MU Electronics and Telecom Engineering (Semester 4)
Wave Theory & Propagation
December 2016
Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary


1(a) Given the potential V=2x2y-5z(V) and a point P (-4, 3, 6) find
a) Electric field intensity at P
b) Electric flux density at P
c) Volume charge density at P
5 M
1(b) State the Maxwell's equations for good dielectric in integral and point for Also state their significance.
5 M
1(c) Explain Super refraction.
5 M
1(d) With the help of neat schematic diagram, explain the working of an Electromagnetic Pump.
5 M
1(e) Compare MOM, FEM and FDM.
5 M

2(a) Teo extensive homogeneous isotropic dielectrics meet on plane z=0. For z>0, εr1=4 and for z<0, εr2=3. A uniform electric field \( \vec{E_1}=5\hat{a_x}-2\hat{a_y}+3\hat{a_z}(kV/m)\)/ exists for z≥0. Find a)\[\vec{E_2}\ \ \text{for} z\leq 0.
b) The angles E1 and E2 make with the interface.
10 M
2(b) State Poynting teorem. Write its final expression and explain the meaning of each term.
5 M
2(c) Obtain the reflection and transmission coefficient of a prependicular polarized wave incident between a dielectric-dielectric boundary with an oblique incidence.
5 M

3(a) Determine the potential at the free nodes in the potential system of Fig.1. using Finite Difference Method ( Band Matrix Method)
!mage
10 M
3(b) Derive Helmholtz equations for electromagnetic fields in free space.
5 M
3(c) Fot the normal incidence, determine the amplitudes of reflected and transmitted \[\vec{E}\ \ \text{and}\ \ \vec{H}\] at interface of two regions at z=0 Given: Incident Ei<\sub>1.5×10-3 (V/m); εr1=8.5; μr1=1; σ=0. Second region is free space.
5 M

4(a) State and drive FRISS transmission euquation.
10 M
4(b) Calculate skin depth and wave velocity at 1.6 Mhz in aluminum with the conductivity 38.2 mS/m and μr=1.
5 M
4(c) What is ionosphere? Which layers are present during day and night time? Where maximum attenuation of electromagnetic waves takes place inside the ionosphere?
5 M

5(a) Obtain an expression of MUF in terms of d, H and fe. If a high frequency communication link is to be established between two points on the Earth 2000 km away, and the reflection region of ionosphere is at height of 200 km and has critical frequency of 5 Mhz, then calculate the MUF for the given path.
10 M
5(b) The receiving antenna is located at 80 km from the transmitting antenna. The height of transmitting antenna is 100m. Find the required height of receiving antenna.
5 M
5(c) Explain the formationn of inversion layer in troposphere.
5 M

6(a) Consider a two element mesh as shown in Fig.2. Using FEM determine the potentials at free nodes.
Node (x,y)
1 (0.8, 1.8)
2 (1.4, 1.4)
3 (2.1, 2.1)
4 (1.2, 2.7)

!mage
10 M
6(b) Define critical frequency as a measure of ionospheric propagration and determine critical frequency for reflection at vertical incidence if the maximum value of electron density is 1.24×106 per CC.
5 M
6(c) Explain formation of duct and condition for duct propagation.
5 M



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