2023 104304

B.Tech. 3rd Semester Examination, 2023

Time 03 Hours

Full Marks 70

Instructions:

The marks are indicated in the right-hand margin.
There are NINE questions in this paper.
Attempt FIVE questions in all.
Question No. 1 is compulsory.

Q.1 Choose the correct answer of the following (Any seven question only):

Q1.1

What is the value of the unit step function $ u(t-T) $ at any time $ t \le T $

a)

1

b)

0

c)

infinite

d)

none of the above

Q1.2

An RC high-pass filter consists of a 820 ohm resistor. What is the value of C is to be taken so that $ X_c $ is ten times less than R at an input frequency of 12 kHz?

a)

81 µF

b)

161 µF

c)

0.161 µF

d)

220 µF

Q1.3

The transient current in an RLC circuit is oscillating when

a)

$R = 2\sqrt{\frac{L}{C}}$

b)

$R = 0$

c)

$R < 2\sqrt{\frac{L}{C}}$

d)

$R > 2\sqrt{\frac{L}{C}}$

Q1.4

A cut set matrix gives relation between

a)

Branch currents and link currents

b)

Branch voltages and tree branch voltages

c)

Branch voltages and link voltages

d)

Branch currents and tree currents

Q1.5

A network consists 4 nodes, 6 branches. How many basic loop can be formed?

a)

3

b)

9

c)

1

d)

2

Q1.6

In a series RLC circuit if C is increased resonant frequency

a)

Increases

b)

Decreases

c)

It remains the same

d)

It is zero

Q1.7

What is the type of filter shown in the figure?

a)

Low pass filter

b)

High pass filter

c)

Band pass filter

d)

All pass filter

Q1.8

Comment on the periodicity of a constant signal?

a)

It is periodic

b)

It is not periodic

c)

It is a mixture of period and aperiodic signal

d)

It depends on the signal

Q1.9

The branches which are not present in a tree is called

a)

twigs

b)

links

c)

co-tree

d)

tie-set

Q1.10

A system is linear if it satisfies

a)

Principle of superposition

b)

Principle of homogeneity

c)

Both (i) & (ii)

d)

Only (i)

Q.2 Solve this question :

Q2.1

A given LTI system has produced an impulse response as shown by $ h(t) $ given in figure below. Find the time response of this LTI system when an input signal $ x(t) $ as shown below is applied to this system.

Q.3 Solve both questions :

Q3.1

What is filter? Discuss the advantages of an active filter over a passive filter.

Q3.2

What is band-pass filter? Derive the gain $ \left| \frac{V_o}{V_{in}} \right| $ of a first order Butterworth active band-pass filter.

Q.4 Solve both questions :

Q4.1

Explain clearly with the help of suitable examples the following terms used in network analysis:
a) Oriented graph
b) Tree
c) Cut Set
d) Tie Set
e) Incidence matrix and its properties.

Q4.2

For a symmetrical two port network prove that $ AD - BC = 1 $

Q.5 Solve both questions :

Q5.1

Obtain the first form of the Foster Network for the driving point impedance of LC network given as: $ Z(S) = \frac{10(S^2+4)(S^2+16)}{S(S^2+9)} $

Q5.2

What is Cauer's form of circuit realization? Describe briefly.

Q.6 Solve this question :

Q6.1

Establish the $ \pi - T / Y - \Delta $ transformation relations. Convert the $ \pi / \Delta $ into an equivalent $ T / Y $ network given below.

Q.7 Solve this question :

Q7.1

For the following circuit draw the oriented graph and obtain the Tie-set matrix.

Q.8 Solve this question :

Q8.1

In the following circuit $ V_s = 200\sqrt{2}\cos 500t $, $ R = 80 \Omega $, $ L = 160 $ mH.
(a) Determine the current drawn from $ V_s $ and power absorbed by the LR circuit.

(b) A capacitor is then connected across the $ V_s $, so that the current now drawn from $ V_s $ is in phase with $ V_s $. Determine the value of the capacitor and the power drawn from $ V_s $.

Q.9 Write short notes on any two of the following:

Q9.1

Active Band pass filter

Q9.2

Causal & non causal signals with examples

Q9.3

Zero order hold circuit

Q9.4

Aliasing and its effect

2023 V4 104304

B.Tech. 3rd Semester Examination, 2023

Time 03 Hours

Full Marks 70

Instructions:

The marks are indicated in the right-hand margin.
There are NINE questions in this paper.
Attempt FIVE questions in all.
Question No. 1 is compulsory.

Q.1 Choose the correct answer of the following (Any seven question only):

Q1.1

What is the value of the unit step function $ u(t-T) $ at any time $ t \le T $

a)

1

b)

0

c)

infinite

d)

none of the above

Q1.2

An RC high-pass filter consists of a 820 ohm resistor. What is the value of C is to be taken so that $ X_c $ is ten times less than R at an input frequency of 12 kHz?

a)

81 µF

b)

161 µF

c)

0.161 µF

d)

220 µF

Q1.3

The transient current in an RLC circuit is oscillating when

a)

$R = 2\sqrt{\frac{L}{C}}$

b)

$R = 0$

c)

$R < 2\sqrt{\frac{L}{C}}$

d)

$R > 2\sqrt{\frac{L}{C}}$

Q1.4

A cut set matrix gives relation between

a)

Branch currents and link currents

b)

Branch voltages and tree branch voltages

c)

Branch voltages and link voltages

d)

Branch currents and tree currents

Q1.5

A network consists 4 nodes, 6 branches. How many basic loop can be formed?

a)

3

b)

9

c)

1

d)

2

Q1.6

In a series RLC circuit if C is increased resonant frequency

a)

Increases

b)

Decreases

c)

It remains the same

d)

It is zero

Q1.7

What is the type of filter shown in the figure?

a)

Low pass filter

b)

High pass filter

c)

Band pass filter

d)

All pass filter

Q1.8

Comment on the periodicity of a constant signal?

a)

It is periodic

b)

It is not periodic

c)

It is a mixture of period and aperiodic signal

d)

It depends on the signal

Q1.9

The branches which are not present in a tree is called

a)

twigs

b)

links

c)

co-tree

d)

tie-set

Q1.10

A system is linear if it satisfies

a)

Principle of superposition

b)

Principle of homogeneity

c)

Both (i) & (ii)

d)

Only (i)

Q.2 Solve this question :

Q2.1

A given LTI system has produced an impulse response as shown by $ h(t) $ given in figure below. Find the time response of this LTI system when an input signal $ x(t) $ as shown below is applied to this system.

Q.3 Solve both questions :

Q3.1

What is filter? Discuss the advantages of an active filter over a passive filter.

Q3.2

What is band-pass filter? Derive the gain $ \left| \frac{V_o}{V_{in}} \right| $ of a first order Butterworth active band-pass filter.

Q.4 Solve both questions :

Q4.1

Explain clearly with the help of suitable examples the following terms used in network analysis:
a) Oriented graph
b) Tree
c) Cut Set
d) Tie Set
e) Incidence matrix and its properties.

Q4.2

For a symmetrical two port network prove that $ AD - BC = 1 $

Q.5 Solve both questions :

Q5.1

Obtain the first form of the Foster Network for the driving point impedance of LC network given as: $ Z(S) = \frac{10(S^2+4)(S^2+16)}{S(S^2+9)} $

Q5.2

What is Cauer's form of circuit realization? Describe briefly.

Q.6 Solve this question :

Q6.1

Establish the $ \pi - T / Y - \Delta $ transformation relations. Convert the $ \pi / \Delta $ into an equivalent $ T / Y $ network given below.

Q.7 Solve this question :

Q7.1

For the following circuit draw the oriented graph and obtain the Tie-set matrix.

Q.8 Solve this question :

Q8.1

In the following circuit $ V_s = 200\sqrt{2}\cos 500t $, $ R = 80 \Omega $, $ L = 160 $ mH.
(a) Determine the current drawn from $ V_s $ and power absorbed by the LR circuit.

(b) A capacitor is then connected across the $ V_s $, so that the current now drawn from $ V_s $ is in phase with $ V_s $. Determine the value of the capacitor and the power drawn from $ V_s $.

Q.9 Write short notes on any two of the following:

Q9.1

Active Band pass filter

Q9.2

Causal & non causal signals with examples

Q9.3

Zero order hold circuit

Q9.4

Aliasing and its effect

2022 104304

End Semester Examination - 2022

Time 03 Hours

Full Marks 70

Instructions:

The marks are indicated in the right-hand margin.
There are NINE questions in this paper.
Attempt FIVE questions in all.
Question No. 1 is compulsory.

Q.1 Choose the correct option/answer of the following: (Answer any seven)

Q1.1

An ideal voltage source should have

a)

Large value of e.m.f

b)

Small value of e.m.f

c)

Zero source resistance

d)

Infinite source resistance

Q1.2

For every tree, there will be _______ number of cut-set matrices.

a)

1

b)

2

c)

3

d)

4

Q1.3

Which of the following expression is true in case of open circuit parameters?

a)

$V_1 = Z_{11}V_1 + Z_{12}I_2$

b)

$V_1 = Z_{11}I_1 + Z_{12}V_2$

c)

$V_1 = Z_{11}I_1 + Z_{12}I_2$

d)

$V_2 = Z_{11}I_1 + Z_{12}I_2$

Q1.4

For a T shaped network, if the Short-circuit admittance parameters are $ Y_{11}, Y_{12}, Y_{21} $ and $ Y_{22} $ then $ Y_{11} $ in terms of Transmission parameters can be expressed as

a)

$Y_{11} = \frac{D}{B}$

b)

$Y_{11} = \frac{C-A}{B}$

c)

$Y_{11} = \frac{-1}{B}$

d)

$Y_{11} = \frac{A}{B}$

Q1.5

The cut-off frequency of the constant k-low pass filter is ?

a)

$1/\sqrt{LC}$

b)

$\frac{1}{\pi\sqrt{LC}}$

c)

$\sqrt{LC}$

d)

$\pi\sqrt{LC}$

Q1.6

Which condition determines the causality of the LTI system in terms of its impulse response?

a)

Only if the value of an impulse response is zero for all negative values of time

b)

Only if the value of an impulse response is unity for all negative values of time

c)

Only if the value of an impulse response is infinity for all negative values of time

d)

Only if the value of an impulse response is negative for all negative values of time

Q1.7

A graph with n vertices and n-1 edges that is not a tree, is

a)

A circuit

b)

Euler

c)

Connected

d)

Disconnected

Q1.8

If a network function has zeros only in the left-half of the s-plane, then it is said to be

a)

A stable function

b)

A non-minimum phase function

c)

A minimum phase function

d)

An all-pass function

Q1.9

Define tree, twigs and links of a graph.

Q1.10

What do you mean by natural response and forced response of a network?

Q.2 Solve all questions :

Q2.1

Define the following terms: (i) Branch (ii) Node (iii) Tree (iv) Loop

Q2.2

Define and state the properties of incidence matrix.

Q2.3

For the graph shown below, find the incidence and cut set matrices.

Q.3 Solve both questions :

Q3.1

Discuss in brief the Z parameters, Y parameters, hybrid parameters and ABCD parameters.

Q3.2

Find the Z and Y parameters for the following circuit.

Q.4 Solve both questions :

Q4.1

Check whether the following polynomial is Hurwitz or not: $ s^4 + 7s^3 + 4s^2 + 18s + 6 $

Q4.2

A driving point impedance is given by: $ Z_{LC}(s) = \frac{s(s^2+1)(s^2+6)}{(s^2+1)(s^2+5)} $. Obtain the first form of Cauer network.

Q.5 Solve both questions :

Q5.1

If the bandstop filter shown in below figure is to reject a 200 Hz sinusoid while passing other frequency, Calculate the value of L and C, take $ R = 150 \Omega $ and bandwidth as 100 Hz.

Q5.2

Explain Low pass filter, high pass filter, band pass filter and band stop filter with proper diagram and derivation.

Q.6 Solve both questions :

Q6.1

The output $ y(t) $ of a linear time invariant system is related to its input $ X(t) $ by following equation: $ y(t) = 0.5X(t-t_d+T) + X(t-t_d) + 0.5X(t-t_d-T) $. What is s Filter transfer function $ H(w) $.

Q6.2

What is the system? What are the different types of system?

Q.7 Solve both questions :

Q7.1

Obtain the first and second Foster forms of the below reactance function: $ Z(s) = \frac{s(s^2+9)}{(s^2+4)(s^2+16)} $

Q7.2

Show all possible cut-sets of the below network graph.

Q.8 Solve both questions :

Q8.1

Obtain the values of L and C for a prototype T and $\pi$ shape low pass filters with $ R_0 = 500 \Omega $ and cut off frequency $ f_c = 2KHz $.

Q8.2

A second-order band pass filter is to be constructed using RC components that will only allow a range of frequencies to pass above 1kHZ and below 30kHz. Assuming that both the resistors have values of 10k$\Omega$, calculate the values of the two capacitors required.

Q.9 Write short notes on any two of the following:

Q9.1

Image impedance and its relation to open circuit and short circuit impedances.

Q9.2

Transient response of R L series circuit to impulse signal.

Q9.3

Inverse hybrid parameter of a 2 port network.

2022 V4 104304

End Semester Examination - 2022

Time 03 Hours

Full Marks 70

Instructions:

The marks are indicated in the right-hand margin.
There are NINE questions in this paper.
Attempt FIVE questions in all.
Question No. 1 is compulsory.

Q.1 Choose the correct option/answer of the following: (Answer any seven)

Q1.1

An ideal voltage source should have

a)

Large value of e.m.f

b)

Small value of e.m.f

c)

Zero source resistance

d)

Infinite source resistance

Q1.2

For every tree, there will be _______ number of cut-set matrices.

a)

1

b)

2

c)

3

d)

4

Q1.3

Which of the following expression is true in case of open circuit parameters?

a)

$V_1 = Z_{11}V_1 + Z_{12}I_2$

b)

$V_1 = Z_{11}I_1 + Z_{12}V_2$

c)

$V_1 = Z_{11}I_1 + Z_{12}I_2$

d)

$V_2 = Z_{11}I_1 + Z_{12}I_2$

Q1.4

For a T shaped network, if the Short-circuit admittance parameters are $ Y_{11}, Y_{12}, Y_{21} $ and $ Y_{22} $ then $ Y_{11} $ in terms of Transmission parameters can be expressed as

a)

$Y_{11} = \frac{D}{B}$

b)

$Y_{11} = \frac{C-A}{B}$

c)

$Y_{11} = \frac{-1}{B}$

d)

$Y_{11} = \frac{A}{B}$

Q1.5

The cut-off frequency of the constant k-low pass filter is ?

a)

$1/\sqrt{LC}$

b)

$\frac{1}{\pi\sqrt{LC}}$

c)

$\sqrt{LC}$

d)

$\pi\sqrt{LC}$

Q1.6

Which condition determines the causality of the LTI system in terms of its impulse response?

a)

Only if the value of an impulse response is zero for all negative values of time

b)

Only if the value of an impulse response is unity for all negative values of time

c)

Only if the value of an impulse response is infinity for all negative values of time

d)

Only if the value of an impulse response is negative for all negative values of time

Q1.7

A graph with n vertices and n-1 edges that is not a tree, is

a)

A circuit

b)

Euler

c)

Connected

d)

Disconnected

Q1.8

If a network function has zeros only in the left-half of the s-plane, then it is said to be

a)

A stable function

b)

A non-minimum phase function

c)

A minimum phase function

d)

An all-pass function

Q1.9

Define tree, twigs and links of a graph.

Q1.10

What do you mean by natural response and forced response of a network?

Q.2 Solve all questions :

Q2.1

Define the following terms: (i) Branch (ii) Node (iii) Tree (iv) Loop

Q2.2

Define and state the properties of incidence matrix.

Q2.3

For the graph shown below, find the incidence and cut set matrices.

Q.3 Solve both questions :

Q3.1

Discuss in brief the Z parameters, Y parameters, hybrid parameters and ABCD parameters.

Q3.2

Find the Z and Y parameters for the following circuit.

Q.4 Solve both questions :

Q4.1

Check whether the following polynomial is Hurwitz or not: $ s^4 + 7s^3 + 4s^2 + 18s + 6 $

Q4.2

A driving point impedance is given by: $ Z_{LC}(s) = \frac{s(s^2+1)(s^2+6)}{(s^2+1)(s^2+5)} $. Obtain the first form of Cauer network.

Q.5 Solve both questions :

Q5.1

If the bandstop filter shown in below figure is to reject a 200 Hz sinusoid while passing other frequency, Calculate the value of L and C, take $ R = 150 \Omega $ and bandwidth as 100 Hz.

Q5.2

Explain Low pass filter, high pass filter, band pass filter and band stop filter with proper diagram and derivation.

Q.6 Solve both questions :

Q6.1

The output $ y(t) $ of a linear time invariant system is related to its input $ X(t) $ by following equation: $ y(t) = 0.5X(t-t_d+T) + X(t-t_d) + 0.5X(t-t_d-T) $. What is s Filter transfer function $ H(w) $.

Q6.2

What is the system? What are the different types of system?

Q.7 Solve both questions :

Q7.1

Obtain the first and second Foster forms of the below reactance function: $ Z(s) = \frac{s(s^2+9)}{(s^2+4)(s^2+16)} $

Q7.2

Show all possible cut-sets of the below network graph.

Q.8 Solve both questions :

Q8.1

Obtain the values of L and C for a prototype T and $\pi$ shape low pass filters with $ R_0 = 500 \Omega $ and cut off frequency $ f_c = 2KHz $.

Q8.2

A second-order band pass filter is to be constructed using RC components that will only allow a range of frequencies to pass above 1kHZ and below 30kHz. Assuming that both the resistors have values of 10k$\Omega$, calculate the values of the two capacitors required.

Q.9 Write short notes on any two of the following:

Q9.1

Image impedance and its relation to open circuit and short circuit impedances.

Q9.2

Transient response of R L series circuit to impulse signal.

Q9.3

Inverse hybrid parameter of a 2 port network.

2020 104304

B.Tech Examination, 2020

Time 3 hours

Full Marks 70

Instructions:

The marks are indicated in the right-hand margin.
There are NINE questions in this paper.
Attempt FIVE questions in all.
Question No. 1 is compulsory.

Questions

Q1

Choose the correct answer of the following (any seven):

a)

The output $y(t)$ and the input $x(t)$ of a system are related by the equation $y(t) = x(t) + c$ , where $m$ and $c$ are constants. The system (i) is linear (ii) is non-linear (iii) may be linear or non-linear depending on $y(t)$ and $x(t)$ (iv) None of the above.

b)

Which one of the following is a linear system? (i) $y(t) = 2u(t)$ (ii) $y(t) = 2u(t) + 5$ (iii) $y(t) = 2u^2(t)$ (iv) $y(t) = 2u^2(t) + 5$

c)

The graph of a network has six branches with three tree branches. The minimum number of equations required for the solution of the network is (i) 2 (ii) 3 (iii) 4 (iv) 5

d)

The condition for over-damped response of an $RLC$ series circuit is (i) $\frac{R^2}{4L^2} = \frac{1}{LC}$ (ii) $\frac{R^2}{4L^2} < \frac{1}{LC}$ (iii) $\frac{R^2}{4L^2} > \frac{1}{LC}$ (iv) $\frac{R^2}{4L^2} \le \frac{1}{LC}$

e)

The value of the impulse function $\delta(t)$ at $t=0$ is (i) 0 (ii) $\infty$ (iii) 1 (iv) indeterminate

f)

In a two-port network containing linear bilateral passive circuit elements, which one of the following conditions for $z$-parameters would hold? (i) $z_{11} = z_{22}$ (ii) $z_{12}z_{21} = z_{11}z_{22}$ (iii) $z_{11}z_{12} = z_{22}z_{21}$ (iv) $z_{12} = z_{21}$

g)

If $f(t)$ is a periodic waveform with even symmetry, then its Fourier series expansion does not contain (i) sine terms (ii) cosine terms (iii) odd harmonics (iv) even harmonics

h)

In a series resonant circuit, to obtain a low-pass characteristic, across which element should the output voltage be taken? (i) Resistor (ii) Inductor (iii) Capacitor

i)

A high-pass filter circuit is basically (i) a differentiating circuit with low-time constant (ii) a differentiating circuit with large-time constant (iii) an integrating circuit with low-time constant (iv) an integrating circuit with large-time constant

[14 Marks]

Q2

Answer the following:

a)

Define the following functions:

[4 Marks]

b)

Determine whether the system defined by $y(t) = \sin[x(t)]$ is time-invariant.

[5 Marks]

c)

Determine whether the following continuous-time systems are stable:

[5 Marks]

Q3

Answer the following:

a)

Derive the expression for transient voltage across the resistor and capacitor when switch $S$ is on in Fig. 1:

[8 Marks]

b)

In Fig. 2 the switch $K$ is closed. Find the time when the current from the battery reaches to $500\text{ mA}$ .

[6 Marks]

Q4

Answer the following:

a)

What is 'network topology'?

[2 Marks]

b)

State the advantages offered by the graph theory as applied to electric circuit problems.

[4 Marks]

c)

Write down the incidence matrix and cut-set matrices for the network shown in Fig. 3:

[8 Marks]

Q5

Answer the following:

a)

Discuss the advantages of the Laplace transform method over the conventional classical methods of solving the linear differential equations with constant coefficients.

[3 Marks]

b)

Explain gate function. Obtain the equation of a gate function starting at origin and duration $T$ .

[3 Marks]

c)

Find the response current of a series $RL$ circuit consisting of a resistor $R = 3\text{ }\Omega$ and an inductor $L = 1\text{ H}$ when each of the following driving force voltage is applied:

[8 Marks]

Q6

Answer the following:

a)

What are the open-circuit impedance parameters of a two-port network? Why are they so called?

[3 Marks]

b)

What are transmission parameters? Where are they most effectively used?

[3 Marks]

c)

Obtain the $z$-parameters for the circuit shown in Fig. 4:

[8 Marks]

Q7

Answer the following:

a)

What are different types of filters?

[4 Marks]

b)

In a series $LCR$ type band-pass filter, $L = 50\text{ mH}$ , $C = 127\text{ nF}$ and $R = 63\text{ }\Omega$ . Determine (i) the resonance frequency and (ii) the bandwidth.

[4 Marks]

c)

Design a low-pass filter with $RC$ and $RL$ circuits.

[6 Marks]

Q8

Answer the following:

a)

Check whether the following polynomials are Hurwitz or not:

[7 Marks]

b)

Determine whether the following polynomials are positive real:

[7 Marks]

Q9

Answer the following:

a)

Find the first and second Cauer forms of $LC$ networks for the impedance function: $Z(s) = \frac{s^4+10s^2+9}{s^3+4s}$

[7 Marks]

b)

Determine whether the following polynomials are positive real:

[7 Marks]

2019 031505

B.Tech Examination, 2019

Time 3 hours

Full Marks 70

Instructions:

The marks are indicated in the right-hand margin.
There are NINE questions in this paper.
Attempt FIVE questions in all.
Question No. 1 is compulsory.

Questions

Q1

Write short notes on any seven of the following terms:

a)

Laplace transform of $t \sin t$

b)

Bandwidth

c)

Cut-off frequency

d)

Initial value theorem and final value theorem

e)

Transfer function

f)

ABCD parameter

g)

Driving point impedance

h)

Poles and Zeros of network function

i)

Twigs and links

j)

Planner and non-planner graphs

[14 Marks]

Q2

Answer the following:

a)

In a source-free $R\text{-}L$ circuit at $t=0$ , the current is $I_0$ . Obtain the expression of inductor current and voltage at $t>0$ . A $4\text{ H}$ inductor with initial current $2\text{ A}$ connected through a resistor $R = 8\text{ }\Omega$ at $t=0$ . Find the current through inductor for $t>0$ .

[8 Marks]

b)

Find the inverse transform of $\frac{7s+5}{s^2+s}$ .

[6 Marks]

Q3

Answer the following:

a)

Define $z$-parameter of two-port network. Write down the condition for reciprocity and symmetry.

[7 Marks]

b)

Obtain $z$-parameters for the network shown in the figure below:

[7 Marks]

Q4

Answer the following:

a)

Derive the expression for step response of $R\text{-}L$ circuit with initial inductor current $I_0$ . Plot its voltage response and current response.

[6 Marks]

b)

The switch in the figure given below has been closed for a long time. It opens at $t=0$ . Find $i(t)$ for $t>0$ :

[8 Marks]

Q5

Given the transfer function $H(s) = \frac{V_o(s)}{V_i(s)} = \frac{10}{s^2+3s+10}$ . Realize the function using the circuit in the figure given below:

a)

Select $R=5\text{ }\Omega$ , and find $L$ and $C$ .

b)

Select $R=1\text{ }\Omega$ , and find $L$ and $C$ .

[14 Marks]

Q6

Determine the hybrid parameters for the network in the figure given below:

[14 Marks]

Q7

Determine what type of filter is shown in the figure given below. Calculate the corner or cutoff frequency. Take $R=2\text{ k}\Omega$ , $L=2\text{ H}$ and $C=2\text{ }\mu\text{F}$ :

[14 Marks]

Q8

Fig. I and Fig. II given below show circuit diagram tree and co-tree respectively. Find (a) incidence matrix for the orientation shown, (b) $f$-cut set matrix and (c) $f$-loop matrix:

[14 Marks]

Q9

Answer the following:

a)

Write a technical note on Hurwitz polynomials.

[6 Marks]

b)

Test whether the following polynomials is Hurwitz:

[8 Marks]

2018 031505

B.Tech Examination, 2018

Time 3 hours

Full Marks 70

Instructions:

The marks are indicated in the right-hand margin.
There are NINE questions in this paper.
Attempt FIVE questions in all.
Question No. 1 is compulsory.

Questions

Q1

Choose the correct answer (any seven) :

a)

A network has 15 nodes and 12 independent loops. The number of branches in the network is

a)

(i) 25

b)

(ii) 26

c)

(iii) 27

d)

(iv) 28

b)

The transfer function of a low-pass R-C network is

a)

(i) $(RCs)(1 + RCs)$

b)

(ii) $\frac{1}{1 + RCs}$

c)

(iii) $\frac{RCs}{1 + RCs}$

d)

(iv) $\frac{s}{1 + RCs}$

c)

A two-port network is symmetrical, if

a)

(i) $z_{11}z_{22} - z_{12}z_{21} = 1$

b)

(ii) $AD - BC = 1$

c)

(iii) $h_{11}h_{22} - h_{12}h_{21} = 1$

d)

(iv) $y_{11}y_{22} - y_{12}y_{21} = 1$

d)

In an m-derived low-pass filter, the value of m is

a)

(i) $\sqrt{1 - (\frac{f_{\infty}}{f_c})^2}$

b)

(ii) $\sqrt{1 - (\frac{f_c}{f_{\infty}})^2}$

c)

(iii) $\sqrt{1 + (\frac{f_{\infty}}{f_c})^2}$

d)

(iv) $\sqrt{1 + (\frac{f_c}{f_{\infty}})^2}$

e)

The number of roots of $s^3 + 5s^2 + 7s + 3 = 0$ in the left half of s-plane is

a)

(i) zero

b)

(ii) one

c)

(iii) two

d)

(iv) three

f)

A $\pi$-section filter network consists of a series arm inductor of 20 mH and two shunt arm capacitors of 0.16 $\mu$F. The cut-off frequency is

a)

(i) 2.5 kHz

b)

(ii) 4.3 kHz

c)

(iii) 1.5 kHz

d)

(iv) 3.98 kHz

g)

A two-port network is define by the following pair of equations: $I_1 = 2V_1 + V_2$ , $I_2 = V_1 + V_2$ . Its impedance parameters ($z_{11}, z_{12}, z_{21}, z_{22}$) are

a)

(i) 2, 1, 1, 1

b)

(ii) 1, -1, -1, 2

c)

(iii) 1, 1, 1, 2

d)

(iv) 2, -1, -1, 1

h)

The Laplace transform of $\frac{1 - e^{-t}}{t}$ is

a)

(i) $\log[\frac{s}{s + 1}]$

b)

(ii) $\log[\frac{1}{s(s + 1)}]$

c)

(iii) $\log[\frac{s + 1}{s}]$

d)

(iv) $\log[s(s + 1)]$

i)

Which of the following is the representation of $y$-parameters in terms of $z$-parameters?

a)

(i) $\begin{bmatrix} \frac{z_{22}}{\Delta z} & \frac{-z_{12}}{\Delta z} \\ \frac{-z_{21}}{\Delta z} & \frac{z_{11}}{\Delta z} \end{bmatrix}$

b)

(ii) $\begin{bmatrix} \frac{z_{11}}{z_{21}} & \frac{\Delta z}{z_{21}} \\ \frac{1}{z_{21}} & \frac{z_{22}}{z_{21}} \end{bmatrix}$

c)

(iii) $\begin{bmatrix} 1 & \frac{-z_{12}}{z_{11}} \\ \frac{z_{21}}{z_{11}} & \frac{\Delta z}{z_{11}} \end{bmatrix}$

d)

(iv) $\begin{bmatrix} \frac{z_{11}}{\Delta z} & \frac{1}{z_{12}} \\ \frac{1}{z_{12}} & \frac{z_{22}}{z_{21}} \end{bmatrix}$

j)

As the poles of a network shift away from the x-axis, the response

a)

(i) remains constant

b)

(ii) becomes less oscillating

c)

(iii) becomes more oscillating

d)

(iv) None of the above

Q2

Answer the following:

a)

Derive the $z$-parameters in terms of ABCD parameters.

b)

Obtain the open circuit $z$-parameters of the network shown in Fig. 1 :

Q3

For the network shown in Fig. 2, draw the graph, write the tie-set schedule and hence obtain the equilibrium on loop basis. Calculate the values of branch currents and branch voltages :

Q4

Answer the following:

a)

The switch in the network in Fig. 3 is closed at $t = 0$ . Determine the voltage across the capacitor: Use Laplace transform :

b)

In the network of Fig. 4, the switch is closed at $t = 0$ , with the network previously unenergized. Determine currents $i_1(t)$ and $i_2(t)$ . (Use Laplace transform) :

Q5

Answer the following:

a)

Derive the expression for characteristic impedance of a $\pi$-network. Also, express in terms of open-circuit impedance ($Z_{oc}$) and short-circuit impedance ($Z_{sc}$).

b)

Design a band-pass constant $k$ filter with cut-off frequencies of 3 kHz and 7.5 kHz and nominal characteristic impedance of 900 $\Omega$ . Draw a T-section configuration.

Q6

Answer the following:

a)

Write the necessary conditions for transfer functions (restrictions on pole and zero).

b)

Compute $V_2/V_1$ and $I_2/I_1$ , i.e., voltage transfer function and current transfer function respectively for the network shown in Fig. 5 :

Q7

Answer the following:

a)

Determine the Foster forms of realization of the R-C impedance function (Foster forms I and II) $Z(s) = \frac{(s + 1)(s + 4)}{s(s + 2)(s + 5)}$ .

b)

Synthesize the network, if $Z(s) = \frac{s^5 + 5s^3 + 4s}{s^4 + 3s^2 + 1}$ as Cauer-I form.

Q8

Answer the following:

a)

Determine $y$-parameters for the network shown in Fig. 6 :

b)

Find the step response of the voltage across the capacitor in the network as shown in Fig. 7 :

Q9

Write brief notes on any three of the following :

a)

Fundamental circuit matrix and fundamental cut-set matrix (with example)

b)

Time domain behaviour from pole-zero plot

c)

Classification of filters with characteristics of each

d)

Inverse hybrid parameters

2017 031505

B.Tech Examination, 2017

Time 3 hours

Full Marks 70

Instructions:

The marks are indicated in the right-hand margin.
There are NINE questions in this paper.
Attempt FIVE questions in all.
Question No. 1 is compulsory.

Questions

Q1

Choose the correct answer (any seven) :

a)

In the circuit of Fig. 1 shown below, the voltage $V(t)$ is

a)

(i) $e^{at} - e^{bt}$

b)

(ii) $e^{at} + e^{bt}$

c)

(iii) $ae^{at} - be^{bt}$

d)

(iv) $ae^{at} + be^{bt}$

b)

When a unit-impulse voltage is applied to an inductor of 1 H, the energy supplied by the source is

a)

(i) $\infty$

b)

(ii) 1 J

c)

(iii) $\frac{1}{2}$ J

d)

(iv) 0

c)

The graph of an electrical network has $n$ nodes and $b$ branches. The number of links with respect to the choice of a tree is given by

a)

(i) $b - n + 1$

b)

(ii) $b + n$

c)

(iii) $n - b + 1$

d)

(iv) $n - 2b - 1$

d)

A system is represented by the transfer function $\frac{10}{(s + 1)(s + 2)}$ . The DC gain of this system is

a)

(i) 1

b)

(ii) 2

c)

(iii) 5

d)

(iv) 10

e)

For a two-port network to be reciprocal, then

a)

(i) $z_{11} = z_{22}$

b)

(ii) $y_{21} = y_{12}$

c)

(iii) $h_{21} = +h_{12}$

d)

(iv) $AD - BC = 0$

f)

The passband of a typical filter network with $z_1$ and $z_2$ as the series and shunt-arm impedances is characterized by

a)

(i) $-1 < \frac{z_1}{4z_2} < 0$

b)

(ii) $-1 < \frac{z_1}{4z_2} < 1$

c)

(iii) $0 < \frac{z_1}{4z_2} < 1$

d)

(iv) None of the above

g)

If $F_1(s)$ and $F_2(s)$ are two positive real functions, then the function which is always positive real, is

a)

(i) $F_1(s) F_2(s)$

b)

(ii) $\frac{F_1(s)}{F_2(s)}$

c)

(iii) $\frac{F_1(s) F_2(s)}{F_1(s) + F_2(s)}$

d)

(iv) $F_1(s) - F_2(s)$

h)

Each of the two series elements of a T-section low-pass filter consists of an inductor of 60 mH having negligible resistance and a shunt element having a capacitance of 0.2 $\mu$F. The nominal impedance is

a)

(i) 547.72 k$\Omega$

b)

(ii) 54.72 k$\Omega$

c)

(iii) 547.72 $\Omega$

d)

(iv) 5.477 $\Omega$

i)

For a two-port symmetrical bilateral network, if $A = 3$ and $B = 1$ , the value of the parameter $C$ will be

a)

(i) 4

b)

(ii) 6

c)

(iii) 16

d)

(iv) 8

j)

The Laplace transform of a unit-ramp function starting at $t = a$ is

a)

(i) $\frac{1}{(s + a)^2}$

b)

(ii) $\frac{e^{-as}}{(s + a)^2}$

c)

(iii) $\frac{e^{-as}}{s^2}$

d)

(iv) $\frac{a}{s^2}$

Q2

Answer the following:

a)

Derive $ABCD$ parameters in terms of $y$-parameters.

b)

Determine the $y$-parameters for the two-port shown in Fig. 2 below:

Q3

For the network shown in Fig. 3 below, draw network graph, selecting 2, 4, 5 as tree branches. Obtain loop incidence matrix and loop equations:

Q4

In the network shown in Fig. 4 below, the switch is closed at $t = 0$ . Find the currents $i_1(t)$ and $i_2(t)$ when initial current through the inductor is zero and initial voltage on the capacitor is 4 V:

Q5

Answer the following:

a)

For the network shown in Fig. 5 below, find $G_{21} = V_2/V_1$ :

b)

Define driving-point functions. Write down driving-point functions for a two-port network.

Q6

Derive the following expressions for a constant $k$ high-pass filter:

a)

Nominal impedance

b)

Cut-off frequency

c)

Attenuation constant

d)

Phase constant

e)

Characteristic impedance

f)

Design of filter

Q7

Answer the following:

a)

Realize the foster form of the following impedance function: $Z(s) = \frac{s(s^2 + 4)}{2(s^2 + 1)(s^2 + 9)}$

b)

Realize the Cauer-II form of the following impedance function: $Z(s) = \frac{8(s^2 + 1)(s^2 + 3)}{s(s^2 + 2)(s^2 + 4)}$

Q8

Answer the following:

a)

Find the short-circuit and open-circuit impedances of the network shown in Fig. 6 below and hence obtain its $\pi$ equivalent:

b)

In the circuit of Fig. 7 below, switch $S$ is closed and steady-state conditions reached. Now at time $t = 0$ , switch $S$ is opened. Obtain the expression for the current through the inductor:

Q9

Write brief notes about the following:

a)

Incidence matrix

b)

Loop matrix or circuit matrix

c)

Transfer functions in two-port network

2017 031605

B.Tech Examination, 2017

Time 3 hours

Full Marks 70

Instructions:

The marks are indicated in the right-hand margin.
There are NINE questions in this paper.
Attempt FIVE questions in all.
Question No. 1 is compulsory.

Questions

Q1

Choose the correct answer of any seven questions. $2 \times 7 = 14$

a)

A dc voltage source is connected across a series R-L-C circuit. Under steady-State conditions the applied voltage drops entirely across the

a)

(a) R only

b)

(b) L only

c)

(c) C only

d)

(d) R and L only

b)

In terms of ABCD parameters, a two-port network is symmetrical if and only if

a)

(a) $A = B$

b)

(b) $B = C$

c)

(c) $C = D$

d)

(d) $D = A$

c)

Two two-port networks $\alpha$ and $\beta$ having ABCD parameters as $A_{\alpha} = D_{\alpha} = 4, A_{\beta} = D_{\beta} = 3, B_{\alpha} = 5, C_{\alpha} = 3$ and $B_{\beta} = 4$ and $C_{\beta} = 2$ are connected in cascade in order of $\alpha, \beta$ . The equivalent 'A' parameter of the combination is

a)

(a) 17

b)

(b) 22

c)

(c) 24

d)

(d) 31

d)

The number of links for a network graph having 'n' nodes and 'b' branches is

a)

(a) $b - n + 1$

b)

(b) $n - b + 1$

c)

(c) $b + n - 1$

d)

(d) $b - n$

e)

For a given network the reduced incidence matrix is given as $Ai = \begin{bmatrix} 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ 1 & 0 & 0 & 1 & 0 & -1 & 1 \\ -1 & -1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & -1 & 1 & 0 & 0 \end{bmatrix}$ The parallel branches in the graph are

a)

(a) 1 and 2

b)

(b) 2 and 3

c)

(c) 6 and 7

d)

(d) none of these

f)

For a transfer function $H(s) = \frac{P(s)}{Q(s)}$ ,

a)

(a) the degree of $P(s)$ is always greater than the degree of $Q(s)$

b)

(b) the degree of $P(s)$ and $Q(s)$ are the same

c)

(c) the degree of $P(s)$ is independent of the degree of $Q(s)$

d)

(d) the maximum degree of $P(s)$ and $Q(s)$ differ at the most by one

g)

The driving point impedance of the circuit shown in Fig. 1 is given by $Z(s) = \frac{0.2s}{s^2 + 0.1s + 2}$ the component values are

a)

(a) $L = 5 \text{ H}, R = 0.5 \Omega, C = 0.1 \text{ F}$

b)

(b) $L = 0.1 \text{ H}, R = 0.5 \Omega, C = 5 \text{ F}$

c)

(c) $L = 5 \text{ H}, R = 2 \Omega, C = 0.1 \text{ F}$

d)

(d) $L = 0.1 \text{ H}, R = 2 \Omega, C = 5 \text{ F}$

h)

The first critical frequency nearest to the origin of the complex frequency plane for an R-L driving impedance function will be

a)

(a) a zero in the left-half plane

b)

(b) a zero in the right-half plane

c)

(c) a pole in the left-half plane

d)

(d) either a pole or a zero in the left-half plane depending on the connection

i)

A band stop filter

a)

(a) attenuates frequencies lying between two cut-off frequencies $f_1$ and $f_2$ and passes all other frequencies.

b)

(b) attenuates all frequencies less than lower cut-off frequency.

c)

(c) attenuates all frequencies above the cut-off frequency, $f_2$ .

d)

(d) passes frequencies between the two cut-off frequencies, $f_1$ and $f_2$ .

j)

For a proto-type filter, the $Z_o$ value is

a)

(a) resistive in pass band

b)

(b) inductive in pass band

c)

(c) capacitive in pass band

d)

(d) complex impedance in pass band

Q2

Answer the following:

a)

Find the current $i_L(t)$ for $t > 0$ in the circuit shown in Fig. 2 using Laplace transform. (7 marks)

b)

Determine $i(t)$ and $v(t)$ for $t > 0$ for the circuit shown in Fig. 3. The switch is closed at $t = 0$ . using Laplace transfer (7 marks)

Q3

For the circuit shown in Fig. 4, find poles, zeros and scale factor of the transfer impedance function, $Z_{12}(s) = V_2(s)/I_1(s)$ . (14 marks)

Q4

Answer the following:

a)

For the circuit shown in Fig. 5 determine the hybrid parameters. (7 marks)

b)

Find $V_1$ and $V_2$ in the network shown in Fig. 6 if $y$-parameters are $Y_{11} = \frac{3}{2}\mho, Y_{22} = \frac{5}{6}\mho, Y_{12} = Y_{21} = -\frac{1}{2}\mho$ . (7 marks)

Q5

For the network shown in Fig. 7, write the tie-set matrix and determine the loop currents and branch currents using network graph theory. (14 marks)

Q6

Answer the following:

a)

Synthesize the impedance function $Z(s) = \frac{(s^2 + 1)(s^2 + 3)}{s(s^2 + 2)}$ in second cauer form. (7 marks)

b)

Synthesize the impedance function $Z(s) = \frac{(s + 1)(s + 5)}{(s + 3)(s + 7)}$ in first Foster form. (7 marks)

Q7

For passive filter, derive the fundamental filter equation, with the help of this equation, derive the expressions for cut-off, frequency, attenuation constant and phase shift constant for constant-K low-pass filter. (14 marks)

Q8

Answer the following:

a)

In the circuit shown in Fig. 8, the switch is moved from a to b at $t = 0$ . Using Laplace transform find $i(t)$ for $t > 0$ , assuming that the switch was at position a for a long time. (7 marks)

b)

Derive the reciprocity condition for a two-port network in terms of h-parameters. (7 marks)

Q9

Answer the following:

a)

A reduced incidence matrix of a network graph is given below. Draw the oriented graph. $Ai = \begin{bmatrix} 1 & 1 & 0 & 0 & 0 & 0 & 1 \\ -1 & -1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & -1 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & -1 & -1 & -1 & 0 \end{bmatrix}$ (7 marks)

b)

Check the positive realness of the function $F(s) = \frac{s^2 + s + 6}{s^2 + s + 1}$ . (7 marks)

2016 031505

B.Tech Examination, 2016

Time 3 hours

Full Marks 70

Instructions:

There are Nine Questions in this paper.
Attempt Five questions in all.
Question No. 1 is compulsory.
The marks are indicated in the right-hand margin.

Questions

Q1

Answer the following:

Q2

Answer the following:

Q3

Answer the following:

Q4

Answer the following:

Q5

Answer the following:

Q6

Answer the following:

Q7

Answer the following:

Q8

Answer the following:

Q9

Answer the following:

2015 031505

B.Tech Examination, 2015

Time 3 hours

Full Marks 70

Instructions:

All questions carry equal marks.
There are NINE questions in this paper.
Attempt FIVE questions in all.
Question No. 1 is compulsory.

Questions

Q1

Answer the following:

Q2

Answer the following:

Q3

Answer the following:

Q4

Answer the following:

Q5

Answer the following:

Q6

Answer the following:

Q7

Answer the following:

Q8

Answer the following:

Q9

Answer the following:

2014 031505

B.Tech Examination, 2014

Time 3 hours

Full Marks 70

Instructions:

All questions carry equal marks.
There are NINE questions in this paper.
Attempt FIVE questions in all.
Question No. 1 is compulsory.

Questions

Q1

Answer the following:

Q2

Answer the following:

Q3

Answer the following:

Q4

Answer the following:

Q5

Answer the following:

Q6

Answer the following:

Q7

Answer the following:

Q8

Answer the following:

Q9

Answer the following:

2013 031505

B.Tech Examination, 2013

Time 3 hours

Full Marks 70

Instructions:

All questions carry equal marks.
There are NINE questions in this paper.
Attempt FIVE questions in all.
Question No. 1 is compulsory.

Questions

Q1

Answer the following:

Q2

Answer the following:

Q3

Answer the following:

Q4

Answer the following:

Q5

Answer the following:

Q6

Answer the following:

Q7

Answer the following:

Q8

Answer the following:

Q9

Answer the following: