In the following (long) discussion it is talking about a 15 foot
mobile vertical for 160 meters. The radiation resistance is in the
order of .3 ohms! The resistance in the loading coil alone is around
10 ohms. So you can see where most of the power will go when trying to
fed a short radiator! This is assuming a perfect no loss ground. If
there are ground losses (as in real life) that .3 ohms radiation
resistance becomes an even smaller fraction of the overall system
resistance. Meaning you will get even less power into the antenna to
radiate.

----------------------------------------
Note that radiation efficiency is almost directly related to radiation
resistance but that is because that is a result of how much actual
power you can get into the antenna. It is not because a low radiation
resistance antenna radiates any less than one with a high radiation
resistance.
----------------------------------------

The following is from W8JI's web sit. A discussion on short top loaded
mobile antennas. Go to his site for more details. He is talking about
a center loading coil antenna.
http://www.w8ji.com/mobile_and_loaded_antenna.htm


Degrees Vs Radiation Resistance

This upper four feet of this antenna resonates near 24 MHz with the
hat. We can assume it is 90 degrees long at 24 MHz, which would
translate to 6.9 degrees on 1.85 MHz. Following that same logic, this
would mean the loading coil would be about 83 degrees long
electrically. Using the incorrect logic proposed by others where the
loading coil "makes up the difference in electrical degrees", there
would be almost no current past the loading coil. Obviously this is
not the case, the loading coil has very little "electrical length".
As a matter of fact, the electrical length is about equivalent to the
physical length!

This goes back to radiation theory, and my favorite saying: "Five
hundred feet of wire in a one foot long tube is still one foot of
antenna". Some CB manufactures sell antennas to consumers with the
claim they use 5/8 or 3/4 wavelength of wire in an eight-foot
fiberglass whip, so the antenna has more gain. Obviously this is not
true. Let's not let such silly claims spread into amateur radio!

Related topics:

Inductors

The spice inductor model shows one example of how unequal current is
created. The model demonstrates a coil having significant distributed
capacitance to the point of current return in the system compared to
terminating impedance of the coil. In a monopole this return path
would be to the groundplane, or anything closer to the potential of
the groundplane than the area above the loading coil's position in the
antenna system.
Another Practical Antenna Example

Let's assume we have a lossless 15.3 foot long 0.2 inch diameter
conductor over a perfect groundplane. Eznec gives the 1.821 MHz base
impedance as .3004 -2169j. In other words, the antenna "looks like"
..3004 ohms of load resistance in series with 40.32pF on 1821kHz. The
return path for current is through the .3004 ohm resistance and
40.32pF capacitance, back to the ground of the antenna (it is a
Marconi antenna).

Such a termination (load) would require a series inductance of 2169j
(189.57µH) to cancel feedpoint capacitive reactance. A typical 190µH
inductor would be rather large, requiring somewhere around 53 turns
when using a 4" by 4" form factor. One would expect a physically large
inductor to have noticeable but very small displacement currents to
the groundplane, when the small stray coil capacitance is compared to
the 40.32pF termination capacitance. This raises two very important
design guidelines:

* When installing a loading coil of substantial inductance in an
electrically short antenna, sheetmetal and dielectrics should be kept
away from the coil and areas of antenna above the loading coil. This
would include dielectrics on or near the inductor, since the presence
of dielectrics would increase undesirable capacitance.
* When inductive reactance requirements are large, as when short
thin "stingers" without hats are used above a coil, the coil form
factor should lean more towards long and thin. Capacitances near the
open end of the coil (high voltage end) should be minimized. This
would be true even when the coil length increase results in a small
reduction in mutual turns coupling, since the stray capacitance may
result in a larger loss penalty than the slight increase in
accumulated resistance from additional wire length.

Efficiency

Efficiency in any antenna near earth is almost always dominated by
ground related losses, short-height Marconi antennas are no exception.
The overall effect of loading inductor Q and matching system losses
are "diluted" or "swamped-out" by ground losses. Ground losses cause
most systems to have greatly reduced sensitivity to inductor design.

The only consistently predictable factor in efficiency in fractional
wavelength Marconi antennas with limited size ground systems is
radiation resistance. Efficiency increases almost directly in
proportion to radiation resistance.
Radiation Resistance and Power Radiated

Radiation resistance is probably the most poorly defined term used
with antennas. The lack of clear definition creates errors and
misjudgments when predicting antenna performance. If you wish more
detailed information, this page contains information on radiation
resistance. For the purposes of this discussion and to avoid pitfalls
associated with using feedpoint impedance as radiation resistance,
I'll use the same definitions Jasik, Balmain, and others have used.
This definition is based on the IRE definition of radiation resistance
being equal to the net or effective current causing radiation squared
divided by the power radiated as EM energy, or Rr=Pr/I^2.

Using this definition, a folded dipole has a radiation resistance
identical to a conventional dipole of the same physical dimensions (
~70 ohms).

Radiation is caused by charge acceleration, there is no magic. The
only thing affecting radiation resistance in a short vertical antenna
near ground is current distribution over the linear area occupied by
the radiation portion of the antenna. The general rules a

Radiation resistance of a Marconi vertical in the maximum possible
radiation resistance case for a given height (this is the case where
current is uniform throughout the structure) is equal to 1580*(H/L)^2
where H equals height and L equals wavelength and both are expressed
in the same units. Using degrees, we see a 10-degree tall antenna has
a maximum possible radiation resistance of 1580*(10/360)^2 or
1580*.000772 = 1.22 ohms. This would apply even if the antenna is a
vertical, DDRR, Fractal, or folded unipole with considerable top
loading.

If current is triangular, radiation resistance would decrease by a
factor of four to 0.305 ohms.

Power radiated is given by I^2*Rr

With 100-watts applied to a 10-degree tall antenna, net current in a
lossless antenna with uniform current distribution would be 9.05
amperes. With triangular distribution, such as appears in a small
diameter short base loaded whip, current would be approximately 18.1
amperes. We are in serious problems if the inductor reduces current
along its length, since the only possible way to radiate 100 watts
would be to have somewhere around 9 amperes of effective current
integrated over the 10-degree vertical area of space for the radiator!
Ground Losses

All current flowing (or displaced) vertically into the antenna must
equal current flowing out of the ground or counterpoise system. Even
though ground losses are distributed losses, we must normalize all
losses to the feedpoint in order to compare systems. There are cases
where this will not always occur, causing us to falsely assume we have
lower losses than really exist.

In this tutorial and comparison, I have normalized ground losses to
the same point where radiation resistance is considered.
System Losses

(Measured data below of actual antenna given below was from 1995 data
taken at a different location near Atlanta with a slightly different
loading coil and antenna. There is a slight disagreement with current
data. I left this all in so you can see the departure from
measurements and models using 8 year old data.)
Base Loaded (Triangular Antenna Current Distribution) with no ground
loss

Assuming we have a base-loaded antenna, and the operating frequency
has a wavelength of 550 feet (around the 160-meter band), a 15.3 foot
vertical would fit the above 10-degree value. Interestingly enough
when we compare Eznec to formulas available in older (1950 vintage)
engineering textbooks, we find radiation resistance predicted by Eznec
is .3003 ohms while the triangular current estimate for the same
height radiator is .305 ohms! This is an amazing degree of agreement,
illustrating what we could do before modeling programs became
available. (With perfect top loading, both Eznec and longhand
calculations show approximately 1.2 ohms of radiation resistance.)

Assuming our 15.3 foot tall (10-degree) base-loaded antenna uses a
coil Q of 200, the coil has 10.845 ohms of ESR. Total resistance with
a perfect ground would be 10.85+.3= 11.15 ohms. Current into this
system with 100 watts applied would be around 3 amperes, resulting in
~2.7 watts radiated and ~97.3 watts lost as heat in the inductor.

Doubling coil Q (400) would provide 5.73 ohms of base resistance with
4.18 amperes. Power radiated would be 5.2 watts, power lost as heat
would be 94.8 watts. Efficiency does not quite double, changing from
2.7 to 5.2%. This results in a 2.8dB change in signal level.
Top Loaded (with no ground loss)

If we added a four-wire hat with 15-foot wires, current would no
longer be triangular. While we wouldn't quite reach the optimum
uniform distribution, current at the top would be about 78% of current
at the antenna base. Feedpoint impedance would become 0.97 -551j, and
the antenna would look like 0.97 ohms in series with 159pF.

Using a coil Q of 200, we would now have 2.76 ohms of inductor loss.
Current becomes 5.18 amperes. Radiated power is 26 watts, while power
lost as heat becomes 74 watts. Even in the perfect ground case, the
change in efficiency caused by top loading is large. Top loading (with
only the hat) results in 9.8 dB change in signal level when compared
to the base loaded case when coil Q remains 200. Efficiency is 26%.
The coil remains at ground level for easy matching and frequency
change.

In this case current at each terminal of the loading coil would be
essentially the same regardless of poor coil mounting techniques. In
order to have significant current taper in the coil or in the bottom
of the mast, shunt capacitance would have to be a significant compared
to 160pF. The antenna's high input capacitance relaxes inductor and
antenna mounting electrical requirements.
Base Loaded (high ground loss)

My F-250HD Super Cab pickup truck, when parked over open medium
quality pasture land, has a ground resistance of about 20 ohms
(normalized to the feedpoint) on 160 meters. Applying this ground loss
to the base loaded antenna, the system has a feedpoint resistance of
20+.3=20.3 ohms. (This is reasonably close to actual feedpoint
resistances measured with a similar operating antenna.) Adding coil
losses, the system has 20.3+10.85=31.15 ohms. (NOTE: Current coil is
~8 ohms ESR, 10.85 ohms is from ~8 year old data) Current is sqrt
(100/31.15) or 1.79 amperes.

This results in .96 watts radiated, and 99.04 watts lost as heat.
Efficiency is now around .96%.

Substitution of a coil with a Q of 400 results in 25.7 ohms feed
resistance, or 1.97 amperes antenna current at 100 watts. In this case
efficiency is now 1.16% for 1.16 watts radiated. The change caused by
doubling coil Q with high system ground losses is about 0.8dB,
compared to almost 3dB in the perfect ground case! With a poor ground
(in this case typical of a very large vehicle), a large change in coil
Q produces little change in system efficiency.
Another Top Loaded (high ground loss) System Example (made prior to
the EZNEC model above)

Using a large hat isn't practical in a moving mobile, although it
could apply to fixed stations suffering with poor ground systems. When
the hat is smaller, such as a mobile requires, the loading inductor
can be moved higher in the system. Such a move would produce uniform
current below the loading coil, with a current shape above the coil
dictated by the construction of the upper portion of the antenna. My
own mobile uses a six-foot diameter hat manufactured from stainless
steel automobile antennas arranged in a spoke. I have no problems with
wind or occasional obstructions. While unsightly, a modest hat is
workable.

In order to keep the systems comparable I'll use the same radiation
resistance provided by a large hat, but intentionally add high ground
loss as a lumped resistance. This model ignores field losses near the
antenna.

In this case we have 0.97 -551j as the inductor termination presented
by the antenna. With ground losses normalized at 20 ohms and an
inductor Q of 200, we have 20+2.76+.97 = 23.73 ohms of feedpoint
resistance. Current is 2.05 amperes, and power radiated is 4.1 watts.
Power lost is 95.9 watts.

Efficiency is 4.1%, a 6.3dB increase over a base-loaded triangular
current system with the same lossy ground. This system is 8dB down
from the same "top-loaded" distribution using a perfect ground.

When the system has significant fixed losses, increasing radiation
resistance four times by top loading provides a similar dividend in
system efficiency. At the same time a substantial increase in coil Q
provides only minimal change in field strength.