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  #51   Report Post  
Old September 19th 05, 04:20 AM
Cecil Moore
 
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Richard Harrison wrote:

Ian Jackson wrote:
"Maybe 377 ohms?"

Arnold B. Bailey in "TV and Other Receiving Antennas" shows his
calculations of radiation resistance at the current maximum point for a
center-fed thin dipole at its various resonances:

1st--------------------------------72 ohms
2nd------------------------------200 ohms
3rd-------------------------------102 ohms
4th-------------------------------260 ohms
5th-------------------------------117 ohms
6th-------------------------------295 ohms
7th-------------------------------127 ohms
8th-------------------------------321 ohms
9th-------------------------------135 ohms
10th-----------------------------340 ohms


Note that those are not the feedpoint impedances. They are
based on the current maximum points which often occur
somewhere besides the feedpoint.
--
73, Cecil http://www.qsl.net/w5dxp


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Old September 19th 05, 01:42 PM
pezSV7BAXdag
 
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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


  #53   Report Post  
Old September 19th 05, 03:27 PM
Cecil Moore
 
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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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Old September 19th 05, 03:49 PM
Cecil Moore
 
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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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Old September 19th 05, 05:29 PM
Richard Harrison
 
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Cecil, W5DXP wrote:
"Note that those are not the feedpoint impedances.".

Well, the imprdance I qupted was the radiation resistance, which is the
voltage to current ratio of an antenna at the maximum current point in
the antenna. I was just too lazy to post the complete Table given by
Bailey.

Only when the order of resonance in a center-fed dipole is odd, 1st,
3rd, 5th, etc, is the feedpoint resistance the same as the radiation
resistance. In odd-ordered resonances, the antenna feedpoint resistance
is te same as the radiation resistance. In odd-orfered resonances, the
antenna feedpoint is at s current loop.

In even-ordered resonances, the value of the feedpoint resistance is
equal to the feedpoint impedance squared, divided by the radiation
resistance value. Bailey has worked it all out for us.

Best regards, Richard Harrison, KB5WZI



  #56   Report Post  
Old September 19th 05, 06:34 PM
pezSV7BAXdag
 
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| -----------------------------------------------------------------
| Subject...: 73 Ohms, How do you get it?
| Sent......: Monday, September 19, 2005 5:27 PM
| Newsgroups: rec.radio.amateur.antenna
| From......: "Cecil Moore"
| -----------------------------------------------------------------
| [...]
| 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

| -----------------------------------------------------------------

Do you mean that
since the length is infinite
there is no reflected wave?
But then here it is,
once again,
one of the most controversial issues...

Well,
I think we are in the front of a case in which
the limit depends on the way we approach it.
Every logical way to approach a limit is permissible.
And these ways are infinite in number of course.
But the convergence is too demanding:
"She" wants all these limits to be equal.
If just two of them are unequal
the convergence simply does not exist.
Mathematically this is not a rare case,
they say.

Sincerely,

pezSV7BAXdag



  #57   Report Post  
Old September 19th 05, 07:19 PM
Reg Edwards
 
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"Ian Jackson" wrote in
message ...
In message , Reg
Edwards writes
What is the impedance at the centre of an infinitely long dipole

(in
free space)?


===============================
Its not very different from -

Zin = 120 * Ln( Wavelength / d ) ohms.

where d = conductor diameter, both measured in metres.

Thus, at wavelength = 80 metres with 14 gauge copper wire, input
impedance = 1300 ohms approx.

If you don't believe me, just measure it.
----
Reg.



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.

I've just done a search on 'Wu+dipole+impedance', and one of the

results
is
http://www.fars.k6ya.org/docs/antenn...nce-models.pdf
I'll have a read of it today.

Cheers,
Ian.
--



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Old September 19th 05, 07:19 PM
Reg Edwards
 
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"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.

I've just done a search on 'Wu+dipole+impedance', and one of the

results
is
http://www.fars.k6ya.org/docs/antenn...nce-models.pdf
I'll have a read of it today.

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

The characteristic impedance of an infinitely long wire is Zo.

If we cut the line and measure between the two ends we obtain an input
impedance of twice Zo. Which is the answer to our problem.

Zo is a function of wavelength, conductor diameter and conductor
resistance R where R includes the uniformly distributed radiation
resistance. On a high Zo line the radiation resistance is small
compared with Zo and the only effect of the radiation resistance is to
give Zo a small negative angle. Which when estimating Zo can be
ignored. (It is conductor resistance which at HF gives Zo of ALL
lines a very small negative angle).

In the problem posed, the current is also uniformly distributed along
the low-loss line and radiation resistance is not the value we are
familiar with and what we might do with it.

And so we get approximately -

Rin = 120 * ( Ln( Wavelength / 2 / d ) - 1 )

At a wavelength of 2 metres and a conductor diameter of 10mm the input
resistance = 433 ohms.

I cannot guarantee the above formula to be correct. But is it low
enough for you? ;o)

Mr Wu calculates radiation resistance which is not the same as input
impedance unless correctly referenced. It is usual in technical papers
to calculate Radres at one end of the antenna. Or it may be the
distributed value. I havn't the time to find and study the full text.
From past experience, with me, it usually ends up as a wild goose
chase.
----
Reg.


  #59   Report Post  
Old September 19th 05, 07:45 PM
Cecil Moore
 
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pezSV7BAXdag wrote:
Do you mean that since the length is infinite
there is no reflected wave? But then here it is, once again,
one of the most controversial issues...


Yep, it's my digital logic in action. :-) If there's no end,
then there cannot be reflections from the ends. And please
note that I am not saying that the characteristic impedance
of a dipole is constant all up and down the line. I'm only
concerned about the apparent characteristic impedance at
the feedpoint, i.e. Vfor/Ifor.

Consider an open circuit transmission line. At 1/4WL, it
exhibits a very low impedance. At 1/2WL it exhibits a very
high impedance. As the transmission line length is increased
to infinity, because of losses, the "stub" impedance will spiral
into the Z0 characteristic impedance point. A similar concept
should apply to a dipole.
--
73, Cecil http://www.qsl.net/w5dxp

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Old September 19th 05, 07:55 PM
Cecil Moore
 
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Reg Edwards wrote:
In the problem posed, the current is also uniformly distributed along
the low-loss line and radiation resistance is not the value we are
familiar with and what we might do with it.


Reg, in the real world, an antenna has radiation losses so
the current decays along its length. Is there any formula
that includes an attenuation factor for a traveling wave
antenna? It would be akin to the attenuation factor for
a transmission line but presumably higher.

I have estimated that, for a 1/2WL dipole, the reflected
voltage and current have dropped by approximately 10% below
the forward voltage and current during the round trip to the
ends of the antenna and back.
--
73, Cecil http://www.qsl.net/w5dxp

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