Re: Space winding question

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

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. 


>
> 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.