Richard Clark wrote:
First I will start with a conventionally sized quarterwave and by
iteration approach the short antenna and observe effects. I am using
the model VERT1.EZ that is in the EZNEC distribution and modifying it
by turns. For instance, I immediately turn on the wire loss.
40mm thick radiator 10.3 meters tall:
Impedance = 36.68 + J 2.999 ohms
which lends every appearance to expectation of Rr that could be
expected from a lossless perfect grounded world.
Best gain is
-0.03dBi
next iteration:
cut that sucker in half:
Impedance = 6.867 - J 301 ohms
which, again, conforms to most authorities on the basis of Rr.
best gain
0.16dBi
How about that! More gain than for the quarterwave (but hardly
remarkable).
This is indeed an interesting result, even though it's small. As a
dipole or monopole gets shorter than a resonant length, the current
distribution changes from sinusoidal to triangular. In the ideal case
(and in the absence of loss), this results in the shorter antenna having
a slightly fatter pattern and therefore slightly less gain. An
infinitesimally short antenna has a gain of less than 0.5 below that of
a resonant one, due to this (and again, in the absence of loss). So the
trend you observed was backwards. The first two things I checked --
segmentation and wire loss -- proved to not be the reason. It appears to
be the effect of the current distribution on the reflected wave from the
ground. The radiation from each part of the antenna reflects from the
ground, and the nature of the reflection depends on the angle at which
it strikes the ground. Radiation from different parts of the antenna
strike at different angles, and the shorter antenna has its current,
therefore its radiation, apportioned differently. It's this difference
that causes the slight backward trend in gain. I wouldn't put too much
weight on it, however, both because of its being small, and that EZNEC
and similar programs use a pretty simple ray-tracing method of
calculating ground reflection rather than a more complex method which
includes diffraction and other effects. You'll see the theoretical trend
if you change the ground type to Perfect, and likely a slightly
different trend if you change the ground constants.
This makes me wonder why any futzing is required except
for the tender requirements of the SWR fearing transmitter (which, by
the way, could be as easily taken care of with a tuner).
next iteration:
load that sucker for grins and giggles:
load = 605 Ohms Xl up 55%
Impedance = 13.43 + J 0.1587 ohms
Did I double Rr? (Only my hairdresser knows.)
best gain
0.13dBi
Hmm, losing ground for our effort, it makes a pretty picture of
current distribution that conforms to all the descriptions here (sans
the balderdash of curve fitting to a sine wave). I am sure someone
will rescue this situation from my ineptitude by a better load
placement, so I will leave that unfinished work to the adept
practitioners.
As I pointed out above, going from a sinusoidal to a triangular
distribution changes the gain less than 0.5 dB, so this change in
distribution changes the gain even less. And again, the interaction with
real ground reverses the trend. With Perfect ground, you'll see that
there's actually a 0.02 dB gain improvement with the new distribution.
This is, of course, insignificant, but it does show that things are
working as they should.
next iteration:
cut that sucker down half again (and remove the load):
Impedance = 1.59 - J 624.6 ohms
Something tells me that this isn't off the scale of the perfect
comparison.
best gain:
0.25dBi
Hmm, the trend seems to go counter to intuition.
That's because you didn't understand the reason for the trend in the
first place. What's happening now is that the gain reduction caused by
the changed distribution is no longer overwhelmed by the gain increase
caused by the interaction with real ground. Again, go to Perfect ground
and you'll see that the trend of less gain as the antenna shortens is
continuing as exepected.
next iteration:
-sigh- what charms could loading bring us?
load = 1220 Ohms Xl up 55%
Impedance = 3.791 + J 1.232 ohms
more than doubled the Rr?
best gain:
0.23dBi
And with Perfect ground, the gain is the same within 0.01 dB with and
without the load -- the modified current distribution wasn't enough to
make any significant difference in the pattern and hence the gain.
Now, all of this is for a source that is a constant current generator;
we've monkeyed with the current distribution and put more resistance
(Rr?) into the equation with loading; and each time loading craps in
the punch bowl.
So much for theories of Rr being modified by loading.
Everything you've done shows that Rr is modified by loading. Rr at the
feedpoint is simply the resistance at the feedpoint. And it clearly
changes when you insert the load. What makes you think that the Rr isn't
changing?
I would
appreciate other effort in kind to correct any oversights I've made
(not just the usual palaver of tedious "explanations" - especially
those sophmoric studies of current-in/current-out).
Perhaps you're expecting the gain to vary in the same way as Rr. But you
see, gain will change with Rr only if the pattern shape stays the same.
And each time you insert the load, the current distribution changes,
which changes the shape of the pattern, which changes the gain. This is
the gain change you're seeing as you change the antenna length and add
loading. The main relationship between Rr and gain is the efficiency.
The antennas you've modeled are so close to being 100% efficient that
increasing Rr has no appreciable effect on gain. Check it yourself --
make the antenna 100% efficient by removing the wire loss and notice
that there's no change in gain (maybe 0.01 dB with the full size antenna).
But now repeat your experiments with, say, a 10 ohm resistive load at
the base to simulate ground system loss. And you'll see that the gain
improves dramatically as your loading increases Rr (the feedpoint
resistance). This is due to the improved efficiency you gain by
increasing Rr.
Roy Lewallen, W7EL
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