1 (a)
Determine the ABCD parameter of the network shown in fig. No. 1(a)

5 M

1 (b)
Test whether P(s)=S

^{5}+12S^{4}+45S^{3}+60S^{2}+44S+48 is Hurwitz polynomial.
5 M

1 (c)
The combined inductance of two coils connected in series is 0.6 H or 0.1 H depending on relative directions of currents in the two coils. If one of the coil has a self inductance of 0.2 H. Find (a) Mutual inductance (b) Coefficient of coupling.

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1 (d)
Find Foster I and II Cauer I and II Circuits for the driving points admittance \( y(s) = \dfrac {s^2+1}{s} \)

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2 (a)
Find the current in the 10Ω resistor using Thevenin's theorem for the network shown in fig 2(a).

10 M

2 (b)
Find the value of V

_{x}in the network shown in fig 2(b) using nodal analysis.

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2 (c)
Check if the following polynomials are Hurwitz polynomials

i) S

ii) S

i) S

^{5}+ S^{3}+ Sii) S

^{4}+ S^{3}+ 2S^{2}+ 3S +2.
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3 (a)
Synthesize the driving point function \(F(s) = \dfrac {(S^2 +1)(S^2+3)}{S(S^2+2)}\) when F(s) is a driving point (i) Impedance (ii) Admittance

Test if the circuit obtained are canonic:

Test if the circuit obtained are canonic:

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3 (b)
State and prove initial value theorem.

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3 (c)
The parameters 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 and propagation constant at a frequency of 1 GHz.
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4 (a)
Determine z and y parameters of the network shown in fig 4(a).

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4 (b)
Determine the voltage transfer function \( \dfrac {v_2}{v_1} \) for the network shown in fig 4(b).

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4 (c)
Test whether \( F(s)= \dfrac {2S^3 + 2S^2 + 3S+2}{S^2+1} \) is a positive Real Function.

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5 (a)

The network shown in fig 5(a), a steady state is reached with the switch open. At t=0 the switch is closed. Determine V_{C}(0^{-}), i_{1}(0^{+}), i_{2}(0^{+}), \( \dfrac {di_1}{dt}(0^+) \text{ and }\dfrac {di_2}{dt}(0^+) \)

10 M

5 (b)
Find the voltage across the 5Ω resistor in network shown in fig, 5(b).

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5 (c)
Find the function v(t) using the pole-zero of the following function. \( V(s) = \dfrac {(S+2)(S+6)}{(S+1)(S+5)} \).

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6 (a)
A unit impulse applied to two terminal black box procedure a voltage V

_{O}(t)=2e^{-t}-e^{-3t}. Determine the terminal voltage when a current pulse of 1A heigh and a duration of 2 seconds in applied at the terminal.

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6 (b)
Determine the driving point impedance of the network shown in fig. 6(b)

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6 (c)
Draw the following normalized quantities on the smith chart:

(2 + j2)Ω

ii) (4-j2)Ω

iii) (1,0)Ω

iv) (j1, 0)Ω

(2 + j2)Ω

ii) (4-j2)Ω

iii) (1,0)Ω

iv) (j1, 0)Ω

5 M

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