Small antennas and radiation resistance
Radiation Resistance
Related pages on Antennas , radiation
and fields , mobile and short
verticals
My 2004 Dayton Hamvention Power Point presentation on Small Verticals can be
downloaded here… DAYTON 2004.
When dealing with
small antennas, the main
points to remember are:

There is no magic bullet or magical cure that causes
a small antenna to act like a large antenna. The problem and solution comes down to net
or effective commonmode current distribution
over linear spatial distance (current movement in a direct line across a
distance of physical space) . 
Small antennas require extraordinary care to
obtain high efficiency.
How do we make a small antenna as efficient as
possible?
 We make current as uniform as possible over the length of the
antenna by using
as much
capacitance as
possible at the
antenna ends.  We use lowloss loading such as optimum form
factor (size, length, and
diameter) loading coils.  We make the antenna as large and
as straight
in a line as possible. We
don’t fold, bend, zigzag, or curve the antenna…… or fold or zigzag the
least amount possible….especially in the high
current areas!  We keep the high voltage points (the open ends) away from
lossy things
(such as lossy earth
or wet foliage).  We keep the high current areas away from other large lossy
conductors.  If we have a Marconi antenna with a small ground system, we isolate that
system from lossy earth. This generally includes line isolators for coax
shields at the feedpoint, so the only earth path is through the
groundisolated counterpoise.
The steps
outlined above maximize radiation resistance
and
minimize loss. Let’s
look at the
interaction between radiation resistance and loss
resistance.
Radiation Resistance
Radiation resistance is
both the most useful
and the least useful
antennarelated term.
Radiation resistance
can easily be
misused and rendered
useless. This is because
radiation resistance
has multiple
poorlydefined meanings. When a term has several nebulous meanings
or uses, it is only
natural that misuse
or mixing of terms appear. Lack of a firm,
single, wellaccepted, definition
allows the term “radiation resistance” to slip from one
definition into another. This
often results in
wellintentioned, but
totally erroneous
conclusions, that seem to follow accurate,
logical, thought!
Common Uses
There are two commonlyused “correct” meanings
of radiation resistance, and one totally incorrect use. The
“correct” uses are:

The resistive part
of an antenna’s
feedpoint
impedance that is
created solely by radiation from the antenna (This is the feedpoint
resistance less and loss resistances in the system) 
The total power radiated in all directions divided by the
square of maximum net (or effective) current causing the radiation (This is
the IRE definition)
Neither of the above definitions include loss resistances of any
type! The moment loss resistance is included, we have a third commonlyused
(but totally useless) definition. This definition, which includes losses,
could
be considered “incorrect” because it
includes resistances that have nothing
to do with radiation. The misused,
or nearly useless, definition is:
3. The simple real (or resistive) part of an antenna’s feedpoint
impedance, irrespective of whatever the feedpoint is in relationship to the radiating
current maximum or any losses.
The correct name for
numbers 1 and 3 “radiation resistance” are
actually the antenna feedpoint resistance. They do not show the
real radiation
resistance!
Of the above good
or useful definitions, the first
definition is most commonly abused through mistake. The second definition is
an IRE definition (albeit a good one that never caught on). In every case, the second good definition,
which is also the least commonly used, provides the most direct
and useful answer.
Examples of Misuse
In
order to understand
what is right, we
sometimes have to
learn what is wrong.
Let’s look at a few
examples where
radiation resistance
is misused to give
nonsensical answers.
Folded Monopoles
Folded monopoles provide the
clearest common example of radiation resistance
misuse. Quite often, in discussions of
vertical antenna
ground system loss,
claims are made that multiple drop
wires increase radiation resistance and lower
earth or ground
system losses. The
justification is
multiple drop wires,
or a folded monopole
element, increases
radiation resistance.
The increased
radiation resistance
reduces ground
currents and ground
losses. This concept
is justified and/or
rationalized through
use of another commonly misused and abused
formula:
eff % = 100 * Rrad/(Rrad + Rloss) .
In order to use the formula above, all losses must be
normalized to the
same point where radiation resistance is taken. Without doing that, the
efficiency formula
above does not work!
Many articles, especially folded monopole articles, either
ignore the fact that
loss resistances
must be normalized
to the feedpoint, or
authors are
unaware of that
fact.
Let’s look at what actually happens in a folded element, and use
it to understand how the poor definition of radiation resistance causes
efficiency
misunderstandings.
Consider the unipole
to the left. Let’s
assume it is 1/4
wavelength tall.
Let’s assume we short
or close the open gap and feed it as a normal
1/4 wave Marconi vertical with a feedpoint at the
point where I3 is
shown. I3 is ALWAYS the vector sum or inphase combination
of currents I1 and I2. With continuity through each leg, I1 and I2
equally share all of
the ground current. This happens regardless of where the feedpoint is located in
the lower portions of the antenna.
With 1/4wl height and
with a reasonable element diameter, the
radiation resistance (fed as a traditional monopole) would be about 36ohms.
Let’s assume ground loss, normalized to the point where we measure I3,
is14 ohms.
Applying 500 watts
makes I3 a current
of
3.16 amperes. Power loss in ground resistance would be I^2R, or 3.16^2 times
14, about 140 watts. Feedpoint resistance would be 50 ohms. Feedpoint power,
as a check, would be 3.16^2 times 50 ohms or 500 watts. With equal diameter
legs, this current would divide and 1.58 amperes would flow in each upper leg
at I1 and I2.
Let’s use the
formula eff %= 100*Rrad/(Rrad+Rloss). We have
36/36+14 = .72 so the result is 72% efficiency,
or 28% loss. 28% loss times 500
watts is 140 watts in ground losses. This matches the other method just
above.
Opening the
gap and feeding as a folded unipole,
half of the radiator current is in I1 while the other half is in I2. Current is
halved to 1.58 amperes at the feedpoint and power remains the same. The
feedpoint resistance now becomes 200 ohms. We can confirm this with I squared R,
or 1.58^2 *200=500 watts. It all works out great so far!
Now let’s
misuse the same efficiency formula, like Bill Orr did in
his Radio Handbook and others do in various
articles. We have 200/200+14 =
.9346 or 93.46 % efficiency.
It seems by using
the folded monopole
element we have
increased efficiency
from 72% to 93.5%!
We know we still have 3.16 amperes flowing as I3, and we know
ground resistance is still 14 ohms (normalized to the point where I3 is
measured). IsquaredR losses are 3.16^2 * 14 = 140 watts! We have exactly the
same power loss in
the ground.
Let’s transform the ground loss value that was normalized at
14ohms where I3 is measured to the feedpoint by the same impedance
multiplication as the feed resistance, or 1:4. We’d now
have a normalized ground
loss resistance
of 4*14 = 56 ohms. 56 ohms of the
200ohm feedpoint resistance is loss. Trying
that same efficiency formula, we get:
144/144+56 = .72, or 72% efficiency!!! Now everything checks out
fine.
Radiation
Resistance,
most common mistake
Many people use the first definition of radiation
resistance, the portion of the terminal resistance of the feedpoint responsible
for radiation. Unfortunately they fail to normalize ground losses to the
same point where the radiation resistance
is taken! We can not use a formula that is based on everything being
normalized to one point
and not normalize to
that point for every term in the
formula! There is no change in efficiency when the NET radiator current
remains the same and when
net ground current remains the same.
Without changing power dissipated in losses compared to power radiated, we can
move the feedpoint resistance all around to anything we like and efficiency
remains the same.
Even if used properly, in many cases, losses are external to the antenna system.
These losses appear exactly as if they are due to radiation. For example, a
Marconi vertical can be 5 dB down from theoretical due to losses out in the
Fresnel region, or from local induction field dissipation, and not appear to
have an abnormally high feed resistance.
To know efficiency and field strength, we really must measure field strength!
Using The Second (IRE) Definition of Radiation Resistance
If we use the second definition of radiation resistance,
the one defined years ago by the IRE, where the effective current causing radiation is compared to power radiated, we
find folding the element does not change efficiency. Using the IRE definition of
radiation resistance, a folded dipole or monopole has the same radiation
resistance as a regular dipole or monopole the same size. Using the IRE
definition, a small loop antenna has
the same radiation resistance regardless the number of turns. All of this fits
perfectly with real life antennas.
Using the IRE definition, the magic “free lunch” vanishes.
You can read about this in textbooks. The “Antenna
Engineering Handbook” by Jasik in 313, 193, and in other sections uses
correct definitions and descriptions.
Quad’s and other Loops
We find the same efficiency misconceptions in articles about
small loops and large quads. Authors sometimes assume, incorrectly,
radiation resistance changes in a favorable proportion to loss resistance as feed impedance increases. What we really are doing is placing the
feedpoint in series with a smaller portion of NET current causing radiation.
The quad antenna has
two current
maximums, and the
feed line only
connects to one of
them.
With a large fullsize
quad element the pattern under some
conditions will slightly change, but efficiency remains basically the same. With
a small
“magnetic” loop antenna, losses
usually increase with more turns!
This is why most
commercial
transmitting loops
only have a single
turn.
Folded Dipoles
Folded dipoles, like
folded monopoles,
are another example
of a system where
radiation resistance
can have two
significantly
different values,
depending on which
definition is used.
As
with the monopole,
the folded dipole
only has half of the
normal dipole
current in each
conductor. The sum
of I1 and I2 is
identical to a
simple traditional
dipole. Using the
IRE definition of
radiation
resistance,
freespace radiation
resistance of a thin
folded dipole is
approximately 73
ohms. Using the less
useful feedpoint
resistance method,
radiation resistance
would be
approximately 292
ohms. Some engineering books use the IRE definition, and clearly state a folded
dipole has about 73 ohms radiation resistance, while other lessprofession texts
use the real part of feedpoint resistance.
In amateur circles, the Coaxial Dipole (or Double Bazooka) misuses the formula
eff % = 100 * Rrad/(Rrad + Rloss) to claim the coaxial dipole or
double bazooka has gain over a regular dipole. This is one of the most abused
formula in articles.
Terminated Folded Elements
Another abuse of radiation resistance is found in terminated
antennas. Some manufacturers and authors claim a resistance can be inserted in
series with one leg of a folded monopole or folded dipole, and the other leg
fed. The usual armwaving claim is the antenna isn’t really resistor loaded, and
that efficiency is very good because radiation resistance is high.
Once again the claim
is incorrect, and
the root of the
problem is not
normalizing losses
to the feedpoint.
A large terminated
rhombic is wellknown to have poor
efficiency. Rhombic gain is actually low compared to other antennas having the
same sin/sin x antenna pattern, because rhombic efficiency is generally less
than 50%. At least half of the power is consumed in termination and ground
losses below the antenna. The actual gain may be reasonably high compared to a
dipole, but not to other efficient antennas with the same halfpower beam width.
The typical manufacturing buzzword is that terminated monopole
and dipole antennas are “traveling wave antennas” and by some magic
(that even large terminated rhombic antennas can’t achieve) have broad bandwidth
and very high efficiency.
A rhombic focuses energy (that is not transformed into heat)
into a narrow beam that has considerable gain, but if it sprayed the radiation
around in a nonfocused pattern, a regular dipole would win hands down. Throw a
resistor on that dipole to smooth SWR variations, or on a vertical, and
efficiency suffers. I listened to a station on 75 meters 600 miles away testing a
Sommer T25 vertical. He was 30 over nine using a dipole, and dropped to S6 with
the vertical. The European he was working reported a similar change. By removing
the termination resistor and baseloading the same vertical, a local Ham gained
almost 25dB on 80 meters!
When we abuse or misuse radiation resistance, we can invent all
kinds of magical antennas. We can have CFA’s, EH antennas,
fractal loops, terminated dipoles,
small magnetic loops, and verticals with all sorts of magical claims. Few, if
any, of the claims are ever correct. Any time we see a claim that
efficiency changes a large amount because of a feed method change,
or that an antenna makes exceptional efficiency without proper supporting field
strength measurements, it should be a red flag.
Increasing Radiation Resistance
Radiation resistance, at least under the useful IRE definition,
can be defined by the following formula:
which would translate to:
Where He is the effective height center of accelerating
charges that cause radiation. In other words, He is the effective
height, expressed in fractions of a wavelength, of the distributed commonmode