Read the following passage and answer the questions that follow : Antennas have become increasingly importance to the society and at present, they are indispensable. They are being used every places. They are available in vast varieties. They are operating at various frequencies which are depending on different application. They operate on the principle of Maxwell's equation. They have different types of radiation patterns. There are several atmospheric losses in the way of propagation of waves. Due to which signal fades down, when it travels from transmitter to receiver antennas. Based on the above para, answer the following questions :
The expression given below is : \(P_{r}=P_{t}\dfrac{A_{et}\cdot A_{er}}{r^{2}\lambda^{2}}\ \left(\text{W}\right)\)
Friis transmission formula
This is the Friis transmission formula written in terms of effective apertures — option 3.
\(P_{r}=P_{t}\dfrac{A_{et}A_{er}}{r^{2}\lambda^{2}}\)
Two features identify it at once. It involves an effective aperture for each of two antennas, so it must describe a one-way link between a transmitter and a receiver; and it falls as \(1/r^{2}\), which is the inverse-square spreading of a wave over a single path.
Why option 4 is the discriminating distractor. The radar equation looks similar but falls as \(1/r^{4}\):
\(P_{r}=\dfrac{P_{t}G^{2}\lambda^{2}\sigma}{\left(4\pi\right)^{3}r^{4}}\)
because the wave travels out to the target and back, suffering inverse-square spreading twice. The expression given has \(r^{2}\), so it cannot be a radar equation. It also contains a target cross-section \(\sigma\) in the radar case and none here.
Why the other two are wrong in kind. The Poynting vector is a power density in watts per square metre at a point, not a total power received; and a "power gain factor" would be a dimensionless ratio, whereas this expression is explicitly labelled in watts.
Deriving it in two steps shows why the aperture form is natural. The transmitter spreads its power over a sphere, and its aperture concentrates it:
\(S=\dfrac{P_{t}G_{t}}{4\pi r^{2}}\ \text{W/m}^{2}\)
and the receiving antenna collects \(P_{r}=SA_{er}\). Substituting the relation between gain and aperture,
\(G=\dfrac{4\pi A_{e}}{\lambda^{2}}\)
converts the familiar gain form into the aperture form given.
What the formula says about design. The \(\lambda^{2}\) in the denominator means that for fixed physical apertures, a shorter wavelength delivers more received power — which is why microwave links use dishes. That runs opposite to the more familiar gain form, where \(\lambda^{2}\) sits in the numerator for fixed gains; the two are consistent, and which one applies depends on whether the antennas are specified by size or by gain.
Hence, the expression is the Friis transmission formula.
Similar Questions
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:
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 :
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:
