The dipole feedpoint

The dipole is a half-wavelength antenna fed in the center. Figure 6-2 shows the voltage (V) and current (I) distributions along the length of the half-wavelength radiator element. The feedpoint is at a voltage minimum and a current maximum, so you can assume that the feedpoint is a current antinode.
At resonance, the impedance of the feedpoint is Ro = V/I. 

There are two resistances that make up Ro. The first is the ohmic losses that generate nothing but heat when the transmitter is turned on. These ohmic losses come from the fact that conductors have electrical resistance and electrical connections are not perfect (even when properly soldered). Fortunately, in a well-made dipole these losses are almost negligible. 

The second contributor is the radiation resistance Rr of the antenna. This resistance is a hypothetical concept that accounts for the fact that RF power is radiated by the antenna. The radiation resistance is the fictional resistance that would 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 the transmission-line impedance. Maximum power transfer always occurs (in any system) when the source and load impedances are matched. In addition, if some applied power is not absorbed by the antenna (as happens in a mismatched system), then the unabsorbed portion is reflected back down the transmission line toward the transmitter. This fact gives rise to standing waves, and the so-called standing wave ratio (SWR or VSWR) discussed in Chap. 3. This is a problem to overcome. Matching antenna feedpoint impedance seems to be simplicity itself because the free-space feedpoint impedance of a simple dipole is about 73 Ω, seemingly a good match to 75-Ω coaxial cable. Unfortunately, the 73-Ω feedpoint impedance is almost a myth. Figure 6-3 shows a plot of approximate radiation resistance (Rr) versus height above ground (as measured in wavelengths). As before, we deal in approximations 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 radiation 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 freespace impedance (72 Ω). At the higher frequencies, it might be possible to install a dipole at a height of many wavelengths. In the 2-m amateur radio band (144 to 148 MHz), 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 (3.5 to 4.0 MHz), however, one wavelength is on the order of 262 ft, so “many wavelengths” is a practical impossibility. There are three tactics that can be followed. First, ignore the problem altogether. In many installations, the height above ground will be such that the radiation resistance will be close enough to present only a slight impedance mismatch to a standard coaxial cable. The VSWR is calculated (among other ways) as the ratio:

good engineering practice (there are sometimes practical reasons) it is nonetheless necessary to install a dipole at less than optimum height. So, if that becomes necessary, what are the implications of feeding a 60-Ω antenna with either 52- or 75-Ω standard coaxial cable? Some calculations are revealing: For 75-Ω coaxial cable:

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 an impedance matching scheme to reduce the VSWR. In Chap. 23, you will find information on various suitable (relatively) broadbanded impedance matching methods including Q-sections, coaxial impedance transformers, and broadband RF transformers.“Homebrew” and commercially available transformers are available to cover most impedance transformation tasks. The third approach is to mount the antenna at a height (Fig. 6-3) at which the expected radiation resistance crosses a standard coaxial cable characteristic impedance. The best candidate seems to be a height of a half-wavelength because the radiation resistance is close to the free-space value of 72 Ω, and is thus a good match for 75-Ω coaxial cable (such as RG-11/U or RG-59/U).

From Practical Antenna Handbook : Joseph J. Carr