus log .

12.What are the main advantages of Bode plot?

The main advantages are:

i) Multiplication of magnitude can be in to addition.

ii) A simple method for sketching an approximate log curve is available.

iii) It is based on asymptotic approximation. Such approximation is sufficient

if rough information on the frequency response characteristic is needed.

iv) The phase angle curves can be easily drawn if a template for the phase

angle curve of 1+ j is available.

13.Define Corner frequency?

The frequency at which the two asymptotic meet in a magnitude plot is called corner

frequency.

108

CONTROL SYSTEM14. Define Phase lag and phase lead?

A negative phase angle is called phase lag.

A positive phase angle is called phase lead.

15. What are M circles?

The magnitude of closed loop transfer function with unit feed back can be shown to be in

the for every value if M.These circles are called M circles.

16.What is Nichols chart?

The chart consisting if M & N loci in the log magnitude versus phase

diagram is called Nichols chart.

17. What are two contours of Nichols chart?

Nichols chart of M and N contours, superimposed on ordinary graph. The M contours are

the magnitude of closed loop system in decibels and the N contours are the phase angle locus of

closed loop system.

18. How is the Resonant Peak(Mr), resonant frequency(Wr ) , and band width determined

from Nichols chart?

i) The resonant peak is given by the value of .contour which is tangent to G(j )

locus.

ii) The resonant frequency is given by the frequency of G(j ) at the tangency point.

iii) The bandwidth is given by frequency corresponding to the intersection point of

G(j ) and –3dB M-contour.

19.What are the advantages of Nichols chart?

The advantages are:

i) It is used to find the closed loop frequency response from open loop

frequency response.

ii) Frequency domain specifications can be determined from Nichols chart.

iii) The gain of the system can be adjusted to satisfy the given specification.

109

CONTROL SYSTEMPart-B

1. How do you find the stability of the system by using a) POLAR PLOT b) BODE PLOT &

c) Nichols chart

2. How do you find the stability of the system by using gain margin and phase margin?

UNIT-IV


1.Define BIBO stability.

A linear relaxed system is said to have BIBIO stability if every bounded input results in a

bounded output.

2.What is the necessary condition for stability.

The necessary condition for stability is that all the coefficients of the characteristic

polynomial be positive.

3.What is the necessary and sufficient condition for stability.

The necessary and sufficient condition for stability is that all of the elements in the first

column of the routh array should be positive.

4.What is quadrantal symmetry?

The symmetry of roots with respect to both real and imaginary axis called quadrantal

symmetry.

5.What is limitedly stable system?

For a bounded input signal if the output has constant amplitude oscilllations Then the

system may be stable or unstable under some limited constraints such a system is called limitedly

stable system.

6. What is synchro?

A synchro is a device used to convert an angular motion to an electrical signal or viceversa.

110

CONTROL SYSTEM7. What is steady state error?

The steady state error is the value of error signal e(t) when t tends to infinity.

8.What are static error constants.

The Kp Kv and Ka are called static error constants.

9 What is nyquist contour

The contour that encloses entire right half of S plane is called nyquist contour.

10. State Nyquist stability criterion.

If the Nyquist plot of the open loop transfer function G(s) corresponding to the nyquist

control in the S-plane encircles the critical point –1+j0 in the counter clockwise direction

as many times as the number of right half S-plane poles of G(s),the closed loop system is

stable.

11.Define Relative stability

Relative stability is the degree of closeness of the system,it an indication of strength or

degree of stability.

12.What are the two segments of Nyquist contour.

i. An finite line segment C1 along the imaginary axis.

ii. An arc C2 of infinite radius.

13.What are root loci.

The path taken by the roots of the open loop transfer function when the loop gain is

varied from 0 to α are called root loci.

13. What is a dominant pole.

The dominant pole is a air of complex conjugate pair which decides the transient

response of the system.

14. What are the main significances of root locus.

i. The main root locus technique is used for stability analysis.

ii. Using root locus technique the range of values of K, for as table system can be

determined

111

CONTROL SYSTEM15 What are the effect of adding a zero to a system.

Adding a zero to a system increases peak overshoot appreciably.

16. What are N circles.

If the phase of closed loop transfer function with unity feedback is α, then tan α will be in

the form of circles for every value of α. These circles are called N circles.

Part-B

1. Explain how stability is determined from Routh – Hurwitz table?

2. State Nyquist stability criterion

3. Draw & Explain the Nyquist plot.

4. find the root locus.

UNIT-V


1. What are the two types of compensation

i. Cascade or series compensation

ii. Feedback compensation or parallel compensation

2. What are the three types of compensators

i. Lag compensator

ii. Lead compensator

iii. Lag-Lead compensator

3. What are the uses of lead compensator

speeds up the transient response

increases the margin of stability of a system

increases the system error constant to a limited extent.

4. What is the use of lag compensator

*Improve the steady state behavior of a system, while nearly preserving its transient

response.

112

CONTROL SYSTEM5. When is lag lead compensator is required

The lag lead compensator is required when both the transient and steady state response

of a system has to be improved

6. What is a compensator

A device inserted into the system for the purpose of satisfying the specifications is called

as a compensator.

7.State – Angle criterion.

The Angle criterion states that s=sa will be a point on root locus for that value of s, ,

∟D(s) = ∟G(s)H(s) =odd multiple of 180°

8. What is a dominant pole

The dominant pole is a pair of complex conjucate pair which decides the

transient response of the system.

9.What is quadrantal symmetry?

The symmetry of roots with respect to both real and imaginary axis called quadrantal

symmetry.

10.What is limitedly stable system?

For a bounded input signal if the output has constant amplitude oscilllations Then the

system may be stable or unstable under some limited constraints such a system is called limitedly

stable system.

11.Define Corner frequency?

The frequency at which the two asymptotic meet in a magnitude plot is called corner

frequency.

12. Define Phase lag and phase lead?

A negative phase angle is called phase lag.

A positive phase angle is called phase lead.

Part-B

113

CONTROL SYSTEM1.Explain the lag compensator.

2.Explain the lead compensator.

114

Ece - Ilyr - Ivsem - Qb

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