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6-2 Graph of current, voltage, and impedance along half-wavelength dipole
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144 High-frequency dipole and other doublet antennas 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 37 A is measured, what is the radiation resistance Rr = = = 73 P I2 1000 W (37)2 [63] [64] [65]
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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 , seemingly a good match to 75- coaxial cable Unfortunately, the 73- 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 , to around 100 , as a function of height At heights of many wavelengths, this oscillation of the curve settles down to the freespace impedance (72 ) 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 65 ft (ie, 2 m 328 ft/m), so many wavelengths is relatively easy to achieve at reasonably attainable heights In the 80-m band (35 to 40 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: 1 Zo > Rr: VSWR = Zo Rr [66]
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2 Zo < Rr:
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The dipole feedpoint 145
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80 Radiation resistance Rr 72 70 Free space Rr
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Height above ground (wavelengths) 6-3 Radiation resistance versus height above ground
VSWR =
Rr Zo
[67]
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-wavelength, such that the radiation resistance is 60 Although not recommended as
146 High-frequency dipole and other doublet antennas 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- antenna with either 52- or 75- standard coaxial cable Some calculations are revealing: For 75- coaxial cable: VSWR = Zo Rr 75 = 125:1 60 [68]
= For 52- coaxial cable: VSWR = =
[69]
Rr Zo 60 = 115:1 52
[610]
[611]
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 , and is thus a good match for 75- coaxial cable (such as RG-11/U or RG-59/U)
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