Wire diameter vs Impedance
 

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From page 22.2 of the 2005 ARRL Handbook

"CONDUCTOR SIZE"

"The impedance of the antenna also depends on the diameter of the
conductor in relation to the wavelength. If the diameter of the
conductor is increased, the capacitance per unit length increases
and
the inductance per unit length decreases. Since the radiation
resistance is affected relatively little, the decreased L/C ratio
causes the Q of the antenna to decrease so that the resonance curve
becomes less sharp with change in frequency. This effect is greater
as
the diameter is increased, and is a property of some importance at
the
very high frequencies where the wavelength is small."

Lots of interesting graphs and charts in the ARRL Antenna Handbook
as
well.
======================================
A nice summary.

But to be more precise, it is the ratio of conductor diameter over
length which matters.

Inductance and capacitance change very slowly with diameter/length.
The changes are hardly noticeable.

L = 0.2 * Length * ( Ln( 4 * Length / Dia ) -1 ) microhenrys.

C = 55.55 * Length / ( Ln( 4 * Length / Dia ) -1 ) picofarads.

Zo = Sqrt( L / C ) = 60 * Ln( 4 * Length / Dia ) -1 ) ohms.

Antenna Q = 2 * Pi * Freq * L / (Distributed Radiation Resistance).

For a half-wave dipole the distributed radiation resistance is 146
ohms, or twice the feedpoint resistance.
----
Reg.

Wire diameter vs Impedance
 

On 30 Apr 2006 20:12:15 -0700, "AC7PN" wrote:

I'm sure the larger conductor has less inductance

Hi Robert,

For a wire, that is not in dispute.

but as Yuri
Blanarovich pointed out earlier the bigger conductor has more
capacitance to free space and that effect must dominate the effect
inductance reduction.

And yet it does not. Components that are significant in size with
relation to wavelength do not exhibit the same qualities. That much
is glaringly obvious.

The problem here is one of a Transform acting upon the expected
outcome. It is generally cautioned here not to treat an antenna as a
transmission line, but this is cautious to the point of ignoring the
solution.

Schelkunoff developed a general formula for the dipole by employing a
biconical structure. This structure operates in the TEM mode and fits
radial expressions for fields naturally described in Maxwell's curl
equations which would be tedious to describe here - so we simple cut
to the chase.

Schelkunoff reveals, mathematically, that this transmission line
analysis presents a finite terminating condition for the current
traveling radially (that is, along the wire out towards the end).
Hence, the biconical form as transmission line never terminates in an
open.

In developing this model towards the thin radiator, the angle of the
cones of the biconical structure fall to a very small value. With
this, the biconical math also simplifies. This simplification does
approach the transmission line condition of an open termination.

The thick radiator falls in between as it is obviously neither thin,
nor conical in shape. As a consequence, neither is it a transmission
line that has an uniform Zc along its length. The formulas usually
used to describe its Zc are an average.

The easy answer comes from this. The two conditions of going from
thick to thin involve two different mathematical basis (providing you
aren't simply going from kind-of-thin to kind-of-thick). This
mathematical basis is transmission line math built on wave mechanics,
not inductors and capacitors. Those are components whose geometries
and size wavelength has condemned to less than useful analogies.

73's
Richard Clark, KB7QHC

Wire diameter vs Impedance
 

I think it's a BIG mistake to be writing about "velocity factor" in
this thread (and perhaps also in some current, related threads). The
reason is that it presupposes behaviour that is just like a TEM
transmission line, and clearly it is not when you get to the fine
details. Until we better understand just what is going on, I propose
that we simply say that resonance occurs for a wire shorter than 1/4
freespace wavelength, when that wire is fed against a ground plane to
which it is perpendicular, and that the thicker the wire, the shorter
it is at resonance when compared with the freespace wavelength. The
effect can be described with an emperical equation, of course. But to
invoke "velocity factor" assumes something about the solution which may
well lead you away from the correct explanation.

I don't really expect many will take this seriously--there seems to be
too much invested in explaining everything in terms of behaviour that
seems familiar. It's a bit like saying a photon is a particle (or a
wave). It is not--it is simply a quantum; and it behaves differently
from particles we know, and behaves differently from waves we know from
our macro-world experience.

The transmission-line analog is a very useful one for practical antenna
engineering, just as considering loading elements as lumped reactances
(perhaps with parasitic lumped reactance and resistance as appropriate)
is useful for practical engineering. But that doesn't mean it fully
explains the behaviour in detail.

Cheers,
Tom

Wire diameter vs Impedance
 

K7ITM wrote:
But to
invoke "velocity factor" assumes something about the solution which may
well lead you away from the correct explanation.

For the feedpoint impedance to be purely resistive, i.e.
resonant, for a standing wave antenna, the reflected wave
must get back into phase with the forward wave. Velocity
factor is a way of explaining how/why that happens. The
diameter of the conductor no doubt appears in the VF
equation.
--
73, Cecil http://www.qsl.net/w5dxp

Wire diameter vs Impedance
 

Thanks for fulfilling my expectation.

Cheers,
Tom

Wire diameter vs Impedance
 

K7ITM wrote:
Thanks for fulfilling my expectation.

EZNEC can be used to verify the relationship of conductor
diameter to velocity factor. Once the conductor diameter
exceeds a certain limit, the standing wave current at the
ends of that conductor undergo a 180 degree phase change,
indicating a longer length than resonance.

Tom, when you can determine the position and velocity of
every electron in the system, please get back to us. :-)
--
73, Cecil http://www.qsl.net/w5dxp

Wire diameter vs Impedance
 

EZNEC can be used to verify the relationship of conductor
diameter to velocity factor. Once the conductor diameter
exceeds a certain limit, the standing wave current at the
ends of that conductor undergo a 180 degree phase change,
indicating a longer length than resonance.

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

A cylinder has a flat circular end. Antenna wires and rods are
cylinders. You should be reminded that the true length of the antenna
is its straight length PLUS the radius of the flat circular end.
----
Reg.

Wire diameter vs Impedance
 

Reg Edwards wrote:

A cylinder has a flat circular end. Antenna wires and rods are
cylinders. You should be reminded that the true length of the antenna
is its straight length PLUS the radius of the flat circular end.
----
Reg.

What do you mean by "true" length?

Roy Lewallen, W7EL

Wire diameter vs Impedance
 

What do you mean by "true" length?


You know very well what I mean. Have you nothing else better to do
with your time?

Wire diameter vs Impedance
 

Reg Edwards wrote:
What do you mean by "true" length?


You know very well what I mean. Have you nothing else better to do
with your time?

No, I don't know what you mean. And your response doesn't give me a
great deal of confidence that you do, either.

The reactance of an infinitely thin half wavelength dipole is 42.5 ohms,
meaning that it isn't resonant. An infinitely thin dipole of length
0.496 wavelength, or about 1% shorter, is resonant. So my first question
is whether the "true length" of an infinitesimally thin resonant dipole
is 0.496 or 0.5 wavelength. (If 1% is too little to quibble about, why
are we concerned about a length difference of a wire diameter?)

If we increase the diameter of the antenna to 1/50 its length, the "true
length" would then be 1.02 times the "true length" of the
infinitesimally thin dipole. Yet we have to reduce the antenna length by
nearly 7% to maintain resonance. So the "true length" doesn't have
anything obvious to do with resonant length, nor does it provide a way
to predict the resonant length based on wire diameter.

If the meaning of "true length" is obvious, most other readers must know
what it means. Would someone please be so kind as to explain to me what
it means and how it's used?

Roy Lewallen, W7EL