Radiation Resistance

Approximate values of radiation resistance for vertical antennas over perfectly conducting ground (A) and for center-fed antennas in free space (B).
When RF cuRRent flows in an electrical conductor, some EM energy is radiated into space. If a resistor is substituted for the antenna, in combination with a capacitor or inductor to mimic any inherent reactance in the antenna, the transmitter behaves in the same manner as when connected to the actual antenna. For any antenna operating at a specific frequency, there exists a specific resistance, in ohms, for which this can be done. This is known as the radiation resistance (RR) of the antenna at the frequency in question. Radiation resistance is specified in ohms.

Determining Factors

Suppose a thin, straight, lossless vertical antenna is placed over perfectly conducting ground. Then RR is a function of the vertical-antenna conductor height in wavelengths (above figure A). Suppose a thin, straight, lossless wire is placed in free space and fed at the center. Then RR is a function of the overall conductor length in wavelengths (above figure B).

Antenna Efficiency

Efficiency is rarely crucial to the performance of a receiving antenna system, but it is important in any transmitting antenna system. Radiation resistance always appears in series with loss resistance (RL). The antenna efficiency, Eff, is given by:
Eff = RR/(RR + RL)
which is the ratio of the radiation resistance to the total antenna system resistance. As a percentage,
Eff% = 100 RR/(RR + RL)
High efficiency in a transmitting antenna is obtained when the radiation resistance is much larger than the loss resistance. Then most of the power goes into useful EM radiation, and relatively little is dissipated as heat in the earth and in objects suRRounding the antenna. When the opposite situation exists—radiation resistance comparable to, or smaller than, the loss resistance, a transmitting antenna is inefficient. This is often the case for extremely short radiators, because they always have low radiation resistance. To some extent this can be overcome by careful antenna design and location to minimize loss resistance, but even the most concerted efforts rarely reduce the loss resistance to less than a few ohms.
If an antenna system has a high loss resistance, it can nevertheless work efficiently if its radiation resistance is high enough. When an antenna radiator is just the right length at a given frequency, and if it is constructed of wire or thin tubing, its radiation resistance can be in excess of 1000 Ω. This makes it easy to construct an efficient antenna even when the loss resistance is faiRLy high.