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The mystery of radials
Erecting the antenna above ground (II) The first effect of placing a 1/4l vertical at ground level is that the mirror-image of the "missing half" has consequences on the feed point impedance that displays about half the impedance of a dipole, or about 35 ohms plus ground loss resistance. At the risk to being repetitious, its lower end displays a low-voltage/high-current, conform to its large lobe firing all the output power at 0° and not higher above the horizon. But other effects look more amazing... Some manufacturers state for example in their advertisings that they sell high performing antennas that do not request any radial or counterpoise (ground plane). Does it mean that if we raise our vertical a couple of meters above the ground, we can remove all our radials and keep its efficiency ? No, you can't. This is not really so simple, except if you are willing to loose all its efficiency... and your money. Do
you remember the 120 radials 1/2l long
each lay on the ARRL's estate to make up all ground losses... ? Good
news ! According to Bencher one more time, "at
heights between 2 and 8 m about ground [...], four 1/4-waves
radials for 40 meters do suffice to provide enough capacitive
coupling to earth to work on 40, 75, 80 and even 160 m bands". Indeed, to avoid the detuning of wires running at ground level
and reduce the ground currents you must raise the radials as low
as 1 meter off the earth. Of course you will raise the antenna by
the same occasion, and probably much higher as we will see in one
moment. In
fact here also some amateurs confuse the height of radials above
ground and the height of the antenna above ground. As both
constitute the radiative part of a vertical antenna and that one without
the other is ineffective, the melting is understandable. But try to
see clearly in this new shallow fog. For example, if one states like Bencher
that for the 40-m band radials can be placed between 2 and 8 m high
(1/20l to 1/5l
high) to remove all ground effects, the antenna itself displays its
best radiation pattern when placed at least... 3/4l
above ground (see table below), so about 30 m high ! Find the
mistake... Both values seem incompatible, but they are not. In fact
your radials will raise with your antenna and will be thus placed
high enough above ground to be "out of reach" from the
soil effects. Ground
plane antennas
We
have not told yet, but although our vertical is now raised in
height, it needs always its mirror-image to work properly. In
this case, the earth is too far and our connection running to the
ground will be detuned as we told before. So, instead of being
grounded the vertical works against a simulated ground made of some
1/4l
radials or stubs attached to the base of the antenna to create an artificial
ground plane at a few meter high, hence its name.
These radials are either open at 45° like a tripod or attached
perpendicular to the antenna axis. For mobile operations the radials
are removed at the benefit of loading coils in order to reduce their
profile. If
we raise the antenna base at a height of 1/2l or
so as states Bencher, usually four or six 1/4l
radials only provide about the same efficiency as dozen or even an
hundred 1/2l radials running underground.
However, whatever state advertisings, when the height above ground
decreases say below 1m, the number of radials required to get the same efficiency
increases naturally. This is pure technical question, not of
marketing... Height
of antenna center (l) Takeoff
angle 1/4 0°
or almost on the horizon From
14 MHz and above (because it is impracticable on lower bands) the
best radiation pattern for a vertical appears from 3/4l
high above ground where an additional lobe appears at 43° of
elevation. At 1.5l high the
vertical antenna sees its main radiation lobes splitted in 4 parts,
the main horizontal one splitting in 3 parts at 0°, 20° and 43°
of elevation and a fourth one appearing at 90° (vertical). The
"Bencher" configuration using some 1/4l
radials placed in height is called a counterpoise. Used in HF and V/UHF
bands, these Ground plane antennas are installed on small and light masts from
2 to 9 m high usually erected above the common obstacles using as few as three
radials or stubs. Rather efficient, these vertical antennas are largely used,
not only by amateurs but also by other services using
shortwaves, hence the presence of a large amount of V/UHF Ground
plane antennas here and there at the HQ of many companies. If
you have a restricted place to install a vertical antenna or have
possible issues with condominium (coproprietary) rules or with the
neighborhood, erecting an antenna very high can be an impossible
task. As
we saw in the table displayed above, for a vertical cut for the 20-m
band, say 5 m high if we use its mirror-image in the ground, the best
efficiency is reached erecting the antenna center up to 30 m high
(100 ft) ! Waow, not easy for everybody. If some amateur installations exceed
largely this height, for most of us this is
neither feasible or economical. So for the lower bands of 40 to 160
m, amateurs have found some hybrid solutions, like using together
a vertical from 9 to 15 m high associated to a radial system made of
only 4 wires as long buried in the ground. The antenna being less than
1/4l
high, the input reactance without loading is capacitive. In this
case a simple series loading coil placed at the base of the antenna
will ensure the matchting to the feed line and the transceiver.
QST
magazine and the other publications edited by ARRL about
antennas have provided several models of such designs (including
several models using wire antennas tight in inverted-V or forming a
loop). Radiation
and SWR : the antenna efficiency Another
question arises when speaking of efficiency : what becomes the power
put in the antenna and how losses affect the SWR ? First
let's do a bit of theory. The
antenna efficiency (er,
also named antenna radiation efficiency) is the radio of the radiated power
Pout
to the input power Pin
of the antenna :
er
= Pout
/ Pin While
it is a number without dimension between 0 and 1 (or expressed as
a percentage), it can also be quoted in decibels.
Knowing that the power ratio in dB = 10 log Pout/Pin,
an efficiency of 0.1 or 10% is 10 log 0.1, so er
= -10 dB, and an efficiency of 0.5 is -3 dB.
The antenna efficiency (er)
is different from the antenna "total efficiency" (eT). This
later considers the antenna system as whole. The total
efficiency of an antenna is the radiation efficiency multiplied by
the impedance mismatch loss of the antenna, when connected to a
transmission line or "receiver", a radio receiver or a
transceiver. This can be summarized by the next relation :
eT
= ML
* er
where
eT
is the antenna total efficiency, ML
is the antenna loss due to impedance mismatch, and er
is the antenna radiation efficiency.
Note
that many consumer products show a low antenna efficiency,
typically ranging from 0.3 to 0.7 or -5 to -15 dB.
Calculating
the efficiency, the 3R equation
Calculating
the antenna efficiency using the above relations can not be easily
performed manually. This calculation requires to measure the above
factors by means of tools that we rarely find in ham shacks like an
antenna analyzer or better, its graphical version, the vector
network analyzer (see end of page).
However,
it is not enough to own such an analyzer to use it properly. Many
novices consider the SWR readout as equivalent to the resonant point
of the antenna. Not necessary. It is only true when the input impedance
display a 50
W resistivity (R=50, X=Fj).
For other non reactive values, both the transmission line (coax) and
the analyzer will alter this result by an amount depending of the
mismach amplitude. So the first to do to prevent errors, is to
perform this measurement not ta a few meters away on the coax line but almost
at the contact of the antenna (within a few centimetres).
Three
main factors can modify the antenna efficiency : -
Ground losses, Rg -
Radiation resistance, Rr -
Coil losses, Rc The
total loss (RT)
is practically, we will see why, the sum of all these "3R"
: RT
= Rg
+ Rr
+ Rc Now,
the antenna total efficiency (eT)
is the ratio between the radiation resistance (Rr)
and the total loss (RT)
: eT
= Rr
/ RT As
above, you can express this result in dB using the relation 10 log (Rr
/ RT). Note
that if in laboratory we can get a very high efficiency almost on
any band with a short antenna, according to tests performed by ARRL
staff using a 3.15 m (10.5') whip, in the field figures are much
lower : 0.1% on 160 m, 7% on 80 m, 31% on 40 m, 69% on 30 m and 88%
on 20 m. Let's
review now each loss type affecting the antenna efficiency. Ground
losses dominate the other losses and thus must be kept as low as
possible. Ground losses depend on many factors like the antenna
mounting, how the antenna is wired and bonded, where the ground
plane (mass of metal) begins, how much metal is used beneath the
antenna in order it radiates properly at low elevation (<15°),
how coax is terminated and whether it is in good state, how chocke and coils are designed, etc. Radiation
resistance is another word for input impedance or resistive
losses. It is a concept,
a mathematical function, rather than a parameter that we can measure
as it. It defines the effective electrical length (not the physical
length) and how the current flows in this circuit. The longer the
antenna electrical length, the higher is the radiation resistance. Its
value change as a square law function (x2)
: from a whip 2-m high to 3-m high, the radiation resistance is
roughly multiplied by 2. Changing a 2-m whip for a 4-m high antenna,
the radiation resistance will be 4 times higher. With a value of 0.2
W for an antenna cut
for the 80-meter band, the radiation resistance can reach 36
W on
the 10-meter band. The
radiation resistance also increases in using cap hats on vertical
antennas. Properly designed, they increase the effective electrical
length and increase the current node. This accessory is the most
efficient on the lower bands where correctly installed the radiation
resistance can be multiplied by 4. For
short, better using a long antenna, specially in portable or mobile
operations, than a short one. You
will find more information about effects of current in the article
describing degree-amperes
and field strenght written by Edmund A. Laport. Coil
losses are by definition losses in all antenna systems using loading
coils. There are mainly installed on small portable and mobile antennas without
to forget shortened beams that often included coils on all elements
(reflector, driven and directors) to
compensate losses. Indeed,
coils are used in all "small" antennas shorter than l/4
on the working frequency, and thus displaying a capacitive reactance
(know a -j). A coil is then added showing an opposite value, thus a
positive reactance (+j). Of course, logically, the smaller the
antenna is cut, the larger the coil reactance will be. Consequently,
all else being equal, will note an increase in coil losses. As
we explained in Basics of antennas
about the Q-factor and the interest of installing a capacitance hat
(cap hat), one can easily increase coil losses in trying to improve
the performances of a small vertical. Indeed, if the cap hat is
place just on top of the coil, the antenna system will display an
excess capacitance and coil losses will increase. In
the same way, although using large coils vs small ones can increase
the Q-factor on specific frequencies or on the low bands, they also
become very lossy at the same low bands. At
last, we stated above that the total loss is "practically" the sum of the
3Rs because there are always additional very small losses in all
metallic accessories connected to the antenna : in the mast, the
whip, the material in which the antenna is made of (stainless steel
affect more for the lower bands), the possible trailer hitch
mounting, and even depending on the diameter of the antenna tubing.
Some will add serial losses, others capacitives losses, serial or in
parallel with the input impedance.
Results
in the field Now
that we installed our antenna system and know what factors can affect its
performances and how to correct them, let's see what really happens
in the field, and specially what values do we measure and calculate. The
radiation resistance or RF energy radiated by your
antenna has to be consider as a "good lost" compared to
the lost induced by the ground and conductor resistance that are
consider as a total loss. Thus, knowing that some
"conductors" (including traps, loading coil, etc) loose
more energy than others, we can use the concept of form factor, the
famous Q-factor. But
due to ground losses, than can easily exceeded the losses in
conductors, traps and coils, a well tuned vertical cut at 1/4l
can display a high SWR in the middle of a band (over 2:1) what means
that some dozen of ohms vanished in pure ground loss resistance.
Here are some tests made in situ. The first shows the efficicency
before (first row) and after (second row) installing 6 radials of 2m long at ground level
around the base of a 1/4l
vertical : Antenna SWR Line
Impedance (ohms) Radiation Resistance
(ohms) Total
Losses (ohms) Efficiency 1/4l
vertical 2:1 50 35 65 35% 1/4l
vertical 1:1 50 35 15 70% SWR
is measured at the antenna feed point in place of the RTX
end to avoid transmission losses and increase the accuracy. Total losses
are due to
radiation lost in coax, traps, loading coils, and ground
loss resistances. The efficiency is expressed
as the ratio of power radiated to the total power fed to
it (or the ratio between the radiation resistance to total losses). Below
is the efficiency
before and after installing 6 radials at the base of the
previous vertical but resonating at half-frequency (e.g.
on 80m in place of 40m), the
third case using 120 radials to reach a zero ground
resistance : Antenna SWR Line
Impedance (ohms) Radiation Resistance
(ohms) Total
Losses (ohms) Efficiency 1/8l
vertical 3:1 50 12 138 8% 1/8l
vertical 1.5:1 50 12 63 16% 1/8l
vertical 1.5:1 50 12 5 16% For
comparison purposes, here is the efficicency of a dipole : Antenna SWR Line
Impedance (ohms) Radiation Resistance
(ohms) Total
Losses (ohms) Efficiency 1/2l
dipole 1:1 75 12 1 90% From
these figures we can conclude that several parameters are very
important to get the highest efficiency of a vertical : 1°.
The radiation resistance must be kept as high as possible, but it
depends on total losses thus, 2°.
The radiation resistance depends on the height of the vertical, but
as height over 1l are not always
practicable, we can reduce the ground loss resistance using as many
radials as possible in using high-Q loading inductors of large
diameter. Therefore the slim loading coils and traps made of thin
wire encasted in metal usually found in ham stores are NOT at all
adapted to this usage. 3°.
A low value of SWR does not mean that your antenna system is
operating efficiently. Even the fence installed in the end of your
backyard or an electric heater could be fine-tuned with an ATU to
display a SWR 1:1 but it will not radiate the least watt of power as
explained on this page dealing
with SWR. Antenna
Gain and Directivity The
antenna gain (G) is related to the antenna efficiency (er)
and the antenna directivity (D) as next : G
= er
D The
gain is quoted in decibel (dB). The antenna radiation pattern can be
expressed as a function in spherical coordinates (polar angle q
and azimut f). In
a diagram in cartesian coordinates showing the elevation plane, the
radiation pattern is only a function of the polar angle q
: F(q,f)
= Ö
(sin q) F(q,f)
= (sin q)5
In
using of one of these equations, and plotting the values for each
angle in a cartesian graph (polar angle vs decibel), you can easily
plot the radiation pattern of an antenna in elevation and display
its lobes as below right. At left, the similar plotting in polar
coordinates (sometimes faulty named "3D radiation
pattern") showing the azimuth plane pattern. Document
Cisco. Software
and antenna analyzer
Of
course, all measures and calculations executed manually can be
performed automatically either using electronic devices or software. There
are free solutions like Smith Charts
from AC6LE or the VOACAP
propagation prediction program (see also this review)
that includes a EZNEC module
from W7EL, but you must know the specifications of your antenna.
These
programs do not calculate the total efficiency and are limited to
the SWR and lobe pattern calculations. EZNEC+ is also able to display Smith
charts, return loss, and reflection coefficient magnitude while EZNEC
Pro also includes the loss in wire insulation among many other
features.
More
complete but more expensive, you can purchase an antenna
analyzer like MFJ-259C
(or the previous model MFJ-259B) from MFJ Enterprises. Its price of 299.95$ and much lower on the
second hand market makes it available to amateurs.
At
last, with a lot money, you can also purchase a professional vector network analyzer
like Keysight
E5061B ENA. But even if you are lucky and found an used model on
the second hand market (there are very scarce), it will cost more
the 17000$ knowing that a brand new model costs more than 27000$.
So, it is not really in reach of the "poor ham radio operator", but who knows.
To
read : Catalog
of Vector network analyzers, UCL University
From
left to right, the MFJ-259C
antenna analyzer from MFJ Enterprises, the Keysigh
(ex-Agilent) E5061B
ENA vector network analyzer, and a plotting from EZNEC
module included in VOACAP
propagation prediction program (see also this review). By
way of conclusion I
think that this time we emerged safe and sound from our fog so much
dreaded. We discovered that a ground plane radial system is recommended
as it provides low-loss "return" paths to currents that can be
"recycled" in the antenna, that might otherwise flow on
the lossy earth. If these return of current come back to the shack
they can be stopped using a current choke, a variant of balun 1:1. Even
if a "no-radial" system displays a low SWR, by itself it
tells us nothing about the antenna efficicency, and mainly how the
ground interacts with the system. For short, a simple vertical 8-m
long (26.6 ft) using radials and a commercial "no-radial" vertical will display
the same performances, but the SWR of the second antenna at the feed
point can reach 20:1 or more without losing any energy but without neither emitting the
least watt ! When
an antenna is placed near ground level, the earth losses are the
major factor limiting the antenna performances, and no antenna tuner
or matching device can do anything about that physical law, except maybe some bad
advisers and vendors. Thus
if you have to remember only one think, that will be the next one
: radials reduce the ground losses and increase the antenna
efficiency. A side effect, too few or too short radials affects the SWR. With
all this information, it looks no more as an idle fancy or diligence from
a manufacturer if he tells us that radials are useful ! Now you know
why. For
more information
Basics
of antennas (on this site)
SWR,
the radiation resistance (on this site)
All
about transmission lines (on this site)
From dB to S-point : Learn to play with power units
(on this site)
The
ARRL Antenna Book 1998, (PDF), QRZ.ru How
Many Radials Does My Vertical really Need?, Rudy Severns, N6LF,
QEX, May/June 2008 (PDF, 700 KB)
ARRL Antenna Book,
ARRL, specially chapter 16 about the efficiency, also available on CD-ROM
Vertical Antenna Classics, ARRL RADIAL_3.EXE,
Reg Edwards, G4FGQ, calculates the efficiency of any system of
radials
Degree-amperes
and field strenght, by Edmund A. Laport (about antenna
currents). Another
Look At Reflections, by Walter Maxwell, W2DU (sk), QST
magazine, 1973-1976 (PDF on K6MHE website)
In QEX
magazine,
May/June
2011, p39, Alan Payne, G3RBJ wrote an interesting article about the
coil theory. In
QST magazine, 1973-1976, Walter Maxwell, W2DU (sk) wrote articles
dealing with
antennas, SWR and line lossses titled Another
Look At Reflections (PDF) In
QST magazine, September 2006 issue,
pp56-57, VE2CV explains how to use an antenna
analyzer and EZNEC to calculate the antenna efficiency (in this case
of a mobile antenna). Page 56 also describes SWR. Page
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