Re: Space winding question

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Malcolm Watts by way of Terry Fritz <twftesla-at-uswest-dot-net>" <m.j.watts-at-massey.ac.nz>

On 11 Mar 01, at 12:53, Tesla list wrote:

> Original poster: "by way of Terry Fritz <twftesla-at-uswest-dot-net>"
> <Mddeming-at-aol-dot-com>
> 
> In a message dated 3/10/01 4:45:00 PM Eastern Standard Time,
> tesla-at-pupman-dot-com writes: 
> 
> Terry & All, 
> 
> It has been said that nothing ruins a good discussion like someone
> with facts. However, I for one appreciate the fact that Terry has
> again "Done the Math" before answering the question. IMVHO this
> approach enhances both the List's and his personal credibility. 
> 
> Matt D. 

In that case I should apologize for my first reply to your question 
since I did a mental calc to arrive at the aanswer. However, I do 
believe that there is a greater difference between the capacitances
than the figures calculated below suggest. Medhurst's tabular 
approach certainly shows it.

Regards,
Malcolm
 
> >
> > Your questions is straight forward and we can figure it out. 
> >
> > The coil's resonant frequency is determined basically by it's
> > inductance and effective capacitance.  "Sort of" like a simple LC
> > circuit.  "I" don't think wire length has anything at all to do with
> > it and wire gauge does not have much affect either. 
> 
> 
> 
> 
> 
> >
> > So we have two 1000 turn coils 12 x 54 and 12 x 60. 
> >
> > The inductance of a coil is given by the following to with about 1%
> > accuracy: 
> >
> > L = (N x R)^2 / (9 x R + 10 x H) 
> >
> >
> > L = inductance of coil in microhenrys (µH) 
> > N = number of turns 
> > R = radius of coil in inches (Measure from the center of the coil to
> > the middle of the wire.) H = height of coil in inches 
> >
> > Putting in our numbers: 
> >
> > L = (1000 x 6)^2 / (9 x 6 + 10 x 54) == 60600uH = 60.6mH 
> >
> > L = (1000 x 6)^2 / (9 x 6 + 10 x 60) == 55000uH = 55.0mH 
> >
> > So now we know the inductance of both coils... 
> >
> > For the capacitance, we can use the famous Medhurst equation also at
> > the site above that is about 1% accurate: 
> >
> > C = 0.29 x L +0.41 x R + 1.94 x SQRT(R^3/L) 
> >
> > C = self capacitance in picofarads 
> > R = radius of secondary coil in inches 
> > L = length of secondary coil in inches 
> >
> > for the first coil I get C = 22.0pF 
> > for the second coil I get C = 23.54pF 
> >
> > So now we know the effective capacitances for both coils. 
> >
> > Using the resonant circuit formula (also at the site above): 
> >
> > F = 1 / (2 x pi x SQRT(L x C) 
> >
> > F = frequency in hertz 
> > L = inductance in henrys 
> > C = capacitance in farads 
> >
> > The first coil gives: 
> >
> > F = 1 / (2 x 3.14159 x SQRT(0.0606 x 22 x 10^-12) = 137.84KhZ 
> >
> > and the second coil gives: 
> >
> > F = 1 / (2 x 3.14159 x SQRT(0.0550 x 23.54 x 10^-12) = 139.87KhZ 
> >
> > Thus, the two coils have very close to the same frequency around
> > 139kHz. 
> >
> > See how easy that is :-))  Ok, there are a bunch of computer
> > programs around that will do all this easily but this is the "stuff"
> > behind how those programs work. 
> 
> 
> 
> 
> 
> 
>