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Rudy Severns, N6LF
PO Box 589, Cottage Grove, OR 97424; n6lf@arrl.net
A Closer Look at Vertical
Antennas With Elevated
Ground Systems—Part 2
N6LF shares his results from further HF vertical antenna experiments.
[Part 2 concludes this article, which began
in the Mar/Apr 2012 issue of QEX . — Ed.]
Multiband Verticals
For a single band antenna we can avoid
the problems of long radials by simply using
radials that are short enough or by increas-
ing the number of radials, but what about the
case of multiband antennas where you typi-
cally have four λ/4 radials for each band? For
example, if you have 40 m λ/4 radials, these
will be λ/2 on 20 m, ¾ λ on 15 m, and so on.
In light of the information we found for G a
as a function of L in Part 1, is that a prob-
lem? I don’t have the space here to explore
it in detail with modeling, but I have looked
at multiband elevated verticals experimen-
tally. The information was in Part 5 of my
QEX series, “Experimental Determination
of Ground System Performance for HF
Verticals.” Part 5 was in the July/August
2009 issue of QEX , pp 15-17. That series
of articles is available for viewing on my
website: ( www.antennasbyn6lf.com ). The
experimental work indicated that as long as
there are a large number of radials (whether
they are the same length or of different
lengths) you don’t have a problem but if
you try to use only a few long radials you
will have problems. Read the article for the
details.
Figure 27 — Examples of the voltage from a radial wire to ground with different numbers of
radials. The input power to the vertical is 1500 W, the operating frequency is 3.5 MHz and the
radial system is elevated 8 feet above ground.
I think this Figure makes it clear why you
want to keep the radials out of reach! Note
that as more radials are added the potential
difference between the radials and ground
drops signiicantly and becomes more uni-
form as we go away from the base of the
antenna. This is a relection of the reduction
in E-ield amplitude with more numerous
radials, as was shown in Figures 24, 25 and
26 in Part 1 of this article (Mar/Apr 2012
QEX ). Even with a large number of radials
that voltage is still high. This voltage will
vary with the square root of the power level
so that going down from 1500 W to 100 W,
a change of 15:1 (0.067), the voltage only
drops by 0.26! Be careful!
Potentials on the Radials
As Laport stated, elevated ground sys-
tems can have very high voltages between
the wires and ground. Figure 27 shows
examples of the voltage from a radial wire
to ground for ideal 4, 12 and 32 λ 0 /4 radial
systems.
Feed Point Impedances
The behavior of the feed point imped-
ance over the band (3.5 to 3.8 MHz for these
24 QEX – May/June 2012
Reprinted with permission © ARRL
 
examples) as we vary H, L, J, N and soil
characteristics is an important factor. The
point I want to make in this section is how
widely the input impedance of ground-plane
antenna can vary as we change one or more
of the variables. There is no one number for
Z in ! We will also look at variations in SWR
bandwidth.
A graph of the feed point impedance
(Z in = R in + j X in ) from 3.5 to 3.8 MHz for
different numbers of radials is shown in
Figure 28. Note that in Figures 28 to 31,
H = L and is adjusted so that the model is
resonant at 3.65 MHz for each variation
of parameters. As the parameters N, J and
soil characteristics are changed, the values
for H and L vary somewhat. From Figure
28 we can see that N has a strong effect on
the feed point impedance (Z in ) although that
effect diminishes as N increases. As shown
in Figure 29, we can convert the informa-
tion in Figure 28 to SWR. In this case the Z 0
impedance for the SWR calculation is taken
to be R in at resonance (3.65 MHz) for each
value of N.
Figure 29 shows that the 2:1 SWR band-
width increases somewhat as N is increased
but by N = 16 we are approaching the point
of vanishing returns for bandwidth.
Figure 30 shows the effect of height
above ground of the radial fan (J) on Z in for
N = 4. It’s pretty clear that the value for J has
a strong effect on Z in . The effect of differ-
ent soil characteristics for a given value of J
(8 feet in this example) is shown in Figure 31.
The information in Figures 28 to 31 rep-
resents only a few possible combinations, but
the graphs make the point that the feed point
impedance of an elevated radial vertical is a
strong function of all the variables, so that
each installation is unique.
We can also see the behavior of Z in over
the band for different combinations of H
and L that are resonant at 3.65 MHz. Some
examples are given in Figure 32 and the
associated graphs for SWR, are given in
Figures 33 and 34. N = 4 and the H&L com-
binations are shown on the graphs.
The combination H = 73.25 feet and
L = 43.11 feet has the very nice property
that Z in = 50 Ω at 3.65 MHz. As shown in
Figure 33, this results in a relatively wide
2:1 SWR bandwidth compared to the other
combinations.
The greater match bandwidth is not just
because Z in = 50 Ω at resonance. The com-
bination also has intrinsically more band-
width as shown in Figure 33, where the Z 0 at
resonance is set to R in at resonance for each
combination of H and L separately.
The idea of increasing the feed point
impedance at resonance to 50 Ω by making
the vertical taller and the radial fan radius
smaller has actually been around for many
Figure 28 — X in versus R in (Z in = R in + j X in ) where frequency varies from 3.5 MHz (lower left
ends of the curves) to 3.8 MHz (upper right ends of the curves) for different values of N.
Frequency is stepped in 25 kHz intervals.
Figure 29 — Feed point SWR as a function of N.
years: R in at resonance can be increased by
sloping the radials downwards from the base.
In effect you are making the vertical taller
and reducing the radial fan radius, which is
what we did in the above example.
Figure 9 (in Part 1) showed how L r varied
for different values of N and H. For H = 69 feet,
L r decreased rapidly as more radials were
added. We can play this game to ind designs
where Z in = 50 Ω at resonance. Figure 35 is
a graph where L is varied from 15 feet to
100 feet for two values of H (72 feet and
77.6 feet). Note that H in the range of 72 feet
<=> 77.6 feet represents the limit that allows
R in = 50 Ω . Longer or shorter values for H
do not have a point where R in = 50 Ω for
L = 15 feet <=> 100 feet. The combination of
H = 72 feet, L = 25 feet, N = 16 and J = 8 feet
QEX – May/June 2012 25
Reprinted with permission © ARRL
 
over average ground will give us Z in = 50 Ω at
3.65 MHz. Figure 36 shows the comparison
for SWR between two combinations where
N = 4 and N =16. This illustrates one of the
advantages of using more radials.
For H = 72 feet and N = 16, L is only
25 feet that represents a drastic reduction in
the radius of the radial fan. In exchange for
an increase in height on the order of 6 feet,
we have a good match over a wide portion
of the band and a small diameter radial fan.
Instead of increasing the height we could
have just added a couple of short top-loading
wires. This is very nice but it's not entirely
for free. When compared to the normal four
radial system (H = 67 feet, L = 67.7 feet), G a
for the H = 72 feet, L = 25 feet combination
is lower by about 0.25 dB. You sacriice a
small amount of gain. Whether that is accept-
able for the improvement in matching is an
individual decision.
In a private communication with Dick
Weber, K5IU, he made a suggestion that
overcomes the reduction in gain associated
with small radial length: use longer radials.
This will result in X in ≠ 0 but you can tune
out the reactance with a series impedance.
He has also pointed out that if X in is inductive
(+) then you can tune out the reactance with
a series capacitor at the feed point. Looking
back at Figure 35, we see that this trick will
work for H > 72 feet. (That is for this particu-
lar case, where N = 16, J = 8 feet over average
ground!). If we chose H = 75 feet, L = 70 feet,
N = 16 and adjust the series capacitor at the
feed point as we move across the band, we
get the result shown in Table 1. Note that X in
is given in the Table, but C s (the added series
capacitor) tunes it out.
What we see is a vertical that can have
a very low SWR across the entire 75/80 m
band. It isn’t necessary that C s be adjusted
at every point. Three or four values of C s
switched with relays would probably still
provide acceptable SWR over the entire band.
For the case where H = 72 feet, L = 25 feet
and N = 16, G a = –5.52 dB. When we change
to H = 75 feet, L = 70 feet and N = 16, G a =
–5.03 dB. That’s an improvement of +0.5 dB
in signal strength.
There is another option to make
Z in = 50 + j 0 Ω at resonance. Instead of mak-
ing the antenna taller (or top-loading it) and
the radials shorter, you can simply shift the
feed point up into the vertical to a point where
R in = 50 Ω. This is just a matter of moving the
base insulator up into the antenna. You won't
get quite as much match bandwidth as with
the taller vertical but it will be close and you
can use longer radials that give a better G a .
Whether this trick is mechanically feasible
depends on the particular implementation.
All the examples to this point have
assumed that the excitation at the base of the
Table 1
Z in and SWR from 3.5 to 4.0 MHz for H = 75 Feet, L= 70 Feet and n = 16
Frequency (MHz)
R in (Ω)
X in (Ω)
C s (pF)
SWR
3.50
43.7
69.6
654
1.14
3.65
49.4
113.7
384
1.01
3.80
56.0
159.4
263
1.12
4.0
66.6
223.6
178
1.33
Figure 30 — The effect of height above ground on Z in .
Figure 31 — The effect of different soil characteristics on Z in .
26 QEX – May/June 2012
Reprinted with permission © ARRL
 
sion for Weber’s 80 m vertical with four radi-
als. Figure 38 shows two things: the radial
current division between the radials is far
from equal and the division ratios change as
we move across the band. Unfortunately, this
is typical of elevated ground systems with
only a few radials, as shown in Table 2.
Weber explains this behavior by pointing
out that a horizontal radial above ground is
actually a section of single wire transmission
line open-circuited at the far end so that in
the region where L ≈ λ 0 /4 it acts like a series
resonant circuit. Figure 39 shows an equiva-
lent circuit.
Individually the radials may have differ-
vertical was isolated from ground: a choke
(balun) was used in series with the feed line.
If a choke is not used and the coaxial feed line
is simply connected to the antenna and run
down to ground, usually with the shield con-
nected to the radials and the center conductor
to the vertical, there will be additional ground
currents that increase loss. In a 4-radial
elevated system, G a typically falls -0.25 to
–0.5 dB or even more for lossy soils if a
choke is not used. If 12 to 16 radials are used,
the increased loss is much smaller, usually
only a few tenths of a dB. You might argue
that when N is large a choke is not needed
but I think it is better to be cautious and use a
choke even in that case.
Earlier we saw how the radial length (L)
affected the eficiency (G a ) of the antenna.
We also saw that the effect was reduced
when more radials were used. It is useful to
look at Z in as both N and L are varied, espe-
cially around values of L near λ 0 /4. Figure 37
shows the effect of varying L on X in .
Figure 37 is particularly interesting in that
it shows how sensitive the X in component of
Z in is to radial length when only a few radials
are used. The R in component is not nearly as
sensitive. This becomes important when we
look at current asymmetries in the radials.
Adding more radials reduces the sensitivity
of Z in to radial length and also the susceptibil-
ity to radial current asymmetry. Dick Weber,
K5IU (see Note 43) generated a graph very
similar to Figure 37 by assuming the radi-
als were open circuit transmission lines and
plotting the impedance at the feed point as
more radials were added in parallel. I have
more on radials as transmission lines in the
next section.
installations and, if there is, do we need to
be concerned about it? To answer the irst
part of this question, Dick Weber, K5IU,
made a series of measurements on repre-
sentative 80 m and 160 m verticals with two
and four elevated radials. Dick’s work was
published in “Optimum Elevated Radial
Vertical Antennas,” in the Spring 1997 edi-
tion of Communication Quarterly . (See Note
9 in Part 1 of this article.) I have summarized
some of his data in Table 2 but I strongly rec-
ommend reading his complete article.
Data tables are helpful but sometimes
a graph of the data has more impact.
Figure 38 compares the radial current divi-
Effect of Asymmetries in the Radial
Fan
Is there significant current division
asymmetry among the radials of typical
Figure 32 — Z in variation for different combinations of H and L that are resonant at 3.65 MHz.
Table 2
Radial Current Comparisons from K5IU Measurements
(See Note 9 in Part 1 of this article for a reference to the source of this data.)
Relative
Relative
Relative
Relative
Current
Current
Current
Current
Antenna #
Station ID
Frequency (MHz) Radial 1
Radial 2
Radial 3
Radial 4
1
K5IU
3.528
1.00
0.52
0.27
0.27
1
K5IU
3.816
0.96
1.00
0.51
0.51
1
WXØB
1.805
1.00
0.01
-----
-----
1
WXØB
1.885
1.00
0.05
-----
-----
2
WXØB
1.805
1.00
0.80
-----
-----
2
WXØB
1.885
1.00
0.10
-----
-----
1, 0.125 λ radials, w/inductor
WXØB
1.805
1.00
0.83
-----
-----
1, 0.125 λ radials, w/inductor
WXØB
1.885
1.00
0.76
-----
-----
1
W7XU
1.805
1.00
0.00
0.00
0.00
1st trim
W7XU
1.805
0.03
1.00
0.10
0.07
Last trim
W7XU
1.805
1.00
0.00
0.00
0.00
Last trim
W7XU
1.900
0.03
1
0.10
0.07
QEX – May/June 2012 27
Reprinted with permission © ARRL
Figure 33 — SWR for various combinations of resonant H and L. Z 0 = 50 Ω for all curves.
Figure 34 — SWR with Z 0 equal to R in at resonance for the particular combination of H and L.
28 QEX – May/June 2012
Reprinted with permission © ARRL
 

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