Simple Halfwave Dipole Antennas

The simple dipole, or doublet, is a case in point. This antenna is also sometimes called the Hertz, or hertzian, antenna because radio pioneer Heinrich Hertz reportedly used this form in his experiments. The half-wavelength dipole is a balanced antenna consisting of two radiators (Fig. 6-1) that are each a quarter-wavelength, making a total of a half-wavelength. The antenna is usually installed horizontally with respect to the earth’s surface, so it produces a horizontally polarized signal.  

Let say you have L long dipole antenna .

for halfwave dipole antenna L = 1/2L = 1/4 L + 1/4L

In its most common configuration (Fig. 6-1), the dipole is supported at each end by rope and end insulators. The rope supports are tied to trees, buildings, masts, or some combination of such structures. The length of the antenna is a half-wavelength. Keep in mind that the physical length of the antenna, and the theoretical electrical length, are often different by about 5 percent. A free-space half-wavelength is found from
 
                                                         L = 492/Fmhz   feet   [6.1]





In a perfect antenna, that is self-supported many wavelengths away from any object, Eq. 6.1 will yield the physical length. But in real antennas, the length calculated above is too long. The average physical length is shortened by up to about 5 percent because of the velocity factor of the wire and capacitive effects of the end insulators. A more nearly correct approximation (remember that word, it's important) of a half-wavelength antenna is
 
                                                                L = 468/Fmhz  ft [6.2]
 
where L is the length of a half-wavelength radiator, in feet F MHz is the operating frequency, in megahertz
 
Example Calculate the approximate physical length for a half-wavelength dipole operating on a frequency of 7.25 MHz. Solution:
                                                                L = 468/Fmhz  ft

                                                                   = 468/7.25 ft 

                                                                   = 64.55 ft
 
or, restated another way:
                                                                 L = 64 ft 6.6 in
 
It is unfortunate that a lot of people accept Eq. 6.2 as a universal truth, a kind of immutable law of The Universe. Perhaps abetted by books and articles on antennas that fail to reveal the full story, too many people install dipoles without regard for reality. The issue is resonance. An antenna is a complex RLC network. At some frequency, it will appear like an inductive reactance (X = +jXL), and at others it will appear like a capacitive reactance (X =–jXC). At a specific frequency, the reactances are equal in magnitude, but opposite in sense, so they cancel each other out: XL – XC = 0. At this frequency, the impedance is purely resistive, and the antenna is said to be resonant. The goal in erecting a dipole is to make the antenna resonant at a frequency that is inside the band of interest, and preferably in the portion of the band most often used by the particular station. Some of the implications of this goal are covered later on, but for the present, assume that the builder will have to custom-tailor the length of the antenna. Depending on several local factors (among them, nearby objects, the shape of the antenna conductor, and the length/diameter ratio of the conductor) it might prove necessary to add, or trim, the length a small amount to reach resonance.