EC-602 Antenna and Wave Propagation - May 2023 Question Paper

Under each question, How to answer lists the points an answer should cover, outlined by CampusPrep from the syllabus. Check the details against your textbook.

1. 7 Marks
   aDerive expressions for the components of the radiated field of an alternating current element.
   How to answer

   • Define alternating current element (Hertzian dipole) with assumptions
   • Write retarded vector potential and field relations
   • Derive $E_\theta, E_r, H_\phi$ components in spherical coordinates
   • Identify radiation (far-field) vs induction and electrostatic terms
2. 7 Marks
   bDefine antenna beam width and directivity and obtain the relation between them.
   How to answer

   • Define beam width (HPBW, FNBW) and directivity
   • Define radiation intensity and average power
   • Derive relation between directivity, beam area and beam width
   • Give approximate formula $D \approx 4\pi/\Omega_A$
3. 7 Marks
   aWhat is Retarded Potential? Explain different approaches to solve radiation Problems.
   How to answer

   • Define retarded potential with time delay $R/c$
   • Explain scalar and vector retarded potentials
   • Describe approaches: Maxwell equations, potential method, Poynting vector
   • Explain application to radiation problems
4. 7 Marks
   bProve the reciprocity theorem as applicable to antennas and hence show the equality of directional pattern for transmission and reception by same antenna.
   How to answer

   • State reciprocity theorem for antennas using two antennas with sources
   • Prove using Lorentz reciprocity / reaction concept
   • Show transfer impedance equality
   • Conclude transmit and receive directional patterns are identical
5. 7 Marks
   aIn order to scan the beam of a linear array to 300 off broad side. Calculate the inner element phase shift required if the elements are spaced at 3 cms and the frequency is 64 KHz.
   How to answer

   • Write beam scanning condition $\psi = kd\cos\theta + \beta$
   • Calculate wavelength from $f = 64\ \text{kHz}$
   • Substitute $d = 3\ \text{cms}$ and scan angle off broadside
   • Compute inter-element phase shift $\beta$
6. 7 Marks
   bAn end fire array consisting of several half wave length long isotropic radiators having directive gain of 30. Find the length of array for broad side antenna?
   How to answer

   • State directive gain formula for end-fire array
   • Relate gain $G=30$ to number of elements / length
   • Use half-wave isotropic radiator condition
   • Calculate array length
7. 7 Marks
   aDerive the construction and basic principles of operation of a helical antenna under

   1. i)Normal mode of operation
   2. ii)Axial mode of operation
   How to answer

   • Describe helical antenna construction: helix, ground plane, feed
   • Explain normal mode: dimensions $<< \lambda$, broadside radiation
   • Explain axial mode: circumference $\approx \lambda$, end-fire circular polarization
   • Give applications and radiation characteristics
8. 7 Marks
   bDesign Yagi-Uda antenna of 6 elements to provide gain of 12 dB if the operating frequency is 200 MHz.
   How to answer

   • State Yagi-Uda gain vs number of elements relation
   • Calculate wavelength at $200\ \text{MHz}$
   • Determine lengths of reflector, driven element and directors
   • Determine element spacings for 6-element $12\ \text{dB}$ design
9. 7 Marks
   aDerive an expression for radiated electric field strength of a traveling wave radiation of length 'l'.
   How to answer

   • Assume traveling wave current $I(z)=I_0 e^{-j\beta z}$ on length $l$
   • Integrate retarded vector potential contributions
   • Derive far-field $E_\theta$ expression
   • Discuss pattern dependence on $l/\lambda$
10. 7 Marks
    bDiscuss the principle of operation and the consideration which have to be gone into the design and construction of parabolic reflector antenna.
    How to answer

    • Explain paraboloid geometry and feed placement at focus
    • Explain collimation principle: spherical to plane wavefront
    • Discuss design factors: f/D ratio, aperture efficiency, feed blockage
    • Discuss construction: reflector surface, feed, supports
11. 7 Marks
    aExplain in detail Flat sheet and corner reflector antennas in detail.
    How to answer

    • Describe flat sheet reflector with dipole and image theory
    • Describe corner reflector geometry and angle
    • Compare radiation patterns and gain
    • Give applications
12. 7 Marks
    bA rectangular microstrip antenna is designed in such a way so that it will resonate at 2 GHz. The idealistic lossless substrate (RT/Duroid 6010.2) has a dielectric constant of 10.2 and a height of 0.05 in. (0.127 cm). Determine the physical dimensions (width and length) of the patch (in cm).
    How to answer

    • Calculate width $W$ using $c, f_r, \varepsilon_r$
    • Calculate effective dielectric constant and length extension $\Delta L$
    • Calculate effective and physical length $L$
    • Convert dimensions to cm
13. 7 Marks
    aDerive the relation between Maximum Usable Frequency (MUF) and skip distance.
    How to answer

    • Define MUF, critical frequency and skip distance geometry
    • Use secant law $MUF = f_c \sec\theta_i$
    • Relate incidence angle to earth geometry and virtual height
    • Derive $MUF$ vs skip distance formula
14. 7 Marks
    bDescribe the troposphere and explain how ducts can be used for Microwave propagation.
    How to answer

    • Describe troposphere structure and refractive index
    • Define duct formation: temperature inversion, humidity
    • Explain trapping and super-refraction mechanism
    • Explain use for extended microwave propagation
15. 7 Marks
    aShow that Ionosphere act as a variable refractive index medium.
    How to answer

    • Write Appleton-Hartree / refractive index formula with electron density
    • Show $n = \sqrt{1-81N/f^2}$ variation with height
    • Explain dependence on ionization density $N$
    • Conclude ionosphere as inhomogeneous variable-$n$ medium
16. 7 Marks
    bWhat is Critical Frequency? What is Virtual Height? Find the maximum distance that can be covered if the virtual height of the ionospheric layer is 250 kms.
    How to answer

    • Define critical frequency $f_c$ and virtual height $h_v$
    • Explain reflection condition and equivalent triangular path
    • Write skip/maximum distance formula in terms of $h_v$
    • Substitute $h_v = 250\ \text{kms}$ to find maximum distance