My first thought was a short antenna for 160M that would fit into a 30'
cube as 30' is about as high as I can go around here for various reasons.

Everything that follows was done at 1.9 MHz, which is a wavlength of
518 feet with a wire size of #12.

The first thing was to see what a 30' vertical with 4 15' radials spaced
1' over real ground presents.

In the below, R0 means wire resistance zero, Rc means wire resistance
copper, G0 gain with zero resistance, Gc gain with copper, and the
elevation angle of maximum gain turned out to be 19 degrees for all cases.

30' vertical (.058 wavelengths)

Rc R0 X G0 Gc
2.1 1.8 -1961 3.11 3.11

Note the slight difference in the resistive part. There was no significant
change in anything else.

Now cut the size by a half.

15' vertical (.029 wavelengths)

Rc R0 X G0 Gc
..6 .4 -3939 3.13 1.88

OK, now we see a drop in gain as the wire resistance starts to become
a significant fraction of the radiation resistance, so lets change
to a 15' cube which contains the antenna.

I would think a 0.029 wavelength antenna qualifies as short.

Now stick in a loading coil and see what that does at various heights,
denoted by h and in terms of percent of total height. L is the inductance
in microhenrys required to get X below |1| Ohm. This is all with a wire
resistance of zero

h L R0 X G0
10 268 .4 -.5 3.0
20 200 .6 .7 3.0
30 326 .7 .1 3.0
40 383 .8 1 3.1
50 444 1 .4 3.1
60 546 1 -.6 3.1
70 706 1 -.2 3.1

Note that as the inductor height goes up, the required inductance goes
up as does the gain ever so slightly.

The next step was to optimize the height and inductance against gain,
raising the height and adjusting the inductance until the gain stopped
increasing by less than 0.01 dB.

This resulted in a optimum height of 66.4% and an inductance of 626 uH
and a gain of 3,12 dB.

Now it is time to add a top hat of 4 15' wires and see what they do and
also look at the results with copper.

The first set of results are for an h=50%, L=177 uH, and the second for
h=66.4% and L=179 uH.

Note that with a top hat the required inductance drops significantly
and is much less effected by the placement height.

Rc R0 X G0 Gc
2.0 1.7 .5 3.01 2.16
1.9 2.3 .5 3.00 2.15

Some observations:

Total gain varies only slightly until resistive losses are concidered.

An elevated loading coil increases the impedance from about .5 Ohm to
about 1 Ohm. This is a good thing.

An elevated loading coil increases the inductance needed by a factor
slightly over 2. This is a bad thing.

A real inductor will have a real resistance and ohmic losses which
will add to the other ohmic losses in the antenna.

Therefore even greater care is required to ensure the Q of the elevated
loading coil is as high as possible.

Adding a top hat increases the the impedance from about 1 Ohm to about
2 Ohms. This is a good thing.

Adding a top hat decreases the inductance needed by a factor slightly
over 3. This is a good thing.

The currents in the top hat are very small compared to the current in
the vertical radiator, so they can for all practical purposes be ignored
as a source of loss.

It is not shown, but by changing the material from #12 copper wire
to 1.5" aluminum tubing all the numbers are very close to the
lossless numbers.

Some comments on connections:

Some years ago I was involved with this thing my company was attempting
to build which had a 100 A power supply and all sorts of "strange"
things were occuring.

Long story short, after we obtained a precision milliohmeter and looked
at all the connections, both internal and external to the power supply,
did we realize that at 100A, a few milliohms here and a few there were
causing all the problems.

For lowest resistance, crimped on connectors have to be soldered in
addition to the crimp.

Screw connections have to a large an area as possible and TIGHT. We
had to develop torque specs to ensure that happened in production.

A high Q inductor is wasted if the end connections are 100 milliohs.

We are still faced with the issue of matching a 50 Ohm transmitter
to a 2 Ohm antenna, but for now I am more interested in seeing if
there is some way to further increase the antenna impedance.



--
Jim Pennino