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

Cec, what is your best estimate of the input impedance of an
infinitely long dipole. Just a number please.

Remember Lord Kelvin!
----
Reg.

Reg Edwards wrote:
===================================

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).

This assumption is correct only when the transmission line conductors
are closely spaced. That isn't at all true for the halves of a dipole.

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)

I can't see how it can possibly be correct. Unless I'm mistaken, you've
completely ignored the effect of radiation in calculating the radiation
resistance. It sure makes the calculation a lot simpler, though!

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.

It depends on the author. Kraus uses feedpoint resistance and radiation
resistance interchangeably when loss is assumed to be zero. It's
traditional in AM broadcasting to give radiation resistance referred to
a current maximum. The conclusion is that radiation resistance can be
referred to any point along an antenna you wish, which means that it's
essential to state what point you're using as a reference.

Roy Lewallen, W7EL

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

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.
==============================

Yes, I know. Just insert "approximately" before "uniformly"

On a long terminated non-resonant line I guess the current falls off
crudely exponentially at a rate of about 1 dB per wavelength.

The situation is similar to that very long, low, terminated antenna
wire whose name I can't remember. And whose input resistance at LF is
about 550 ohms. Putting two of them back-to-back gives an input
resistance of twice that = 1100 ohms. Which indicates the answer to
our infinitely long dipole problem.
----
Reg.

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

Roy, if you don't like my simple approximate formula, can YOU produce
a better one without plagiarising?
----
Reg.

Reg Edwards wrote:
Roy, if you don't like my simple approximate formula, can YOU produce
a better one without plagiarising?
----
Reg.

Sure. 42. It might not be better, but it's just as good. Formulas can be
made very simple if you simply ignore any inconvenient facts. Like
radiation from an antenna.

Roy Lewallen, W7EL

"Roy Lewallen" wrote
Reg Edwards wrote:
Roy, if you don't like my simple approximate formula, can YOU
produce
a better one without plagiarising?
----
Reg.
======================================
Sure. 42. It might not be better, but it's just as good. Formulas
can be
made very simple if you simply ignore any inconvenient facts. Like
radiation from an antenna.

Roy Lewallen, W7EL
=====================================
Don't be silly. I didn't ignore radiation resistance. I said it was
small enough in comparison with Zo, as an approximation, to forget
about.

And remember Lord Kelvin.
----
Reg.

Reg Edwards wrote:


And remember Lord Kelvin.
----
Reg.


"To measure is to know."

also

"X-rays will prove to be a hoax."

http://zapatopi.net/kelvin/quotes/

ac6xg