Radiation Efficiency

Author: Edmund A. Laport

Low-frequency antennas characteristically have low radiation resistance and relatively high capacitive reactance. The most practical form of power feed employs series resonance in the antenna circuit, using an inductance to neutralize the antenna reactance. The design of this tuning inductance is an important part of the design of an antenna system. Because of the high currents that flow through the inductance, its resistance becomes a prominent, if not dominant, component of the resistance of the system. Therefore, the tuning inductance becomes a limiting factor in ultimate efficiency of the transmitting plant.

In the absence of more precise information, one may assume that a well-designed low-frequency antenna and ground system will have a radiation efficiency of roughly 75 percent of the equivalent electrical length in degrees of the antenna system at the working frequency. In other words, an antenna system having a vertical height of 11 degrees, with top loading that makes it equivalent to 25 electrical degrees, should have a radiation efficiency of the order of 18 percent. excluding tuning-coil losses. While this estimate is necessarily a rough one, it will serve as a reasonable starting point for computations.

The best guide for initial assumptions is information on systems that have already been built and measured. Such direct information can then be applied to a new problem by similitude. Some reference information of this nature is included later.

The antenna-design problem will always assume one of three basic forms: the limitations on the ultimate design to be those of a reasonable investment; or a maximum height (where physical height is limited by conditions other than cost); or a fixed amount of money available. The design considerations are weighed differently for each of these three forms. Height is the most costly dimension for an antenna system, and so the determination of height is one of the most important considerations in any given problem. It is also the most important choice with respect to maximum realizable radiation efficiency, since radiation resistance is in general proportional to the square of the height.

Since the radiation pattern is not under control in low-frequency-antenna design, the radiation efficiency is purely a circuit problem. The object is to obtain the highest ratio of radiation resistance to total antenna-circuit resistance.

The total antenna resistance is the sum of five separate components:

• Radiation resistance R_τ
• Ground-terminal resistance R_g
• Resistance of tuning inductance R_c
• Resistance equivalent of insulation loss R_i
• Resistance equivalent of conductor loss R_w

The radiation efficiency of an antenna is therefore

Ground resistance often is larger than the radiation resistance even when large investments are made in the ground system. The tuning-coil resistance may be relatively large, even after careful engineering design, because of the large reactance usually necessary and because of practical limitations in minimizing the dissipation factor Q. The characteristically high operating potentials on the antenna, owing to its small resistance and high reactance, cause insulator-loss equivalent resistance to become appreciable and sometimes of great importance in relation to the radiation resistance. The conductor resistance can also become appreciable in systems where mechanical considerations dictate the use of high-strength alloy materials having effective resistivities two to three times greater than copper. Also, the great lengths of wire required for low-frequency antennas add to conductor-loss equivalent resistance.

The absolute values of ground, insulation, and conductor resistance are unattainable by direct measurement and must in any event be estimated from final system-resistance measurements. In the design stage, unfortunately, no significant estimates can be made because of the great range of values encountered within the scope of low-frequency design. From a knowledge of the current distribution in the antenna, the conductor resistance referred to the feed point can be computed by making a summation of PR losses over the complete system.