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INDIAN

INSTITUTE

OF TECHNOLOGY

Department of

Electrical Engineering

END AUTUMN SEMESTER

EXAMINATION-2011

Date: 23.11.2011 · Time: 3 hours

Sub. Name: Signals Networks

Instructions:

Answer

any five

questions.

Full Marks: 100

No. of Students:

240

Sub. No.

EE21101

1 a) State Millman s theorem. 2)

b) The initial energy in the circuit of Fig. Q1 b) is zero at

t

=0. Assume that v t)=5u t) V .

Find Vo s) using Thevenin s theorem. Apply initial and final value theorems to find v (0) and

vo oo). Obtain the expression of

vJt).

4+2+2)

IF

vit

Fig.

Ql b)

c)

An R-L-C series circuit is to be used to estimate the coefficient of the third harmonic of a

square wave signal. Draw the required connection showing the input and output terminals.

f

the square wave has amplitude of 1

OV

and frequency of 50 Hz and the value of the

capacitance is 30 p then fmd the required value of the inductance. Given a choice over the

value of the quality factor Q), which value will you choose: Q = 1.0 or Q = 10.0? Justify

your answer. Find out the value

ofR

for the chosen value

of

Q.

1+1+1+1+1)

d) Find the transmission (ABCD) parameters of the network shown in Fig. Q1(d). Consider

the transformer as an ideal one. 5)

12.50

Fig. Ql d)

2. a) A load impedance Zo is connected at the output port (port 2) of a two port network. Find

the expression of the input impedance (Zi) of the network in terms of its ABCD parameter

and the load impedance. State the condition under which Zi and

Zo

can be called image

impedances.

f

Zi and o are image impedances and Zi s the input impedance with the

output port open and Zis is the input impedance with the output port short circuited, show

that z

=

lz

z

. 2+1+4)

1 \f 1

 

1

5

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2. b) A current pulse shown in Fig. Q2 b) i) is applied to the

R-L

circuit shown in Fig. Q2 b) ii).

Represent the current pulse in Laplace domain. Find the expression

of

the response

i

 

t).

is t),

2.0

...............

.

1.0

.................................

.

2.0

Fig. Q2 b) i)

t, sec

2+4)

io

2

H

Fig. Q2 b ) ii)

c) For the network shown

in

Fig. Q2 c), draw the oriented graph. Considering branches 4, 5

and 6 as the twigs, write the fundamental cut-set matrix. Using this matrix, find the values of

all the branch voltages.

1+2+4)

B

Fig. Q2 c)

3 a)

f the circuit shown in Fig. Q3 a-ii) is an equivalent representation of the coupled circuit

shown in Fig. Q3 a-i), find the values of the inductances L1. L2 and L12. Consider the initial

currents through the inductors to be zero. 5)

1 0 - - - ~ ~ - - - - - - - - - - - - ~ - - ~ 2

Fig. Q3 a-i) Fig. Q3 a-ii)

b) i)

Define tree and fundamental tie-set of a linear graph.

2)

ii)

f

an unconnected graph is formed by

p

connected sub graphs and has a total of n 1

nodes, then prove that the total number 9ftwigs

of

the graph is n 1 . 2)

iii)

f the circuit matrix and the cut-set matrix of a linear graph are denoted by Ba and Qa

respectively, then prove that

Q a ~

=0 3)

c) Draw the circuit diagram

of

an active high pass filter consisting

of

only one operational

amplifier. 2)

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3. d) The open circuit impedance Z) parameters of the two port networks - network A and

network B are given below:

.

[

1 ]

[4

3]

a 2

5 b 3

2

The networks are connected in cascade. Using the definition find the overall

Z

parameters

of

the composite network. Do not use conversion to any other parameter. {6

4. a) In the circuit shown in Fig. Q4 a), the switch K was closed at time t = -oo, thus connecting

the voltage source, v

t)

=

10 sin

314t to the R-

L C

circuit. The switch is opened at time

t =

12.5ms. Draw the circuit jus t after the switching opening of the switch) in Laplace

domain. Find the time domain expression of the voltage across the inductor. 1+3)

vs

t)

=

10sin314t

Fig. Q4 a)

1

100

mH

b) The short circuit admittance parameters of the two-port network N) shown in Fig. Q4 b)

are

Yll

= 5 S, Y22 = 1 S,

Yt2

=

Y21

=

-2 S.

Find the average power delivered to the two port

network. 4)

2 V

Fig. Q4 b)

c) The fundamental cut-set matrix for a linear graph is given below. What is the number

of

nodes

of

the graph? Find the corresponding fundamental loop matrix. Using these matrices,

write the Kirchoffs Current Law and Kirchoffs Voltage Law for the network.

1+2+2)

1 0 0

-1

0 0

0 0 1

-1

0

0

Q

0 0 0 0

-1

1

0 1 0

-1

1 0

d) i)

Draw a band pass filter circuit using general impedance converter GIC). Find its

transfer function and show the band pass operation. 1+2+1)

ii) Design a GIC band pass filter with.fo

=25kHz

= 8.7 and 0 dB mid band gain. 3)

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I

11

an appropriate Flourescent lamp and work out the numbell

of

lamps required. Plan the

layout and sketch. Each lamp measures 1.25 m in length.

06)

Q

Vs =50V,

50Hz

Sl. No.

1

2.

3.

4.

5.

6.

3Q

Lamp Data

LumenOu

1000 lm

800 lm

2900

lm

2000 lm

5600 lm

14500 lm

lOO J.F

Fig

I

I

I

ut Power Out ut

18W

I 14W

I 28W

I

40W

I

70W

140W

lOQ

j10Q

I

Determine L for I: to be

in phase with V s in the

circuit shown In fig; 1 a)

and estimate the power

delivered by the source.

Also draw the complete

phasor diagram inqicating

phasors V s.I

I1,

I2 and

Vt

(10)

Q 5)

Test results on a 200 V

600

V,

20

k

VA

single

hase

transformer are : i)

OC

Test :

200 V, 12 A and 240 W. ii) S.C Test: 100 V, i A and 1200 W. Draw the relevant

circuit diagrams for both the tests. Determine the eq}livalent circuit representation of the

transformer. Determine the terminal voltages and cuirents on both sides under 50 CJ? load,

if load power factor is 0.9 lagging. i

/

10)

/

I

I

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5. a) Present the modulation property of Fourier transform. In, the light

of

this result explain how

signals may be communicated over a distance using modulation and demodulation.

1

+4)

b)

For a series R,L,C circuit with R

=IOOQ,

L=10mH and C=1)lF) obtain the transfer

function between vout

= vc

and the excitation voltage

v in .

3)

c)What is a Bode plot? The asymptotic approximation of the Bode magnitude) plot of a

system is found to have comer frequencies at

OJ=

0.1,

1, and 4 radls, with the slopes,

in

db/decade, being -20 for OJ 0.1, -40 for 0.1

OJ

1, -20 for 1

OJ

4, and -60 for OJ> 4.

Further, it is seen that i) the asymptotic plot magnitude is 20

db

at OJ=

0.1,

and ii) the

actual magnitude plot exceeds the asymptotic one by about 7 db for

4.

Assuming the

zeros

to

be all in the left half plane, fmd the transfer function of the system. 1+5)

d)

What is meant by transient response? What are the features that characterize such a

response? Explain how the transient response

of

the RLC circuit considered

in.

5 b) above

can be obtained experimentally in the laboratory. 1+2+3)

6. a) Define Laplace Transform of a signal. Obtain the same for a signal given by

0,

O>t

t,

O ~ t <

x t) =

1,

t < 2

3- t

2 ~ t < 3

0,

t;?:3

What is its ROC?

1+4+1)

b) Define transfer function for an LTI system. n the light

of

the convolution theorem explain

the practical significance ofthis definition. 1+2)

c) Define stability of a system. Explain how the same can be ascertained for a system from

the

ROC of

its transfer function. 1+2)

d) Does

H s)

= s

-1)/ s

+ 1) s- 2)) represent some i) stable, ii) stable

as

well

as

causal,

system? Explain your answer.

3)

e) The input

x t)

and output y t) of a causal LTI system with impulse response h t)are

related as

y t)

1

a)ji t) a l a)y t) a

2

y t)

=x t)

For what real values of a is the system guaranteed to be stable? Further, if g t)

=

h t) h t),

how many poles does G s) have? 3+2)

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