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The resonance frequency of a single layer solenoid - DERIVATION

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LAN_403

thermite

Wed Feb 20 2008, 05:32AM

Banned on 02/27/2008
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This is a necessary and focussed split from my previous thread on the definition of a tesla coil.

Basically it is focussed on the DERIVATION of inductance and more importantly the distributed capacitance of the coil.

As you can see that two adjacent turns can have a capacitance.

I am sure this is a solved problem. where to find the paper or book that has the COMPLETE dervation is not clear.

thanks in advance

Coronafix

Wed Feb 20 2008, 10:10AM

Registered Member #160 Joined: Mon Feb 13 2006, 02:07AM
Location: Melbourne, Australia
Posts: 938

Here is a list of all the equations we use.
Once again, google.

Dr. Slack

Wed Feb 20 2008, 10:40AM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

Let's make sure we're not working across a language barrier here!

By "Derivation", do you mean concise approximate formulae like the ones above, or how to get to those formulae with calculus from first principles with Maxwells or Biot Savat, or something else?

thermite

Wed Feb 20 2008, 07:09PM

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NeilThomas wrote ...

Let's make sure we're not working across a language barrier here!

By "Derivation", do you mean concise approximate formulae like the ones above, or how to get to those formulae with calculus from first principles with Maxwells or Biot Savat, or something else?

Goldsphere, thanks for the handy list, which btw does not have the interwinding capacitance and medhurst=???

Neil, I mean the second actually but concise approximation is also part of derivation from the exact since in the end derivation is to understand from analysis to design and design is better off done using approximate when exact is very complicated.

Hope someone can help.

Sulaiman

Wed Feb 20 2008, 09:17PM

Registered Member #162 Joined: Mon Feb 13 2006, 10:25AM
Location: United Kingdom
Posts: 3140

As far as I'm concerned, inter-turn capacitance is unimportant.
Use Wheeler for the inductance and Medhurst for capacitanceof the coil, add topload capacitance.
The answer will be good enough because corona and arcs will lower the resonant frequency.
Detailed analysis is pointless when the result is affected by how near you stand!

Marko

Wed Feb 20 2008, 09:20PM

Registered Member #89 Joined: Thu Feb 09 2006, 02:40PM
Location: Zadar, Croatia
Posts: 3145

This is a very interesting topic, and probably not as solved as you may think.

Here is a list of all the equations we use.
Once again, google.

I was never sure of what this 'medhurst' capacitance meant, and it apparently just *can't* be summed with toroid capacitance like some do!

As far as I figured out this is distributed capacitance which has no meaning for our 'effective' capacitance of fundamental series resonant mode.

One can think of inter-turn capacitance as 'parallel' in this case, and I don't know how it affects Fres. I couldn't verify that, but could it be actually *increasing* the resonant frequency, canceling out the series capacitance?

From other side capacitance between windings and ground can be thought of as something that can be added to toroid capacitance relatively safely.

I think these should be distinguished.

Now the 'effective' inductance is puzzling me even more.

I didn't notice these tables until recently:

Firstly, I don't have a clue what causes such a difference between LF and Fres inductance?
I guess transmission-line-liness of the secondary plays a huge factor there...

Also, take look at AC resistance, how it dramatically increases with reduction of winding ratio!

That definitely isn't constant 1/2 skin effect resistance as I thought before!

Lowest ratio shown has Q only of 3, why so low?
Q seems to increase as secondary gets longer and narrower.

Really, can someone here explain this table a bit more? I think that's of huge importance.

For comparison, I calculated inductance of the same wire straightened out to be only 635.973uH.

The interesting thing is that fundamental resonant frequency of a straight wire (wavelength ~ 1/4 of it's length) is actually going to be much lower than of a typical secondary wound with same wire!

This makes me assume that straight wire must have far larger 'effective' capacitance than the coil, despite all of conductor seems to be much closer together in a coil.

I know I can't proivde much help, only ask lots of questions.
I hope this will get someone interested,

discuss -

Marko

Sulaiman

Wed Feb 20 2008, 09:32PM

Registered Member #162 Joined: Mon Feb 13 2006, 10:25AM
Location: United Kingdom
Posts: 3140

Marko, there are two resonant frequencies of a typical TC secondary,
one is primarily determined by inductance and capacitance (Wheeler and Medhurst)
one is determined by 1/4 wavelength.
The inductance/capacitance resonance seems to dominate.

With a small (or no) topload,
the inductance/capacitance resonant frequency will be higher than the 1/4 wavelength resonant frequency.
With a 'typical' topload the L/C resonant frequency will be lower than the 1/4 wavelength resonant frequency.

I remember reading somewhere how Tesla considered both 1/4 wavelength and L/C resonances.
His aim was different though - maximum voltage and NO arcs/sparks.

The high resistance at high frequency is mainly due to 'proximity-effect'
for a 'typical' coil the ac resistance will be about 3 x dc resistance.
There are tables on the net detailing 'proximity effect' vs. H/D

Marko

Wed Feb 20 2008, 09:52PM

Registered Member #89 Joined: Thu Feb 09 2006, 02:40PM
Location: Zadar, Croatia
Posts: 3145

Marko, there are two resonant frequencies of a typical TC secondary,
one is primarily determined by inductance and capacitance (Wheeler and Medhurst)
one is determined by 1/4 wavelength.
The inductance/capacitance resonance seems to dominate.

Sulaiman, sorry, but are you *sure* what are you talking about? Because statements like this may have spread enormous misconceptions which I fell into too.

There is no such a thing as 'other 1/4 wavelength frequency', the ''inductance/capacitance resonance'' is only kind of electrical resonance that exists and that ever existed.

Any transmission line at it's fundamental mode resonates at wavelength of 4 *electrical* lengths, and this is what *is* it's LC/resonance. Electrical length of TC secondary can deviate a lot from it's physical length.

On example of a straight wire in vacuum - it's 1/4 wavelength frequency is the very same frequency of it's LC resonance, there's no other thing!

If I want to look it from other side, the wire is as long as it is, and speed of light as fast as it is, because permeability and permitivity of the vacuum are as they are.

bb tomorrow, really need to go studying now-

Marko

Ultra7

Thu Feb 21 2008, 01:58AM

Registered Member #1157 Joined: Thu Dec 06 2007, 12:11PM
Location: Houston, TX
Posts: 307

Goldsphere wrote ...

Here is a list of all the equations we use.

Oh man, did you actually read the main site for that link Goldsphere?
Tesla Coils For Christ?

Pearland is about 45 minutes away from my house, so I may just go see what they are all about, but. . .
They are using Tesla Coils For Christ's sake. . . . Literally. . . .
They want donations of pole pigs, NST's, and The GeekGroup Caps. . .

Hell, I may start "Tesla Coils For Budda"
How bout Tesla Coils for Ra. . .
Or. . . well, maybe we better not go for Mohamed.

Finn Hammer

Thu Feb 21 2008, 06:19AM

Registered Member #205 Joined: Sat Feb 18 2006, 11:59AM
Location: SkÃ¸rping, Denmark
Posts: 741

I think the work of Paul Nicholson covers your needs:

Cheers, Finn Hammer

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