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[TowerTalk] wideband 80 meter dipoles (long-delete if irrelevant)

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Subject: [TowerTalk] wideband 80 meter dipoles (long-delete if irrelevant)
From: (L. B. Cebik)
Date: Thu, 27 Nov 1997 08:13:45 -0500 (EST)
Dave Leeson brought to our attention an interesting technique for achieving
wide-band operation on the lower HF bands, derived from mentions in texts
and references in ARRL publications by Frank Witt, AI1H.  The technique
involves choosing a geometric average frequency between two frequencies of
interest--then, for that frequency, cutting a length of 50-ohm coax a
multiple of 0.5 wl (allowing for velocity factor), with a 0.25 wl length of
75-ohm coax (again, allowing for velocity factor) at the station end of the

This is a bit of follow-up that seemed interesting as the numbers emerged
from some modeling exercises.  I thought I would pass them on.

The SWR at the antenna relative to 50 ohms does not change, but line losses
at the lower HF bands are not--for many purposes--sufficiently large to
make a case against this or other wide-banding techniques with coaxial feed
lines.  The factors that produce wide-band operation (using the
conventional <2:1 SWR measure for convenience) include the impedance
transformation along the transmission line at frequencies above and below
the dipole resonant length and the physical lengths of coax cut for that
resonant frequency.

Since the situation described by Dave can be modeled directly in NEC-2 or
NEC-4, using the transmission line feature available on NEC, I decided to
look at some SWR curves across 80 meters.  My dipole was resonated at 3.75
MHz to ensure that the 2:1 SWR points fell within the band.  I used the NEC
mathematical models of 50-ohm, 0.765 VF transmission line for 0.5, 1.0,
1.5, and 2.0 wl, followed by a 0.25 wl section of 75-ohm, 0.66 VF cable to
the feedpoint/station end.

My dipole at 120' over level medium ground had an independent feedpoint Z
of 76 ohms.  I am reading from graphs at this point, but hope to make the
data more precise later.

50-ohm Length  Lower limit    Upper limit    Bandwidth      Lowest SWR
     0.5wl          3.57           3.96        0.39              1.45
     1.0            3.55           3.96        0.41              1.30
     1.5            3.57           3.93        0.36              1.10
     2.0            3.58           3.91        0.33              1.05

The table has several interesting features.  First, for a 0.5 wl 50-ohm
run, there is only one SWR minimum, roughly at the self-resonant frequency
of the dipole.  With an independent feed Z of 76 ohms, the SWR shows a
shallow curve.

Second, for lengths of 50-ohm coax of 1 wl and up, the double minima curve
emerges.  With the given independent dipole feed Z, bandwidth is greatest
with a 1 wl run and diminishes above that.  In fact, as the length of 50-
ohm coax is increased, the rise in SWR is steeper at both the low and high
ends of the band.  However, the minimum SWR become lower with increases in
50-ohm line length.  The SWR at the dipole's self-resonant frequency
remains almost unchanged (1.4 to 1.5) throughout.

I reran the exercise, each time lowering the dipole height by 10' in order
to see what effect an increasing independent feed Z might have on the
curves.  I adjusted the independent dipole length as necessary for
resonance and imported that length to the model with transmission lines. 
First the numbers:

110' up"  Z=83 ohms
50-ohm Length  Lower limit    Upper limit    Bandwidth      Lowest SWR
     0.5wl          3.55           3.97        0.42              1.35
     1.0            3.54           3.96        0.42              1.25
     1.5            3.56           3.93        0.37              1.10
     2.0            3.58           3.91        0.33              1.05

100' up"  Z=89 ohms
50-ohm Length  Lower limit    Upper limit    Bandwidth      Lowest SWR
     0.5wl          3.53           3.97        0.44              1.30
     1.0            3.53           3.96        0.43              1.20
     1.5            3.56           3.92        0.36              1.05
     2.0            3.58           3.90        0.32              1.05

90' up"  Z=92 ohms
50-ohm Length  Lower limit    Upper limit    Bandwidth      Lowest SWR
     0.5wl          3.53           3.99        0.46              1.25
     1.0            3.54           3.96        0.42              1.10
     1.5            3.56           3.92        0.36              1.01
     2.0            3.58           3.90        0.32              1.05

As the independent feedpoint impedance of the dipole increases (within the
boundaries of the test runs), the performance of the 0.5 wl 50-ohm coax run
improves.  The curves over all the tests for this length of line are
largely congruent, and the improved performance with increasing feed Z
occurs because the impedance presented to the 0.25 wl 75-ohm matching
section grows closer to the value needed for a 50-ohm impedance at the
transmitter end.

Although not especially extreme, the slope of the SWR curves for the two
longest runs of 50-ohm line grow steeper with increasing independent dipole
feed Z.  Band edge values are about 5:1 for 2 wl runs and 4:1 for 1.5 wl
runs.  By contrast, with a 1.0 wl run, the band-edge SWRs are close to 3:1,
while with a 0.5 wl run, the band-edge values are about 2.7:1 for the worst
case and 2.5:1 for the best case (at the lower end, with lower values at
the upper end of the band).  These values do not account for dissipative
line losses that ordinarily show up at the shack end of the line as
slightly lower SWR readings.

So, what is the use of all this modeling?  If all one needs are two low-SWR
points within the band, then any of the 50-ohm lengths might be in order. 
However, if one is seeking the maximum possible coverage of 80-75, then one
might consider restricting the length of initial 50-ohm coax run to 0.5 wl
or at most 1.0 wl.  One can insert the 75-ohm matching section at this
point and use 50-ohm coax the rest of the way to the shack.  Since the
impedance values fluctuate across the band by as much above 50 ohms as
below it, some further impedance transformation will occur, but it will be
in virtually all cases less radical at the band edges than would be the
case of using the longer initial 50-ohm runs indicated in the charts.

The numbers and suggestions are limited, of course, by the limitations of
the models and modeling program.  They may require field adjustment in
accord with the circumstances of any given installation.  However, I hope
they are useful to those thinking about using the feed system Dave Leeson
has brought to our attention.



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      /  \   \   \ \       ||    

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