Network Theory - Dec 2014

Electronics & Telecom Engineering (Semester 3)

TOTAL MARKS: 100
TOTAL TIME: 3 HOURS (1) Question 1 is compulsory.
(2) Attempt any four from the remaining questions.
(3) Assume data wherever required.
(4) Figures to the right indicate full marks.

Answer any one question from Q1 and Q2

1 (a) Calculate the current I through 6Ω resistor by applying principle of superposition. (6 marks) 1 (b) The reduced incidence matrix of an oriented graph is: $$A=\begin{bmatrix} 0 &-1 &1 &0 &0 \\0 &0 &-1 &-1 &-1 \\-1 &0 &0 &0 &1 \end{bmatrix} $$ Draw the oriented graph. Also calculate the number of trees possible for this graph.(6 marks) 2 (a) Find the value of load impedance Z_L, so that maximum power can be transferred to it in the circuit shown below. Draw Thevenin's equivalent circuit. (6 marks) 2 (b) Write the incidence matrix, tieset matrix and f-cutset matrix for the graph of a network given below. Select tree {4, 5, 6}. (6 marks)

Answer any one question from Q3 and Q4

3 (a) For the network shown below, find the current expression i.e. i(t) when the switch is changed from the position 1 to 2 at t = 0. (6 marks) 3 (b) In a series RLC circuit, a maximum current of 0.1 A flows through the circuit when the capacitor is of 5 ?F with a fixed frequency and a voltage of 5 V. Determine the frequency at which the circuit resonates, the quality factor, the value of resistance and the bandwidth. (6 marks) 4 (a) In the figure given below, the switch is closed at t = 0. Find:
$$ i, \dfrac {di}{dt} \ and \ \dfrac {d^2i}{dt^2} \ at \ t=o^+ $$ (6 marks) 4 (b) Derive the expression for bandwidth of a series RLC resonance circuit.(6 marks)

Answer any one question from Q5 and Q6

5 (a) Explain the following terms used in filter theory:
(i) Attenuation constant,
(ii) Phase constant, and
(iii) Characteristic impedance(6 marks) 5 (b) Write a short note on attenuators. Also derive the relation between decibel and Neper.(7 marks) 6 (a) A π section filter network consists of a series arm inductor of 20 mH and two shunt-arm capacitors of 0.16 μF each. Calculate the cut-off frequency, attenuation and phase shift at 15 kHz.(6 marks) 6 (b) Design a T-section band-pass, constant K type filter with cut- off frequency of 4 kHz and 10 kHz and nominal characteristic impedance of 500 Ω.(7 marks)

Answer any one question from Q7 and Q8

7 (a) Find Y-parameters of the network shown below: (6 marks) 7 (b) Explain the following:
i) Network functions for one and two port networks.
ii) Pole-zeros of network functions. Also state its significance.(7 marks) 8 (a) Calculate the open-circuit impedance parameters for the network shown below and also check for symmetry and reciprocity of the network. (6 marks) 8 (b) Determine the voltage transfer function $$ \dfrac {V_2}{V_1},$$ for the network shown below. (7 marks)