Radiation resistance
Radiation resistance is that part of an antenna's feedpoint electrical resistance caused by the emission of radio waves from the antenna. A radio transmitter applies a radio frequency alternating current to an antenna, which radiates the energy of the current as radio waves. Because the antenna is absorbing the energy it is radiating from the transmitter, the antenna's input terminals present a resistance to the current from the transmitter.
Radiation resistance is an effective resistance, due to the power carried away from the antenna as radio waves. Unlike conventional ohmic resistance, radiation resistance is not an opposition to current of the imperfect conducting materials the antenna is made of.
The radiation resistance is conventionally defined as the value of electrical resistance that would dissipate the same amount of power as heat, as is dissipated by the radio waves emitted from the antenna. From Joule's law, it is equal to the total power radiated as radio waves by the antenna, divided by the square of the root-mean-square| current into the antenna terminals:
The feedpoint impedance and radiation resistance are determined by the geometry of the antenna, the operating frequency, and the antenna location. The relation between the feedpoint impedance and the radiation resistance depends on the position on the antenna at which the feedline is attached.
The relation between feedpoint impedance and radiation resistance is particularly simple when the feedpoint is placed at the antenna's minimum possible voltage / maximum possible current point; in that case, the total feedpoint impedance at the antenna's terminals is equal to the sum of the radiation resistance plus the loss resistance due to "Ohmic" losses in the antenna and the nearby soil:
When the antenna is fed at some other point, the formula requires a correction factor [|discussed below].
In a receiving antenna the radiation resistance represents the source resistance of the antenna, and the portion of the received radio power consumed by the radiation resistance represents radio waves re-radiated by the antenna.
Cause
s are radiated by electric charges when they are accelerated. In a transmitting antenna, radio waves are generated by time varying electric currents, consisting of electrons accelerating as they flow back and forth in the metal antenna, driven by the electric field due to the oscillating voltage applied to the antenna by the radio transmitter.An electromagnetic wave carries momentum away from the electron which emitted it. The cause of radiation resistance is the radiation reaction, the recoil force on the electron when it emits a radio wave photon, which reduces its momentum.
This is called the Abraham–Lorentz force. 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.
Radiation resistance and loss resistance
The radiation resistance is only part of the feedpoint impedance at the antenna terminals. An antenna has other energy losses which appear as additional resistance at the antenna terminals; ohmic resistance of the metal antenna elements, ground losses from currents induced in the ground, and dielectric losses in insulating materials. When the feedpoint is at a voltage minimum and current maximum, the total feedpoint impedance is equal to the sum of the radiation resistance and loss resistanceThe power fed to the antenna is split proportionally between these two resistances.
where
The power 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. So for minimum power loss it is desirable that the radiation resistance be much greater than the loss resistance. The ratio of the radiation resistance to the total feedpoint impedance is equal to the efficiency of the antenna.
To transfer maximum power to the antenna, the transmitter and feedline must be impedance matched to the antenna. This means the feedline must present to the antenna a resistance equal to the input resistance and a reactance equal but opposite to the antenna's reactance. If these impedances are not matched, the antenna will reflect some of the power back toward the transmitter, so not all the power will be radiated. For antennas a half-wave or larger, in length or perimeter, the radiation resistance is usually the main part of their input resistance, so it mostly determines what impedance matching is necessary and what types of transmission line would match well to the antenna.
Effect of the feedpoint
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 no longer holds.In a resonant antenna, the current and voltage form standing waves along the length of the antenna element, so the magnitude of the current in the antenna varies sinusoidally along its length. The feedpoint, the place where the feed line from the transmitter is attached, can be located anywhere along the antenna element. Since feedpoint resistance depends on the input current, it varies with the feedpoint. It is lowest for feedpoints located at a point of maximum current, and highest for feedpoints located at a point of minimum current, a node, such as at the end of the element.
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 impedance happens to equal the characteristic impedance of the feed line.
In order to give a meaningful value for the antenna efficiency, the radiation resistance and loss resistance must be referred to the same point on the antenna, often the input terminals.
Radiation resistance is by convention calculated with respect to the maximum possible current on the antenna, which for short antennas may not physically occur on the antenna at all. 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 is only mostly the radiation resistance; it is a common fallacy to suppose that it is actually the radiation resistance. However, if the antenna is fed at some other point, the equivalent radiation resistance at that point can easily be calculated from the ratio of antenna currents
where and are the electrical lengths from the current node.
Receiving antennas
In a receiving antenna, the radiation resistance represents the source resistance of the antenna as a source of power. Due to electromagnetic reciprocity, an antenna has the same radiation resistance when receiving radio waves as when transmitting. If the antenna is connected to an electrical load such as a radio receiver, the power received from radio waves striking the antenna is divided proportionally between the radiation resistance and loss resistance of the antenna and the load resistance.The power dissipated in the radiation resistance is due to radio waves reradiated by the antenna. Maximum power is delivered to the receiver when it is impedance matched to the antenna. If the antenna is lossless, half the power absorbed by the antenna is delivered to the receiver, the other half is reradiated.
Radiation resistance of common antennas
In all of the formulas listed below, the radiation resistance is the so-called "free space" resistance, which the antenna would have if it were mounted several wavelengths distant from the ground. Installed antennas will have higher or lower radiation resistances if they are mounted near the ground in addition to the loss resistance from the antenna's near electrical field that penetrates the soil.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 is near enough to the characteristic impedance of common 50 Ω and 75 Ω coaxial cable that it can usually be fed directly without need of an impedance matching network. This is one reason for the wide use of the half wave dipole as a driven element in antennas.
Relationship of monopoles and dipoles
The radiation resistance of a monopole antenna created by replacing one side of a dipole antenna by a perpendicular ground plane is one-half of the resistance of the original dipole antenna. This is because the monopole radiates only into half the space, the space above the plane, so the radiation pattern is identical to half of the dipole pattern and therefore with the same input current it radiates only half the power.This is not obvious from the formulas in the table because the different lengths use the same symbol, the derived monopole antenna, however, is only half the length of the original dipole antenna. This can be shown by calculating the radiation resistance of a short dipole, which is twice the length of the corresponding monopole :
Comparing this to the formula for the short monopole shows the dipole has double the radiation resistance of the monopole:
This confirms the consistency of physically modelling a center-fed dipole as two monopoles, placed end-to-end, with adjacent feedpoints.