radiated as radio waves by the antenna, divided by the square of the RMS current
When the antenna is fed at some other point, the formula requires a correction factor discussed below.
The recoil force is in a direction opposite to the electric field in the antenna accelerating the electron, reducing the average velocity of the electrons for a given driving voltage, so it acts as a resistance opposing the current.
consumed by radiation resistance is converted to radio waves, the desired function of the antenna, while the power
consumed by loss resistance is converted to heat, representing a waste of transmitter power.
For "large" antennas, the radiation resistance is usually the main part of their input resistance, so it determines what impedance matching is necessary and what types of transmission line would match well to the antenna.
When the feedpoint is placed at a location other than the minimum-voltage / maximum current point, or if a "flat" voltage minimum does not occur on the antenna, then the simple relation
The feedpoint, the place where the feed line from the transmitter is attached, can be located anywhere along the antenna element.
[5] It is lowest for feedpoints located at a point of maximum current (an antinode),[c] and highest for feedpoints located at a point of minimum current, a node, such as at the end of the element (theoretically, in an infinitesimally thin antenna element, radiation resistance is infinite at a node, but the finite thickness of actual antenna elements gives it a high but finite value, on the order of thousands of ohms).
[16] The choice of feedpoint is sometimes used as a convenient way to impedance match an antenna to its feed line, by attaching the feedline to the antenna at a point at which its input resistance happens to equal the feed line impedance.
[17][18] Radiation resistance is by convention calculated with respect to the maximum possible current
[5] When the antenna is fed at a point of maximum current, as in the common center-fed half-wave dipole or base-fed quarter-wave monopole, that value
Due to electromagnetic reciprocity, an antenna has the same radiation resistance when receiving radio waves as when transmitting.
[8][9] The power dissipated in the radiation resistance is due to radio waves reradiated (scattered) by the antenna.
[8][9] Maximum power is delivered to the receiver when it is impedance matched to the antenna.
Installed antennas will have higher or lower radiation resistances if they are mounted near the ground (less than 1 wavelength) in addition to the loss resistance from the antenna's near electrical field that penetrates the soil.
[d][1] The above figures assume the antennas are made of thin conductors and sufficiently far away from large metal structures, that the dipole antennas are sufficiently far above the ground, and the monopoles are mounted over a perfectly conducting ground plane.
The zero thickness half-wave dipole's radiation resistance of 73 Ω (approx.
This is one reason for the wide use of the half wave dipole as a driven element in antennas.
This can be shown by calculating the radiation resistance of a short dipole (length
Then the radiation resistance is calculated from the law of conservation of energy, as the resistance the antenna must present to the input current to absorb the radiated power from the transmitter, using Joule's law
At frequencies below 1 MHz the size of ordinary electrical circuits and the lengths of wire used in them is so much smaller than the wavelength, that when considered as antennas they radiate an insignificant fraction of the power in them as radio waves.
This explains why electrical circuits can be used with alternating current without losing energy as radio waves.
[g] As can be seen in the above table, for linear antennas shorter than their fundamental resonant length (shorter than 1/ 2 λ for a dipole antenna, 1/ 4 λ for a monopole) the radiation resistance decreases with the square of their length;[24] for loop antennas the change is even more extreme, with sub-resonant loops (circumference less than 1 λ for a continuous loop, or 1/ 2 λ for a split loop) the radiation resistance decreases with the fourth power of the perimeter length.
For example, navies use radio waves of about 15–30 kHz in the very low frequency (VLF) band to communicate with submerged submarines.
The powerful naval shore VLF transmitters which transmit to submarines use large monopole mast antennas which are limited by construction costs to heights of about 300 metres (980 ft) .
From the table above, a 0.015 λ monopole antenna has a radiation resistance of about 0.09 Ohm.
Since the ohmic resistance of the huge ground system and loading coil cannot be made lower than about 0.5 ohm, the efficiency of a simple vertical antenna is below 20%, so more than 80% of the transmitter power is lost in the ground resistance.
To increase the radiation resistance, VLF transmitters use huge capacitively top-loaded antennas such as umbrella antennas and flattop antennas, in which an aerial network of horizontal wires is attached to the top of the vertical radiator to make a 'capacitor plate' to ground, to increase the current in the vertical radiator.
However at frequencies below about 20 MHz, where static is pervasive, this is not such a problem, since a weak signal from the antenna can simply be amplified in the receiver without the amplifier's noise adding any appreciable amount to the already substantial noise (N) accompanying the signal (S), keeping the ratio S/N as good (or bad) as before.