[TowerTalk] Re: Help! Basic TL theory

[L. B. Cebik]

Steve,

Your situation of wanting a compensating capacitive reactance to reduce
SWR at 3.8 MHz for a resonant 3.5 MHz dipole has several possibilities.

First, HAMCALC (from VE3ERP) has some utilities that can help you see the
impedance changes along a transmission line, including one called in the
Index "transmission line performance" that produces a chart every 5
degrees along a specified line or gives results from a user specified
length of line.  It is based on lossless line, but the results are close
enough for lines less than 1 wl long and at lower HF frequencies.

For your problem, I modeled a resonant 3.5 MHz dipole at 50' up and then
checked the impedance at 3.8 MHz, getting 94 + j155.  These numbers must
be considered ballpark, since the dtails of your precise antenna were
lacking.  However, they will get us started.

We can insert a -j155 ohm capacitive reactance at the antenna feedpoint at
3.8 MHz to effect reactance compensation, and still have the 94 ohms
resistive component.

At the 166 degree point (about 78.8' of 0.66 VF 50-ohm coax) the
uncompensated 3.8 MHz impedance has been transformed to about 30 + j88
ohms.  At this point, a series capacitive reactance of -j88 ohms will
compensate, leaving the 30 ohms resistive.

However, switching a fixed capacitance may be more complex than you need,
if you can obtain a hefty variable capacitor.  Place it in a good
(shielded) box with coax connectors.  Isulate it well from everything (box
and its panel) and connect the coax connectors to the plates to place it
in sereis with the line.  Now you can select the capacitance you need to
compensate for inductive reactance anywhere in the band.

This 1-component ATU works if the line presents the terminals with
inductive reactance.  Many hams in the past have cut their dipoles a
little long, even at 3.5 MHz and then used 180-degree or multiples thereof
at the lowest frequency in the band (3.5) MHz to ensure that the line at
the capacitor box always shows an inductive reactance of a magnitude that
the capacitor can handle.  Your 155-166 degree line appears adequate to
ensure this in your case.

Remember that the max capacitance of the capacitor you use determines the
lowest reactance you can compensate for, while the minimum capacitance
determines the highest reactance.  Since impedances are low, you do not
need a 7kV rated capacitor, but something at 1.5 kV seems wise.

Remember that you still have a resistive component other than 50 ohms, so
your will still have some SWR (about 1.6 or so for the case you set up).
However, losses in coax at 80 meters are relatively low even with SWRs
above 2:1 (which the line will have at 3.8 MHz).

The equations for calculating the impedance along a transmission line are
fairly complex and difficult to reproduce in ASCII, even for lossless
lines. However, there is an item at my site with essentially the same
program as in HAMCALC that includes a BASIC listing from which one can
view at least one way of writing the equations for voltage, current (and
phases angles) and R and jX along a lossless feedline for any Zo.  It is
possible to use the R and jX values at the shack end of the line, and with
appropriate sign changes calculate the antenna impedance as well.  If
memory serves, Walt Maxwell's book has such equations and a Basic program
for that direction.

Future versions of HAMCALC will contain a group of programs drawn from
Peter Dodd's work that show a simple way to measure impedance at the shack
end of the line with voltmeter readings and then to calculate back to the
antenna impedance.  Murph is working on this for Version 31, which I have
reviewed in advance for him.  Unfortunately, the Canadian postal workers
strike prevents me from mailing my suggestions.

I hope these notes are useful to you--and to others who might have
forgotten the old timer's way of stretching the SWR bandwidth of an
80-meter dipole with a series capacitor at the shack end of the line.  It
will also work for 160 meters, with the right dipole, capacitor, and
feedline length range.

-73-

LB, W4RNL



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