alhearn wrote:
Why does the reactance peak occur slightly earlier than
half-wavelength?

Since the monopole is purely resistive around 1/4WL and
around 1/2WL, i.e. the reactance is zero at those two
points, it is simply impossible for it to be be any
other way.
--
73, Cecil http://www.qsl.net/w5dxp



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Cecil Moore wrote ..
Since the monopole is purely resistive around 1/4WL and
around 1/2WL, i.e. the reactance is zero at those two
points, it is simply impossible for it to be be any
other way.

That's very true, but between the 1/4WL and 1/2WL zero-reactance
points, reactance increases with frequency, peaks, and then begins to
decrease to cross zero again at the 1/2WL point. This peak is NOT
half-way between 1/4WL and 1/2WL, but skewed heavily toward the 1/2WL
point. My question is what determines where that peak occurs?

Can the reactance peak be somehow adjusted (frequency position, not
magnitude) for tuning purposes? Magnitude is easily adjusted by simply
adding inductive or capacitive reactance, which doesn't change the
shape or peak position of the reactance curve, but simply moves the
curve up or down to change the points at which it crosses zero
(resonance frequency). Controlling the reactance peak position could
do the same.

The answer may be simple and common knowledge, but I haven't found it.

Al

alhearn wrote:
My question is what determines where that peak occurs?

Mathematically, it will be where the SWR circle is tangent
to the reactance arc. The higher the SWR, the higher the
maximum possible reactance and the closer it is to the
anti-resonance point.
--
73, Cecil http://www.qsl.net/w5dxp



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Cecil Moore wrote in message ...
alhearn wrote:
My question is what determines where that peak occurs?

Mathematically, it will be where the SWR circle is tangent
to the reactance arc.

That is not in general true; do you have reason to believe it's true
for the impedance of a dipole? Consider what happens when you change
the reference impedance for the SWR measurement.

The higher the SWR, the higher the
maximum possible reactance and the closer it is to the
anti-resonance point.

What's the reactance at the anti-resonance point? Is highest SWR at
anti-resonance, or at maximum reactance, or at some point between?

Tom Bruhns wrote:
Cecil Moore wrote:

alhearn wrote:
My question is what determines where that peak occurs?

Mathematically, it will be where the SWR circle is tangent
to the reactance arc.

That is not in general true; do you have reason to believe it's true
for the impedance of a dipole?

When the dipole is at maximum feedpoint reactance, can the SWR be
calculated? Of course. Will that point, when plotted on a Smith Chart
lie on the SWR circle? Of course. Will it also lie on a reactance arc?
of course. Will the SWR circle be tangent to that reactance arc?
Of course. Will the un-normalized value of the maximum feedpoint
reactance be constant? Of course, assuming nothing changes except Z0.

Consider what happens when you change
the reference impedance for the SWR measurement.

It doesn't matter. The Smith Chart reference changes and therefore
the SWR changes but *the value of the antenna feedpoint impedance
stays the same*. The new SWR circle is still tangent to the reactance
arc at the same value of un-normalized reactance even though the
normalized reactance value has changed. Xmax/Z01 is different from
Xmax/Z02 but Xmax has not changed (assuming Z0 is the only change).

The higher the SWR, the higher the
maximum possible reactance and the closer it is to the
anti-resonance point.

What's the reactance at the anti-resonance point?

Always zero, by definition. Examples: A full-wave center-fed dipole
or a half-wave end-fed monopole. ("Anti-resonant" is what we called
such antennas at Texas A&M 50 years ago.)

Is highest SWR at
anti-resonance, or at maximum reactance, or at some point between?

If the Z0 of your transmission line is equal to the feedpoint impedance
at anti-resonance, the lowest SWR will occur at anti-resonance. If the
Z0 of your transmission line is equal to the feedpoint impedance at
maximum reactance, the lowest SWR will occur at maximum reactance. :-)

Depends upon the Z0 of the transmission line. If you choose a Z0 that
is the square root of the resonant impedance times the anti-resonant
impedance, the SWR at resonance and anti-resonance will be the same.
For a dipole that Z0 value is usually between 450 ohms and 600 ohms.
That's why anti-resonance is no problem for ladder-line/open-wire.
--
73, Cecil http://www.qsl.net/w5dxp



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Cec, & Co.

Zo of an antenna wire seems to be an important parameter in your
discussions. Knowledge of its value would appear to be essential before
continuing with calculations. Otherwise nobody will get nowhere.

So how is the value of Zo obtained (without bringing Terman et al into it)?
----
Reg, G4FGQ

Reg Edwards wrote:

Cec, & Co.
Zo of an antenna wire seems to be an important parameter in your
discussions.

Why do you say that? The only thing I have dealt with is
a constant feedpoint impedance at any one frequency.
--
73, Cecil http://www.qsl.net/w5dxp



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Reg Edwards wrote:
Cec, & Co.
Zo of an antenna wire seems to be an important parameter in your
discussions.

Here's an example of what I have been talking about. The feedpoint
impedance of my 130 ft. dipole (according to EZNEC) is:

60+j0 ohms at 3.63 MHz - resonance

2513+j2314 at 6.575 MHz - maximum reactance

5000+j0 at 7.118 MHz - anti-resonance

Assuming the antenna is fed with Z0 = 550 ohm open-wire line, the SWR
ranges from 8.5:1 to 9.2:1 and the impedance at a current maximum
point on the ladder-line ranges from 60 ohms to 65 ohms. The feedpoint
impedances from 3.63 MHz (resonance) to 7.118 MHz (anti-resonance)
describe an imperfect semi-circle on a Smith Chart normalized for 550 ohms.

If one plots the feedpoint impedances for all the different bands on a
Smith Chart normalized for SQRT(Rresonant * Ranti-resonant), it will
resemble an imperfect SWR circle (or imperfect spiral). By feeding my
dipole only at the current-maximum points, I achieve a near-perfect match
on all amateur HF bands without an antenna tuner.

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



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Cecil Moore wrote in message ...
Tom Bruhns wrote:
Cecil Moore wrote:

alhearn wrote:
My question is what determines where that peak occurs?

Mathematically, it will be where the SWR circle is tangent
to the reactance arc.

That is not in general true; do you have reason to believe it's true
for the impedance of a dipole?

When the dipole is at maximum feedpoint reactance, can the SWR be
calculated? Of course. Will that point, when plotted on a Smith Chart
lie on the SWR circle? Of course. Will it also lie on a reactance arc?
of course. Will the SWR circle be tangent to that reactance arc?
Of course.

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? 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.

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

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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