Tom Bruhns wrote:
That's pretty approximate, Cecil. From EZNec for a 10 meter 1mm diam
wire, I got about 2570+j2277 at 27.00MHz. The resistive and reactive
parts differ by over ten percent.

For an approximation that I carry around in my head, 20% accuracy
is good enough for me.

Be that as it may, if you evaluate the SWR tangency thing for a high
reference impedance, you will see that it's a GROSS error, not a tiny
one. You said it wouldn't change with changes in reference impedance,
but it does, and in a major way.

Actually, what I said is that the maximum reactance point on an SWR
circle doesn't depend upon Z0 and proved it with equations.
Xmax/Z01 = X1 normalized for Z01. Xmax/Z02 = X2 normalized for Z02.
X1 and X2 are different but Xmax is the same value no matter what the Z0.

Yes, the error is tiny for your
assumed 2500+j2500 evaluated against Z0 of 50 ohms, but the error is
huge if you evaluate against Z0 of, say, 2000 ohms.

That wouldn't be a logical thing to do. The highest Z0 commonly available
to hams is around 600 ohms. The higher the SWR, the more accurate is this
approximation. Conversely, the lower the SWR the more inaccurate is
this approximation. Since I encounter SWR's in the general range of
10-25, it works pretty well for me.

And we're still back to not having said anything about _why_ the
reactance peaks at the frequency it does relative to the half- and
full-wave resonances.

_Why_ am I sitting at my computer right now? Because I'm not somewhere
else? :-) The reactance seems to peak about 85% of the way between the
1/2WL frequency and the one-wavelength frequency. QED folks seem to
be satisfied with just an equation which doesn't ask or answer, _why?_.
They say, "That's just the way it is."
--
73, Cecil http://www.qsl.net/w5dxp



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