Match the following lists in terms of radiation resistances of various antennas : Choose the correct answer from the codes given below: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. \(400\left(\dfrac{\text{Physical height}}{\lambda}\right)^{2}\)
a-iv, b-i, c-ii, d-iii
Read the variable in each expression — each formula names the dimension that belongs to its own antenna, so the matching can be done by inspection.
d → iii. Half-wave dipole — 73 Ω. The one pure number in the list, and the most quoted figure in antenna theory. It is why 75 Ω coaxial cable exists: the feeder is chosen to match this radiation resistance so that the antenna is matched and reflections vanish. (The full impedance is 73 + j42.5 Ω, made purely resistive by trimming the dipole about 5 % shorter than λ/2.)
a → iv. Short vertical monopole — \(400(h/\lambda)^{2}\). A monopole is described by its physical height above the ground plane, and "physical height" appears in only this expression. The monopole is the image-formed half of a dipole, so its radiation resistance is half the dipole value — which is exactly why the constant 400 is (nearly) half the dipole's 800.
c → ii. Dipole antenna — \(80\pi^{2}(L/\lambda)^{2}\). This is the short (Hertzian) dipole formula, written in terms of the overall length L. Note \(80\pi^{2}\approx790\), twice the monopole constant, confirming the factor-of-two relation.
b → i. Small loop — \(31200\left(A/\lambda^{2}\right)^{2}\). The only formula containing an area, and the only one where the bracket is squared over λ2 — a loop radiates as a magnetic dipole, so its strength depends on the enclosed area rather than on a length.
What the numbers tell you. All the small-antenna formulas vary as (size/λ)2, so radiation resistance collapses as the antenna is made electrically small: a monopole of height λ/20 has \(400/400=1\ \Omega\). With ohmic loss resistance comparable to that, the radiation efficiency
\(\eta=\dfrac{R_{rad}}{R_{rad}+R_{loss}}\)
becomes poor — the fundamental reason small antennas are inefficient and hard to match.
Hence, the correct matching is a-iv, b-i, c-ii, d-iii.
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 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:
