(1) A ground system having a hundred properly
installed radials has negligible loss resistance (Ref
20). AM broadcast stations operating in the 540- to
1600-kHz band use either 120 or 240 radials, while
the FCC requires a minimum of 90. With such a
ground system the terminal impedance of a thin
quarter-wave (X/4) vertical is approximately the
theoretical value of 36.5 + y'22 ohms, and becomes
approximately 32 ohms resistive when the antenna
is shortened to resonance. Thus, when fed with a
50-ohm line, the SWR at resonance will be close to
1.6, rising predictably on either side of resonance.
However, a ground system having only 15 radials
has approximately 16 ohms of ground-loss resistance
with this antenna. Thus, if we remove a few
radials at a time from the 100-radial system, the
increasing ground (loss) resistance adds to the
fixed radiation resistance, increasing the total
resistance terminating the feed line. Hence, as each
radial is removed, the terminating resistance comes
closer and closer to 50 ohms, reducing the SWR.
When enough radials have been removed for the
ground-loss resistance to reach 18 ohms, the terminating
resistance will be 18 + 32 = 50 ohms, for a
perfect one-to-one match! While the SWR went
down, though, so did the radiated power, because
now the power is dividing between 32 ohms of radiation
resistance and 18 ohms of ground resistance!
In cases where losses are very small, it is unnecessary
to improve an impedance mismatch that produces an
SWR of only 1.6:1, because only a 0.24 dB
increase in power will result by reducing the 1.6:1
mismatch to 1:1. However, in this antenna situation,
reducing the 1.6:1 mismatch to 1:1 by removing
radials will cause a 36% decrease in radiated power,
a loss of 1.93 dB in the ground resistance.
Ground resistance with 100 to 120 radials is typically
in the range of 1 to 2 ohms, or less. However,
ground systems having from two to four radials may
have a loss resistance as high as 30 to 36 ohms, so
now the SWR at the resonant frequency will be
around 1.3 or 1.4. However, when operating at other
frequencies, instead of rising from this low value of
SWR, as it should at frequencies away from resonance,
the ground-loss resistance holds the off-resonant
SWR to lower values than would result with a
good ground. The low SWR simply indicates that
the line is well matched, but it offers no clue that
approximately half the power is heating the ground.
Thus, the low SWR in this case is misleading;
instead of verifying that the antenna system is efficient
over a wide frequency band, it is actually
telling us that the efficiency is very poor indeed!
here's the simple, non-technical explanation. the
larger the number of radials used, (to collect the
current radiated by the antenna) the lower the
loss resistance, the higher the radiation efficiency
and the better the performance, both in xmit and
rcve, according to the principle of reciprocity.