Velocity Factor and resonant frequency
 

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.

Velocity Factor and resonant frequency
 

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

Velocity Factor and resonant frequency
 

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.

Velocity Factor and resonant frequency
 

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

Velocity Factor and resonant frequency
 

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

Velocity Factor and resonant frequency
 

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.

Velocity Factor and resonant frequency
 

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.

Velocity Factor and resonant frequency
 

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.

Velocity Factor and resonant frequency
 

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

Velocity Factor and resonant frequency
 

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

Approximations
 

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.

Velocity Factor and resonant frequency
 

On 24 Apr 2006 18:09:17 -0700, "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.

Hi Tom,

Was that because the answer was so simple, or is there some other
anticipated (yet unrevealed) factors to be tossed into the mix?

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

It should, the conflict is already built in.

As I am often tagged with being obscure, it irks me to see someone
struggling to capture the crown. Tom, just what is it that is the
conundrum?

Hint, conundrums are usually emphasized with a question mark - or is
this the classical riddle that expects an answer in a pun?

73's
Richard Clark, KB7QHC

Approximations
 

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

Approximations
 

Richard, your use of the English language is HIGHLY approximate and
therefore prone to errors greater than 59 percent.
----
Reg.

Velocity Factor and resonant frequency
 

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

Velocity Factor and resonant frequency
 

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?

Velocity Factor and resonant frequency
 

Dave wrote:
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?


No ground planes allowed.
73,
Tom Donaly, KA6RUH

Velocity Factor and resonant frequency
 

Dave wrote:

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?


Properly made and installed, G Line shouldn't know the difference.

tom
K0TAR

Velocity Factor and resonant frequency
 

Tom Ring wrote:

Dave wrote:

SNIPPED


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


Properly made and installed, G Line shouldn't know the difference.

tom
K0TAR

Tom, the original question is a single conductor transmission line. A
single conductor transmission line is used to feed a 'classic Windom'.

In that configuration, is it a G line?

For the uninitiated, including this questioner, what is a G line?

Velocity Factor and resonant frequency
 

Dave wrote:

Tom Ring wrote:

Tom, the original question is a single conductor transmission line. A
single conductor transmission line is used to feed a 'classic Windom'.

In that configuration, is it a G line?

For the uninitiated, including this questioner, what is a G line?


I don't believe a single bare wire will operate as a transmission line
in free space. It will radiate. G line, on the other hand, will not.
At least it won't radiate any more than a piece of coax. And it can be
used in reasonably normal situations, but no sharp bends. It is not
practical for HF, however. 70 cm would probably be as low as you would
want to go.

The quick description is that G line is a wire coated with a dielectric
to a specific thickness that is coupled to by a device resembling a
feedhorn on each end, where the horn is a flaring of the shield. As I
remember it, the dielectric discontinuity constrains the E field, and
hence the EM field. The losses are much lower than coax, on the order
of 5 dB per mile at 500 MHz.

For details see -

http://coldwar-c4i.net/G-Line/EE0860/p638.html

tom
K0TAR

Velocity Factor and resonant frequency
 

Tom Ring wrote:
I don't believe a single bare wire will operate as a transmission line
in free space.

Let's say we have a 1/2WL dipole in free space driven by a
self-contained source at the center. If we float a florescent
light bulb around the ends of the dipole, are you saying the
electric fields won't fire the bulb like it does on earth?
--
73, Cecil http://www.qsl.net/w5dxp

Velocity Factor and resonant frequency
 

Some more info he http://www.answers.com/topic/goubou-line

If you search for Goubou line AND Goubau line, you can find lots more.
Older editions of "Reference Data for Radio Engineers" had design info
on them.

The losses, as with any good line, are mainly due to I^2*R loss in the
wire. The current is lower than it would be for the same wire in coax,
for a given power, and thus the loss is lower. "YMMV" when it rains,
or when the line gets coated with soot and grime.

I believe I've seen it described as "quasi-TEM". Clearly if you look
immediately next to the wire, you'll find magnetic field symmetrically
encircling the wire, and electric field is always perpendicular to good
conductors so the electric field is radial. That's the same as in
coax, but if you look at the article Tom posted a reference to, you'll
see that the field lines do not remain perpendicular to the wire
further out.

Cheers,
Tom

Velocity Factor and resonant frequency
 

K7ITM wrote:
Some more info he http://www.answers.com/topic/goubou-line

If you search for Goubou line AND Goubau line, you can find lots more.
Older editions of "Reference Data for Radio Engineers" had design info
on them.

The losses, as with any good line, are mainly due to I^2*R loss in the
wire. The current is lower than it would be for the same wire in coax,
for a given power, and thus the loss is lower. "YMMV" when it rains,
or when the line gets coated with soot and grime.

I believe I've seen it described as "quasi-TEM". Clearly if you look
immediately next to the wire, you'll find magnetic field symmetrically
encircling the wire, and electric field is always perpendicular to good
conductors so the electric field is radial. That's the same as in
coax, but if you look at the article Tom posted a reference to, you'll
see that the field lines do not remain perpendicular to the wire
further out.


According to Goubau's original paper [1] the mode is a surface wave
which is attached to the wire, but decays over a distance of a few
wavelengths sideways from the wire. Unlike a normal TEM wave, the energy
in this surface wave remains confined to its cylindrical near field, and
does not radiate into the far field. Its only direction of long-distance
propagation is along the wire, which is what makes it usable for
transmission-line purposes.

The surface wave also has the rather odd property that on a bare wire of
infinite conductivity, it will not propagate at all! However, it will
propagate successfully if the wire is coated with a magnetic or a
dielectric material, and for practical applications Goubau favoured
various forms of insulated wire.

The practical problem is that the surface wave requires a feedhorn of
several wavelengths in diameter, to selectively excite this particular
mode without also exciting the radiating TEM mode. Out along the wire,
any disturbance to the propagating fields tends to cause mode conversion
back into TEM, which makes the G-line revert to radiating like any
normal wire antenna. When the wire is viewed as a transmission line, any
far-field radiation represents a loss.

To sum up, the G-line surface wave is very different from the normal TEM
waves around an isolated wire. Unless you take specific steps to excite
this particular mode, it won't occur at all, so it isn't relevant to the
main topic under discussion.



[1] Georg Goubau, 'Single-conductor Surface-Wave Transmission Lines'.
Proc IRE, June 1951, pp 619-624.



--
73 from Ian GM3SEK 'In Practice' columnist for RadCom (RSGB)
http://www.ifwtech.co.uk/g3sek

Approximations
 

On Tue, 25 Apr 2006 09:06:24 +0100, "Reg Edwards"
wrote:

Richard, your use of the English language is HIGHLY approximate and
therefore prone to errors greater than 59 percent.
----
Reg.

I'm sorry Reggie, Old Son, but being a native speaker does not elevate
your opinion to that of expert. In fact, your being British is the
single most negative mark against you in that respect. Your precision
is merely adequate to conversing with the corner grocer - luckily your
software code does not tolerate such abiquity. We would have far more
intelligent conversations with you if you stuck with Pascal instead.
Even the sewer rats of Rio would notice you had something to say.

73's
Richard Clark, KB7QHC

Velocity Factor and resonant frequency
 

Cecil Moore wrote:

Tom Ring wrote:

I don't believe a single bare wire will operate as a transmission line
in free space.


Let's say we have a 1/2WL dipole in free space driven by a
self-contained source at the center. If we float a florescent
light bulb around the ends of the dipole, are you saying the
electric fields won't fire the bulb like it does on earth?

Stop acting like an idiot Cecil.

tom
K0TAR

Velocity Factor and resonant frequency
 

It's a mistake to think that just because an antenna looks like it has
one wire (although it really always has two) that it bears any
similarity to a G line in operation. Whatever mode a G line effects, it
isn't the same as an antenna -- a G line doesn't radiate significantly
unless bent or improperly constructed.

Roy Lewallen, W7EL

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

Velocity Factor and resonant frequency
 

Ian White GM3SEK wrote:
snip
To sum up, the G-line surface wave is very different from the normal TEM
waves around an isolated wire. Unless you take specific steps to excite
this particular mode, it won't occur at all, so it isn't relevant to the
main topic under discussion.


Ian,

Thanks for the explanation. It was very helpful as well as concise.

And I didn't think it had much to do with the main topic when I diverted
to this one, except for the phrase "single wire transmission line", but
that never stopped anyone else here before! ;)

tom
K0TAR

Approximations
 

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

Velocity Factor and resonant frequency
 

Reg, G4FGQ wrote:
"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."

Equation 14 on page 48 of Terman`s 1943 edition of "Radio Engineers`
Handbook is:

Lo = 0.00508 l (2.303 log 4l/d - 1+mu/4) microhenrys

Lo is the (approximate) low-frequency inductance and the dimensions are
in inches.

Terman also gives the (approximate) low-frequency inductance formula of
a single-layer solenoid on page 55 of the same book.

One can find the resonant frequency of the coil when using a known
capacitance to resonate the coil at a low frequency. Maybe a dip meter
could be used. Capacitive and inductive reactances are equal at
resonance. Self and stray capacitances are included with the known value
of capacitance used to resonate the coil at the low frequency. The
resonant frequency is lower than the known capacitance by itself would
produce.

The resonance formula used with the actual inductance of the coil will
give the capacitance of the resonant circuit

The difference between the calculated capacitance and the known
capacitor value is equal to the stray and self-capacitance total, so it
is good to minimise stray capacitance when seeking the self-capacitance
value of the coil.

An ARRL Single-Layer Coil Winding Calculator is a slide rule which makes
things easy.

Best regards, Richard Harrison, KB5WZI

Velocity Factor and resonant frequency
 

That's all very nice. Let's see if it's useful for anything.

A while back, Cecil posted a model of a base loaded vertical antenna. It
has an inductor which is vertically oriented. The bottom of the inductor
is 1 foot from the ground and the inductor is 1 foot long and six inches
in diameter. Inductance is 38.5 uH and it's self resonant at 13.48 MHz.
(Moving it very far from ground changes the resonant frequency to 13.52
MHz.)

What's it's velocity factor, and how did you calculate it?

Roy Lewallen, W7EL


Richard Harrison wrote:
Reg, G4FGQ wrote:
"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."

Equation 14 on page 48 of Terman`s 1943 edition of "Radio Engineers`
Handbook is:

Lo = 0.00508 l (2.303 log 4l/d - 1+mu/4) microhenrys

Lo is the (approximate) low-frequency inductance and the dimensions are
in inches.

Terman also gives the (approximate) low-frequency inductance formula of
a single-layer solenoid on page 55 of the same book.

One can find the resonant frequency of the coil when using a known
capacitance to resonate the coil at a low frequency. Maybe a dip meter
could be used. Capacitive and inductive reactances are equal at
resonance. Self and stray capacitances are included with the known value
of capacitance used to resonate the coil at the low frequency. The
resonant frequency is lower than the known capacitance by itself would
produce.

The resonance formula used with the actual inductance of the coil will
give the capacitance of the resonant circuit

The difference between the calculated capacitance and the known
capacitor value is equal to the stray and self-capacitance total, so it
is good to minimise stray capacitance when seeking the self-capacitance
value of the coil.

An ARRL Single-Layer Coil Winding Calculator is a slide rule which makes
things easy.

Best regards, Richard Harrison, KB5WZI

Velocity Factor and resonant frequency
 

Roy Lewallen wrote:
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.


Roy, I can't answer the question you put to Reg, but the capacitance of
an isolated conducting cylinder is approximately that of an isolated
conducting sphere of the same surface area. Any unbalanced charge on a
conductor resides on the surface of the conductor and so the greater the
surface area, the greater the charge you can place on it to raise its
potential by some amount, etc. Obviously the cylinder's electric field
would depart from the radial field of a point charge at the center of
the sphere but I don't think that's relevant in this case. I hear bells
ringing. ;-)

Chuck



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.

Velocity Factor and resonant frequency
 

Roy Lewallen wrote:

What's it's velocity factor, and how did you calculate it?

I can't believe I did that! It must be from spending too much time
reading Internet postings. Of course I meant:

What's its velocity factor, and how did you calculate it?
^^^
I knew better than that by the time I'd finished grade school. Hope it
isn't all downhill from here.

Roy Lewallen, W7EL

Velocity Factor and resonant frequency
 

Roy, W7EL wrote:
"What is the velocity factor, and how did you calculate it?"

Given:
length = 12 inches
diamwter = 6 in.
L = 38.6 microhenry

I used formula (37) from Terman`s Handbook to calculate 25 turns in the
coil. 471 inches of wire are needed in the coil.

The velocity of the EM wave traveling around the turns of the coil is
almost equal to the velocity in a straight wire. But, the time required
to travel 471 inches is 40 times the time required to travel 12 inches.
The velocity factor is the reciprocal of 40 or 0.025.

Best regards, Richard Harrison, KB5WZI

Velocity Factor and resonant frequency
 

Tom Ring wrote:

Cecil Moore wrote:
Let's say we have a 1/2WL dipole in free space driven by a
self-contained source at the center. If we float a florescent
light bulb around the ends of the dipole, are you saying the
electric fields won't fire the bulb like it does on earth?

Stop acting like an idiot Cecil.

It was a technical question. I was just wondering what keeps
the wire from transferring energy when it is located in free
space.
--
73, Cecil http://www.qsl.net/w5dxp

Velocity Factor and resonant frequency
 

Roy Lewallen wrote:

That's all very nice. Let's see if it's useful for anything.

A while back, Cecil posted a model of a base loaded vertical antenna. It
has an inductor which is vertically oriented. The bottom of the inductor
is 1 foot from the ground and the inductor is 1 foot long and six inches
in diameter. Inductance is 38.5 uH and it's self resonant at 13.48 MHz.
(Moving it very far from ground changes the resonant frequency to 13.52
MHz.)

What's it's velocity factor, and how did you calculate it?

13.48 MHz is not exactly the self-resonant frequency of the
coil. At 13.48 MHz, the one foot bottom section is 0.0137
wavelengths long, i.e. 4.9 degrees. So the coil occupies
85.1 degrees, i.e. 0.236 wavelength. The coil length is
coincidentally also one foot so the velocity factor is
4.9/85.1 = 0.058.
--
73, Cecil http://www.qsl.net/w5dxp

Velocity Factor and resonant frequency
 

Richard Harrison wrote:

Roy, W7EL wrote:
"What is the velocity factor, and how did you calculate it?"

Given:
length = 12 inches
diamwter = 6 in.
L = 38.6 microhenry

I used formula (37) from Terman`s Handbook to calculate 25 turns in the
coil. 471 inches of wire are needed in the coil.

The velocity of the EM wave traveling around the turns of the coil is
almost equal to the velocity in a straight wire. But, the time required
to travel 471 inches is 40 times the time required to travel 12 inches.
The velocity factor is the reciprocal of 40 or 0.025.

13.48 MHz is not exactly the self-resonant frequency of the
coil. At 13.48 MHz, the one foot bottom section is 0.0137
wavelengths long, i.e. 4.9 degrees. So the coil occupies
~85.1 degrees at self-resonance. The coil length is coincidentally
also one foot so the velocity factor is 4.9/85.1 = 0.058.

I don't have the Terman Handbook. Does he take adjacent coil
coupling into account in that formula? If not, that's the
difference in the two results.

In either case, the velocity factor is not anywhere near 1.0
as the lumped circuit model would have us believe.

Does anyone have a formula for what percentage of current is
induced in coils farther and farther away from the primary
coil? I haven't found such a formula in my references but it's
got to exist.
--
73, Cecil http://www.qsl.net/w5dxp

Velocity Factor and resonant frequency
 

Cecil, W5DXP wrote:
"I don`t have the Terman Handbook."

Formula (37) on page 55 of the 1943 "Radio Engineers` Handbook is:

Lo = (r sq) (n sq) / 9(r) + 10(l)
Lo = approximate low-frequency inductance of a single-layer solenoid in
microhenries where r is the radius and l is the length of the coil in
inches.

Terman attributes the formula to H.A. Wheeler, "Simple Inductance
Formulas for Radio Coils", Proc. I.R.E., Vol 16, P1398, October 1928.

Best regards, Richard Harrison, KB5WZI

Velocity Factor and resonant frequency
 

Richard Harrison wrote:
Roy, W7EL wrote:
"What is the velocity factor, and how did you calculate it?"

Given:
length = 12 inches
diamwter = 6 in.
L = 38.6 microhenry

I used formula (37) from Terman`s Handbook to calculate 25 turns in the
coil. 471 inches of wire are needed in the coil.

The velocity of the EM wave traveling around the turns of the coil is
almost equal to the velocity in a straight wire. But, the time required
to travel 471 inches is 40 times the time required to travel 12 inches.
The velocity factor is the reciprocal of 40 or 0.025.

Not quite what I was expecting, but let's see if I understand what it
means. This means that if we put a current into one end of the inductor,
it'll take about 40 ns for current to reach the other end, right? So we
should expect a phase delay in the current of 180 degrees at 6.15 MHz,
or about 30 degrees at 1 MHz, from one end to the other?

Roy Lewallen, W7EL

Velocity Factor and resonant frequency
 

"Roy Lewallen" wrote:
Richard Harrison wrote:
The velocity of the EM wave traveling around the turns of the coil is
almost equal to the velocity in a straight wire. But, the time required
to travel 471 inches is 40 times the time required to travel 12 inches.
The velocity factor is the reciprocal of 40 or 0.025.

Not quite what I was expecting, but let's see if I understand what it
means. This means that if we put a current into one end of the inductor,
it'll take about 40 ns for current to reach the other end, right? So we
should expect a phase delay in the current of 180 degrees at 6.15 MHz,
or about 30 degrees at 1 MHz, from one end to the other?

Dr. Corum's VF equation predicts a VF of approximately double
Richard's with corresponding delays of 1/2 of your calculated
values.
--
73, Cecil, W5DXP

Velocity Factor and resonant frequency
 

FWIW, tau=sqrt(L*C); Z0=sqrt(L/C); L=3.86e-5; tau=4e-8
(Please note: That is NOT!! a lumped model!)

implies that C= 41pF and Z0=965ohms

(v.f. = 0.058 is left as an exercise for the reader.)

But if the coil's axis is parallel to a ground plane, that 6" diameter
coil must be spaced about a quarter inch away from the ground plane
(axis 3.25" from ground plane) to get that 41pF capacitance, and that's
assuming a solid tube 3" in radius as a quick model .(An
approximation!)

Cheers,
Tom