## Wave Theory & Propagation - May 2014

### Electronics & Telecomm. (Semester 4)

TOTAL MARKS: 80

TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.

(2) Attempt any **three** from the remaining questions.

(3) Assume data if required.

(4) Figures to the right indicate full marks.
**1(a)** Identify the type of polarization of the Electromagnetic wave with the following Electric fields and justify the same$$ i) \overrightarrow{E} = \sin (\omega t - \beta z)a_x + \sin\left(\omega t - \beta z + \dfrac {\pi}{2}\right )a_y \\ \\
ii) \overrightarrow{E} \left [ E_1 \cos (\omega t)a_x - E_2 \sin (\omega t) a_y \right ]e^{-j\beta z} \ \ \ \ \ \ \ \ \ $$(5 marks)
**1(b)** With regards to the ionosphere discuss the following

i) E Layer

ii) Sporadic E layer(5 marks)
**1(c)** Derive the boundary condition for electric and magnetic field.(5 marks)
**1(d)** With the help of a neat schematic,Explain the working of an electromagnetic pump.(5 marks)
**1(e)** What do you mean by depth of penetration?(5 marks)
**2(a)** state and Explain Faradays Law in both the integral and differential form?(5 marks)
**2(b)** Four 40nC charges are located at A (1,0,0), B(-1,0,0 ), C(0,1,0) and D(0,-1,0). Determine the total force on the charge at A.(5 marks)
**2(c)**

The coefficient matrix for two elements as shown below are given by

$$ C^{(1)} = \begin{bmatrix} 1.2357 &-0.7786 &-0.4571 \\-0.7786 &0.6929 &0.0857 \\-0.4571 &0.0857 &0.3714 \end{bmatrix} \ \ and \ \ \\ C^{(2)} = \begin{bmatrix} 0.5571 &-0.4571 &-0.1 \\-0.4571 &0.8238 &-0.3667 \\-0.1 &-0.3667 &0.4667 \end{bmatrix} \ \ \ \ \ \ \ $$

Determine the global coefficient matrix.

(5 marks)
**2(d)**

Determine the shape function a_{1}, a_{2}, a_{3} from the following element.

(5 marks)
**3(a)** State and explain Maxwells equation in free space integral and differential form.hence explain the difference between conduction and displacement current.(5 marks)
**3(b)** A media has the following properties μ_{r}=8,ϵ_{r}=2,σ=10_{-4}mhp/m at 2Ghz

Determine

(i) attenuation constant

(ii) attenuation constant in db

(iii) phase constant

(iv) propagation constant

(v) wavelength

(vi) phase velocity

(vii) intrinsic impedance

(viii) refractive index

(ix) loss tangent

(x) is the media behaving like a conductor or dielectric.(10 marks)
**4(a)** Derive wave equation in free space(10 marks)
**4(b)** State the Poynting theorem.write its final expression hence explain the mennino of each term.(5 marks)
**4(c)** Solve Laplace's Equation $\Delta^2V=0; \ 0 \leq x \le 1; \ 0 \le y \le 1$ $with \ V(x,1) = 45x (1-x); \ V(x,0)= V(0,y) = V(1, y) =0.$ Assume mesh size as 0.5
(5 marks)
**5(a)** Obtain the reflection and transmission coefficient of a parallel polarized wave incident between a dielectric boundary with an oblique incidence(10 marks)
**5(b)** An electromagnetic wave is incident from air to an medium with dielectric constant 5 and relative permeability 80.If the angle of incidence of 58°determine the angle of reflection and refraction.(10 marks)
**5(c)** what polarization is transmitted in ground wave propagation and why?Hence typically till what is ground wave propagation effective.(5 marks)
**6(a)** Explain Super refraction and tropospheric fading(5 marks)
**6(b)** What is virtual height of a layer? Why is it called so? Is it more or less than the actual height of the layer
(10 marks)
**6(c)** What is ionosphere? Which layers are present during day and night time? Where does maximum attenuation of an electromagnetic wave take place inside the ionosphere? Hence define frequency.
(5 marks)