If the effective area of an antenna becomes \(\frac{2A}{3}\) from its initial value of 'A', while keeping its operating frequency same. Then, the antenna gain becomes \(\left(\frac{2x+4}{15}\right)\) times of its initial value. The value of x will be:
3
The governing relation. The gain of an antenna and its effective aperture (effective area) are linked by
\(G = \dfrac{4\pi A_e}{\lambda^{2}}\)
What is held constant. The operating frequency is unchanged, so λ is unchanged and the factor \(4\pi/\lambda^{2}\) is a constant. Therefore the gain is directly proportional to the effective area:
\(G \propto A_e\)
Step 1 — form the ratio of the new gain to the old.
\(\dfrac{G_{new}}{G_{old}} = \dfrac{A_{e,new}}{A_{e,old}} = \dfrac{2A/3}{A} = \dfrac{2}{3}\)
Step 2 — equate to the expression given in the question.
\(\dfrac{2x+4}{15} = \dfrac{2}{3}\)
Step 3 — cross-multiply and solve.
\(2x+4 = \dfrac{2}{3}\times 15 = 10\)
\(2x = 6 \Rightarrow x = 3\)
Verify. Putting x = 3 back: \((2\times3+4)/15 = 10/15 = 2/3\) ✓, which matches the area reduction of one third.
Concept behind the formula. Effective aperture is the area from which the antenna appears to "collect" incident power, \(A_e = \eta_{ap}A_{phys}\), where the aperture efficiency ηap is typically 0.5–0.7 for a parabolic dish. Because gain scales with Ae/λ², an antenna gets more directive either by growing physically larger or by working at a shorter wavelength (higher frequency). Here the frequency is deliberately fixed so that the whole change comes from the aperture, making the proportionality direct.
Hence, the value of x is 3.
Similar Questions
For a half wave dipole antenna
A. The average value of current is 0.64 (unit).
B. The ratio of electric field intensity just near to the antenna surface and the potential developed on the antenna surface after reception of signal, is equal to the effective height
C. Effective aperture will remain same if antenna gain will be improved by some technique.
D. The effective height will be 0.64 l, where l is the physical length of antenna.
E. If length of antenna becomes l = 0.1λ, then its current distribution become triangular.
Choose the correct answer from the options given below :
Match the following lists in terms of radiation resistances of various antennas :
List – I List – II a. Short vertical monopole i. \(31200\left(\dfrac{\text{Area of Loop}}{\lambda^{2}}\right)^{2}\) b. Small loop antenna ii. \(80\pi^{2}\left(\dfrac{L}{\lambda}\right)^{2}\) c. Dipole antenna iii. 73 ohms d. Radiation resistance of half wave dipole iv. \(400\left(\dfrac{\text{Physical height}}{\lambda}\right)^{2}\) Choose the correct answer from the codes given below:
Match List I with List II
LIST I (Type of Aperture Antenna) LIST II (Beam widtd half power points) A. Uniformly illuminated linear Array I. \(\frac{58}{D_\lambda}\) B. Uniformly illuminated circular aperture II. \(\frac{56}{a_{E\lambda}}\) C. Optimum E-plane rectangular horn III. \(\frac{67}{a_{E\lambda}}\) D. Optimum H-plane rectangular horn IV. \(\frac{51}{L_\lambda}\) Choose the correct answer from the options given below:
Following statements are given :
(a) Beam width between first nulls for a broadside long array is given by \(\dfrac{2\lambda}{nd}\).
(b) Beam width between first nulls for an end fire long array is given by \(2\sqrt{\dfrac{2\lambda}{nd}}\).
(c) Beam width between first nulls for a broadside long array is given by \(\dfrac{\lambda}{nd}\).
(d) Beam width between first nulls for an end fire long array is given by \(\dfrac{\lambda}{nd}\).
Which of the above statements are correct ?
The most basic antenna element is :
The expression given below is :
\(P_{r}=P_{t}\dfrac{A_{et}\cdot A_{er}}{r^{2}\lambda^{2}}\ \left(\text{W}\right)\)
Important Questions from Antennas
Which of the following antennas is the standard reference antenna for the directiveness?
Consider the following statements:
(a) Fiber optic cable is much lighter than copper cable
(b) Fiber optic cable is not affected by power surges or electromagnetic interference
(c) Optical transmission is inherently bidirectional.
Which of the statements is (are) correct?Broadside arrays have
A. Number of dipoles of unequal size
B. Number of dipoles equally spaced
C. Collinear dipoles
D. Dipoles in phase
E. Dipoles are 90 out of phase
Choose the correct answer from the options given below:
To match the impedance of a 'ground penetrating radar antenna' to the ground, impedance of ground is given by the expression, (if ϵ r= 14, μ r= 1, σ = 10 −2 ℧/m, operating frequency = 200 MHz)
For an isotropic antenna P n(θ, φ) = 1, D = 1, for all θ and φ. The beam area for the isotropic antenna is given by:
