Ken, I guess I'm still confused.

As I understand it, one cannot reliably determine the exact resonance of
a dipole by finding the point of minimum SWR. Until this measurement
issue is resolved, there would seem to be little benefit to seeking an
explanation of why the formula appeared not to work.

It is probably too late now, but if you had used an impedance bridge
(MFJ or Autek, for example) you could have found resonance at the point
of zero reactance. All within the limits of the instruments, of course.

Some of the posts suggest other reasons why the formula might not work,
but it is not yet evident to me that it didn't work.

Sorry my earlier post was not more clear. (I'm even sorrier for this
post if you actually used an impedance bridge! Hi.)

73,

Chuck
NT3G

There's good reason for confusion.

Resonance is defined as the frequency at which the reactance is zero.

Antenna resonance is the frequency at which the feedpoint reactance is zero.

At the input end of a feedline, resonance will occur at the same
frequency as antenna resonance only if the antenna resistance is the
same as the feedline characteristic impedance, or if the feedline is a
multiple of a quarter wavelength (yes, quarter) long. So resonance at
the input end of a feedline is often at a different frequency than
antenna resonance. (You could call that "antenna system resonance".)

The reading on an SWR meter is a function of the both the resistance and
reactance of the load presented to the meter.

As the frequency changes, both the feedpoint resistance and reactance
change. So if the resistance is closer to the SWR meter's Z0 when
there's a slight reactance, the SWR meter reading at the feedpoint can
be better than at resonance, when the reactance is exactly zero. When
measured at the feedline input, there's the additional factor of
impedance transformation that can modify the reactance and therefore
resonance.

In practice, though, the point of minimum SWR is nearly always very
close to resonance, at the antenna feedpoint. This is because for most
antennas, the reactance changes much faster with frequency than the
resistance does. And, when the feedpoint resistance is roughly equal to
the feedline Z0, the transformation by a mismatched feedline isn't
extreme, so again the point of minimum SWR is usually close to
resonance. Where you're likely to see a noticeable difference between
resonance and lowest SWR is with antennas with several coupled elements
(where feedpoint R can change more rapidly with frequency), or severely
mismatched feedlines, like when using open wire line to feed a dipole on
several bands.

In the end, it really doesn't matter. There's nothing at all magical
about resonance, so there's no need to try and achieve it. What you're
usually interested in doing is matching the rig to the input of the
feedline, and the common measure of the quality of that match is the
reading on an SWR meter. So the common, and valid, practice is to prune
the antenna for lowest SWR meter reading. If you do that, there's no
need to worry about where resonance might be.

Roy Lewallen, W7EL

chuck wrote:

Ken, I guess I'm still confused.

As I understand it, one cannot reliably determine the exact resonance of
a dipole by finding the point of minimum SWR. Until this measurement
issue is resolved, there would seem to be little benefit to seeking an
explanation of why the formula appeared not to work.

It is probably too late now, but if you had used an impedance bridge
(MFJ or Autek, for example) you could have found resonance at the point
of zero reactance. All within the limits of the instruments, of course.

Some of the posts suggest other reasons why the formula might not work,
but it is not yet evident to me that it didn't work.

Sorry my earlier post was not more clear. (I'm even sorrier for this
post if you actually used an impedance bridge! Hi.)

73,

Chuck
NT3G

So the common, and valid, practice is to prune
the antenna for lowest SWR meter reading. If you do that, there's no
need to worry about where resonance might be.

===================================

An excellent description, Roy.

There's a minor omission. You omitted to say that the SWR meters is
redundant because the actual reading is disregarded. There are other
reasons of course. Only a TLI is needed.
----
Reg

No, the SWR meter is useful in determining the quality of the match. I
was careful to say "SWR meter reading" to distinguish it from the SWR on
a transmission line.

Roy Lewallen, W7EL

Reg Edwards wrote:
So the common, and valid, practice is to prune
the antenna for lowest SWR meter reading. If you do that, there's no
need to worry about where resonance might be.


===================================

An excellent description, Roy.

There's a minor omission. You omitted to say that the SWR meters is
redundant because the actual reading is disregarded. There are other
reasons of course. Only a TLI is needed.
----
Reg

The quality of the match is NOT the SWR on ANY line. Quality is the degree
of conformance to specified requirements. Or how closely the transmitter
load matches the required value.

The meter does NOT measure the SWR on the line between itself and the
antenna. It does NOT measure the SWR on any real line. If only because no
other real line exists The meter is redundant.

As discussed elsewhere, other quantities which an SWR meter purports to
measure are Forward and Reflected power, both at the same place and same
time. Which are just as imaginary as the transmission line the meter assumes
they exist on.

Imaginary quantities can be useful at times. But at least the name of the
imaginary number "j" does not cause anywhere near as much confusion about
what is really happening as the name "SWR Meter" does. Witness the
arguments amongst otherwise sane, logical, intelligent, educated people.
----
Reg.

======================================

"Roy Lewallen" wrote in message
...
No, the SWR meter is useful in determining the quality of the match. I
was careful to say "SWR meter reading" to distinguish it from the SWR on
a transmission line.

Roy Lewallen, W7EL

Reg Edwards wrote:
So the common, and valid, practice is to prune
the antenna for lowest SWR meter reading. If you do that, there's no
need to worry about where resonance might be.


===================================

An excellent description, Roy.

There's a minor omission. You omitted to say that the SWR meters is
redundant because the actual reading is disregarded. There are other
reasons of course. Only a TLI is needed.
----
Reg

Thanks for the information and explanation, Roy.

I do agree that the error introduced by using an SWR minimum as a proxy
for zero reactance would not alone account for Ken's results. I also
agree that resonance is important here only insofar as it is a
definitional element in the nnn/f = L formula. I understand the formula
is an approximation. At issue was whether the approximation held
constant over a frequency excursion of approximately 5%, not an
unreasonable expectation. Ken offered measurements purportedly showing
that the approximation did not hold over that range. I will try to show
that the uncertainty in the reported measurements does not provide
confidence in the conclusion that the "constant" has changed. Whether
the "constant" actually changed, and if so why, does not concern me here.

Ken initially reported a change to the "constant" (i.e., 234) of 2.32 in
going from 9.5665 to 10.1955 MHz by trimming the length of a dipole. He
based this on his measurements of SWR used to determine resonant
frequency and on his measurements of wire length.

What is the required precision in SWR measurement needed to determine
resonant frequency?

An error in measuring the resonant frequency that would produce a
"constant" error of 2.32, is roughly 0.097 MHz. For a 30 meter half-wave
dipole, the feed-point SWR ranges from 1.35 at 9.97 MHz to 1.35 at 10.02
MHz, with 1.34 being the minimum at 10.0 MHz (from Reg Edwards'
swr_freq.exe program). This SWR range corresponds to a frequency
difference of 0.06 MHz. More directly, an SWR measurement error of 0.01
at the antenna could produce an error in computed resonant frequency of
0.06 MHz. Measuring at the end of a transmission line is not likely to
improve this relationship.

So how likely is it that SWRs were actually read with precisions on the
order of 0.01, when the measurements were taken hours or days apart? I
can't do that on my Bird. I think only a digital SWR meter can provide
that kind of precision. On a calm day. With no inherent lsd jitter. And
would it be repeatable after hours or days between measurements? Try it
on your antennas. In any case, to achieve the 500 Hz precision reported
would require something like five significant digits of SWR measurement.
Maybe in a lab with a cutting-edge network analyzer. The issue is not
accuracy, of course, but whether SWR measurements of the required
precision are feasible. Please, no lectures, folks, on how unimportant
such SWR measurements are in normal practice. This is a very unusual
application of SWR measurement.

What is the effect of errors in length measurement on calculated
frequency using the formula?

For the length measurement, Ken reports a precision of 0.001 foot. That
is 0.012 inches, less than 1/64 inch. I don't believe this kind of
precision was achieved either. An inch in a 24 foot length of wire is
actually pretty good, considering the difficulty in holding it taut
without stretching it, etc. But a one inch difference will produce an
equivalent frequency error of 0.03 MHz (by the formula).

Simply adding the 0.06 Mhz and 0.03 MHz errors gives a total uncertainty
of 0.09 MHz, an amount roughly equal to that required to generate an
error of 2.32 in calculating the "constant". I know, I know. These are
not rms errors. But they're what we have.

In other words, no cigar for for showing that the "constant" changes by
2.32 when the frequency changes by five percent.

Perhaps someone can provide a more sophisticated analysis of the
measurement uncertainty involved. Perhaps with a better analysis, we
will find that we can all go out and measure SWR to within 0.01 so we
can calculate resonant frequency to within 500 Hz. Yeah, I know all that
precision is imaginary, thanks to umpteen digit calculators.

And sure, changing the height of the antenna ends could also
explain a change in the "constant". At least the change would be in the
reported direction.

So there it is! I looked at the problem and tried to understand where
the data came from and how they were measured and how much confidence I
should give them. Meanwhile, I missed the whole point of the exercise,
which seemed to be hypothetical: if one were to do such and such and
found that the "constant" changed, what might have caused it. That's
what's great about this group. The rest of you pretty much thought about
the question and went to what is probably the correct answer. Do the
data Ken reported really support that answer? Who knows.

Gotta love this stuff.

73 to all and thanks for your patience on this tediously long post.

Chuck
NT3G

chuck wrote:
I do agree that the error introduced by using an SWR minimum as a proxy
for zero reactance would not alone account for Ken's results.

I have only just now read this thread so I am ignorant of anything
that has been posted before. I just want to add that, using my MFJ-
259B, the minimum SWR is not usually at the same frequency as the
purely resistive reading. Draw your own conclusions from that
measurement.
--
73, Cecil http://www.qsl.net/w5dxp

Sorry to hack just a very short piece out of context, but it's pretty
fundamental to the whole issue. I'll try to comment on the rest later,
as time permits. . .

chuck wrote:

. . .

What is the required precision in SWR measurement needed to determine
resonant frequency?

. . .

There is no amount of precision which will make that possible.

The resonant frequency cannot be determined by measurement of SWR alone
(or more accurately, by an SWR meter reading), except in one very
special case: If the resistance at resonance is equal to the SWR meter's
characteristic impedance, then a reading of exactly 1:1 indicates
resonance at the SWR meter terminals. This is seldom the case for an
antenna or antenna system. In other words, if the SWR meter reads 1:1,
then the load it's connected to is 50 + j0, which is resonant (assuming
a 50 ohm SWR meter). There's no way to determine resonance with any
other reading or for any other resistance -- if the meter dips to, say
1.2:1 at some frequency, you can't know if resonance has occured at that
frequency unless you have some additional information.

Again, in practice, the point of minimum SWR meter reading is often, but
not always, very close to the point of resonance (at the SWR meter). And
again, there's seldom any need to determine resonance.

Roy Lewallen, W7EL