"Harry" wrote
I know that a half-wave dipole in free space has
a feed-point impedance of approximately 73 ohms.

Can anyone tell me **exactly** how this number is calculated.

=======================================
There's no such value as 'exact'.

All you have to do is integrate the power flowing outwards from a
dipole at the centre of an arbitrary sphere with a surface area of x
square metres and equate it to the current flowing in the dipole,
taking into account the distribution of current along the dipole, and
you will obtain the radiation resistance referred to its feedpont.
OK?

But in your case, all you can do is just accept the hearsay value of
73 ohms as being good enough.

Actually it depends on the diameter of the dipole relative to its
length and at HF it is a few percent less. Not that anybody ever
notices such minor discrepancies.
----
Reg, G4FGQ

Hi Tim and Reg,

Thank you for your valuable information. Is there any website or
textbook that actually shows the step-by-step calculation of this magic
number which has been quoted so often in the cable industry?

You know most video cables and connectors have characteristic
impedance, 75 Ohms.

I am not afraid of math. I just like to understand the details of its
derivation.

-- Harry

Harry wrote:
Hi Tim and Reg,

Thank you for your valuable information. Is there any website or
textbook that actually shows the step-by-step calculation of this magic
number which has been quoted so often in the cable industry?

You know most video cables and connectors have characteristic
impedance, 75 Ohms.

I am not afraid of math. I just like to understand the details of its
derivation.

-- Harry


What you're seeking is in the book _Antenna Theory, Analysis and Design_
by Constantine A. Balanis, ISBN 0-471-59268-4.
73,
Tom Donaly, KA6RUH

Transmission line calculations are much easier than antenna calculations.

To a first approximation: Zo = SQRT(L/C); where L = inductance per unit
length, and C = capacitance per unit length.

Harry wrote:
Hi Tim and Reg,

Thank you for your valuable information. Is there any website or
textbook that actually shows the step-by-step calculation of this magic
number which has been quoted so often in the cable industry?

You know most video cables and connectors have characteristic
impedance, 75 Ohms.

I am not afraid of math. I just like to understand the details of its
derivation.

-- Harry

"Ham op" wrote
Transmission line calculations are much easier than antenna
calculations.

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

Antenna conductors ARE transmission lines and the same sort of
calculations apply.
----
Reg.

Reg Edwards wrote:
Antenna conductors ARE transmission lines and the same sort of
calculations apply.

You're right, Reg. Without reflections from the ends of a
dipole, the feedpoint impedance would be hundreds of ohms.
A standing wave antenna is like a lossy transmission line
where the loss is to radiation. And the SWR on a 1/2WL dipole
standing wave antenna is quite high - in the neighborhood of
20:1.
--
73, Cecil http://www.qsl.net/w5dxp


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In message , Cecil Moore
writes
Reg Edwards wrote:
Antenna conductors ARE transmission lines and the same sort of
calculations apply.

You're right, Reg. Without reflections from the ends of a
dipole, the feedpoint impedance would be hundreds of ohms.
A standing wave antenna is like a lossy transmission line
where the loss is to radiation. And the SWR on a 1/2WL dipole
standing wave antenna is quite high - in the neighborhood of
20:1.

Just a quick question.
What is the impedance at the centre of an infinitely long dipole (in
free space)?
Ian.
--

Ian Jackson wrote:
Just a quick question.
What is the impedance at the centre of an infinitely long dipole (in
free space)?

Same as a terminated dipole in an anechoic chamber? 600-800 ohms?
--
73, Cecil http://www.qsl.net/w5dxp


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Ian Jackson wrote:
"What is the impedance at the centre of an infinitely long dipole in
free space?

It is the antenna`s Zo. This depends on the size of the conductor used
to make the dipoole.

Arnold B. Bailey has already worked all this out and presents it in his
1950 edition from Rider`s of "TV and Other Receiving Antennas".

Like the Zo of a transmission line, antenna Zo has nothing to do with
reflections and terminations. When you first apply power, energy must
flow into the antenna at some definite voltage to current ratio. This is
the surge impedance or Zo. If the antenna or line is uniform and
infinitely long, the energy sent away is never heard from again. Zo is
the only impedance anywhere.

Page 345 gives the surge impedance in ohms for a balanced antenna as:

Zo = 276 log 1/P

P is the circumference of the antenna rod, or periphery, expressed as a
fraction of the free-space wavelength (see page 342) This may sound
goofy but Bailey has his reasons.

Bailey`s graph on page 345 gives dipole impedances from 70 ohms to 680
ohms for rod peripheries from 1 wavelength down to 0.00001 wavelength

If you have no reflections or standing waves, the impedance you
calculate should be the Zo.

Best regards, Richard Harrison, KB5WZI

Harry wrote:
Thank you for your valuable information. Is there any website or
textbook that actually shows the step-by-step calculation of this magic
number which has been quoted so often in the cable industry?

"Antenna Theory" by Balanis, second edition, Chapter 4.
--
73, Cecil http://www.qsl.net/w5dxp


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