## 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 i_{1}(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 I_{2}/I_{1}.
(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)