Radiation resistance is that part of an antenna's feedpoint resistance that is caused by the radiation of electromagnetic waves from the antenna, as opposed to loss resistance (also called ohmic resistance) which is caused by ordinary electrical resistance in the antenna, or energy lost to nearby objects, such as the earth, which dissipate RF energy as heat.

The energy depleted by loss resistance is converted to heat radiation; the energy lost by radiation resistance is converted to radio waves. When the feedpoint is at a voltage minimum, the total of radiation resistance and loss resistance is the electrical resistance of the antenna.[1] The ratio of the radiation resistance to the total resistance is the antenna efficiency.

The radiation resistance is determined by the geometry of the antenna, whereas the loss resistance is primarily determined by the materials of which it is made and its distance from and alignment with other nearby conductors or semi-conductors, and what those are made of. Both radiation and loss resistance depend on the distribution of current in the antenna.

## Cause

The total resistance at the feedpoint of the antenna results from voltage or energy loss due to three different causes: radiation loss and conductor loss in the antenna itself, and ground loss from the antenna heating nearby objects which are not a part of the antenna, but which do interact with it, such as the soil below it.

Radiation resistance is caused by the radiation reaction of the conduction electrons in the antenna.[2] The radiation resistance represents reduction of the electrons’ momentum due to the energy lost from creating electromagnetic waves:

The alternation of AC current flowing through an antenna accelerates the electrons in its conductor, pulling them forward and backward in sync with the frequency of the current. When accelerated, electrons radiate electromagnetic waves which also have momentum. The momentum of the departing waves subtracts from the electrons’ momentum, causing the electrons to slow down, which is seen as a drop in voltage.

### Conductor loss

An unavoidable part of the loss resistance comes from electrical resistance in the conductor the antenna is made of. Electrons moving through any metal are scattered off its metallic crystal lattice which also diminishes the electrons' momentum, transferring energy from the electrons to the lattice by impulse. The Ohmic resistance represents the energy lost by the electrons from collision with the metal atoms in the lattice, and the resulting vibrations of the lattice are perceived as heat.

### Ground loss

Loss resistance can also include loss from heating the earth below the antenna and in conductive objects nearby, called ground loss, even though the loss is not always in the earth. Except for aviation, spacecraft, and maritime antennas, the majority of radio antenna power loss is nearly always from heating the soil. The loss results from electrical and magnetic fields generated by the antenna accelerating electrons in the soil or an adjacent conductor, such as the metal roof of a nearby building. The resulting collisions in that material generate heat similarly to the heat losses in the metal lattice of the antenna, discussed in the prior section.

These losses can be understood as disturbance of the antenna’s field lines by an electric or magnetic obstacle, absorbing the fields or diverting the field lines from the most expedient route bridging the gap between one pole of the dipole antenna to the other pole, and thereby impeding the electrical circuit through the antenna; likewise, electric field lines interrupted between a monopole antenna and its counterpoise or ground plane.[a]

All antennas’ most intense fields are local, and rapidly diminish with distance from the antenna, so ground losses can be reduced or effectively eliminated if the antenna can be placed strategically far away from any electrical or magnetic obstacle. For example, very high frequency (VHF) quarter-wavelengths are about 5 feet (1.5 m), so a quarter-wave or half-wave VHF antenna is small enough to be feasibly mounted on a non-conducting mast several quarter-wavelengths above the earth and far from other antennas, metal-clad or cement buildings, or metal-frame structures.

## Calculation

In general, electrical power is calculated by:[2][3]

${\textstyle P=\left|I\right|^{2}R_{r}\,}$

where ${\displaystyle I}$  is the electric current flowing into the feeds of the antenna, ${\displaystyle P}$  is the power in the portion of the resulting electromagnetic field that departs, rather than being re-absorbed, and ${\displaystyle R_{r}}$  is the resistance seen at the antenna feedpoint, above and beyond the resistance caused by heat loss. Usually ${\displaystyle I}$  is the time average of the current (root mean square value). The result is an effective resistance:[2]

${\displaystyle R_{r}={\frac {P}{\left|I\right|^{2}}}\,}$

This effective resistance is called the radiation resistance.

Radiation resistance is sometimes called a “fictitious” resistance, or a “virtual” resistance, but it represents an actual loss of voltage in the antenna feed circuit, proportional to the current, just like the Ohmic resistance. Further, the energy lost via Ohmic resistance and via radiation resistance is carried away by electromagnetic radiation in both cases: heat radiation in the case of Ohmic loss, and radio waves in the case of radiation resistance.[2][3]

## Footnotes

1. ^ Disturbance of magnetic field lines also causes ground loss if the magnetic field is blocked from circulating around a wire in any kind of antenna. However, since many non-metals (including most soils) are very nearly transparent to magnetic fields, the greatest ground loss is usually via interruption of the antenna’s electric field.

## References

1. ^ Milligan, Thomas (1985). Modern Antenna Design. New York, NY: McGraw Hill Book Company. p. 69. ISBN 0-07-042318-0. LCCN 84-17131.
2. ^ a b c d Schelkunoff, Sergei A.; Friis, Harald T. (1966) [1952]. Antennas: Theory and practice. Applied Mathematics Series. New York, NY: John Wiley & sons. LCCN 59-5083.
3. ^ a b Silver, H. Ward; Ford, Stephen R.; Wilson, Mark J., eds. (2011). ARRL Antenna Book (22 ed.). Newington, CT: American Radio Relay League. ISBN 978-0-87259-680-1.