Circuits and Transmission Lines - Dec 2012

Electronics & Telecomm. (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) For maximum power transfer find the value of Z_L if
(i) Z_L is impedance
(ii) Z_L is pure resistance :
(5 marks) 1 (b) find initial value of, f(t)= 20-10t-e^-25t
verify using initial value theorem. (5 marks) 1 (c) In the network given below, initial value of I_L =4A and V_C=100. Find I_C(0⁺):
(5 marks) 1 (d) Current I₁ and I₂ entering at 1 and port 2 respectively of two port network are given by following equation.
I₁ =0.5V₁ - 0.2V₂
I₂ = -0.2V₁ +V₂
Obtain T and Π(pi) representation. (5 marks)

Attempt any FOUR from the following

1 (e) For network shown, find V_C /V and draw pole-zero plot.
(5 marks) 2 (a) Using mesh analysis find power supplied by the dependent source.
(10 marks) 2 (b) Find current supplied by source.
(10 marks) 3 (a) Write B and Q matrix for the Graph shown.
(10 marks) 3 (b) Draw Bode plot for the function G(s). Find gain margin, phase margin and comment on stability.
$$ G(s)= \frac{2(s+0.25)}{s^2(s+1)(s+0.5)} $$(10 marks) 4 (a) Switch is opened at t=0 with initial conditions as shown. Find
$$ v_1, \frac{dv_1}{dt}, \frac{dv_2}{dt}\ at \ time\ 0^+ $$
(10 marks) 4 (b) Find Y parameter using interconnection:
(10 marks) 5 (a) In the network key is closed at t=0. Find i₁ (0⁺), i₂(0⁺ and i₃ (0⁺).
(10 marks) 5 (b) Find i(t).
(10 marks) 6 (a) The circuit attain steady state with switch at position (a) & is moved to position (b) at t=0. Find V(t) for t ≥ 0.
(10 marks) 6 (b) Find Z₁₁, Z₂₁ and G₂₁
(10 marks) 7 (a) Realize following functon in Foster II form

$$ Z(s)=\frac{(s^2+1)(s^2+3)}{s(s^2+2)(s^2+4)} $$ (10 marks) 7 (b) Check following polynomials for Hurtwitz -
$$ \ \left(i\right)\ \ p\left(s\right)=S^4+4s^2+8 $$

$$ \left(ii\right)\ \ p\left(s\right)=s^4+s^3+5s^2+3s+4 $$(10 marks)