Tom Bruhns wrote:
I'm sorry, Cecil, but you lost me there. For any given SWR circle,
there are only two (complex conjugate) points at which reactance arcs
are tangent. Why would we think that the point of max reactance on
the antenna impedance curve will necessarily be at the point of
tangency?

Note: I am talking about the frequencies between the 1/2WL resonant
point and the one-wavelength (anti)resonant point for a fixed dipole.
There will exist a maximum reactance point between those two
frequencies. By definition of the bi-linear transformation rules
involving the Smith Chart, the maximum reactance point will be
located at the point where the SWR circle is tangent to the
reactance arc. It simply cannot be located anywhere else.

It's an obvious geometrical thing, Tom. The SWR circle is centered at
the center of the Smith Chart. The reactance arc (circle) is centered
somewhere else outside of the Smith Chart. Where these two circles are
tangent, the reactance is at a maximum, by definition. If the two circles
are not tangent and not touching, then that cannot possibly be the maximum
reactance point. If the two circles are not tangent and intersect at two
points, then that cannot possibly be the maximum reactance point. In the
latter case, the maximum reactance point lies between those two intersection
points.

The antenna impedance arc of the simple dipole I modelled
indeed does not lie tangent to the max reactance arc at the same point
as the SWR circle that's tangent that reactance arc.

Sorry, you did something wrong or don't understand what I am
saying. It is impossible for the maximum reactance point not to be
tangent to the reactance arc at the maximum reactance point. On the
inductive top part of the Smith Chart, between 1/2WL and 1WL, if the
circles intersect at more than one point, you are not at the maximum
reactance point. If the circles intersect at one and only one point,
they are tangent, by definition, and you are at the maximum reactance
point. If they don't intersect at all, you are not at the maximum
reactance point.

In any event, I don't see that this tells us anything about _why_ the
dipole shows max reactance at that particular frequency.

Because it's an obvious geometrical thing, Tom. It simply cannot be any
other frequency and can be proved with relatively simple geometry.

EXAMPLE: 1/2WL resonant feedpoint impedance is 50+j0 ohms.
One-wavelength (anti)resonant feedpoint impedance is 5000 ohms.
Maximum reactance point has a feedpoint impedance of 2500+j2500 ohms.

The SWR circle (at the frequency of maximum reactance) will pass through
the 2500+j2500 ohm point. Do you disagree?

The reactance arc (at the frequency of maximum reactance) will pass
through the 2500+j2500 ohm point. Do you disagree?

ERGO: The SWR circle will be tangent to the reactance arc at the
2500+j2500 ohm point no matter what Z0 is being used. Do you
disagree?
--
73, Cecil http://www.qsl.net/w5dxp



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I agree that it's an obvious geometrical thing...and it could be that
I'm simply not understanding what you're trying to communicate.
But...do a simulation of the "dipole1.ez" that ships with EZNec, after
first changing the number of segments to 31 so it doesn't complain.
Find the frequency between 300MHz and 600MHz which maximized the
reactance. I believe you will find it at about 494MHz, and the
reactance is +j866.0 ohms. At that frequency, the resistive part is
1085 ohms. Put that on a Smith chart whose reference resistance is 50
ohms. Draw a constant-SWR circle (35.542; magnitude of rho = .9453)
through that point. Note that there are two constant-reactance arcs
tangent to that SWR circle, and note that they are NOT tangent at the
antenna's impedance point. In fact, it's reasonably easy to calculate
them as +/-j887.8. Now change the reference impedance to 2000 ohms,
and note that the constant SWR circle which passes through the antenna
max-reactance impedance point is nowhere near the point that SWR
circle is tangent to a reactance arc. The SWR for 1085+j866 referred
to 2000 ohms is 2.296, magnitude of rho = .3932. The constant SWR
circle in this case is tangent to reactance arcs of +/-j1860.28.

I certainly agree that the point where a reactance arc is tangent with
an SWR circle is the maximum reactance on that SWR circle, but that's
not necessarily (and generally is NOT) also a point on the curve
representing antenna feedpoint impedance versus frequency. -- Did I
miss something fundamental here? Are we not discussing how the
antenna feedpoint impedance changes with frequency, and specifically
the frequency between half and full wave resonances at which the
antenna feedpoint reactance is maximum?

And still, all this does NOTHING to tell us WHY the antenna's
reactance reaches maximum at that particular frequency. Again, maybe
I missed it, but I didn't see anything in your swr circles and
reactance arcs explanation that even mentioned frequency.



Example: Cecil Moore wrote in message ...
Tom Bruhns wrote:
I'm sorry, Cecil, but you lost me there. For any given SWR circle,
there are only two (complex conjugate) points at which reactance arcs
are tangent. Why would we think that the point of max reactance on
the antenna impedance curve will necessarily be at the point of
tangency?

Note: I am talking about the frequencies between the 1/2WL resonant
point and the one-wavelength (anti)resonant point for a fixed dipole.
There will exist a maximum reactance point between those two
frequencies. By definition of the bi-linear transformation rules
involving the Smith Chart, the maximum reactance point will be
located at the point where the SWR circle is tangent to the
reactance arc. It simply cannot be located anywhere else.

It's an obvious geometrical thing, Tom. The SWR circle is centered at
the center of the Smith Chart. The reactance arc (circle) is centered
somewhere else outside of the Smith Chart. Where these two circles are
tangent, the reactance is at a maximum, by definition. If the two circles
are not tangent and not touching, then that cannot possibly be the maximum
reactance point. If the two circles are not tangent and intersect at two
points, then that cannot possibly be the maximum reactance point. In the
latter case, the maximum reactance point lies between those two intersection
points.

The antenna impedance arc of the simple dipole I modelled
indeed does not lie tangent to the max reactance arc at the same point
as the SWR circle that's tangent that reactance arc.

Sorry, you did something wrong or don't understand what I am
saying. It is impossible for the maximum reactance point not to be
tangent to the reactance arc at the maximum reactance point. On the
inductive top part of the Smith Chart, between 1/2WL and 1WL, if the
circles intersect at more than one point, you are not at the maximum
reactance point. If the circles intersect at one and only one point,
they are tangent, by definition, and you are at the maximum reactance
point. If they don't intersect at all, you are not at the maximum
reactance point.

In any event, I don't see that this tells us anything about _why_ the
dipole shows max reactance at that particular frequency.

Because it's an obvious geometrical thing, Tom. It simply cannot be any
other frequency and can be proved with relatively simple geometry.

EXAMPLE: 1/2WL resonant feedpoint impedance is 50+j0 ohms.
One-wavelength (anti)resonant feedpoint impedance is 5000 ohms.
Maximum reactance point has a feedpoint impedance of 2500+j2500 ohms.

The SWR circle (at the frequency of maximum reactance) will pass through
the 2500+j2500 ohm point. Do you disagree?

The reactance arc (at the frequency of maximum reactance) will pass
through the 2500+j2500 ohm point. Do you disagree?

Certainly the +j2500 ohm reactance arc will pass through 2500+j2500.
But that reactance arc is not tangent to the SWR circle that passes
through that point, necessarily. Draw the chart with Zref set to
10,000 ohms, and you'll instantly see this. Draw the chart with
Zref=50 ohms, and it will be difficult to see, but in fact if you go
through the calcs, I believe you'll find a slight discrepancy even
there! The point of tangency is not exactly where R=X, though it's
close for high SWR. But try it for a low SWR circle, and it will be
visually obvious on the Smith chart. For example, on a 50 ohm chart,
SWR=1.63 will be tangent to +/-j25 ohm reactance arcs, but at roughly
55 ohms resistive, no where near 25 ohms resistive.


ERGO: The SWR circle will be tangent to the reactance arc at the
2500+j2500 ohm point no matter what Z0 is being used. Do you
disagree?

Sure do. See numerical examples above.

Tom Bruhns wrote:
I certainly agree that the point where a reactance arc is tangent with
an SWR circle is the maximum reactance on that SWR circle, but that's
not necessarily (and generally is NOT) also a point on the curve
representing antenna feedpoint impedance versus frequency. -- Did I
miss something fundamental here?

I suspect you missed that my input to the discussion assumes a thin wire
at HF frequencies. Try an HF dipole with a thin wire and see what you get.
It will be approximately the same curve as Fig. 10, page 2-10, ARRL Antenna
Book, 15th edition. Since this is the graph of an end-fed antenna, the
dipole response can be obtained by multiplying the frequencies by 2.
Everything I have said has been extrapolated from that graph in the
ARRL Antenna Book which is, as I said before, an "imperfect circle or
imperfect spiral".

Are we not discussing how the
antenna feedpoint impedance changes with frequency, and specifically
the frequency between half and full wave resonances at which the
antenna feedpoint reactance is maximum?

Yes, that's true. Now try it with a thin wire on HF. I believe what
you will find is that at the maximum reactance point, the resistance
is approximately half of the one-wavelength (anti)resonant value.
At the maximum reactance point, the resistance and reactance are
approximately equal. Since the maximum reactance value lies between
two points of pure resistance, doesn't it make sense that it might
be approximately where the resistance is half of the maximum value
of resistance?

Maybe you should just tell us why you disagree with Fig. 10 in the
ARRL Antenna Book, 15th edition, page 2-10.

If you want to see a dipole feedpoint impedance Vs frequency, it
is illustrated in Figs. 2-5, Page 2-3,4, ARRL Antenna Book CD,
version 2.0. Unfortunately, they plotted reactance on a linear
scale and resistance on a log scale and thus messed up the
shape of the "imperfect circle or imperfect spiral". Even with
that, one can see that the point of maximum reactance approximately
equals the resistance at that point and is approximately half the
value of the maximum resistance.
--
73, Cecil http://www.qsl.net/w5dxp



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Tom Bruhns wrote,

(Snip)

And still, all this does NOTHING to tell us WHY the antenna's
reactance reaches maximum at that particular frequency. Again, maybe
I missed it, but I didn't see anything in your swr circles and
reactance arcs explanation that even mentioned frequency.


In Constantine Balanis book _Antenna Theory Analysis and Design_
second edition Section 8.5 page 411, there are a couple of charts of
resistance and reactance that illustrate the original question. On
the facing page (page 410) equations are given for R and X at
current maximum points on a dipole. If these equations are
correct it's not hard to believe that their respective maxima don't
coincide since the equations are different. If anyone wants to
understand where the equations come from he can read chapter
eight in all its gory entirety. It's not simple and requires more than
just a familiarity with a Smith chart. Cecil should read before he
thinks.
73,
Tom Donaly, KA6RUH

Cecil Moore wrote in message ...
....
The SWR circle (at the frequency of maximum reactance) will pass through
the 2500+j2500 ohm point. Do you disagree?

The reactance arc (at the frequency of maximum reactance) will pass
through the 2500+j2500 ohm point. Do you disagree?

ERGO: The SWR circle will be tangent to the reactance arc at the
2500+j2500 ohm point no matter what Z0 is being used. Do you
disagree?

that specific example, using a reference impedance of 50 ohms...

magnitude of rho for 2500.00+j2500.00 = .9801999804
magnitued of rho for 2500.25+j2500.00 = .9801999801
magnitude of rho for 2500.50+j2500.00 = .9801999800
magnitude of rho for 2500.75+j2500.00 = .9801999801
magnitude of rho for 2501.00+j2500.00 = .9801999804

The point of tangency to an SWR circle for the +j2500.00 arc is
therefore NOT at 2500.00+j2500.00. It will be much more obvious if
you recalculate things at a higher reference impedance, say 1000 ohms.
Then following the +j2500 reactance arc, mag(rho) reaches a minimum
when Z is about 2692+j2500. And in any event, I think it highly
unlikely that the antenna's resistance when the reactance peaks at
2500 ohms will be exactly 2500 ohms as well.

Tdonaly wrote:
Cecil should read before he thinks.

Tom, why do you require 6 decimal point precision out
of a ballpark rule-of-thumb estimate? The maximum reactance
point of a thin-wire dipole is in the neighborhood of the maximum
reactance point of the SWR circle as proved by the graphs in the
ARRL Antenna Book CD. The maximum reactance is approximately equal
to 1/2 the maximum resistance. The resistance at the maximum reactance
point is approximately equal to 1/2 the maximum resistance. If someone
carries those ballpark concepts around in his head, he will be
reasonably close to reality. It's all cut-and-try after that.

Exactly what agenda forces you to sacrifice your reputation trying to
find some unusual esoteric exception to my statements? (Never mind,
I already know the answer.)
--
73, Cecil http://www.qsl.net/w5dxp



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Tom Bruhns wrote:
that specific example, using a reference impedance of 50 ohms...

magnitude of rho for 2500.00+j2500.00 = .9801999804
magnitued of rho for 2500.25+j2500.00 = .9801999801
magnitude of rho for 2500.50+j2500.00 = .9801999800
magnitude of rho for 2500.75+j2500.00 = .9801999801
magnitude of rho for 2501.00+j2500.00 = .9801999804

The point of tangency to an SWR circle for the +j2500.00 arc is
therefore NOT at 2500.00+j2500.00.

Good Lord, Tom, do you have to stoop so low as to argue over
0.0000000003? I said it was a ballpark rule-of-thumb estimate
to start with. Just what agenda are you following that requires
greater than 0.0000000003 accuracy out of a ballpark rule-of-
thumb estimate? No need to answer - I already know the answer.
--
73, Cecil http://www.qsl.net/w5dxp



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On Fri, 26 Mar 2004 16:29:59 -0600, Cecil Moore
wrote:

No need to answer - I already know the answer.

On Fri, 26 Mar 2004 16:20:24 -0600, Cecil Moore
wrote:

(Never mind,
I already know the answer.)

Who would've thougth otherwise? Foolish boys.

Cecil Moore wrote:
Good Lord, Tom, do you have to stoop so low as to argue over
0.0000000003? I said it was a ballpark rule-of-thumb estimate
to start with. Just what agenda are you following that requires
greater than 0.0000000003 accuracy out of a ballpark rule-of-
thumb estimate? No need to answer - I already know the answer.

In case anyone has forgotten, here's what I said in an earlier posting:

At least for my multi-band dipole, it appears that the anti-resonant
feedpoint impedance is about 100 times the resonant feedpoint impedance.
The feedpoint impedance at the maximum reactance point is about 5000/2+j5000/2,
i.e. the R is about half the anti-resonant resistance and the Xmax is about
half the anti-resonant resistance times 'j'. These are my rules-of-thumb for
my dipole.

Does everyone understand the meaning of "appears", "about", and "rules-of-thumb"?
In my world, 20% accuracy out of a rule-of-thumb is pretty good. Does anyone else
(besides Tom) have rules-of-thumb that achieve 0.0000000003 accuracy?
--
73, Cecil http://www.qsl.net/w5dxp



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Cecil wrote,

Tdonaly wrote:
Cecil should read before he thinks.

Tom, why do you require 6 decimal point precision out
of a ballpark rule-of-thumb estimate? The maximum reactance
point of a thin-wire dipole is in the neighborhood of the maximum
reactance point of the SWR circle as proved by the graphs in the
ARRL Antenna Book CD.
The maximum reactance is approximately equal
to 1/2 the maximum resistance. The resistance at the maximum reactance
point is approximately equal to 1/2 the maximum resistance. If someone
carries those ballpark concepts around in his head, he will be
reasonably close to reality. It's all cut-and-try after that.


Cecil, I know you have the Balanis book and that you even took a course
from the great man, himself. You can crack the book and look at the
curves as well as anyone can. You can also read the rest of the
explanation, and, with a lot of work, puzzle it out and improve your
understanding so you don't have to rely on rules of thumb that get you
into arguments like this.

Exactly what agenda forces you to sacrifice your reputation trying to
find some unusual esoteric exception to my statements? (Never mind,
I already know the answer.)

I don't have a reputation. If I did it wouldn't mean anything to me anyway.
Balanis is hardly an "unusual esoteric exception." If you think I have an
"agenda" you're letting your paranoia get the better of you. (No, I'm not
looking for a job on Kerry's campaign committee.)

--
73, Cecil http://www.qsl.net/w5dxp


73,
Tom Donaly, KA6RUH