SPPU Electronics and Telecom Engineering (Semester 5)

Electromagnetics and Transmission Lines

December 2015

Electromagnetics and Transmission Lines

December 2015

Solve any one question from Q1 and Q2

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

_{s}'.
6 M

1 (b)
Derive the expression for the capacitance of spherical plate capacitor.

6 M

1 (c)
A current sheet ( \overline K = 9\widehat a y ) A/M is located at Z=0. The region 1 which is at Z<0 has μr

Given: ( \overline H_2 = 14.5\overline a_x + 8 \widehat a z ) A/M.

Find H

_{1}=4 and region 2 which is at Z>0 has μr_{2}=3Given: ( \overline H_2 = 14.5\overline a_x + 8 \widehat a z ) A/M.

Find H

_{1}
8 M

2 (a)
Derive the expression for the capacitance of parallel 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. Centened at origin & edges parallel to the axis.

8 M

Solve any one question from Q3 and Q4

3 (a)
Select values of K such that each of the following pairs of fields satisfies Maxwells's equation [ i) \ \overline E = (K_x - 100t)overline ab_y \ v/m \
\ \ \overline H= (x+20t) \overline a_z \ A/m \ \
\mu = 0.25 \ H/m \ \epsilon =0.01 \ F/m. \
ii) \ \overline D = 5x\overline a \ x-2y \ \overline a \ y+kz \ \overline a z \ \mu c /m^2 \
\ \overline {B} = 2 \overline a_y \ mT \ \ \mu = \mu_0 \ \epsilon = \epsilon_0
]

8 M

3 (b)
Define displacement current and displacement current density & hence
show that ∇×H=Jc+Jd

where JC → conduction current density

Jd → displacement current density.

where JC → conduction current density

Jd → displacement current density.

8 M

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

8 M

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

8 M

Solve any one question from Q5 and Q6

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

6 M

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

R=11Ω/km

G=0.8 μmho/km

L=0.00367 H/km

C=8.35 nF/km.

At a signal of 1 KHz calculate

i) Characteristic impedance Zo

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=11Ω/km

G=0.8 μmho/km

L=0.00367 H/km

C=8.35 nF/km.

At a signal of 1 KHz calculate

i) Characteristic impedance Zo

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

6 (a)
A cable has an attenuation of 3.5 dB/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 10km down the line when line is terminated with Zo.

8 M

6 (b)
Derive the expression for characteristic impedance (Zo) and propagation constant (r) in terms of primary constants of transmission line.

8 M

Solve any one question from Q7 and Q8

7 (a)
Derive the expression for input impedance of a transmission line. Hence
state the effect of open circuit & short circuit of line or input impedance.

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 is impedance matching? Explain necessity of it, What is stub matching?
Explain the single stub matching with its merits & demerits.

8 M

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

10 M

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