Practical_Antenna_Handbook_0071639586

180 p a r t I I I : h i g h - F r e q u e n c y B u i l d i n g - B l o c k A n t e n n a s
is because some of the signal radiated by the dipole strikes the ground directly beneath
the antenna and is reflected straight up, where it induces a second field within
the dipole. Because of the time it takes the radiated field to reach the ground and return,
the induced field is shifted in phase with respect to the original signal in the
dipole. This causes the ratio of voltage to current at the feedpoint to vary with the
height of the antenna, which is simply saying the feedpoint impedance varies with
height. At heights of many wavelengths, this oscillation of the curve settles down to
the free-space impedance (73 Ω) as the effect of the earth becomes negligible. At the
higher frequencies (VHF and above), it becomes practical to install a dipole at a height
of many wavelengths. In the 2-m amateur radio band (144 to 148 MHz), λ ≈ 6.5 ft (i.e.,
2 m × 3.28 ft/m), so a height of “many wavelengths” is relatively easy to achieve. In
the 80-m band (3.5 to 4.0 MHz), however, λ ≈ 262 ft, so “many wavelengths” is a virtual
impossibility for most.
Any of a number of alternative responses can be chosen:
• Ignore the problem altogether. In many installations, the height above ground
will be such that the radiation resistance will be close enough to represent only
a slight impedance mismatch to a standard coaxial cable. For Z 0 > R RAD , the
voltage standing wave ratio (VSWR) is calculated (among other ways) as the
ratio
For Z 0 < R RAD , it is the ratio
Z0
VSWR = (6.5)
R
RAD
where Z 0 = coaxial cable characteristic impedance
R RAD = radiation resistance of antenna
RRAD
VSWR = (6.6)
Z
• Consider mounting the antenna at a height somewhat below a quarterwavelength,
such that the radiation resistance is around 60 Ω. What is the
resulting VSWR when feeding a 60-Ω antenna with either 52- or 75-Ω standard
coaxial cable? Some calculations reveal:
For 75-Ω coaxial cable:
Z
VSWR =
R
0
RAD
0
75
=
60
= 1.25 : 1