To those who supplied information on their stacks, I thank you. Although
not absolutely complete, I have tried to model almost all the stacks "in
principle." Here are the restrictions: the heights are in terms of a
fraction of a wavelength, so you have to translate that into feet. That
will allow you to equate a 10 or 15 meter installation with the modeled 20
meter antennas. Next, the model beams are 3 element "ideals" and you will
have to estimate the amount of gain over the 3-element beam your 4, 5, 6,
or 7, element beam has. The gain numbers will give you a basis for making
relative judgments such as, "Will I gain anything by raising the top beam
in my stack by another fraction of a wavelength?"
In order to handle stacks with up to four beams, I reduced the number of
segments per half wavelength in my NEC-4 models. (The program would have
handled it, but available time was limited by other projects.) Hence, the
tables below start from scratch with some baseline data. That will
validate the comparisons.
Everything will be by way of tables, without commentary. Some unworthy
options will be evident. Others may depend on two factors: a. your own
readout of experience or IONCAP results for paths from your QTH to your
targets, and b. what your operating activities and interests are and hence
what your targets are. These are variables that method of moments cannot
model.
In case of printout misalignment, the headings of columns containing
numbers from left to right are always:
TO angle in degrees; Gain in dBi; F-B ratio in dB; horizontal beamwidth to
-3 dB points in degrees, and Feedpoint impedance given as r +/- jX in ohms.
for numerous options, both a main and a significant secondary elevation
lobe are given. Abbreviations specific to a given chart are presented with
the chart.
1. Baseline 3-element Yagi Characteristics: 1 antenna by height in wl:
Height TO angle Gain F-B Beamwidth Feedpoint Impedance
in wl degrees dBi dB degrees R +/- jX ohms
1/2 25 12.3 25.2 64 24.7 - 0.7
5/8 21 12.9 24.9 64 25.9 + 0.1
3/4 17 13.1 40.1 62 26.5 - 1.2
7/8 15 13.3 29.0 62 25.5 - 1.6
1 14 13.4 25.1 62 25.1 - 0.9
1.5 9 13.7 25.3 62 25.3 - 0.9
2 7 13.8 25.6 62 25.4 - 0.9
2.5 6 13.8 25.9 62 25.5 - 0.9
Note: This model chosen for its generally good performance as a 3-element
Yagi plus the convenience of using simple transmission line modeling
techniques for stacking beams with a resultant 50-ohm overall feed.
2. Two beams stack, single feed at various spacings. Abbreviations: Both
in = both in phase; both out = both, but out of phase; Top only = only top
beam fed, but lower present in stack; Bot only = only bottom beam fed,
although upper present in stack. A second line for an entry indicates a
secondary elevation lobe worth noting.
2a. 2 beams at 1 wl and 1.5 wl up.
Stack TO angle Gain F-B Beamwidth Feedpoint Impedance
set-up degrees dBi dB degrees R +/- jX ohms
Both in 11 15.8 21.3 60 50.6 - 0.9
Both out 50 12.3 18.5 82 45.0 + 7.5
25 11.5 28.8 66
Top only 9 13.6 22.3 60 26.1 - 1.9
Bot only 14 13.3 22.1 62 26.0 - 1.9
2b. 2 beams at 1 wl and 1.63 wl up.
Stack TO angle Gain F-B Beamwidth Feedpoint Impedance
set-up degrees dBi dB degrees R +/- jX ohms
Both in 10 16.2 17.6 62 51.4 - 1.7
Both out 47 12.7 23.1 76 49.0 + 6.5
23 12.5 31.4 64
Top only 9 13.9 18.6 62 22.1 - 1.1
Bot only 13 13.6 17.9 62 24.5 - 1.5
2c. 2 beams at 1 wl and 2 wl up.
Stack TO angle Gain F-B Beamwidth Feedpoint Impedance
set-up degrees dBi dB degrees R +/- jX ohms
Both in 8 15.7 39.3 62 46.7 + 2.3
Both out 20 14.7 22.2 62 51.9 + 1.4
39 12.9 26.6 70
Top only 7 13.7 35.5 62 25.6 - 1.1
Bot only 14 13.4 26.7 62 25.3 - 1.1
2d. 2 beams at 0.7 and 1.4 wl up. (This corresponds roughly to 70-75'
lower and 140-150' upper on 20 meters.)
Stack TO angle Gain F-B Beamwidth Feedpoint Impedance
set-up degrees dBi dB degrees R +/- jX ohms
Both in 11 15.7 15.0 64 50.7 - 5.7
Both out 28 13.8 25.8 64 49.7 + 7.1
58 9.1 18.6 86
Top only 10 13.9 16.4 64 24.4 - 0.8
Bot only 18 13.2 18.9 64 25.5 - 0.2
3. 3 beams stacked at 1, 1.5, and 2 wl. Added abbreviations: Top out =
top out of phase with other two; Mid out = middle out of phase with other
two; Bot out = bottom out of phase with other two; Mid only = middle beam
onlt fed, but with other two present.
Stack TO angle Gain F-B Beamwidth Feedpoint Impedance
set-up degrees dBi dB degrees R +/- jX ohms
All in phase 9 17.25 22.3 60 50.3 - 0.9
Top out 17 13.4 22.1 62 51.4 + 3.6
36 13.2 30.8 68
Mid out 55 13.3 14.3 88 41.3 + 12.9
32 8.9 18.5 68
Bot out 22 14.3 22.1 64 51.9 + 3.3
7 10.3 19.7 60
Top only 7 13.6 24.5 60 26.2 - 2.1
Mid only 9 13.6 19.0 60 26.7 - 3.2
Bot only 14 13.3 23.1 62 25.8 - 2.0
4. 4 beams stacked at 1, 1.5, 2, 2.5 wl up. Beams are designated top,
2nd, 3rd, bot from top to bottom.
Stack TO angle Gain F-B Beamwidth Feedpoint Impedance
set-up degrees dBi dB degrees R +/- jX ohms
All in phase 7 18.3 21.3 60 49.8 - 2.6
Top out 12 15.1 21.8 60 49.5 + 2.8
28 12.2 24.5 64
2nd out 40 13.5 28.2 71 48.9 + 8.6
9 11.3 22.2 60
3rd out 6 12.3 20.6 60 48.6 + 7.8
30 12.0 22.2 66
Bot out 20 14.9 22.3 62 49.4 + 2.9
6 14.1 20.4 60
Top 2 out 17 16.0 20.6 62 52.1 - 0.6
32 13.3 21.8 66
Mid 2 out 26 14.4 24.8 64 52.2 + 2.3
43 13.7 29.8 74
Top/3rd out 57 14.0 12.8 91 38.5 + 16.7
Top only 6 13.7 21.3 60 25.5 - 0.3
2nd only 7 13.5 20.2 60 26.5 - 3.4
3rd only 9 13.4 21.4 60 26.5 - 3.2
Bot only 14 13.2 23.8 62 25.8 - 2.0
Note: "Top 2 out" above is equivalent to "Bot 2 out" and "Top/3rd" out is
equivalent to "2nd/Bot out."
5. 2 beams at 1 wl height, horizontally spaced, where spacing is given in
wl fractions from tip to tip of the elements (add 1/2 wl for boom-to-boom
spacing). Side ears represent side lobes similar to those from an EDZ--
only gain is given. Out of phase condition produces two lobes with a deep
center null. "Split" = degrees each side of center line of the lobes.
Stack TO angle Gain F-B Beamwidth Feedpoint Impedance
set-up degrees dBi dB degrees R +/- jX ohms
a. 1/4 wl sp
In phase 13 16.1 22.8 32 50.3 - 0.6
side ears -2.9
Out of phase 13 13.4 39.8 48.2 + 4.2
split 28
b. 1/2 wl sp
In phase 14 16.5 22.3 26 49.6 + 0.1
side ears 5.8
Out of phase 13 14.2 30.8 50.1 + 3.0
split 24
c. 5/8 wl sp
In phase 13 16.5 24.3 24 49.0 + 0.6
side ears 8.2
Out of phase 13 14.6 27.9 50.4 + 2.4
split 22
d. 1 wl sp
In phase 13 16.4 26.5 18 49.3 + 1.9
side ears 11.7
Out of phase 13 15.4 25.1 50.1 + 1.3
split 18
Note that as the spacing grows wider, the out-of-phase split grows
narrower, but the ears grow larger.
I hope this data is useful to you as a point of departure in your stack
building and revision planning (used in conjunction with other data). I
shall these tables to the stack entry at my web site for reference. You
can access them at http://funnelweb.utcc.utk.edu/~cebik/radio.
-73-
LB, W4RNL
L. B. Cebik, W4RNL /\ /\ * / / / (Off)(423) 974-7215
1434 High Mesa Drive / \/ \/\ ----/\--- (Hm) (423) 938-6335
Knoxville, Tennessee /\ \ \ \ / / || / (FAX)(423) 974-3509
37938-4443 USA / \ \ \ \ || cebik@utk.edu
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