The value of radiation resistance of a Hertzian dipole of length \(\dfrac{\lambda}{80}\) is given by
0.123 Ω
The radiation resistance of a Hertzian (elementary, uniform-current) dipole is
\(R_{r}=80\pi^{2}\left(\dfrac{dl}{\lambda}\right)^{2}\ \Omega\)
Substitute \(dl=\dfrac{\lambda}{80}\), so the ratio is 1/80 :
\(R_{r}=80\pi^{2}\left(\dfrac{1}{80}\right)^{2}=\dfrac{80\times9.8696}{6400}=\dfrac{789.6}{6400}=0.1234\ \Omega\)
which is option 4.
The squared dependence is the whole physics of the result. Radiation resistance falls as the square of the length in wavelengths, so a short antenna is a very poor radiator:
| Length | Rr |
|---|---|
| λ/10 | 7.9 Ω |
| λ/20 | 1.97 Ω |
| λ/50 | 0.32 Ω |
| λ/80 | 0.123 Ω |
Why such a small value is a serious problem. Efficiency is
\(\eta=\dfrac{R_{r}}{R_{r}+R_{loss}}\)
and a real antenna's conductor and ground losses easily amount to an ohm or more. With \(R_{r}=0.123\ \Omega\) against, say, 1 Ω of loss, the efficiency would be only 11 % — almost all the power delivered would heat the wire rather than radiate. This is exactly the difficulty of AM broadcast antennas at long wavelengths and of the short whips used on hand-held VHF radios.
The second problem is matching. A fraction of an ohm of resistance in series with a large capacitive reactance is very hard to match to a 50 Ω feeder, and any matching network's own losses are then comparable with the radiation resistance itself.
Note the contrast with the half-wave dipole, whose radiation resistance is about 73 Ω — six hundred times larger. That is why resonant-length antennas are used wherever there is room for them, and why the Hertzian dipole survives mainly as the theoretical building block from which longer antennas are constructed by integration.
Hence, the radiation resistance is 0.123 Ω.
Similar Questions
The angular distribution of the transmitted power around the antenna is generally known as :
An antenna is polarized in the plane of the field perpendicular to
An antenna is generally a metallic object, often a wire or collection of wires, used to convert high frequency current into electromagnetic waves and vice-versa. Antenna serve either or both of the following two functions, generation or the collection of electromagnetic energy. In a transmitting system, a radio-frequency signal is developed, amplified, modulated and applied to the antenna. The R-F currents flowing through the antenna produce electromagnetic waves which radiate into the atmosphere. In a receiving system, electromagnetic waves "cutting" through the antenna induce alternating currents for use by the receiver.
Efficient operation also requires that the receiving antenna be of the same polarization as the transmitting antenna. Polarization is the direction of the electric field and is therefore, the same as the antennas physical configuration. Thus vertical antenna will transmit vertical polarized light, any antenna having a physical length that is one-half wavelength of the applied frequency is called a Hertz antenna. Hertz antenna are predominantly used with frequencies above 2 MHz. Usually, at frequencies below 2 MHz, a Marconi type of antenna is used. The Marconi antenna is usually a quarter-wave grounded antenna or any odd multiple of a quarter wavelength.
The Yagi-Uda antenna consists of a drivers element and two or more parasitic elements. Yagi-Uda has two parasitic elements, a reflector and a director. This Yagi-Uda antenna provides about 7 dB of power gain with respect to a half-wavelength dipole reference. More complex antennas may be circularly polarized both vertically and horizontally polarized waves are radiated with equal power in both. If the powers are unequal the antenna is said to be elliptically polarized.
A horn is an ideal antenna for terminating a waveguide and may be conical, rectangular or sectorial. Wide band antennas either when the transmissions are wide band or when working of narrow channels over a wide frequency range is the major application. Helical antenna, which consists of a loosely wound helix backed up by a metal ground plane. Loop antennas are often used for direction finding. Loops have many shapes and generally consists of a single turn of wire. Discone is a ground plane antenna evolved from the vertical dipole and having a very similar radiation pattern.
For a half wave dipole the directivity ‘D’ in dB is of the order of :
Important Questions from Basics of Antenna
Arrange the following antennas in ascending order of their radiation resistance.
A. Short dipole (L = \(\frac{\lambda}{10}\) )(I av = l o)
B. Short dipole (L= \(\frac{\lambda}{10}\) )( I av = l o/2)
C. Linear \(\frac{\lambda}{2}\) dipole (sinusoidal current distribution)
D. Small Loop (square loop) single turn of(L = \(\frac{\lambda}{10}\) )
Choose the correct answer from the options given below
If the frequency of the signal is 1 MHz, the minimum height of the transmitting antenna should be:
The Antenna employed in Television receivers
Which of the following is NOT true with respect to antennas?
An instrument to check whether RF power in the transmission line is transferred to the antenna is:
