In message , Cecil Moore
writes
Ian Jackson wrote:
Are you sure it's as high as that, Reg? I once did a Smith Chart plot
of the impedance at the centre of a dipole, the valued being taken
from a table 'compiled by Wu' (LK Wu?). These only catered for a
lengths up to a few wavelengths. As the plot progressed round and
round the Smith Chart, it seemed to be heading for something around
350 to 400 ohms.

Maybe 377 ohms? Remember that any finite length dipole is a standing
wave antenna and the feedpoint impedance is (Vfor+Vref)/(Ifor+Iref)
where Vfor is the forward voltage phasor, Vref is the reflected
voltage phasor, Ifor is the forward current phasor, and Iref is
the reflected current phasor.

For a 1/2WL resonant dipole the feedpoint impedance is low:
R = (|Vfor|-|Vref|)/(|Ifor|+|Iref|) ~ 73 ohms

For a 1WL (anti)resonant dipole the feedpoint impedance is high:
R = (|Vfor|+|Vref|)/(|Ifor|-|Iref|) ~ 5200 ohms (EZNEC)

An infinite dipole would not be a standing wave antenna. It would
be a traveling wave antenna (as in a terminated rhombic). So the
feedpoint impedance of an infinite dipole would be Vfor/Ifor=Z0.
Since the reflections modify the feedpoint impedance, we might
suspect that Vfor/Ifor falls between the feedpoint impedance for
a 1/2WL dipole and a one WL dipole. Seems to me, the Z0 of the
dipole, i.e. Vfor/Ifor, must be in the ballpark of the square
root of the product of those two feedpoint impedances.

Yes, I did think of 377 ohms (which I understand is 'the impedance of
free space'), but I'm no expert in these matters.

As you indicate, the impedance must lie somewhere between 73 and 5200
ohms. You suggest that this might be something like the square root of
the product of those two feedpoint impedances (the geometric mean),
which gives 616 ohms. However, you would see 600 ohms simply by looking
into an infinite length of 600 ohm feeder, which has parallel,
non-radiating conductors. If the length of the feeder was relatively
short (compared with infinity!!), pulling the conductors apart would
increase the impedance (probably to a lot more than 616 ohms). The
question is, 'when does radiation start to influence the impedance?'

If you look at K6OIK's paper at
http://www.fars.k6ya.org/docs/antenn...nce-models.pdf
and look at, for example, page 22, you can see how the feed impedance at
odd halfwaves increases, and at even halfwaves, decreases. I only found
this paper this morning, and haven't had time to look to see which (if
any) of the many formulas was used to obtain the plot. It must be
possible to get close to the infinity condition by entering values for a
very, very long dipole.

Cheers,
Ian.

--

In King and Harrrison's _Antennas and Waves_, they show a plot of
calculated antenna feedpoint impedance as X vs R up to about 5
wavelengths. Antenna wire radius is 0.008496 wavelength. The Z of an
infinite length antenna is indicated by locating the centers of the
circles and noting that the center converges. The point of convergence
for this particular wire radius is about 250 - j170 ohms.

In the chapter on experimental measurements, there's a plot of the
calculated admittance of an antenna of radius 0.000635 wavelength up to
about 10 wavelengths. Superimposed are measured values from another
source which show very good agreement. The theoretical values converge
at 214 - j189 ohms, and the measured values at 218 - j174 ohms.

Dervivation takes about a chapter of very heavy math, and numerical
results were obtained with a computer.

Roy Lewallen, W7EL

Roy Lewallen wrote:
The theoretical values converge
at 214 - j189 ohms, and the measured values at 218 - j174 ohms.

Free space? As a data point, I pushed EZNEC to the limit on 40m
with a 9000 ft. dipole. Resonant feedpoint resistance at
7.152 is 390 ohms. Anti-resonant feedpoint resistance at 7.092
is 1980 ohms. It appears that EZNEC would converge to something
in between those two values for an infinite dipole in free space.
I ran into the segment limit at 66 wavelengths.
--
73, Cecil http://www.qsl.net/w5dxp


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Cecil Moore wrote:

Roy Lewallen wrote:
The theoretical values converge at 214 - j189 ohms, and the measured
values at 218 - j174 ohms.

Free space? As a data point, I pushed EZNEC to the limit on 40m
with a 9000 ft. dipole. Resonant feedpoint resistance at
7.152 is 390 ohms. Anti-resonant feedpoint resistance at 7.092
is 1980 ohms. It appears that EZNEC would converge to something
in between those two values for an infinite dipole in free space.

Forgot to add, EZNEC would also converge to approximately
the same reactance value as above.
--
73, Cecil http://www.qsl.net/w5dxp

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Cecil Moore wrote:

Roy Lewallen wrote:

The theoretical values converge at 214 - j189 ohms, and the measured
values at 218 - j174 ohms.


Free space? As a data point, I pushed EZNEC to the limit on 40m
with a 9000 ft. dipole. Resonant feedpoint resistance at
7.152 is 390 ohms. Anti-resonant feedpoint resistance at 7.092
is 1980 ohms. It appears that EZNEC would converge to something
in between those two values for an infinite dipole in free space.
I ran into the segment limit at 66 wavelengths.

One point: Isn't the input impedance of a dipole normally specified at
a wavelength equal to twice the electrical length of the antenna? As
far as I know, dipoles have infinite DC resistance at zero Hertz. ;-)

ac6xg

Jim Kelley wrote:

One point: Isn't the input impedance of a dipole normally specified at
a wavelength equal to twice the electrical length of the antenna? As
far as I know, dipoles have infinite DC resistance at zero Hertz. ;-)

No, you can calculate or specify the input impedance of a dipole at any
frequency. As frequency approaches zero, a dipole's input resistance
approaches zero and its reactance approaches minus inifnity. That is, it
looks like a capacitor, and the capacitive reactance gets larger as the
frequency gets lower. Which is just what you'd expect from a couple of
electrically very short wires having no DC connection.

Roy Lewallen, W7EL

Roy Lewallen wrote:

Jim Kelley wrote:


One point: Isn't the input impedance of a dipole normally specified
at a wavelength equal to twice the electrical length of the antenna?
As far as I know, dipoles have infinite DC resistance at zero Hertz. ;-)

As frequency approaches zero, a dipole's input resistance
approaches zero and its reactance approaches minus inifnity. That is, it
looks like a capacitor, and the capacitive reactance gets larger as the
frequency gets lower. Which is just what you'd expect from a couple of
electrically very short wires having no DC connection.

Roy Lewallen, W7EL

I'll give you a Mulligan on that one if you like, Roy. ;-)

73, ac6xg

Jim Kelley wrote:
One point: Isn't the input impedance of a dipole normally specified at
a wavelength equal to twice the electrical length of the antenna? As
far as I know, dipoles have infinite DC resistance at zero Hertz. ;-)

That would be true for an electrical dipole but we are obviously
talking about physical poles here, i.e. two infinite conductive
fishing poles. :-)
--
73, Cecil http://www.qsl.net/w5dxp

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| "Roy Lewallen"
| wrote in message ...
| [...]
| The Z of an
| infinite length antenna is indicated by locating the centers of the
| circles and noting that the center converges.
| [...]
| Roy Lewallen, W7EL


If we discuss here
the impedance referenced to the input (base) current
- and not to the maximum one - then
IMHO:

The quoted text above does not prove convergence.

The convergence must be independent
of the way the length goes to infinity.

The centers of whatever circles
may converge to a finite complex number
but their radii have to simultaneously converge to zero,
to have convergence.

But the limit for Z exists
if and only if
both the limits for R and X exist.
Therefore if the limit for R is dependent
on the way the length goes to infinity
then its limit does not exist.

A guess for either a non-existent limit for R
or an infinite one comes out from:
http://antennas.ee.duth.gr/ftp/visua...s/fu010100.zip
[850 KB]
If either of the above is true for R
then the corresponding is true for Z:

The limit for Z does not exist
or is (in general) the complex infinity.

But always and only for the
the impedance referenced to the input (base) current.

Sincerely,

pezSV7BAXdag

pezSV7BAXdag wrote:
The limit for Z does not exist
or is (in general) the complex infinity.

As the length of a dipole is increased, for the same
power input, more energy is radiated during the first
transcient cycle and less is available for reflection
from the ends of the dipole. Reflected energy is what
is causing the feedpoint impedance to change. As the
length of the dipole is incrementally increased, the
magnitude of the reflected energy is incrementally
decreased. I believe Balanis alludes to this characteristic
of standing-wave antennas.

The feedpoint impedance is Zfp = (Vfor+Vref)/(Ifor+Iref)
using phasor addition.

The limit of that equation as Vref and Iref go to zero
is Vfor/Ifor. That's what happens for an infinitely
long dipole. That's also what happens during the transient
phase of a finite dipole. Thus, Vfor/Ifor can be thought
of as the characteristic impedance of the dipole. Seems
to me, Vfor/Ifor could actually be measured during the
transient phase of a long finite dipole. Will a TDR
report the ratio of V/I for an RF pulse?
--
73, Cecil http://www.qsl.net/w5dxp

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