Cecil, what formula do you use for the velocity factor of a coil of
diameter D, length L, and N number of turns, in metric units if its
convenient.

Do you have a formula for the self-resonant frequency?
----
Reg.

Reg Edwards wrote:
Cecil, what formula do you use for the velocity factor of a coil of
diameter D, length L, and N number of turns, in metric units if its
convenient.

Reg, it's equation (32) from Dr. Corum's paper at:

http://www.ttr.com/TELSIKS2001-MASTER-1.pdf

There is a test in the preceeding paragraph to see if
that equation is appropriate for a particular coil.
Equation (32) is derived from empirical data collected
on coils that pass that test.

Just be sure the diameter, pitch, and wavelength are
all in meters and it will be metric.

I'll send you a .gif file of that page of Dr. Corum's
paper. The graph in Fig. 1 is for equation (32).

While you are at it, take a look at equation (47) for
the characteristic impedance of the coil and let us
know what you think.

Do you have a formula for the self-resonant frequency?

Here's what I have been doing lately:

1. Using as close as EZNEC can come to my 75m bugcatcher
coil stock, create enough turns for the modeled coil to
be self-resonant on 4 MHz. My 75m bugcatcher coil stock
is ~0.5 ft diameter and 48 turns per foot.

2. Delete enough turns to make it look like my real-
world bugcatcher coil. Use that coil for EZNEC modeling
at 4 MHz.

3. Assume the velocity factor didn't change appreciably
when deleting those turns.

4. Calculate the number of linear feet occupied by the
coil by dividing the length of the coil by the velocity
factor.

5. Calculate the percentage of a wavelength occupied by
the coil by dividing the results of (4.) above, by 246
feet, a wavelength at 4 MHz.

Of all the measurements and modeling so far, this is what
I have come up with as the most accurate estimate of the
percentage of a wavelength occupied by the coil.

And no, it is not 90 degrees minus the rest of the antenna.
The requirement for a purely resistive feedpoint impedance
is that the superposition of the forward and reflected voltages
have the same phase angle as the superposition of the forward
and reflected currents - nothing more.
--
73, Cecil http://www.qsl.net/w5dxp

Dear Cec,

After 3/4 of a bottle of Australian Cabernet Sauvignon, I plucked up
sufficient courage to present my printer with Corum's paper.

Lo and behold, it worked perfectly. Even the small amount of color was
accurately reproduced.

After speed-reading it I came to the conclusion it is unnecessarily
over-complicated. What on Earth does "Voltage Magnification by
Coherent Spatial Modes" mean?

For years, my approach to loading coils at HF has been to calculate
the inductance and capacitance per unit length of coil from DC
principles. And then calculate the velocity factor and Zo from
transmission line principles. Which gives results in the right ball
park according to what few experiments I have made with actual anennas
and helices on the 160 and 80 meter bands.

Then there was G3YXM who deliberately put more turns on the coil on
the grounds it was easier to remove them than add to them in case
pruning was required. Pruning was required and he ended up by removing
all the excess turns.

Have you compared VF's (a critical parameter) in my programs with
Corum's values for close-wound coils of usual proportions? I must try
to find time to do it myself.

Thanks very much for posting me Corum's paper. I am pleased to see
the University of Nis has not been seriously affected by the bombing
and guided missiles during the US Yugoslavian attacks. Have the
bridges across the Danube been replaced yet?
----
Reg.

Reg Edwards wrote:
After speed-reading it I came to the conclusion it is unnecessarily
over-complicated.

Maybe making it over-complicated also makes it over-accurate? :-)

What on Earth does "Voltage Magnification by
Coherent Spatial Modes" mean?

It means that super high SWRs result in super high voltages.
It's the usual VSWR = Vmax/Vmin for coherent signals.

Have you compared VF's (a critical parameter) in my programs with
Corum's values for close-wound coils of usual proportions?

I haven't yet figured out the English unit to Metric unit
conversion procedure for turns on a coil. :-)
--
73, Cecil http://www.qsl.net/w5dxp

Reg Edwards wrote:
. . .
For years, my approach to loading coils at HF has been to calculate
the inductance and capacitance per unit length of coil from DC
principles. And then calculate the velocity factor and Zo from
transmission line principles. Which gives results in the right ball
park according to what few experiments I have made with actual anennas
and helices on the 160 and 80 meter bands.

How do you calculate the coil C to use in the transmission line formulas?

Roy Lewallen, W7EL

How do you calculate the coil C to use in the transmission line
formulas?

Roy Lewallen, W7EL
===================================

I'm surprised a person of your knowledge asked.

Go to Terman's or other bibles, I'm sure you'll find it somewhere, and
find the formula to calculate the DC capacitance to its surroundings
of a cylinder of length L and diameter D.

Then do the obvious and distribute the capacitance uniformly along its
length.

The formula will very likely be found in the same chapter as the
inductance of a wire of given length and diameter.

I have the capacitance formula I derived myself somewhere in my
ancient tattered notes but I can't remember which of the A to S
volumes it is in.

I'm 3/4 ot the way down a bottle of French Red plonk. But Terman et
al should be be quite good enough for your purposes.

And its just the principle of the thing which matters. It's simple
enough. I don't suppose you will make use of a formula if and when
you find one.
----
Reg.

I did a search quite some time ago and failed completely in finding the
formula you describe, in Terman or any other "bible". The formula for
the capacitance of an isolated sphere is common, but not a cylinder. The
formula for a coaxial capacitor is common also, but the capacitance
calculated from it approaches zero as the outer cylinder diameter gets
infinite.

Maybe you could take a look after the wine wears off, and see if you can
locate the formula. By your earlier posting, it sounds like you've used
it frequently, so it shouldn't be too hard to find. I'd appreciate it
greatly if you would. And yes, I would make use of the formula -- I'm
very curious about how well a coil can be simulated as a transmission
line. The formula you use would be valid only in isolation, so
capacitance to other wires, current carrying conductors, and so forth
would have an appreciable effect. I showed not long ago that capacitance
from a base loading coil to ground has a very noticeable effect. Do you
have a way of taking that into account also?

Roy Lewallen, W7EL

Reg Edwards wrote:
How do you calculate the coil C to use in the transmission line
formulas?
Roy Lewallen, W7EL
===================================

I'm surprised a person of your knowledge asked.

Go to Terman's or other bibles, I'm sure you'll find it somewhere, and
find the formula to calculate the DC capacitance to its surroundings
of a cylinder of length L and diameter D.

Then do the obvious and distribute the capacitance uniformly along its
length.

The formula will very likely be found in the same chapter as the
inductance of a wire of given length and diameter.

I have the capacitance formula I derived myself somewhere in my
ancient tattered notes but I can't remember which of the A to S
volumes it is in.

I'm 3/4 ot the way down a bottle of French Red plonk. But Terman et
al should be be quite good enough for your purposes.

And its just the principle of the thing which matters. It's simple
enough. I don't suppose you will make use of a formula if and when
you find one.
----
Reg.

Just find the capacitance for a wire of length L and diameter D.

A wire of length L and diameter D is a cylinder.

I vaguely remember seeing, in Terman, in graphical or tabular form,
the capacitance to its surroundings of a vertical wire of length L,
the bottom end of which is at a height H above a ground plane.

If you can't find an equation for capacitance then use the equation
for inductance. The velocity factor for an antenna wire is 1.00 or
0.99. From inductance per unit length you can calculate what the
capacitance per unit length must be to give a velocity factor of 1.00
That's the perfectly natural way I sort things out. My education must
be altogether different to yours.

The equation for capacitance in terms of length and diameter must be
of the same form as inductance with a just a reciprocal involved.

I'm even more certain you will find an equation for inductance of an
isolated wire of length L and diameter D somewhere in the bibles.
From which the equation for capacitance can be deduced.
----
Reg.

Hmmm...this is getting back really close to what I was trying to get at
when I posted the capacitance-of-a-wire-conundrum basenote a few weeks
ago that went nowhere. But since you've opened it up again, I'll toss
out some conundrum-ish things about it.

Consider a wire that's perpendicular to a ground plane; obviously this
is interesting for a doublet configuration also, because of symmetry.

I believe I can, without too much trouble, find the inductance of a
cylinder of current--current in the shallow skin depth of the wire,
which is different than the inductance at low frequencies--per unit
length. I believe it will be relatively unaffected by distance along
the wire.

I believe I can, with a little more difficulty, find the (DC, as you
say) capacitance to the ground plane of a section of wire that's short,
in isolation from the rest of the wire (as if the rest of the wire
weren't there). But I believe that capacitance will be a much stronger
function of distance from that short section to the ground plane than
was the case for inductance.

That leaves me with a velocity, sqrt((capacitance/unit
length)*(inductance/unit length)), that is not particularly constant
along the length of wire. I know that things really are like you say:
the velocity along that wire will be nearly the speed of light.

So that tells me that something is wrong, and three things come
immediately to mind: either the inductance is more variable with
distance from the ground plane than I think it is, or the capacitance
is less variable, or the DC analysis does not hold when we are dealing
with things propagating at about the speed of light.

In fact, there is a clue in the fact that for the whole wire, with one
end spaced a very small distance from the ground plane and the other
end far away, in a DC case the charge would be clustered near the
ground plane, with very little charge at the tip...but in a resonant
antenna, there is often a LOT of charge out near the end that's far
away from the ground plane.

OK, that ought to be enough to get lots of conflicting responses going!

Cheers,
Tom

K7ITM wrote:
Hmmm...this is getting back really close to what I was trying to get at
when I posted the capacitance-of-a-wire-conundrum basenote a few weeks
ago that went nowhere. But since you've opened it up again, I'll toss
out some conundrum-ish things about it.

Consider a wire that's perpendicular to a ground plane; obviously this
is interesting for a doublet configuration also, because of symmetry.

I believe I can, without too much trouble, find the inductance of a
cylinder of current--current in the shallow skin depth of the wire,
which is different than the inductance at low frequencies--per unit
length. I believe it will be relatively unaffected by distance along
the wire.

I believe I can, with a little more difficulty, find the (DC, as you
say) capacitance to the ground plane of a section of wire that's short,
in isolation from the rest of the wire (as if the rest of the wire
weren't there). But I believe that capacitance will be a much stronger
function of distance from that short section to the ground plane than
was the case for inductance.

That leaves me with a velocity, sqrt((capacitance/unit
length)*(inductance/unit length)), that is not particularly constant
along the length of wire. I know that things really are like you say:
the velocity along that wire will be nearly the speed of light.

So that tells me that something is wrong, and three things come
immediately to mind: either the inductance is more variable with
distance from the ground plane than I think it is, or the capacitance
is less variable, or the DC analysis does not hold when we are dealing
with things propagating at about the speed of light.

In fact, there is a clue in the fact that for the whole wire, with one
end spaced a very small distance from the ground plane and the other
end far away, in a DC case the charge would be clustered near the
ground plane, with very little charge at the tip...but in a resonant
antenna, there is often a LOT of charge out near the end that's far
away from the ground plane.

OK, that ought to be enough to get lots of conflicting responses going!

Cheers,
Tom


What is the transmission mode in a single conductor transmission line?
Does a coil support TEM waves, TM, or TE? Is there some type of
cutoff frequency?
How do you compute the phase velocity? How do you know the phase
velocity of an electromagnetic wave on a coil of wire isn't greater
than the speed of light in the helical direction?
People like Reg and Cecil like to simplify things to the point of
absurdity. Things that complicate the picture and disagree with their
simplifications are promptly ignored. I hope no one reading these posts
is under the false impression he's learning transmission line theory.
73,
Tom Donaly, KA6RUH