Coils are transmission lines
 

ALL coils are distributed in space. They have a conductor. Therefore
they can be analysed in the same manner as transmission lines.

They ARE transmission lines, no matter what length. They can't help
it!

Program COILINE demonstrates how a simple coil-loaded vertical antenna
can be designed by using classical transmission line mathematics.

Enter length, diameter and number of turns on the coil, the length of
the top rod or whip or wire, and you can examine how the thing behaves
at any frequency. You can design anything from a bottom loaded long
wire to a helical for 160 metres.

Coils can vary between a few turns on an empty toilet roll tube to a 4
feet long, 1 inch diameter, plastic pipe wound with 1000 turns.

You can prune the whip to obtain resonance at a given frequency
without having to go out in the freezing cold back yard.

Discover the velocity factor, nano-seconds per meter, and other
numbers for your particular coil. All will be of interest to the
participants in the interminable civil war still raging on another
thread. Ammunition galore!

Download program COILINE from website below and run immediately. Only
47 kilo-bytes. Its quite entertaining.

By the way, it has just occurred to me, I forgot to include coil Q in
the results. But it hardly matters - there's little to be done with
the number even if you know it.
----
.................................................. ..........
Regards from Reg, G4FGQ
For Free Radio Design Software go to
http://www.btinternet.com/~g4fgq.regp
.................................................. ..........

Coils are transmission lines
 

Reg Edwards wrote:
(snip)
By the way, it has just occurred to me, I forgot to include coil Q in
the results. But it hardly matters - there's little to be done with
the number even if you know it.

Thanks.

But what about comparing different ways of obtaining the same
inductance to find those with higher or lower Q?

Coils are transmission lines
 

Reg Edwards wrote:
Discover the velocity factor, nano-seconds per meter, and other
numbers for your particular coil.

Reg, would you care to share your formula for velocity factor?
--
73, Cecil http://www.qsl.net/w5dxp

Coils are transmission lines
 

But what about comparing different ways of obtaining the same
inductance to find those with higher or lower Q?

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

To double Q, whatever it is, just double length and diameter of the
coil, wind on a number of turns of much thicker wire for the same
inductance, and Bingo, Q is doubled. The value of Q is unecessary.

Efficiency and bandwidth can be deduced by calculating from the known
values of wire and radiation resistances. But I suppose Q, once
available, would be a short cut to crudely estimating bandwidth.
Additional information is needed.

The loss in the coil may not be the dominating factor. What matters is
the System Q. It can be considerably worse than coil Q.
----
Reg.

Coils are transmission lines
 

Reg, would you care to share your formula for velocity factor?
==========================================

Cec, can't you find it in your bibles?

Velocity = 1 / Sqrt( L * C) metres per second

where L and C are henrys and farads per metre.

What you really want to know is how to calculate L and C from coil
dimensions. But you won't find that from any bible.

As a special favour, I'll attach the source code for the program to an
e-mail. Read it with a non-proportional text editor such as Notepad.

In your discussions on the other thread you have mentioned a coil's
self-resonant frequency. In the source code you will also find a
formula for Fself. Which, again, cannot be found in any bible. It is
a fairly straightforward 2 or 3-line formula.

Fself is not used anywhere in the program. It is available solely out
of interest. It is fairly accurate. I have measured it on many coils
of all proportions and numbers of turns from 1 inch to 6 feet long
with 1500 turns.
----
Reg, G4FGQ

Coils are transmission lines
 

Reg Edwards wrote:
Velocity = 1 / Sqrt( L * C) metres per second

Well now, W7EL, a pretty smart fellow questioned that equation,
as I remember before a bottle of CA Sutter Home Cabernet Sauvignon,
circa 2001. (Not bad for a 5 year old red.)

Dr. Corum's equation is a mite more complicated involving
fractional powers of diameter, turns per inch, and wavelength
and it closely agreed with my self-resonant measurements.

If we work backwards from Dr. Corum's fairly accurate
VF, can we calculate the L and C of the coil?
--
73, Cecil http://www.qsl.net/w5dxp

Coils are transmission lines
 

Reg Edwards wrote:
Reg, would you care to share your formula for velocity factor?
==========================================

Cec, can't you find it in your bibles?

Velocity = 1 / Sqrt( L * C) metres per second

where L and C are henrys and farads per metre.

What you really want to know is how to calculate L and C from coil
dimensions. But you won't find that from any bible.

. . .

What seems to be getting lost in the discussion is that L is *series* L
per meter and C is *shunt* C per meter -- that is, the C to another
conductor(*). C is not the self-capacitance of the inductor.

(*) Conductors also have capacitance to free space, but I'm not at all
sure the transmission line equations for such things as velocity are
valid if this is used for C. The equation for the resonant length of a
wire in space is very complex and can't be solved in closed form, and
even approximate formulas are much more complex than those for
transmission lines. So while transmission lines and antennas -- or
radiating inductors -- share some characteristics, you can't blindly
apply the equations for one to the other and expect valid results.

Roy Lewallen, W7EL

Coils are transmission lines
 

L and C are neither in series or in parallel with each other.

They are both DISTRIBUTED as in a transmission line.

To calculate the self-resonant frequency what we are looking for is an
equivalent shunt capacitance across the ends of the inductance.

Turn to turn capacitance is is a very small fraction of the total
capacitance. If there are 10 turns then there are 10 turn-to-turn
capacitances all in series. After a few turns there is very little
capacitance which can be considered to be across the coil.

Consider two halves of the coil. We have two large cylinders each of
half the length of the coil. Diameter of the cylinders is the same as
coil diameter. Nearly all the capacitance across the coil is that due
to the capacitance between the two touching cylinders (excluding their
facing surfaces).

The formula for VF is true for any transmission line with distributed
L and C. And a coil has distributed L and C.

Agreed, L and C are approximations for very short fat coils. But any
approximation is far better than none at all. All antennas have to be
pruned at their ends.
----
Reg.
"Roy Lewallen" wrote

Velocity = 1 / Sqrt( L * C) metres per second

where L and C are henrys and farads per metre.

What seems to be getting lost in the discussion is that L is
*series* L
per meter and C is *shunt* C per meter -- that is, the C to another
conductor(*). C is not the self-capacitance of the inductor.

(*) Conductors also have capacitance to free space, but I'm not at
all
sure the transmission line equations for such things as velocity are
valid if this is used for C. The equation for the resonant length of
a
wire in space is very complex and can't be solved in closed form,
and
even approximate formulas are much more complex than those for
transmission lines. So while transmission lines and antennas -- or
radiating inductors -- share some characteristics, you can't blindly
apply the equations for one to the other and expect valid results.

Roy Lewallen, W7EL

Coils are transmission lines
 

Of course I understand that both L and C are distributed. But the C in
the transmission line formula isn't a longitudinal C like the C across
an inductor; it's the (distributed, of course) shunt C between the two
conductors of the transmission line. I don't believe you can justify
claiming that the C across an inductor is even an approximation for the
C from the inductor to whatever you consider to be the other
transmission line conductor.

Roy Lewallen, W7EL

Reg Edwards wrote:
L and C are neither in series or in parallel with each other.

They are both DISTRIBUTED as in a transmission line.

To calculate the self-resonant frequency what we are looking for is an
equivalent shunt capacitance across the ends of the inductance.

Turn to turn capacitance is is a very small fraction of the total
capacitance. If there are 10 turns then there are 10 turn-to-turn
capacitances all in series. After a few turns there is very little
capacitance which can be considered to be across the coil.

Consider two halves of the coil. We have two large cylinders each of
half the length of the coil. Diameter of the cylinders is the same as
coil diameter. Nearly all the capacitance across the coil is that due
to the capacitance between the two touching cylinders (excluding their
facing surfaces).

The formula for VF is true for any transmission line with distributed
L and C. And a coil has distributed L and C.

Agreed, L and C are approximations for very short fat coils. But any
approximation is far better than none at all. All antennas have to be
pruned at their ends.
----
Reg.
"Roy Lewallen" wrote

Velocity = 1 / Sqrt( L * C) metres per second
where L and C are henrys and farads per metre.

What seems to be getting lost in the discussion is that L is
*series* L
per meter and C is *shunt* C per meter -- that is, the C to another
conductor(*). C is not the self-capacitance of the inductor.

(*) Conductors also have capacitance to free space, but I'm not at
all
sure the transmission line equations for such things as velocity are
valid if this is used for C. The equation for the resonant length of
a
wire in space is very complex and can't be solved in closed form,
and
even approximate formulas are much more complex than those for
transmission lines. So while transmission lines and antennas -- or
radiating inductors -- share some characteristics, you can't blindly
apply the equations for one to the other and expect valid results.

Roy Lewallen, W7EL

Coils are transmission lines
 

Roy Lewallen wrote:
Of course I understand that both L and C are distributed. But the C in
the transmission line formula isn't a longitudinal C like the C across
an inductor; it's the (distributed, of course) shunt C between the two
conductors of the transmission line. I don't believe you can justify
claiming that the C across an inductor is even an approximation for the
C from the inductor to whatever you consider to be the other
transmission line conductor.

Agreed. They are as different as a shunt element and a series element
in a pi filter.