## Antennas & Propagation - Dec 2014

### Electronics & Communication (Semester 6)

TOTAL MARKS: 100

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

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

(3) Assume data wherever required.

(4) Figures to the right indicate full marks.
**1 (a)** With the help of Maxwell's equation, explain how radiation and reception of EM takes place?(6 marks)
**1 (b)** Explain the following terms as related to antenna system:

i) Directivity ii) HPBW iii) Effective length iv) Beam efficiency.(8 marks)
**1 (c)** Show that the directivity for unidirectional operation is 2(n+1) for an intensity variation of U-U_{m}cos^{n}θ.(6 marks)
**2 (a)** Write a neat diagram, obtain an expression for maximum effective aperture of a λ/2 dipole.(7 marks)
**2 (b)** Derive relationship between effective aperture and directivity of an antenna.(8 marks)
**2 (c)** Find the maximum power received at a distance of 0.75 km over free space 110 MHz circuit consisting of a transmitting antenna of 30dB gain and a receiving antenna of 25dB gain. If the power i/p to the transmitting antenna is 120 watts.(5 marks)
**3 (a)** Starting from fundamentals derive the equation for radiation resistance of Hertzian dipole.(8 marks)
**3 (b)** A dipole antenna of length 5cm is operated at a frequency of 100MHz with terminal current, I_{0}-120mA. At time t=1 sec, 0=45° and r=3m, Find: (i) E_{r}; (ii) E_{θ} and (iii) H_{ϕ}(8 marks)
**3 (c)** Calculate the radiation resistance of a length=λ/5. (Assume triangular current distribution).(4 marks)
**4 (a)** Derive the far field expressions for small loop antenna.(8 marks)
**4 (b)** Derive an expression and draw the field pattern for an array of two isotropic point source with equal amplitude and opposites phase. Take d=λ/2.(8 marks)
**4 (c)** Find half power beam width directivity of a linear broadside array of four isotropic point sources of equal strength widht d=λ/2?(4 marks)
**5 (a)** Write explanatory note on: i) Folded-dipole antenna; ii) Yagi-Uda antenna.(10 marks)
**5 (b)** Find the length, L-H plane aperture and flare angles 0_{E} and θ_{H} of a pyramidal horn for which E-plane aperture is 10λ. Horn is fed by a rectangular wavelength with TE_{10} mode. Assume ?=0.2λ in E-plane and 0.375λ in H-plane. Also find E-plane, H-plane beam widths and directivity.(6 marks)
**5 (c)** A dish antenna operating at a frequency of 1.43 GHz has a diameter of 64mts and is fed by directional antenna. Calculate HPBW, BWFN and gain with respect to λ/2 dipole with even illumination.(4 marks)
**6 (a)** Write short notes on:

i) Parabola reflectors

ii) periodic antenna(12 marks)
**6 (b)** Determine the cut off frequencies and bandpass of a log periodic dipole array with a design factor of 0.7. Ten dipoles are used in the structure, the smallest having a dimension L/2 equal to 0.3m.(8 marks)
**7 (a)** Define a wave tilt of a surface wave propagation. Also prove that wave tilt $$ \alpha = \tan^{-1} \dfrac {E_n}{E_v} = \tan ^{-1} \left [ \dfrac {1}{\sqrt{\epsilon_r}} \cdot \dfrac {1}{[1+x^2]^{1/4}} \right ] $$(10 marks)
**7 (b)** Derive the expression for resultant field strength at a point due to space wave propagation.(5 marks)
**7 (c)** For a VHF communication link, a 35 watt transmitter is operating at 90MHz. Determine the distance up to which LOS would be possible given that height of the transmitting and receiving antenna are 40 m and 25m respectively. Evaluate the held strength at the receiving point.(5 marks)
**8 (a)** Define the following: i) MUF; ii) Critical frequency; iii) Virtual height; iv) Skip distance.(8 marks)
**8 (b)** Calculate the value of the operating frequency of the ionosphere layer specified by refractive index of 0.85 and an electron density 5×10^{5} electron/m^{3}. Calculate the critical frequency and MUF of the system with θ_{1}=30°.(6 marks)
**8 (c)** Calculate the critical frequencies for f_{1}, f_{2} and f_{3} and E layers, for which the maximum ionic densities are 2.3×10^{6}, 3.5×10^{6} and 1.7×10^{6} elections/cm^{3} respectively.(6 marks)