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Disparaging Helical Antennas for AO-40...some notes

<Or 'dissing' as our kids say nowadays.  Or is that already passe?>

What prompted this missive is from "Success with 4-foot dish" by Fred
W0FMS, whom I'll quote here:

> I think the key is to not mess around with helixes too much-- do small 
> dishes.  Back when I used to do WEFAX, I tried a loop yagi first-- but when 
> In discovered a 2 foot MA/COM dish outperfomed the loop yagi, I've never 
> looked back since.  (OK, I tried a 33 turn 2401 helix-- but even a 18" dish 
> seems to work better)

I don't know what sources folks use to design their helical antennas,
but if it's ARRL-based it's inaccurate.  All my ARRL literature quotes
the original Kraus work (from the '50s!) 

	G=15*N*C^2*S/lambda^3		where C=circumference in wavelengths, S=turn
spacing in wavelengths

which obviously increases without end as the helix is made longer
(increasing N).  I understand that Kraus based his leading term of 15 on
an assumed constant gain-beamwidth product of (4pi) steradians or 41,253

Side note:  A common directivity estimator is G=41253/(hpbw1)(hpbw2)
where hpbw1 is the half-power beamwidth in one plane, and hpbw2 the
half-power beamwidth in an orthogonal plane.  Many will probably be
familiar with this expression.  You can define a gain-beamwidth formula
by rearranging G*(hpbw1)*(hpbw2)=41253.

The most widely quoted helical antenna measurement campaign is that of
King and Wong ("Characteristics of 5- to 35-turn Uniform Helical
Antennas, IEEE Transactions on Antennas and Propagation, March 1980, pp.
291-296; also reproduced in Johnson and Jasik, "Antenna Engineering
Handbook", 2nd Ed., chapter 13).  King and Wong's measurements clearly
show that (1) for short helices, the gain-bandwidth product is a fair
amount less than 41,253; and (2) as the helix gets longer, the
gain-bandwidth product decreases rapidly.

Bottom Line:  The longer you make a helix, the gain doesn't go up
forever.  And it's a LOT less than Kraus' original formulation for
moderate-length helices.

Another reference:

Practically...the ubiquitous 60cm dish on S-band is around 20.5dBi with
a good feed (that's 50% illumination/spillover efficiency).  If we take
King and Wong as completely correct, then you just about can't get there
from here.  The longest helix they measured (35 turns and 8.5
wavelengths long) came out only to 17.8dBi peak gain, and the
gain-beamwidth product was down to around 22,000 (nearly 3dB down from

As another example, the oft-quoted 16 turn helix will probably really
get you only 15.3dBi or so (again based on King and Wong's
measurements).  That's 5dB less than the dish and a lot of margin to
give up!

And Pieter's 72-turn helix, well from extrapolation on the King and Wong
data it would have been around 19.8dBi; close to the dish but a pretty
long stick!

I should also point out that the King and Wong measurements used helixes
that were backed not by a flat ground-plane, but a "cup" or cavity. 
Other investigators (references not handy at the moment) have found that
the "cup" gives about 2dB additional forward gain.  If you're building
with a flat ground plane, you could take off 2 more dB.  The web
reference above claims that the use of radials rather than a solid
groundplane is another 3.5dB gain penalty.  Those are pretty significant

To Fred's comment that I opened with:  an 18" dish at S-band would be
around 18dBi.  A fully-featured 33 turn helix would be pretty close to
this (17.7dBi or so, but maybe only 15.7dBi without cup, or maybe 12dBi
if it had a radial groundplane?).  But the tone of the comment leads me
to believe he expected much better out of helix, and he
didn't--couldn't--get it.
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