## 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)