Straight, Uniform Vertical Radiator

Author: Edmund A. Laport

The fundamental frequency f₀ of a vertical radiator is the lowest frequency for which the reactance is zero at the feed point between the lower end of the radiator and ground. At this frequency, the electrical length of the antenna is 90 degrees, or one-quarter wavelength.

In practice, an antenna that is a quarter wavelength electrically is somewhat shorter than a quarter wave long physically. The difference is due to end effect, which results from the finite ratio of antenna length to antenna diameter. Table 1.2 shows the effect of height (length)-to-diameter ratio h/d on physical length G for a cylindrical vertical radiator for the condition of zero reactance with no artificial end loading.

From this table, the fundamental frequency of a vertical radiator can be determined from its geometry. For example, a cylindrical conductor with h/d = 200 has a physical height of 85 degrees. Its fundamental wavelength is λ₀ = 360h/85.0, and its fundamental frequency is

For an idealized uniform vertical antenna without end effect, the fundamental wavelength in meters is

These relations are useful in deriving a simple equivalent vertical antenna that has the same fundamental frequency as an antenna of any arbitrary configuration. The current distribution along the vertical portion can thus be determined and from that the radiation resistance, and eventually the field strength per ampere at a unit distance can be calculated.