Wire diameter vs Impedance - correction
 

John - KD5YI wrote:
Reg Edwards wrote:

You should supply your "secrets" along with your formulae.


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

At my time of life I don't have time to write a book!

You'll just have to read between the lines. ;o)
----
Reg.




Fine. From now on, I will assume you have no time to explain your
"secrets" when you post so I will ignore your formulae. This approach is
much better than being misled if I do not read between your lines properly.

Is it important that antennas that won't work have to conform to the
formulae of antennas that do? 8^)

- 73 de Mike KB3EIA -

Wire diameter vs Impedance
 

I agree with Roy on this, that an accurate understanding will take some
fairly serious analysis. For example, the top hat in my example had
_less_ shortening effect than simply using a wire with radius only 1/4
as large as the length of the top hat radials. Also, calculations of
the capacitance of a spherical capacitor, compared with capacitance per
unit length of the antenna wire, don't give me any confidence that the
end capacitance fully explains the shortening effect.

Cheers,
Tom

Wire diameter vs Impedance
 

Opps!

ALPHA and BETA got transformed into ? and j?




Dave wrote:

Cecil Moore wrote:

K7ITM wrote:

Those sources also don't tell me anything about
"velocity factor" as far as I can tell.



What RF engineers call "velocity factor" is related to the phase
constant in the complex propagation constant embedded in any
transmission line equation in any decent textbook. Do your
sources tell you anything about the complex propagation constant?


Complex propagation constant is ? = ? +j? :

Whe

? is the attenuation in Nepers/wavelength

? is the phase shift in Radians/wavelength

Did I pass ??????????

Wire diameter vs Impedance
 

Cecil Moore wrote:

Dave wrote:

Complex propagation constant is ? = ? +j? :
? is the attenuation in Nepers/wavelength
? is the phase shift in Radians/wavelength
Did I pass ??????????


If I remember correctly, SQRT(Z*Y) results in a
dimensionless quantity.

Alpha and Beta got transformed into ? and j?. Gamma also got transformed
into ?.

What kind of bait are you throwing out about SQRT[Z*Y] ?

Wire diameter vs Impedance
 

Dave wrote:
Alpha and Beta got transformed into ? and j?. Gamma also got transformed
into ?.

Now it makes more sense. :-) What is scarey is that some
browsers may display Greek characters correctly and some
may not.

What kind of bait are you throwing out about SQRT[Z*Y] ?

Z is the distributed series impedance and Y is the distributed
shunt admittance. The equation for the propagation constant
is gamma = alpha + j*beta = SQRT(Z*Y). Doesn't multiplying
an impedance by an admittance result in a dimensionless
quantity?
--
73, Cecil http://www.qsl.net/w5dxp

Wire diameter vs Impedance
 

SQRT[Z*Y] = SQRT [[Z11 + jZ12]*[Y11 + jY12]] = Z11*Y11 - Z12*Y12
+jZ12*Y11 +jY12*Z11 [I think I got all the terms correct.]

So, the attenuation constant is still a complex number and it is
dimensionless.

In the transmission line equations the attenuation constant is
multiplied by line length yielding an expression in Nepers
[dimensionless] and radians [dimensionless].
Cecil Moore wrote:

Dave wrote:

Alpha and Beta got transformed into ? and j?. Gamma also got
transformed into ?.


Now it makes more sense. :-) What is scarey is that some
browsers may display Greek characters correctly and some
may not.

What kind of bait are you throwing out about SQRT[Z*Y] ?


Z is the distributed series impedance and Y is the distributed
shunt admittance. The equation for the propagation constant
is gamma = alpha + j*beta = SQRT(Z*Y). Doesn't multiplying
an impedance by an admittance result in a dimensionless
quantity?

Wire diameter vs Impedance
 

Dave wrote:
So, the attenuation constant is still a complex number and it is
dimensionless.

The attenuation constant is a real number, not a complex number.
--
73, Cecil http://www.qsl.net/w5dxp

Wire diameter vs Impedance
 

My error ... I meant propagation constant.

Cecil Moore wrote:

Dave wrote:

So, the attenuation constant is still a complex number and it is
dimensionless.


The attenuation constant is a real number, not a complex number.

Wire diameter vs Impedance
 

Presumably you meant "propagation constant" (which is anything but
constant for real lines). In any event it is most certainly is not
dimensionless. If it were and you multiplied it by a length, your
result would have units of length. Oh, and I think you left the sqrt
off the right side of the equation. I guess Z11 is resistance per unit
length, Z22 is the radian frequency times the inductance per unit
length, etc?? Sigh.

Cheers,
Tom

Wire diameter vs Impedance
 

Here's an interesting quote from S.A. Schelkunoff, "Theory of Antennas
of Arbitrary Size and Shape", Proc. of the I.R.E., September, 1941
(footnote 17): "From the point of view developed in this paper there is
no difference between 'end effect' and radiation."

This is the paper in which Schelkunoff develops his often-quoted
approximate equations for antenna feedpoint impedance (the ones
including sine and cosine integral -- Si and Ci -- terms). He says,
basically, that an antenna acts like a transmission line -- a conical
antenna like a constant-Z line and a cylindrical (e.g., wire or tubing)
antenna like a variable-Z line -- *except at the ends*. At the ends,
modes other than TEM are excited, resulting in radiation, modification
of antenna impedance, and modification of current distribution. The
radiation, he says, can be modeled as either a terminating impedance or
as a distributed impedance (R and L) along the line. You can find an
abbreviated version of this explanation in Kraus' _Antennas_.

A transmission line is similar to an antenna in only some respects, and
assuming they act exactly the same leads to erroneous conclusions. Among
the many mistakes made in recent postings is the assumption that a
complete reflection takes place from the end of an antenna wire. As
Schelkunoff, Kraus, and others explain, this isn't correct.

Roy Lewallen, W7EL

Wire diameter vs Impedance
 

Roy Lewallen wrote:
A transmission line is similar to an antenna in only some respects, and
assuming they act exactly the same leads to erroneous conclusions.

A capacitor and resistor is similar to a stinger in only some
respects, and assuming they act exactly the same leads to
erroneous conclusions.
--
73, Cecil http://www.qsl.net/w5dxp

Wire diameter vs Impedance
 

On Wed, 03 May 2006 15:55:23 -0700, Roy Lewallen
wrote:

This is the paper in which Schelkunoff develops his often-quoted
approximate equations for antenna feedpoint impedance (the ones
including sine and cosine integral -- Si and Ci -- terms). He says,
basically, that an antenna acts like a transmission line -- a conical
antenna like a constant-Z line and a cylindrical (e.g., wire or tubing)
antenna like a variable-Z line -- *except at the ends*. At the ends,
modes other than TEM are excited, resulting in radiation, modification
of antenna impedance, and modification of current distribution.

Otherwise expressed as a finite Z instead of a zero current (infinite
Z) point at the end. Of course, finite and infinite are relative even
for Schelkunoff.

The
radiation, he says, can be modeled as either a terminating impedance or
as a distributed impedance (R and L) along the line. You can find an
abbreviated version of this explanation in Kraus' _Antennas_.

Hi All,

Pretty much what I've offered in the past and recently in this thread
(same source, Schelkunoff through Robert Collin). Anyway, I see no
formulas offered and as I don't have Kraus to see if they are missing
there too:
Zc = Z0 · ln (cot (theta/2)) / pi
for
Z0 = 377 Ohms
theta 5°
or
Zc = Z0 · (ln(2) - ln(theta))) / pi
for
theta 5°
where theta is the half angle of the cone section.

This, of course, says nothing of the variable Zc for a thick radiator
(which is not conical, but cylindrical). The "average" Zc:
Zc = 120 · (ln (l/a) - 1)
for
l: length
a: diameter

The Zc as a function of position:
Zc(z) = 120 ln (2 · z / a)

73's
Richard Clark, KB7QHC

Wire diameter vs Impedance
 

"Roy Lewallen" wrote:
The
radiation, he says, can be modeled as either a terminating impedance or
as a distributed impedance (R and L) along the line. You can find an
abbreviated version of this explanation in Kraus' _Antennas_.

A transmission line is similar to an antenna in only some respects, and
assuming they act exactly the same leads to erroneous conclusions. Among
the many mistakes made in recent postings is the assumption that a
complete reflection takes place from the end of an antenna wire. As
Schelkunoff, Kraus, and others explain, this isn't correct.

What they seem to be saying is that a quarter-wave monopole
could be modeled like this:

======1/4WL 600 ohm line======12K load

The 12K load dissipates approximately the same amount
of power radiated by a 1/4WL monopole so the conditions
at the feedpoint will be similar to the 1/4WL monopole.

Just because it can be modeled in that fashion doesn't mean
that the radiation is from the same place as the 12k load.

This does seem to be a good way to understand the forward
and reflected waves occurring in a 1/4WL monopole. Guess
what the feedpoint impedance is?

Another way to model the antenna would be with resistance
wire instead of transmission line wire. Then we wouldn't need
the 12K load resistor. We could just specify 1 dB loss between
the forward power and reflected power.
--
73, Cecil, W5DXP