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 I₂ 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)