At 07:19 AM 5/11/2005, Bill Tippett wrote:
>Hi Jim,
>
>At 08:43 AM 5/11/05, Jim Lux wrote:
>
>>Yes, indeed, the gain (or vertical beamwidth, which is related to the
>>gain/directivity) won't change very much for pretty significant phase
>>errors.
>>
>>However, the direction that the beam points WILL change quite a bit. Say
>>you've got two20m antennas spaced 30 ft apart (call it 10 meters, a rough
>>half wavelength : 180 deg of phase). If you have an extra 10 degrees in one
>>of the antennas, the beam will be shifted by arctan(10/180) = about 3
>>degrees. (same effect if you have one antenna where the phase center is
>>shifted a couple feet).
>
> What do you mean "direction"???
Elevation angle of main beam.
My calculation was for isotropic antennas. Because you have to lay that
pattern on top of the actual beam patterns for the two antennas, the shift
won't be as great. That is, the underlying elevation patterns of the two 15
dBi yagis dominates over the array pattern which is only 3dBi.
> All antennas are assumed
>to be in the same azimuthal direction. The combined vertical "direction"
>is hardly affected by small phase differences, e.g. the bottom two Yagis
>in my 10m stack (70'/35') using Eznec over Average flat ground:
>
>In-phase: 16.85 dBi @ 8 deg TOA, VBW 8.9 deg
>10 deg: 16.83 dBi @ 8 deg TOA, VBW 9.0 deg
>20 deg: 16.76 dBi @ 8 deg TOA, VBW 9.0 deg
>30 deg: 16.63 dBi @ 8 deg TOA, VBW 9.1 deg
I did a model in NEC4 using a pair of simple 3 element 20m yagis, made of
aluminum, over Sommerfield ground (13,5), just exciting the antennas with
voltages (so mutual coupling might result in excitations that aren't quite
the same phase). I put the antennas at 17 and 27 meters (56 and 89 ft)
(just because I happened to have a single yagi model at 17 meters, and just
used a GM to duplicate it 10 meters higher).
Changing the phasing by + and - 30 degrees, I got the following data:
-30 12.8 deg 14.73 dB
0 12.4 deg 15.09 dB
30 12.0 deg 14.74 dB
which is quite similar to your data. What I found very interesting,
though, was the depth of the null between the main and next lobe up (a few
tenths of a degrees in main lobe elevation isn't going to make much
difference). Here we go:
-30 30.2 deg 3.82dB (very broad null)
0 28.4 deg -6.94 dB (fairly sharp)
30 26.8 deg, -3.83 dB (fairly sharp)
Here you see the expected several degree steering (mostly because nulls
aren't as affected by the individual element patterns as much).
Just for reference, the upper antenna, by itself, has a gain of 13.93 dB,
peaking at an elevation angle of 10.8 deg. The lower antenna peaks at
13.46 dB, at an elevation angle of 16.6 deg. The relative squint between
the beams is why the array gain isn't 3 dB more than the element gain (i.e.
16-17dB), but is only 15 dB. The beam formed in the array neatly straddles
the two beams, at about the -1dB point.
>Phase increments were added to bottom antenna only. I didn't model
>for the top one only but the results should not be significantly different.
>Eznec does not give more resolution than 1 degree for the TOA gain
>peak, but these are all clearly less than 1 degree...nowhere near 3.
>
>>A three degree change in vertical take off angle might have a significant
>>gain because you've moved into a different part of the antenna pattern,
>>especially for takeoff angles close to horizontal, where the gain changes
>>rapidly.
So, while the main beam doesn't move much, the null does move. That moving
null is probably the advantage of various array stacking schemes (i.e. the
whole Top/Bottom/BIP/BOP thing doesn't move the elevation angle of the main
lobe much (some 6 degrees in the example I modeled), but it does move the
null (and second order sidelobes) a lot. Particularly if you want that
nice sharp null to replace the main lobe (switching from BIP to BOP, for
instance), 30 degrees of phase shift might result in significant changes.
>>Mutual coupling, mechanical differences, the fact that one antenna is closer
>>to the ground, etc., could easily result in a 10 degree phase shift.
>
> Mutual coupling and proximity to ground are both
>taken care of in Eznec. Not sure what you mean by "mechanical"
>differences (feed system?), but they should also be taken care of
>in a properly constructed model.
Differences between the NEC model and the physical reality. In particular,
the reactive component at the feedpoint, which varies quite strongly in
high gain Yagi antennas.
In my simple 3 element model, which happens to resonate at 14.02 MHz, the
phase you'd actually radiate (if driven from a 50 ohm source) would vary
from -10 to 60 degrees over the range from 14.0 to 14.2 MHz. The antenna
is a pretty high Q resonator (about 50), so phase shifts change rapidly
with small changes in frequency (or, more imporantly, with dimensions and
spacings). And, don't forget that the feedpoint impedance will be
transformed by the transmission line to wherever the summing point is.
Relating back to the original question about matching dissimilar antennas,
the odds that both antennas "track" in phase over even a pretty small range
is pretty small. Especially if one antenna is, for instance, a 2 element
and the other a 3 element, so the Q's are very different. You might get it
all nicely phased up at one frequency, with no wind, and no bird sitting on
the antenna, but as soon as you move 50 kHz, or the wind moves the elements
around, and it's a whole new ballgame (at least as far as the nulls go...
the main lobe won't move much).
The whole problem of accounting for the reactive component in a phased
array antenna, particularly one that has to work over a relatively wide
band (more than a fraction of a percent), is a very challenging part of
array design. There's a reason why array designers like low gain (i.e. low
Q) elements, or why they use techniques such as swamping pads on receive
arrays.
Combine that with the typical power amplifier output impedance
characterics, and it gets even more challenging.
This is fundamentally why I think that the value in stacks is the fact that
you can change things at all (in an elevation plane sense), not that you
can actually predict it. It gives you a knob to turn quickly, and your
ears can quickly determine which of the 4 settings works best, at that
frequency, that time, and that configuration.
Agonizing about inches (or feet) of transmission line is probably
pointless, as long as you stay away from something pathological (you can
get some weird effects with just the right length lines connecting antennas
(or with mutual coupling).. in phased array radars it's called scan
blindness). The NEC models (or, even simpler phasing models) can probably
help you in the planning process to avoid "bad" lengths.
Jim, W6RMK
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