Dave Leeson brought to our attention an interesting technique for achieving
wideband 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
interestthen, for that frequency, cutting a length of 50ohm coax a
multiple of 0.5 wl (allowing for velocity factor), with a 0.25 wl length of
75ohm coax (again, allowing for velocity factor) at the station end of the
line.
This is a bit of followup 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 notfor many purposessufficiently large to
make a case against this or other widebanding techniques with coaxial feed
lines. The factors that produce wideband 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 NEC2 or
NEC4, 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 50ohm, 0.765 VF transmission line for 0.5, 1.0,
1.5, and 2.0 wl, followed by a 0.25 wl section of 75ohm, 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.
50ohm 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 50ohm
run, there is only one SWR minimum, roughly at the selfresonant frequency
of the dipole. With an independent feed Z of 76 ohms, the SWR shows a
shallow curve.
Second, for lengths of 50ohm 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
50ohm line length. The SWR at the dipole's selfresonant 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
50ohm 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
50ohm 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
50ohm 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 50ohm 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 75ohm matching
section grows closer to the value needed for a 50ohm impedance at the
transmitter end.
Although not especially extreme, the slope of the SWR curves for the two
longest runs of 50ohm 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 bandedge SWRs are close to 3:1,
while with a 0.5 wl run, the bandedge 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 lowSWR
points within the band, then any of the 50ohm lengths might be in order.
However, if one is seeking the maximum possible coverage of 8075, then one
might consider restricting the length of initial 50ohm coax run to 0.5 wl
or at most 1.0 wl. One can insert the 75ohm matching section at this
point and use 50ohm 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 50ohm 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.
73
LB, W4RNL
L. B. Cebik, W4RNL /\ /\ * / / / (Off)(423) 9747215
1434 High Mesa Drive / \/ \/\ /\ (Hm) (423) 9386335
Knoxville, Tennessee /\ \ \ \ / /  / (FAX)(423) 9743509
379384443 USA / \ \ \ \  cebik@utk.edu
URL: http://funnelweb.utcc.utk.edu/~cebik/radio.html

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