SPPU Electronics and Telecom Engineering (Semester 5)
Electromagnetics and Transmission Lines
June 2015
Total marks: --
Total time: --
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

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 'ΡL'.
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 = 9ay A/m is locate at z=0. The region 1 which is at z<0 has μr1=4 and region 2 which is at z>0 has μr2=3.
Given H2 =14.5ax + 8az A/m Find H1.
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 (Z0 ) 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 Z0.
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 Z0
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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