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'[EE:] Inductance and capacitance'
2004\07\15@020722 by

This old basic info is getting hard to find!

I need to find the inductance and capacitance of a wire rod of known diameter and length, in free space.  I found a formula in an old ARRL handbook, but it makes Mathcad throw up. I suspect something's dimensionally wrong with it, like dividing microhenries by cucumbers.

I also need to find the # of turns required to create inductance L, when wire diameter is known, close spacing, air core, but coil length is not known.
Again, ARRL gets me close, but their formula wants length as an input, when I don't know the number of turns yet.. N*Dia = L in this case.

Anyone have good info?

--

> This old basic info is getting hard to find!
>
> I need to find the inductance and capacitance of a wire rod of known
diameter and length, in free space.  I found a formula in an old ARRL
handbook, but it makes Mathcad throw up. I suspect something's dimensionally
wrong with it, like dividing microhenries by cucumbers.

Check this out - not much but may help

*************************************************
Roy Hopkins   :-)

Tauranga
New Zealand
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>
>Check this out - not much but may help
>

It's the same thing, I need to know the length of the coil in order to calculate the # of turns. I'm looking for the close wound case, where the number of turns determines the length.

--

I have here my trusty Coil Design and Construction Manual, Babini and
Bernards  press ( 30pence ), still in print but no longer that cheap
and it has been updated.

Anyhow it doesn't use AWG so you'll have to convert British SWG to US

and length into uH and various other things.

2004 edition and it is called LCFR

Also the RSGB book used to have all this info in it as a series of
nomagraphs.

Wheelers formula

L = r^2 * N^2 /9r + (10 * length) OR

N^2 = r^2 /9 * r + (10 * length)

N = Sqrt (L * N^2)

Winding pitch = N/length.

The example in the book is

single layer air coil of 197uH diameter 1" , 2.5 " long

1^2 / 9 * 1 + 10 * 2.5 = N^2/34

197uH * 34 = 6698

N = sqrt 6698 = 81 turns

Pitch = 81 turns / 2.5" long = 32.4 turns per inch, and as it proudly
states this equals SWG 22 double silk covered wire in appendix A

For metric I have seen this formula - but I think there may be an
error in it.

N = 5/r * sqr L(10 * lenght + 9r)

where r is the outside radius of the coil in inches and N is the
number of turns

Colin
--
cdb, bodgy1optusnet.com.au on Thursday,15 July,2004

I have always been a few Dendrites short of an Axon and believe me it
shows.

Light travels faster than sound. That's why some people appear bright
until they speak!

--

Do it iteratively.

Assume a length.

Compute the turns.

If the number of turns don't match the length, adjust them and repeat.

Bob Ammerman
RAm Systems

{Original Message removed}
Or you could come up with your own equation giving length for a number
of turns, and use some calculus...
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Bob Ammerman wrote:
{Quote hidden}

--

At 10:08 AM 7/15/2004 -0400, Bob Ammerman wrote:

>Do it iteratively.
>
>Assume a length.
>Compute the turns.
>If the number of turns don't match the length, adjust them and repeat.

Particularly icky to do in mathcad.

--

Or, better yet... program your favorite math software to do it iteratively,
perhaps by operating on an array of coil lengths, then plot it and just pick
your size from the graph.  Print the plot and never worry about it again!
:-D

{Original Message removed}
> From:         David VanHorn[SMTP:dvanhornCEDAR.NET]
> Sent:         Thursday, July 15, 2004 2:36 AM
> To:   PICLISTMITVMA.MIT.EDU
> Subject:      Re: [EE:] Inductance and capacitance

>>
>>Check this out - not much but may help
>>

> It's the same thing, I need to know the length of the coil in order to calculate
> the # of turns. I'm looking for the close wound case, where the number of
> turns determines the length.

In the original formula, substitute N*diam for L. This will give you an N inside
of the formula and another N on the left side of the equation. Rearrange terms
so that all terms containing N are on one side of the equation, factor that side
into N times something, and divide both sides of the equation by "something".
For example, if

N = a + b*len, then N = a+b*(N*diam) and N(1 - b*diam) = a. Therefore

N = a / (1 - b*diam)

The problems begin when the resulting equation cannot be solved. This
would mean an equation of third order or higher. The actual equation
will be quadratic, as you can see by using this equation for a single layer
coil:

L = [ N * N * A * A ] / [ 9 * A + 10 * B ]

L is the inductance in microhenries, N is the number of turns, A is the
mean radius of the coil (to the center of the wire) in inches, and B is
the length of the coil in inches. Let B = N * D where D is the wire
diameter. Then

L = [ N * N * A * A ] / [ 9 * A + 10 * N * D ]

Clear the fraction by multiplying both sides by [ 9 * A + 10 * N * D ]

L * [ 9 * A + 10 * N * D] = N * N * A * A

This gives  (A ^ 2) * (N ^ 2) - ( 10 * L * D ) * N - 9 * A * L = 0

This quadratic equation can be solved for N. There will be two
solutions; use the positive real root if there is one. If not, there
is no solution.

John Power

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'[EE:] Inductance and capacitance'
2004\08\11@114217 by
That again..

Boy I tell you, sometimes you look at a thing, and it seems so simple..

I'm looking at the series combination of four large inductors, and a relatively small rod.  I know from direct observation that the system is series resonant near 250kHz, with a low impedance notch.

The four inductors are Miller PN 6306, 10mH inductors with a DC resistance of 31 ohms, and a parasitic C of 5.025pF.  Modeling this gives me exactly what Miller predicts for self-resonance, at 0.71 MHz.

The inductors are physically arranged to minimize coupling, so I should be able to consider them as four parallel RLC circuits, connected in series.

The antenna capacitance is a little dodgy. I haven't found a formula for the capacitance of a rod or cylinder in space, so I assumed that over any reasonable distance, the rod looks like a sphere, and took the sphere formula, and solved for C per unit of surface area, then applied that to the rod's surface area.  That gives me 0.766pF for a 17 inch 3/8 diameter rod.  Since my shop isn't empty space, I add 1pF for strays in the real world, and 1pF for other near-field junk.

So.. Seems simple enough to calculate impedance of the inductors over a range, sum four of those, and then add the antenna impedance also in series, right?

Only problem is, when I scan the impedance over frequency, I get only one interesting point, up around 710kHz.

I am using ZL=2piFL and ZC=(-1)/(2piFC), which has been working up to this point.
For the inductor impedance, it's ((ZL+RL)*ZLc)/((ZL+RL)+ZLc), taking inductive reactance in series with DC resistance as a sum, and then parasitic capacitance in parallel.

What I think it should look like, is the series circuit of four units, each unit is an inductor in series with a resistor, and a capacitor across that pair. The antenna C then should add in series on the end.  I'm pretty sure I can ignore it's inductance.

I haven't tickled my AC analysis neurons this much in years, am I looking at this wrongly?

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On Wed, 11 Aug 2004, Dave VanHorn wrote:

<snip>

> I haven't tickled my AC analysis neurons this much in years, am I
> looking at this wrongly?

Dave,

I'm not sure if you're looking at this correctly or not. In my experience
with capacitance sensor analysis, I've often been surprised at how wrong
my intuition can be! Since you have a real physical thing that you can
measure, it may be useful to create as an accurate as possible schematic
representing your system. Then you could experiment with it by varying
physical parameters and seeing how the system responds.

You may wish to purchase Charles Walker's book "Capacitance, Inductance
and Crosstalk Analysis":

http://antennas.argospress.com/book-0890063923.htm

It ain't cheap, but it has tons of different wiring geometries that may

Another approach may be to get a book on Antenna design. Stuzman and
Thiele's "Antenna Theory and Design" has a whole section on wire antennas.
There's also a section on radiation of monopoles from a finite ground
plane.

http://antennas.argospress.com/book-0471025909.htm

I'm not an expert in this area, but my opinion is that the lumped
equivalent circuit model for antenna design is really insufficient. At
best, you may be able to identify dominant poles in frequency response.

Scott

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At 11:25 AM 8/11/2004, Scott Dattalo wrote:

>On Wed, 11 Aug 2004, Dave VanHorn wrote:
>
><snip>
>
>>I haven't tickled my AC analysis neurons this much in years, am I
>>looking at this wrongly?
>
>Dave,
>
>I'm not sure if you're looking at this correctly or not. In my experience
>with capacitance sensor analysis, I've often been surprised at how wrong
>my intuition can be! Since you have a real physical thing that you can
>measure, it may be useful to create as an accurate as possible schematic
>representing your system. Then you could experiment with it by varying
>physical parameters and seeing how the system responds.

Up to a point, things seem to be going well, but in this system, parasitics are relatively large, and even desired!

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> I'm looking at the series combination of four large inductors, and a
relatively small rod.  I know from direct observation that the system is
series resonant near 250kHz, with a low impedance notch.

The mini-NEC antenna modelling program may help.
I've never used it ...

Available many places including here

He has other interesting related programs too.

RM

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At 12:06 PM 8/11/2004, Russell McMahon wrote:

>> I'm looking at the series combination of four large inductors, and a
>relatively small rod.  I know from direct observation that the system is
>series resonant near 250kHz, with a low impedance notch.
>
>
>The mini-NEC antenna modelling program may help.
>I've never used it ...
>
>Available many places including here
>

The "antenna" isn't intended to behave as an antenna, in the classical sense.
It's a capacitor, starting with it's own value in the space, and then increasing to some higher value as the hand is brought near.

It's radiation efficiency is abysmally low.

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Dave,

Everything you've said so far reminds me of a Theremin.  If that's not the
case, I think there's still a chance you will find your answers in that
area, as a lot of information has been accumulated since the 1920s.  Here's
one interesting site that may be applicable.
http://www.dogstar.dantimax.dk/theremin/thersens.htm

Romulus, MI

{Quote hidden}

sense.
> It's a capacitor, starting with it's own value in the space, and then
increasing to some higher value as the hand is brought near.
>
> It's radiation efficiency is abysmally low.
>
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You want the inductors coupled imho. the way they are set up now, you see
four parallel RLC resonators in series towads a load, and they form an
efficient bandpass.

To make the inductor work as you want it, you have to have a coil whose
self capacitance is much lower than the load's. This is nearly impossible
in your situation. What you could try is to use a tuned parallel circuit
and couple the antenna at the top and the feed at a tap or small secondary
to the coil. Or use an inductive antenna. Two crossed ferrite rods should
work perfectly at that frequency.

To continue the way you do it now, you would have to add a parallel
resistor to each coil to reduce its self resonant Q below that of the
calculated target Q of your desired assembly (with the rod). You are
aiming for Q=2..10 probably, for each coil. Basically if the Q of your
adapter is half that of the antenna + driver's then the antenna will
dominate the tuning. The target Q must include the drive impedance.

>The "antenna" isn't intended to behave as an antenna, in the classical
>sense. It's a capacitor, starting with it's own value in the space, and
>then increasing to some higher value as the hand is brought near.
>
>It's radiation efficiency is abysmally low.

Ah, that's different. Still, for such a low capacitance at a low
frequency, you should try to put the stick at the top of a parallel LC
resonant circuit and either use it as a bandpass filter or as an absorber.
The hand will detune it. The Theremin uses something like this (detuning
parallel resonant circuit) for the volume control.

Basically you have an oscillator at fixed frequency, coupling weakly into
the sensor tank circuit (I used a twiddlecap). A high impedance detector
(JFET) measures the amplitude in the tank. The tank is tuned for maximum
output (or half output) then any object coming closer or moving farther
causes an amplitude change at the output. For a peaked tank the amplitude
falls on both sides, for the slope, it can indicate direction (closer or
farther). Tuning this is best done remotely using a varicap ;-)

Peter

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At 08:12 PM 8/12/2004, Peter L. Peres wrote:

>You want the inductors coupled imho. the way they are set up now, you see
>four parallel RLC resonators in series towads a load, and they form an
>efficient bandpass.

I understand, but I'm trying to model an existing device that deliberately set them up with minimal coupling. Most designs would use a single large inductor, but LARGE is the word, at about 3.5" diameter, and maybe 14-20 inches long.

>To make the inductor work as you want it, you have to have a coil whose
>self capacitance is much lower than the load's. This is nearly impossible

Yes. About 6-ish pF is practical

> What you could try is to use a tuned parallel circuit
>and couple the antenna at the top and the feed at a tap or small secondary
>to the coil. Or use an inductive antenna. Two crossed ferrite rods should
>work perfectly at that frequency.

http://www.dvanhorn.org/TankCkt.gif This is the circuit in question, which does work pretty well. I'm trying to optimize it.

>To continue the way you do it now, you would have to add a parallel
>resistor to each coil to reduce its self resonant Q below that of the
>calculated target Q of your desired assembly (with the rod). You are
>aiming for Q=2..10 probably, for each coil. Basically if the Q of your
>adapter is half that of the antenna + driver's then the antenna will
>dominate the tuning. The target Q must include the drive impedance.

Dosen't low Q make for instability?

{Quote hidden}

It does, but this is the pitch side.

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> I understand, but I'm trying to model an existing device that
> deliberately set them up with minimal coupling. Most designs would use a
> single large inductor, but LARGE is the word, at about 3.5" diameter,
> and maybe 14-20 inches long.

10mH coils have a lot of parasitic capacitance no matter who makes them
(even if pelerine pitch wound with litz wire). I also think that your
measured 700kHz self resonant frequency is due to multiple sections
(layers) resonating while being tightly coupled. This corresponds to a
much higher self capacitance than you calculated. 10 to 30pF should be
about right for that size of coil, if it is good.

>http://www.dvanhorn.org/TankCkt.gif

Is the tank at the right a part of the oscillator ? If so, and you are
trying to tune the osc. I think it would be easier to use a capacitive
divider to insert the antenna and not use L1 at all. I.e. replace L1 with
a small capacitor and see with what Ctrim value it works best.

My limited experience with Theremin lead me to quickly abandon direct
tuning of the oscillator and use indirect tuning. I had an XO that was
weakly coupled to two identical tanks using twiddlecaps. Each tank had a
short antenna, one for pitch, one for volume. Each tank also had a JFET
peak rectifier. The pitch rectifier drove a varicap in the 'real' pitch
osc, which beat against the XO, and the volume rectifier drove another
JFET mounted as volume control. So I had only one critical coil to tune
(the one for the beat osc). I used 6 transistors and a voltage regulator
(78L05). There was a lot of rf leakage into the (external) audio amp but
the amp did not mind. It all ran on 10mA or less from a 9V battery. The
circuit was built 'dead bug' style on a small piece of weissblech. I used
a 10 MHz crystal I think. After I finished playing with it I dismantled
it.

I also think that you can control the pitch without an antenna by putting
the osc in a plastic box and just putting your hand on or near it (the
bottom would be shielded with foil), if the frequency is high enough. 27
MHz should work great.

A high Q antenna usually causes trouble since the transmitter can see a
complex impedance that changes even with modulation sidebands. It can
easily self-oscillate like this.

good luck,

Peter

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At 08:06 PM 8/15/2004, Peter L. Peres wrote:

>>I understand, but I'm trying to model an existing device that
>>deliberately set them up with minimal coupling. Most designs would use a
>>single large inductor, but LARGE is the word, at about 3.5" diameter,
>>and maybe 14-20 inches long.
>
>10mH coils have a lot of parasitic capacitance no matter who makes them
>(even if pelerine pitch wound with litz wire). I also think that your
>measured 700kHz self resonant frequency is due to multiple sections
>(layers) resonating while being tightly coupled. This corresponds to a
>much higher self capacitance than you calculated. 10 to 30pF should be
>about right for that size of coil, if it is good.

?? I ran that through mathcad taking the SRF and inductance as constants, and I measured the SRF to conform to the data sheet.

>>http://www.dvanhorn.org/TankCkt.gif
>
>Is the tank at the right a part of the oscillator ? If so, and you are
>trying to tune the osc. I think it would be easier to use a capacitive
>divider to insert the antenna and not use L1 at all. I.e. replace L1 with
>a small capacitor and see with what Ctrim value it works best.

There is a maginfication effect that is very important, that happens when the antenna coil, and the antenna (with all the parasitics) is resonant just above the pitch oscillator's operating point.

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>There is a maginfication effect that is very
>important, that happens when the antenna coil,
>and the antenna (with all the parasitics) is
>resonant just above the pitch oscillator's
>operating point.

This sounds like it is one of those shop doorway security things.

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At 11:38 AM 8/16/2004, Alan B. Pearce wrote:

>>There is a maginfication effect that is very
>>important, that happens when the antenna coil,
>>and the antenna (with all the parasitics) is
>>resonant just above the pitch oscillator's
>>operating point.
>
>This sounds like it is one of those shop doorway security things.

Nope. The first electronic instrument.
http://www.thereminworld.com/

If you think you know what it sounds like, well..
Find anything by Clara Rockmore, particularly "Vocalise".

The point that I'm trying to model, is proving a bit intractable, but I know it's there from measurements of real life instruments.

The parallel point of the tank circuit is where it oscillates.
The series circuit of the antenna coil, and all it's parasitics, shifts the parallel point of the tank.

If you make no effort to tune the system, then you get no real gain, because the antenna system's resonant point will be too far away from the tank circuit.

If you tune around on the tank, you should be able to cross the antenna's resonant point, this is characterized by a sudden jump, as the oscillator can't actually run at the point where they collide.

If you tune the antenna system close to the tank, then you get the situation where the antenna is slightly inductive with no hand capacitance, and transitions to slightly capacitive with the hand near the antenna.  This results in the best playable range.   I'm trying to model this behavior in mathcad, so I can optimize it.

There are issues of sensitivity, in that most instruments produced today are TOO sensitive, and linearity but this last in a musical sense, in that I'd like to get all the octaves to translate into the same physical control distance.   I'm also working with the shape of the antenna rod on this, experimenting with airfoiled tubing to reduce the sudden increase in capacitance in the last little bit of range.  In the far-field, the airfoiled tubing acts just like a rod, since it has the same surface area. In the near field, the thin edge takes the effective surface area down a notch.

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>If you tune around on the tank, you should be able to cross the antenna's
>resonant point, this is characterized by a sudden jump, as the oscillator
>can't actually run at the point where they collide.

I think that you are talking about a Q rule side effect. In that case the
jump would be very abrupt.

The Q rule says that in an oscillator with several frequency-determining
elements (more or less equally coupled), the one with the higher Q factor
will determine the resonant frequency.

The sudden jump is well known from grid-dip-meter work where it is easy to
have the grid dip oscillator 'hijacked' by a high Q tank circuit (assuming
it is a direct oscillator type). This is exactly the Q rule at work. The
GDO will escape the capture from the tank when the bandpass effect of the
GDO and tank circuit will attenuate enough at the tank circuit's frequency
that the GDO tank can take over again.

For linear control as in thermin you probably want to avoid this jump. One
way would be to make sure that the antenna circuit has a larger Q than the
oscillator's tank (the opposite of what I was preaching until now ?), so
it would dominate tuning. This could be done by damping the oscillator
tank (in your scheme) with a small resistor. I'd try 30 ohms in series
with the tank tuning capacitor.

Peter

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