radial_system_design_and_efficiency_in_hf_verticals.pdf

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Radial System Design
And
Efficiency In HF Verticals
Rudy Severns N6LF
September 2008
The efficiency of an HF vertical depends on its associated ground system and the soil over which the
antenna is erected. The most direct way to determine the efficiency of an antenna is to determine
the fraction of the input power which is actually radiated. However, there is a small complication,
what do we mean by "radiated power" and how might we determine it? It turns out that there are a
couple of ways to define radiated power depending on what we're using the antenna for. One
practical way to address this question is to use NEC modeling which can provide the actual radiated
power and that's where the information in this note was derived from. Modeling results are
discussed below but details of the modeling itself are given in reference [2].
A related efficiency question is the long standing "conventional wisdom" that shorter radials work
better with shorter verticals. It can be argued that because shorter verticals have significantly higher
field intensities close to the base of the antenna (for a given input power), which leads to higher
ground losses, that it makes sense that more attention be given to the radial system close in. While
this sounds reasonable I couldn't find any quantitative justification. So I extended the modeling
study to include shorter antennas to see if the conventional wisdom had any quantitative basis.
Efficiency
Power ( Pi ) is delivered to the feedpoint from the source, some of this power will be radiated ( Pr ),
some will be dissipated in the soil ( Pg ) and some will be dissipated in the conductors and any
loading elements that may be present. For the purposes of this discussion we will ignore the losses
due to conductors and loading elements.
Efficiency ( η ) can be expressed in several ways but the most obvious is as the ratio of radiated
power to input power:
Pr
η
Pi
(1)
We usually state efficiency in percent (%). However, in a vertical what we are concerned with is the
change in signal strength for a given change in the ground system and many times it can more
useful to express efficiency in terms of dB:
1
989410602.129.png
Pr
⎛
⎞
η
=
10
log
⎝
⎠
Pi
(2)
For example, if the antenna has an efficiency of 90% that represents a signal loss of about -0.46 dB
compared to a lossless antenna. On the other hand if the efficiency is only 60% then the signal loss
is -2.22 dB. In most of the following discussion this is the form I will use, although for some graphs
it's more convenient to use the conventional % representation.
Radiated power (Pr)
Our definition of efficiency is a direct function of Pi and Pr . The meaning of "input power" is obvious
but what do we mean by "radiated power" and how do we determine it? One way of finding Pr is to
compute the total power passing through a virtual surface completely enclosing the antenna. For
antennas over ground this surface is typically a constant radius hemisphere some distance ( r ) from
the antenna. In the absence of ground losses (i.e. perfect ground) Pr = Pi everywhere in space and
the choice of r doesn't matter. However, if lossy ground is present then the value for r does matter.
As we go further from the base of the antenna (larger r ) ground loss increases and Pr will decrease.
If your only interest is skywave propagation for DX then you will be interested only in the power
radiated into space. Ground loss in the near field, energy that propagates as a ground wave and
reflection losses in the far field are all losses that reduce the "radiated" or skywave signal. NEC will
compute Pr directly for the case where the radius of the hemisphere is infinite. This is the average
gain ( Ga ). Ga represents the fraction of the input power which is radiated at an infinite distance, i.e.
the "skywave radiation".
Pr
=
GaPi
(3)
Dividing through by Pi we get:
Pr
η
Ga
=
Pi
(4)
EZNEC gives Ga in two forms, a decimal value and in dB. The decimal value multiplied by 100 is
the efficiency in percent. Over perfect ground no power is lost and Ga = 1, or equivalently, 0 dB.
Over real ground Ga still represents the radiated power but Ga will have some -dB value which takes
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989410602.140.png 989410602.150.png
into account the power dissipated in the ground surface out to infinity. The curvature of the earth is
not taken into account in the NEC Ga calculation but that has only a very small effect.
While stating efficiency in terms of sky-wave radiation makes a good deal of sense, it's more
common to think of efficiency in terms of only the near-field losses within 1/2 to 1 wavelength of the
base of the antenna. This is the region within which it may be practical to install a ground system to
reduce Pg and thereby increase Pr for a given Pi . For that reason when calculating Pr the radius of
the hemisphere is typically made 1/2 to 1 wavelength and integration of the radiated power density
over that surface gives us Pr . We then can go on to determine η .
The problem with this approach is that NEC does not automatically do this for you. You have to first
use NEC to compute the complex values of the E and H fields over the surface of the hemisphere
and then take the vector cross product to get the power density on that surface. Finally you need to
integrate over the surface to get Pr . This is complicated and you have to have some mathematical
skill. Taking this approach you will get values for η which reflect what is going on in the immediate
region of the antenna.
This information may be interesting but if your only interest is in determining the improvement in your
DX signal a given radial system improvement will provide, then you can just use the average gain
calculation. No math skills required! The incremental change in signal will be very similar for both
methods but the absolute values for η will be different.
7.2 MHz Modeling results
Figures 1 and 2 show the efficiency for r = 1 wavelength for two different soils.
0.00
7.2 MHz
0.005/13 soil
r=40m
-0.50
128 radials
-1.00
-1.50
64 radials
-2.00
32 radials
-2.50
16 radials
-3.00
8 radials
-3.50
-4.00
-4.50
4 radials
-5.00
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Radial length [wavelengths]
Figure 1, efficiency in dB as a function of radial number and length in average soil. r =40 m.
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0
7.2 MHz
0.02/30 soil
r=40m
128 radials
-0.5
64 radials
-1
32 radials
16 radials
-1.5
-2
8 radials
-2.5
4 radials
-3
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Radial length [wavelengths]
Figure 2, efficiency in dB as a function of radial number and length in very good soil. r =40 m.
These two figures very clearly illustrate what is to be "gained" by using more and longer radials.
However, looking at figure 1 (average ground) we see something funny. When using only four
radials, as we increase the length from 1/8-wave the efficiency goes down, not up. The same thing
happens for eight radials only not quite as much. More copper means more loss not less!
We do not see this effect in figure 2 which is for the same antenna over very good ground. In this
case when there are only a few radials, increasing the radial length does no harm but also does little
good. A few long radials in good soils are a waste of copper. The loss effect seen in figure 1 stems
from a radial resonance which can increase ground loss. This effect is described in reference [1].
Alternately we can graph efficiency in terms of Ga as shown in figures 3 and 4. Unfortunately this
also shows how inefficient verticals are even over very good ground. Very depressing! For example,
with very good soil (0.02/30) and 128 1/2-wave radials, the efficiency of a 1/4-wave vertical is still
only -2.76 dB (53%)!
4
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-3
7.2 MHz
0.005/13 soil
r=infinity
128 radials
-3.5
-4
64 radials
-4.5
32 radials
-5
-5.5
16 radials
-6
-6.5
8 radials
-7
-7.5
4 radials
-8
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
Radial length [wavelengths]
Figure 3, Efficiency in terms of Ga for average soil.
-2.5
7.2 MHz
0.02/30 soil
r=infinity
128 radials
-3
64 radials
-3.5
32 radials
-4
16 radials
-4.5
8 radials
-5
4 radials
-5.5
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
Radial length [wavelengths]
Figure 4, Efficiency in terms of Ga for very good soil.
This observation does not imply we should abandon verticals! In many cases, particularly on
the low bands where support height is usually limited, verticals can often provide a stronger signal at
the desired low angles for DXing than a practical horizontal antenna. Incorporated into arrays
verticals provide a practical way to have gain arrays with steerable patterns on the low bands.
5
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