On Thu, 27 Jun 2013 16:11:50 -0700, Jeff Liebermann
wrote:

I'm stuck at home today with a foot problem. So, I get to sit at the
computer instead of the workbench. I'll throw together a web page
showing that cutting the antenna short does NOT reduce it's gain and
efficiency very much (but does mangle the pattern and VSWR). Stay
tuned.

5 hours (minus dinner) later and I'm dead tired. What started as a
simple little demonstration turned into a time burning nightmare.
Here's where I stopped:
http://www.11junk.com/jeffl/antennas/Monopole/index.html
The various sub-directories are NEC2 models for various length
monopole antennas over a perfect ground plane. That a rough
approximation of what one would expect to see on the roof of a car
with a large metal roof at VHF/UHF frequencies. It's not quite
correct, but close enough for this exercise.

The directories are named after the length of the monopole antenna.
For example:
monopole_0_625
is a 0.625 or 5/8th wavelength antenna. The underscores were used
because Windoze XP detests more than one period in a filename.

The NEC deck is really simple.

CM Monopole antenna over perfect ground.
CM by Jeff Liebermann AE6KS 06/25/2013
CE
SY LENGTH = 0.625 'Length in wavelengths
GW 1 21 0 0 0 0 0 LENGTH 0.001
GE 1
GN 1
EK
EX 0 1 1 0 1 0
FR 0 0 0 0 299.8 0
EN

The only value that changes for each antenna is the label:
LENGTH = X.XXX
The 0.001 is 0.001 wavelengths for a wavelength = 1 meter, which is a
2mm diameter monopole antenna. The 299.8 MHz frequency is a
convenient trick to make 1 wavelength equal to 1 meter, making all the
dimension appear in wavelengths. That allow this antenna to be easily
scaled to any frequency.

If you feel ambitious, download and install 4NEC2 from:
http://www.qsl.net/4nec2/
and try it. If you're really into big models, I suggest you also get
the multi-core/processor NEC2 engine from:
http://users.otenet.gr/~jmsp/
which really speeds things up.

So much for the background stuff...

Start with the 1/4 wave antenna at:
http://www.11junk.com/jeffl/antennas/Monopole/monopole_0_250/index.html
http://www.11junk.com/jeffl/antennas/Monopole/monopole_0_250/slides/monopole_0_250.html
Note that the gain is 5.19dBi. At this point, I usually get an
outrage from everyone who knows that a dipole is 2.15dBi and that this
monopole can't possibly have more. Well, we have a perfectly
reflective ground under this antenna, that reflects 100.0% of
everything that hits it, effectively doubling the gain.
2.15dBi + 3.01dB doubling = 5.16dBi
You'll see the extra 3dB gain throughout the various pages.

The common misconception is that shorter antennas have less gain. Yes,
they do, but it's not really proportional to the length. For example,
the 1/4 wave monopole may have 5.19dBi gain,
http://www.11junk.com/jeffl/antennas/Monopole/monopole_0_250/slides/monopole_0_250.html
but the 1/8th wave monopole still has 4.86dbi gain
http://www.11junk.com/jeffl/antennas/Monopole/monopole_0_125/slides/monopole_0_125.html
and the 1/20th wave monopole still has 4.79dBi gain.

Going the other direction with longer monopole antennas, the full wave
monopole at:
http://www.11junk.com/jeffl/antennas/Monopole/monopole_1_000/slides/monopole_1_000.html
has 7.06dBi gain or less than 2dB more than a 1/4 monopole. One might
expect that having 4 times as much wire as the 1/4 wave monopole would
produce a 6dB gain increase, but that's not how it works.

I did some tweaking and arranged to produce the antenna impedance in
polar form. For example, the 1/4 wave antenna at:
http://www.11junk.com/jeffl/antennas/Monopole/monopole_0_250/slides/monopole_0_250.html
has an impedance of 48.7 ohms with a phase angle of 30.2 degrees.
Close enough to 50 ohms.

However, as we get into even multiples of 1/4 wavelength, the
impedances become very high. For example, the infamous 1/2 wave
monopole shows 934 ohms:
http://www.11junk.com/jeffl/antennas/Monopole/monopole_0_500/slides/monopole_0_500.html
which is not going to be easy to match.

On the short end of the scale, the 1/8th wave antenna at:
http://www.11junk.com/jeffl/antennas/Monopole/monopole_0_125/slides/monopole_0_125.html
shows 254 ohms, which will work with a 2:1 turns ratio transformer.

If you look at the antennas that are odd multiples of 1/4 wavelength,
you'll notice that their impedances are tolerably close to 50 ohms.
For example, the 1.25 wavelength antenna is 72.9 ohms, which will
probably work without any matching xformer.
http://www.11junk.com/jeffl/antennas/Monopole/monopole_1_250/slides/monopole_1_250.html

If you look at the patterns at:
http://www.11junk.com/jeffl/antennas/Monopole/index.html
you'll see some interesting things. The pattern for the 1/2 wave
monopole and shorter are all very similar. The gain is also fairly
constant. I can't say the same for the impedance, which varies
radically and the takeoff angle, which keeps creeping upward as the
antenna gets longer. As the antenna gets really long, such as this 5
wavelength monopole monster:
http://www.11junk.com/jeffl/antennas/Monopole/monopole_5_000/slides/pattern.html
the major lobes are almost straight up, which might be useful for
talking to satellites but not terrestrial repeaters. Note that the
gain has increased to 10.7dBi or 5.5dB more than the 1/4 wave
monopole.

Lots more can be extracted from the simulations. I'll clean up the
mess, contrive a web page, make it pretty, but not tonite.








--
Jeff Liebermann
150 Felker St #D http://www.LearnByDestroying.com
Santa Cruz CA 95060 http://802.11junk.com
Skype: JeffLiebermann AE6KS 831-336-2558