1 (a)
Prove that F(s)=(s+?) where ? is a non-zero positive integers, is Hurwitz. Hence show that the polynomial P(s)=(s+6)

^{2}(s+4)^{6}is also Hurwitz.
5 M

1 (b)
State and prove initial Value Theorem.

5 M

1 (c)
Determine the ABCD parameters of the netwrork shown in fig. 1(c) considering the network as a cascade of two sub-networks.

5 M

1 (d)
Find Foster I and II, and Cauer I and II circuits for the driving point admittance \[ Y(s)= \dfrac {s^2+1}{s} \] Comment on your result.

5 M

2 (a)
Find the value of the variable resistance R in the circuit shown in Fig. 2(a) such that the power delivered to the load resistance R

_{i}=2 ohm is maximum. Evaluate the maximum value of the power.

10 M

2 (b)
Two identical 2-port networks are connected in cascade. If the y-parameters of each network are y

_{11}=-y_{12}=-y_{21}-y_{22}=10 mho determine the y-parameters of the composite network.
5 M

2 (c)
In the circuit shown in Fig. 2(c) find V

_{x}.

5 M

3 (a)
Test if \[ Z(s)=\dfrac {(s+1) (s+9)}{s(s+4)} \] represents a diving point impedance of an RL, RC or LC circuit. Sketch Z(σ) or Z(ω) curves whichever is applicable. Fost Foster II canonical circuit for the function.

10 M

3 (b)
State and prove Final Value Theorem.

5 M

3 (c)
The parameters of a transmission line are: 0.25 ? mho/km, 6&Omega/km, 2.22 mH/km, 005 ?F/km. Find the characteristics impedance Z

_{0}and propagation constant ? at 1 Khz.
5 M

4 (a)
Derive an expression for current I in the circuit shown in Fig 4(a) under the condition ?

^{2}LC=0.5, where ? is the radian frequency of the ac voltage V. Hence show that |I| is independent of the impedance Z_{x}.

10 M

4 (b)
Test if \[ F(s) = \dfrac {s^3+10s^2+27s+18}{(s+1)(s+3)(s+5)} \] is a Positive Real Function. Realize the function as driving point impedance in Foster I form.

5 M

4 (c)
Determine V

_{1}for the network shown in Fig. 4(c) when L=CR^{2}and V_{1}is a pulse of height 10V and width 1 S.

5 M

5 (a)
A unit step voltage is applied to a circuit consisting of only passive elements (each has numerical value I). The current supplied by the source is exponentially decreasing as shown in Fig. 5(a). Find the circuit with the minimum number of elements possible.

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5 (b)
Define and give the significance of the following:

i) Characteristics Impedance

ii) Propagation constant

iii) Reflection coefficient

i) Characteristics Impedance

ii) Propagation constant

iii) Reflection coefficient

5 M

5 (c)
State the conditions for a reciprocal 2-port network in terms of y-parameters and then convert it in terms of ABCD parameters.

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6 (a)
Write a brief note on Smith chart under the following heads.

i) VSWR circles

ii) Characteristics

iii) Applications.

A lossless 75? transmission line is terminated by an impedance of 150+j150?. Using Smith chart determine the following.

i) VSWR

ii) reflection coefficient

i) VSWR circles

ii) Characteristics

iii) Applications.

A lossless 75? transmission line is terminated by an impedance of 150+j150?. Using Smith chart determine the following.

i) VSWR

ii) reflection coefficient

10 M

6 (b)
Find Thevenin resistance of the circuit shown in Fig. 6(b) across the terminals AB.

5 M

6 (c)
Determine the Laplace transform of v

_{1}(t) shown in Fig. 6(c)(i). Hence find the Laplace transform of v_{2}(t) shown in Fig. 6(c)(ii).

Fig. 6(c)(i)

Fig 6(c)(ii)

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