A quarter wavelength is related to frequency by the equation:
Lft = 246v/fo
where Lft represents λ/4 in feet, fo represents the frequency in megahertz, and v represents the velocity factor. If the length is expressed in meters as Lm, then the formula is:
Lm = 75v/fo
For a typical wire conductor, v = 0.95 (95 percent); for metal tubing, v can range down to approximately 0.90 (90 percent). A λ/4 antenna must be operated against a low-loss RF ground. The feed-point impedance over perfectly conducting ground is approximately 37 Ω. This represents radiation resistance in the absence of reactance, and provides a reasonable impedance match to most coaxial transmission lines.
The simplest vertical antenna is a λ/4 radiator mounted at ground level. The radiator is fed with a coaxial cable. The center conductor is connected to the base of the radiator, and the shield is connected to a ground system.
Unless an extensive ground radial system is installed, a ground-mounted vertical is likely to be inefficient unless the surface happens to be an excellent conductor (saltwater or a salt marsh, for example). Another problem is the fact that vertically polarized antennas receive more human-made noise than horizontal antennas. In addition, the EM fields from ground-mounted transmitting antennas are more likely to cause interference to nearby electronic devices than are the EM fields from antennas installed at a height.
Basic quarter-wave verticals. At A, ground-plane antenna. At B, coaxial antenna.
A ground-plane antenna is a vertical radiator, usually measuring λ/4, operated against a system of λ/4 conductors called radials. The feed point, where the feed line joins the antenna radiator and the hub of the radial system, is elevated. When the feed point is at least λ/4 above the ground, only three or four radials are necessary to obtain a low-loss RF ground system. The radials extend outward from the base of the antenna at an angle between 0° and 45° with respect to the horizon. Above figure A illustrates a typical ground-plane antenna with four horizontal radials.
A ground-plane antenna should be fed with coaxial cable. The feed-point impedance of a ground-plane antenna having a λ/2 radiator is about 37 Ω if the radials are horizontal; the impedance increases as the radials droop, reaching about 50 Ω at a droop angle of 45°.
The radials in a ground-plane antenna can extend straight downward, and then can be merged to form a λ/2 cylinder or sleeve that is concentric with the feed line. In this case, the feed-point impedance is approximately 73 Ω. This is known as a coaxial antenna (above figure B).