THEORY EXAMINATION (SEM–VI) 2016-17 ANTENNA AND WAVE PROPAGATION

ANTENNA AND WAVE PROPAGATION (NEN023)

Time: 3 Hours  Max Marks: 100

SECTION – A (Short Answer Questions)

(10 × 2 = 20 Marks)

(a) Directional antenna efficiency & directivity of isotropic antenna

A directional antenna concentrates radiated power in a particular direction, hence it has higher efficiency than an isotropic antenna which radiates equally in all directions.
Directivity of isotropic antenna:

D=1(0 dB)D = 1 \quad (0\,\text{dB})D=1(0dB) 

(b) Parameters for receiving antenna design

Important parameters are:                                             Gain

Directivity                                                                       Bandwidth

Polarization                                                                    Input impedance

Effective aperture

(c) Disadvantages of binomial array

Low directivity                                                                Broad beamwidth

Reduced gain compared to uniform arrays                   Complex amplitude distribution

(d) Relation for electric field strength

Electric field strength at distance d:                              E∝1dE \propto \frac{1}{d}E∝d1​

Thus, as distance increases, electric field strength decreases.

(e) Why sky wave propagation is not possible above 30 MHz

At frequencies above 30 MHz, ionospheric layers cannot reflect radio waves back to earth due to insufficient electron density.

(f) Broadside vs End-fire array

(g) Radiation pattern for U=Umcos⁡θU = U_m \cos \thetaU=Um​cosθ

Unidirectional: Single main lobe                           Bidirectional: Two lobes opposite to each other

(h) Directivity over half-sphere

Directivity:    D=2D = 2D=2 

(i) Power gain of paraboloidal reflector

Given aperture = 10λ10\lambda10λ:

G=(πDλ)2=(10π)2G = \left(\frac{\pi D}{\lambda}\right)^2 = (10\pi)^2G=(λπD​)2=(10π)2 GdB=20log⁡10(10π)≈29.9 dBG_{dB} = 20\log_{10}(10\pi) \approx 29.9\,\text{dB}GdB​=20log10​(10π)≈29.9dB 

(j) HPBW and BWFN

HPBW: Half Power Beam Width                           BWFN: Beam Width Between First Nulls

Relation:

D∝1BeamwidthD \propto \frac{1}{\text{Beamwidth}}D∝Beamwidth1​ 

SECTION – B (Long Answer Questions)

(Attempt any FIVE – 5 × 10 = 50 Marks)

2(a) Aperture & Effective Aperture

Aperture is the physical area that intercepts energy.
Effective aperture:                                                 Ae=Gλ24πA_e = \frac{G\lambda^2}{4\pi}Ae​=4πGλ2​

If gain is reduced to ¼, effective aperture also becomes ¼.

2(b) Maximum received power (Friis equation)

Given:
Distance = 0.5 km
Frequency = 1 GHz                                              Pt=150 WP_t = 150\,WPt​=150W
Gt=25 dBG_t = 25\,dBGt​=25dB                           Gr=20 dBG_r = 20\,dBGr​=20dB

Using Friis formula:

Pr=PtGtGr(λ4πR)2P_r = P_t G_t G_r \left(\frac{\lambda}{4\pi R}\right)^2Pr​=Pt​Gt​Gr​(4πRλ​)2

Substituting values gives the maximum received power.

2(c) Antenna array & normalized field

An antenna array is a group of radiating elements arranged to obtain desired radiation characteristics.

For uniform linear array:

Enorm=sin⁡(Nϕ/2)Nsin⁡(ϕ/2)E_{norm} = \frac{\sin(N\phi/2)}{N\sin(\phi/2)}Enorm​=Nsin(ϕ/2)sin(Nϕ/2)​ 

2(d) MUF & ionospheric refraction

MUF (Maximum Usable Frequency):

MUF=fcsec⁡θ\text{MUF} = f_c \sec \thetaMUF=fc​secθ

Radio waves bend due to gradual change in refractive index of ionosphere.
Ionosphere consists of D, E, F₁, F₂ layers.

2(e) Corner vs Parabolic reflector & reciprocity theorem

Comparison:

Reciprocity theorem:
Transmission and reception characteristics of an antenna are identical.

Mutual impedance:

Zm=V2I1Z_m = \frac{V_2}{I_1}Zm​=I1​V2​​ 

2(f) Binomial array & end-fire numerical

Far-field pattern derived using pattern multiplication.

Given directivity = 30 (end-fire array):
Array length and beamwidth calculated using standard formulas.

For broadside array, length is smaller and beamwidth is wider.

2(g) Small loop antenna & Yagi antenna

Small loop antenna far-field:

Eθ∝IAsin⁡θrE_\theta \propto \frac{I A \sin\theta}{r}Eθ​∝rIAsinθ​

Yagi antenna:
Highly directional antenna with one reflector, one driven element, and multiple directors.

Design for 61–68 MHz includes spacing ≈ 0.2λ.

2(h) Rhombic antenna

Rhombic antenna works on traveling wave principle.
Maximum field intensity is obtained by proper choice of side length and termination resistance.

SECTION – C (Very Long Answer Questions)

(Attempt any TWO – 2 × 15 = 30 Marks)

3(a) Directivity of end-fire array

For two isotropic sources:

D=2[1+sin⁡(2πdλ)]1+(2πdλ)D = \frac{2\left[1+\sin\left(\frac{2\pi d}{\lambda}\right)\right]}{1+\left(\frac{2\pi d}{\lambda}\right)}D=1+(λ2πd​)2[1+sin(λ2πd​)]​ 

3(b) Beamwidth and directivity

Directivity:

D=41257θEθHD = \frac{41257}{\theta_E \theta_H}D=θE​θH​41257​ 

4(a) Radiation resistance

Radiation resistance of short dipole:

Rr=80π2(Lλ)2R_r = 80\pi^2\left(\frac{L}{\lambda}\right)^2Rr​=80π2(λL​)2 

4(b) Critical frequency and skip distance

Critical frequency: Highest frequency returned vertically

Virtual height: Apparent reflection height

Skip distance: Minimum distance for sky wave return

Silence zone: Region without reception

5(a)–(c) Short Notes

VLF & LF antennas: Very large size, used for submarine communication

Ground wave propagation: Earth conductivity affects attenuation

Conical spiral antenna: Frequency independent, wide bandwidth