The dipole feedpoint

The dipole is a half-wavelength antenna fed in the center. Figure 6-2 shows the volt-age (V) and current (I) distributions along the length of the half-wavelength radia-tor element. The feedpoint is at a voltage minimum and a current maximum, so youcan assume that the feedpoint is a current antinode.At resonance, the impedance of the feedpoint is Ro=V/I. There are two resis-tances that make up Ro. The first is the ohmic losses that generate nothing but heatwhen the transmitter is turned on. These ohmic losses come from the fact that con-ductors have electrical resistance and electrical connections are not perfect (evenwhen properly soldered). Fortunately, in a well-made dipole these losses are almostnegligible. The second contributor is the radiation resistance Rrof the antenna.This resistance is a hypothetical concept that accounts for the fact that RF power isradiated by the antenna. The radiation resistance is the fictional resistance thatwould dissipate the amount of power that is radiated away from the antenna.

 For example, suppose we have a large-diameter conductor used as an antenna,and it has negligible ohmic losses. If 1000 W of RF power is applied to the feedpoint,and a current of 3.7 A is measured, what is the radiation resistance?

 It is always important to match the feedpoint impedance of an antenna to thetransmission-line impedance. Maximum power transfer always occurs (in any sys-tem) when the source and load impedances are matched. In addition, if some appliedpower is not absorbed by the antenna (as happens in a mismatched system), thenthe unabsorbed portion is reflected back down the transmission line toward thetransmitter. This fact gives rise to standing waves, and the so-called standing waveratio (SWR or VSWR) discussed in Chap. 3. This is a problem to overcome.Matching antenna feedpoint impedance seems to be simplicity itself because thefree-space feedpoint impedance of a simple dipole is about 73 Ω, seemingly a goodmatch to 75-Ωcoaxial cable. Unfortunately, the 73-Ωfeedpoint impedance is almosta myth. Figure 6-3 shows a plot of approximate radiation resistance (Rr) versusheight above ground (as measured in wavelengths). As before, we deal in approxi-mations in Fig. 6-3; in this case, the ambiguity is introduced by ground losses.Despite the fact that Fig. 6-3 is based on approximations, you can see that radi-ation resistance varies from less than 10 Ω, to around 100 Ω, as a function of height.At heights of many wavelengths, this oscillation of the curve settles down to the free-space impedance (72 Ω). At the higher frequencies, it might be possible to install adipole at a height of many wavelengths. In the 2-m amateur radio band (144 to 148MHz), one wavelength is around 6.5 ft (i.e., 2 m ×3.28 ft/m), so “many wavelengths”is relatively easy to achieve at reasonably attainable heights. In the 80-m band (3.5to 4.0 MHz), however, one wavelength is on the order of 262 ft, so “many wave-lengths” is a practical impossibility.There are three tactics that can be followed. First, ignore the problem alto-gether. In many installations, the height above ground will be such that the radiationresistance will be close enough to present only a slight impedance mismatch to astandard coaxial cable. The VSWR is calculated (among other ways) as the ratio:

 where
 Zo is the coaxial-cable characteristic impedance 
Rr is the radiation resistance of the antenna Consider an antenna mounted at a height somewhat less than a quarter-wave-length, such that the radiation resistance is 60 Ω. Although not recommended as good engineering practice (there are sometimes practical reasons) it is nonethelessnecessary to install a dipole at less than optimum height. So, if that becomes neces-sary, what are the implications of feeding a 60-Ωantenna with either 52- or 75-Ωstandard coaxial cable? Some calculations are revealing

 In neither case is the VSWR created by the mismatch too terribly upsetting.The second approach is to mount the antenna at a convenient height, and use animpedance matching scheme to reduce the VSWR. In Chap. 23, you will find infor-mation on various suitable (relatively) broadbanded impedance matching methodsincluding Q-sections, coaxial impedance transformers, and broadband RF trans-formers. “Homebrew” and commercially available transformers are available to covermost impedance transformation tasks.The third approach is to mount the antenna at a height (Fig. 6-3) at which theexpected radiation resistance crosses a standard coaxial cable characteristic imped-ance. The best candidate seems to be a height of a half-wavelength because the ra-diation resistance is close to the free-space value of 72 Ω, and is thus a good matchfor 75-Ωcoaxial cable (such as RG-11/U or RG-59/U
Reference : Practical Antenna  Handbook by Joseph Carr