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MU Electronics and Telecom Engineering (Semester 3)
Circuits and Transmission Lines
May 2016
Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

1(a) Determine Y-parameters for the network shown in fig 1(a)

5 M
1(b) Test if F(s) = S4+s3+5s2+3s+4 is a Hurwitz polynomial.
5 M
1(c) Two coils connected in series have self inductance 80 mH & 20 mH respectively
The total inductance of the circuit is found to 140 mH. Determine the
(i) mutual inductance between two coils and
(ii) The coefficient of coupling
5 M
1(d) Synthesize the following function into a network.
$$Z(s)=\dfrac{s^2+2s+2}{s^2+s+1}$$ using cauer -I form.
5 M

2(a) Find the Thevenin's equivalent across the terminals XY for the circuit shown in fig2(a)

10 M
2(b) Determine the node voltage at node (1) & (2) of the Network Shown in fig 2(b) by using nodal analysis.

5 M
2(c) Test Whether
$$F(s)=\dfrac{s(s+3)(s+5)}{(s+1)(s+4)}$$ is a positive real function.
5 M

3(a) Synthesize the driving point function using Foster-I and Foster-II form $Z(s)=\dfrac{2(s^2+1)(s^2+9)}{s(s^2+4)}$
10 M
3(b) State and prove Initial value theorem.
5 M
3(c) A transmission line has distributed parameters R=6 Ohms / km, L-2.2 mH/km C=0.005 μF/km & G=0.005 μ mho/km
Determine characteristics impedance and propagation constant at 1KHz frequency.
5 M

4(a) Find ABCD parameters for the two port Network shown in fig 4(a).

10 M
4(b) Find Network functions $$\dfrac{V_1}{I_1},\dfrac{V_2}{I_1},\dfrac{V_2}{V_1}$$ for the network shown in fig 4(b)

5 M
4(c) A transmission line has a characteristics impedance of 50+j 100Ω and is terminated in a load impedance of 73-j 42.5 Ω. Calculate
(a) The reflection coefficient
(b) The standing wave ratio.
5 M

5(a) The Network shown in fig 5(a), switch K is closed at t=0, Assume all initial conditions as zero. Find $$i,\frac{di}{dt}$$ & $$\dfrac{d^2i}{dt^2}\ \text{at}\ t=0^+$$

10 M
5(b) Write the KVL equations in standard form for the N/W shown in fig 5(b)

5 M
5(c) Find poles and zero of the impedance Z(s) for the Network Shown in fig 5(c)

5 M

6(a) Why is the Impedance matching required? Draw the following normalized quantities on the smith chart.
(i) (3+i3) Ω
(ii) (1.0) Ω
(iii) (2-j1) Ω
(iv) j 1.0 Ω
5 M
6(b) Write short note on:
Time domain analysis using Laplace Transform.
5 M
6(c) Define the following terms
(i) Phase Velocity
(ii) Characteristics impedance
(iii) Reflection coefficients
5 M

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