SPPU Electronics and Telecom Engineering (Semester 5)

Electromagnetics and Transmission Lines

June 2015

Electromagnetics and Transmission Lines

June 2015

Answer any one question from Q1 and Q2

1 (a)
Derive the expression for electric field intensity E at a point 'P' due to infinite line charge with uniform line charge density 'Ρ

_{L}'.
6 M

1 (b)
Derive Laplace and Poisson equations for electronics & hence state physical significance of Laplace & Poisson equations.

6 M

1 (c)
A current sheet k = 9a

Given H

_{y}A/m is locate at z=0. The region 1 which is at z<0 has μ_{r1}=4 and region 2 which is at z>0 has μ_{r2}=3.Given H

_{2}=14.5a_{x}+ 8a_{z}A/m Find H_{1}.
8 M

2 (a)
Derive the expression for the capacitance of spherical plate capacitor.

6 M

2 (b)
Derive expression for Biot & Savart law using magnetic vector potential.

6 M

2 (c)
\[ \overline D = \dfrac {5x^3} {2} \widehat a x \ c/m^2 . \] Prove divergence theorem for a volume of cube of side 1m. Centered at origin & edges parallel to the axis.

8 M

Answer any one question from Q3 and Q4

3 (a)
Define displacement current and displacement current density & hence show that \[ \nabla \times H = J_c + J_d \\
\begin {align*} where & J_c \rightarrow \ conduction \ current \ density \\ &J_d \rightarrow \ Displacement \ current \ density \end{align*} \]

8 M

3 (b)
Select values of K such that each of the following pairs of fields satisfies Maxwell's equation. \[
i) \ \overline E = (Kx - 100t) \overline a_y \ V /m \\ \ \ \overline H = (x+20t)\overline a_z \ A/m \\ \ \ \mu=0.25 H/m \ \varepsilon=0.01F /m \\ \\ ii) \overline D = 5x \widehat a_x - 2 y \widehat a_y + Kz \widehat a _z \ \mu c/ m^2 \\ \ \ \overline B = 2 \overline a_y \ mT \\ \ \ \mu = \mu_0 \ \varepsilon= \varepsilon_0 \]

8 M

4 (a)
What is mean by uniform plane wave, obtain the wave equation travelling in free space in terms of E.

8 M

4 (b)
Derive Maxwell's equations in differential and integral form for time varying and free space.

8 M

Answer any one question from Q5 and Q6

5 (a)
Derive the expression for characteristic impedance (Z

_{0}) and propagation constant (r) in terms of primary constants of transmission line.
8 M

5 (b)
A cable has an attenuation of 3.5dB/Km and a phase constant of 0.28 rad/km. If 3V is applied to the sending end then what will be the voltage at point 10 km down the line when line is terminated with Z

_{0}.
8 M

6 (a)
Explain the phenomenon of reflection of transmission line and hence define reflection coefficient.

6 M

6 (b)
A transmission line cable has following primary constants.

R=11 Ω / km, G=0.8 μ℧ / km

L=0.00367 H/Km C=8.35 nF/km

At a signal of 1 kHz calculate

i) Characteristic impedance Z

ii) Attenuation constant (α) in Np/Km

iii) Phase constant (β) in radians / Km

iv) Wavelength (λ) in Km

v) Velocity of signal in Km/sec.

R=11 Ω / km, G=0.8 μ℧ / km

L=0.00367 H/Km C=8.35 nF/km

At a signal of 1 kHz calculate

i) Characteristic impedance Z

_{0}ii) Attenuation constant (α) in Np/Km

iii) Phase constant (β) in radians / Km

iv) Wavelength (λ) in Km

v) Velocity of signal in Km/sec.

10 M

Answer any one question from Q7 and Q8

7 (a)
What is the impedance matching? Explain necessity of it, what is stub matching? Explain the single stub matching with its merits and demerits.

9 M

7 (b)
Explain standing wave and why they generate? Derive the relation between the SWR and magnitude of reflection coefficient?

9 M

8 (a)
What do you mean by distortionless line. Derive expression for characteristic impedance and propagation constant for distortionless line.

8 M

8 (b)
The VSWR on a lossless line is found to be '5' and successive voltage minima are 40 cm a part. The first voltage minima is observed to be 15 cm from load. The length of a line is 160cm and characteristic impedance is 300 Ω Using Smith chart find load impedance, sending end impedance.

10 M

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