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

Dear nitpickers, Tom and Tom,

Have you never heard of the word "approximation".

The Whole World is founded on Good Approximations.

The art lies in making them.
----
Reg.

On Tue, 25 Apr 2006 07:27:27 +0100, "Reg Edwards"
wrote:

The Whole World is founded on Good Approximations.

The art lies in making them.

Hi Reggie,

The lies are in the art of making them. Whole debates are founded on
±59% error being "close enough."

73's
Richard Clark, KB7QHC

Regarding the use of English, I will interpret your opening line as
excluding Tom and me from the ranks of nitpickers. Thank you for the
comma.

Indeed, we build our world on approximations. Even Maxwell and friends
gave us only approximations, though ones that are far better than we
need for the things we do with our HF or even microwave antennas.

But if I'm given two DIFFERENT ways to approximate the same thing, and
they give me VERY different answers, then I'd like to understand the
situation better. In other words, I'm exactly interested in that art
you mention, and in being able to judge when others claim to know that
art but in fact do not. They can try to lead me astray, but I don't
have to let them.

In other words, if you or anyone else gives me answers, directly or
through graphs or computer programs or whatever, I'd like to be able to
judge the validity of those answers for what I'm trying to accomplish.
I trust that's not a goal you'd disagree with, but perhaps you will.

I also am much more wary of people who just give answers with no
indication of the degree to which they are approximations, than I am of
people who explain that their answers are approximations and to what
degree and why they are.

In this case, I happen to think that it's worthwhile understanding WHY
the DC capacitance isn't very useful in the dynamic situation of an
antenna. Thankfully, for those who can't figure that out for
themselves, there are some decent explanations kicking around.

Cheers,
Tom

Tom Donaly wrote:


What is the transmission mode in a single conductor transmission line?

That is a good question. I'd never thought about it. Anyone here have
experience with G Line?

tom
K0TAR

Tom Ring wrote:

Tom Donaly wrote:


What is the transmission mode in a single conductor transmission line?


That is a good question. I'd never thought about it. Anyone here have
experience with G Line?

tom
K0TAR

The questions needs further refinement. Over a plane or in free space?