Circuit Theory - May 2015

Electronics Engineering (Semester 3)

TOTAL MARKS: 80
TOTAL TIME: 3 HOURS (1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Assume data if required.
(4) Figures to the right indicate full marks. 1 (a) Find the thevnin's equivalent network for terminals A and B. (4 marks) 1 (b) For the network shown, the switch is closed at t=0. Find the current i₁(t) t>0. (4 marks) 1 (c) State the condition for reciprocity of h-parameter and prove it.(4 marks) 1 (d) Obtain S-domain equivalent circuit of an inductor and capacitor having non-zero initial conditions.(4 marks) 1 (e) What are scattering parameters. State their properties.(4 marks) 2 (a) In the given network, what will be the R_L to get maximum power delivered to it. Calculate power. (8 marks) 2 (b) For the network shown, determine the current i(t) when the switch is closed at t=0 with zero initial condition. (8 marks) 2 (c) List the types of damping in series R-L-C circuit and mention the condition for each damping.(4 marks) 3 (a) Design a single stub match for a load of (150 + j232.5)Ω for 75Ω transmission line at 500 Mhz using smith chart.(8 marks) 3 (b) Define T-parameters and relate them to other parameter as indicated
i) A and C in terms of z-parameters
ii) B in terms of y-parameter(6 marks) 3 (c) Compare Foster form-I and Foster form-II of an L.C. network. $$ Z(s) = \dfrac {6s(s^2+4)} {(s^2 +1) (s^2+64)}. $$(6 marks) 4 (a) Check the positive real functions $$ i) \ F(s) = \dfrac {s^2+ 6s+5}{s^2 +9s+14} \ and \\ ii) \ F(s)= \dfrac {s^3 + 6s^2 +7s +3}{s^2 + 2s+1} $$(8 marks) 4 (b) Derive an expression for characteristics equation of a transmission line. Also obtain α, β and γ of the line.(8 marks) 4 (c) What are standing waves. Define reflection coefficient and V.S.W.R. of a transmission line.(4 marks) 5 (a) Test whether the following polynomials are Hurwitz, use continuous fraction expansion. $$ i) \ s^7 + 2s^6 + 2s^5 + s^4 + 4s^3 + 8s^2 + 8s +4 \\ ii) \ s^4 + 2s^2 + 2 $$(10 marks) 5 (b) Find teh characteristics impedances, cut off frequency and passband frequency for given network. (5 marks) 5 (c) Obtain pole-zero plot for I₂/I₁. (5 marks) 6 (a) Two identical sections of the network shown are connected in cascade manner. Obtain the transmission line parameters of over all connection (8 marks) 6 (b) Find the current through 15-Ω resistor. (6 marks) 6 (c) Compare Cauer form-I and Cauer form-II of RC Network. $$ Z(s) = \dfrac {3(s+2)(s+6)} {s(s+4)}. $$(6 marks)