Inductor coil parasitic capacitance, using the cosh function - diyAudio
 Inductor coil parasitic capacitance, using the cosh function
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 11th January 2017, 05:53 PM #1 diyAudio Member   Join Date: Jul 2004 Location: Scottish Borders Inductor coil parasitic capacitance, using the cosh function I have a formula for predicting the capacitance of an air core inductor. Cparallel (pF per turn) = B * Er / {11.45*cosh^-1(S/D)} where B = coil diameter mm Er = dielectric constant (of air) = 1 S = gap between the coil turns mm D wire diameter mm I think cosh^-1 is the inverse cosh function. Can I get a scientific calculator to give that answer, when S/D = 1? If I press 2ndF, then hyp, then cos (1), I get 0 or hyp, then 2dF then cos (1), I get 0 or hyp, then cos (1), I get 1.54 Any idea if any of these answers could be correct? __________________ regards Andrew T. Sent from my desktop computer using a keyboard Last edited by AndrewT; 11th January 2017 at 05:58 PM.
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Quote:
 Originally Posted by AndrewT I have a formula for predicting the capacitance of an air core inductor. Cparallel (pF per turn) = B * Er / {11.45*cosh^-1(S/D)} where B = coil diameter mm Er = dielectric constant (of air) = 1 S = gap between the coil turns mm D wire diameter mm I think cosh^-1 is the inverse cosh function. Can I get a scientific calculator to give that answer, when S/D = 1? If I press 2ndF, then hyp, then cos (1), I get 0 or hyp, then 2dF then cos (1), I get 0 or hyp, then cos (1), I get 1.54 Any idea if any of these answers could be correct?
cosh(x)=(e^x+e^(-x))/2=(e^x+1/e^x)/2

If cosh(x)=1, then the only option is e^x=e^(-x)=1 (since y+1/y=2 has y1=y2=1 as solution), which in turn means x=0.

 12th January 2017, 05:28 AM #3 diyAudio Member   Join Date: Jul 2004 Location: Scottish Borders Unfortunately that makes the C/turn to be infinity since the cosh^-1 is in the divisor. __________________ regards Andrew T. Sent from my desktop computer using a keyboard
 12th January 2017, 09:38 AM #4 diyAudio Member   Join Date: May 2007 I guess that means the formula is wrong. Is it possible that you have misunderstood the formula, and perhaps S is not the space between turns but the distance from wire centre to wire centre? That means that turns which are touching will have S=D, at which point you might expect quite high capacitance. Not infinite capacitance, but the formula probably only works when there is some space.
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I copied the formula from here and although they say that S = distance between , the drawing does show what you suggested. Centre to centre rather than gap/space.
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 capacitance of coil.png (74.1 KB, 86 views)
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regards Andrew T.
Sent from my desktop computer using a keyboard

 12th January 2017, 09:50 AM #6 diyAudio Member   Join Date: Jul 2004 Location: Scottish Borders Back to the question: how can I use a scientific calculator to find cosh^-1? so that I can see comparisons of close spaced coils with wider spaced coils. __________________ regards Andrew T. Sent from my desktop computer using a keyboard
 12th January 2017, 10:29 AM #7 diyAudio Member   Join Date: May 2007 On my calculator (Casio fx-570) it appears that 'hyp' and 'inv' can be pressed in either order to get inverse cosh. I suggest you play around with a few known values (cosh itself is easy to calculate, as it is the average of two exponentials).
 12th January 2017, 10:46 AM #8 diyAudio Member   Join Date: Jul 2004 Location: Scottish Borders My Sharp does the same: hyp > 2ndF > cos (number) gives the same result as 2ndF > hyp > cos (number). And for S/D = 1.005 (very thin insulation on touching coils) cosh^-1 (1.005) results in 0.09996 and for big gaps equal to wire diameter cosh^-1 (2) = 1.317 i.e. the capacitance has gone down by 92%. That's an enormous reduction in parasitic capacitance. But the inductance will also have gone down so I would need more coils pushing the capacitance back up a bit. Thanks Waly & DF. However there are a few discussions on calculating parasitic capacitance of single layer coils and there seems to be much disagreement on what formulae can be relied on to give sensible answers. One formula gives Cparasitic = coil diameter * X irrespective of the number of turns nor of the wire diameter. __________________ regards Andrew T. Sent from my desktop computer using a keyboard Last edited by AndrewT; 12th January 2017 at 10:54 AM.
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Quote:
 Originally Posted by AndrewT Back to the question: how can I use a scientific calculator to find cosh^-1?.
If it isn't on your physical calculator, you can use the windows scientific calculator:
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 Wincalc.png (46.3 KB, 75 views)
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 12th January 2017, 11:10 AM #10 diyAudio Member   Join Date: Jul 2004 Location: Scottish Borders Again, thanks. I use the scientific Windows calculator and it loads up that way why I open it. But I forgot to go and look ! And it gives the same answer, provided I enter the number first and then inv > cosh. __________________ regards Andrew T. Sent from my desktop computer using a keyboard

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