## Circuits and Transmission Lines - May 2015

### 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)** Determine y-parameter for the network.
(5 marks)

**1 (b)** The constants of a transmission line are R=6Ω/km, L=2.2 mH/Km.G=0.25×10^{-6} ℧/km, C=0.005×10^{-6} F/km.

Determine the characteristics impedance, propagation constant and attenuation constant at 1 KHZ. (5 marks)

**1 (c)** Test if F(S)=2S^{6}+4S^{5}+6S^{4}+8S^{3}+6S^{2}+4S+2 is a Hurwitz polynomial. (5 marks)

**1 (d)** The current I(S) in network is given by $$ I(S) = \dfrac {2(S)} {(S+1)(S+2)}. $$ Plot the pole-zero pattern in the S-plane and hence obtain i(t). (5 marks)

**2 (a)** Find the current through 10Ω resistor using Norton's theorem.
(10 marks)

**2 (b)** Find the current i(t) for t>0.
(10 marks)

**3 (a)** Find Foster I and Foster II forms of the driving points function: $$ F(S) = \dfrac {S^3 + 9S^2 + 23S + 15 } {S(S^3+ 12S^2 + 44S + 48)} $$ (10 marks)

**3 (b)** Determine ABCD parameters of the network shown:
(10 marks)
**4 (a)** A transmission line has a characteristics impedance of 150 Ω and terminated in a load Z_{L}=75 - J100&Omega. Using switch chart, find

i) VSWR

ii) Reflection coefficient

iii) Input impedance at a distance 0.1λ from the load.

iv) location of first voltage maximum and first voltage minimum from the load.(10 marks)

**4 (b)** Find I_{2} using mesh analysis.
(10 marks)

**5 (a)** For the network shown, capacitor C has an initial voltage V_{C}(-0) of 10V and at the same instant current in the inductor L is zero. The switch is closed at time t=0. Obtain the expression for voltage V(t) across the inductor L.
(10 marks)

**5 (b)** For the network shown, determine $$ \dfrac {V1} {I_1} \ and \ \dfrac {V_2} {I_1} $$ . Plot the poles and zeros.
(10 marks)

**6 (a)** For the network shown, find the equivalent T-network.
(10 marks)

**6 (b)** Derive condition for reciprocity in terms of Z parameters and symmetry in terms of h parameters. (10 marks)