## Network Theory - Jun 2015

### 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)** Obtain Thevenin and Norton equivalent circuits for the network shown in fig. 1
(6 marks)
**1 (b)** For the graph and tree given in Fig. 2. find complete incidence matrix, tieset matrix and F-cutset matrix:
(6 marks)
**2 (a)** For the network shown in Fig. 3, determine the current I_{2} using superposition theorem.
(6 marks)
**2 (b)** For the given incidence matrix, draw oriented graph and determine number of possible trees. $$ A=\begin{bmatrix}
-1&\ 1 &\ 1 &\ 0 &\ 0 &\ 0 \\ \ 0
&-1 &\ 0&-1 &\ 1 & \ 0 \\ \ 0
&\ 0 &-1 &\ 1 &\ 0 &\ 1
\end{bmatrix} $$(6 marks)

### Answer any one question from Q3 and Q4

**3 (a)** Find the expression for V_{c}(t) in the network shown in Fig .4.
(6 marks)
**3 (b)** A series resonant circuit consists of R=10Ω, L=100 mH and C=10 nF. Find resonant frequency ω_{r}, F_{r}, quality factor Q_{r} at resonant frequency, bandwidth. Also find current flowing through circuit at resonance if the applied voltage is 100V.(6 marks)
**4 (a)** For the network shown in Fig. 5, obtain the expression for i_{L}(t).
(6 marks)
**4 (b)** A parallel resonant circuit has a coil of 100 μH with Q factor of 100 and is resonated at 1 MHz. Find:

i) Capacitance

ii)o Resistance of coil

iii) Bandwidth

iv) Impedance at parallel resonance.(6 marks)

### Answer any one question from Q5 and Q6

**5 (a)** A Pi-section constant K filter consists of series arm inductance of 20 mH and two shunt arm capacitors of 0.1 μF each. Calculate cut-off frequency, attenuation at 1.5 kHz. Also find nominal impedance Z_{π} at f=0 and f=f_{c}.(7 marks)
**5 (b)** For a T-section symmetrical network derive the expression for Z_{oc}, Z_{sc} and characteristic impedance Z_{o}.(6 marks)
**6 (a)** For the system with 500 Ω resistance design T and Pi attenuators to have 100 dB attenuation. Also draw T and Pi attenuators showing the designed component values.(7 marks)
**6 (b)** Draw the T section and Pi section contant K Band pass filter circuits and write equations for components in series arm and shunt arm(6 marks)

### Answer any one question from Q7 and Q8

**7 (a)** Explain different network functions for one port and two port networks.(7 marks)
**7 (b)** Determine Z parameters for the network shown in Fig 6.
(6 marks)
**8 (a)** Determine the impedance function Z(s) for the network shown Fig. 7. Also draw its pole zero plot.
(7 marks)
**8 (b)** Determine Y parameters of the network shown in Fig. 8
(6 marks)