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[TowerTalk] More stack data from NEC

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Subject: [TowerTalk] More stack data from NEC
From: cebik@utkux.utcc.utk.edu (L. B. Cebik)
Date: Thu, 27 Feb 1997 08:05:31 -0500 (EST)
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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