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Re: Calculation of Q?



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On Sat, 08 Mar 1997 18:11:22 -0600 Tesla List <tesla-at-pupman-dot-com> writes:
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>Date: Sat, 08 Mar 1997 15:53:45 -0500
>From: Steve Falco <sfalco-at-worldnet.att-dot-net>
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>Subject: Calculation of Q?
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>I came across an equation for calculating the Q of a solonoid coil in
>the ITT book "Reference Data for Radio Engineers". The formula is:
>  Q = A * d * sqrt(f)
>where A is a coefficient that varies with the ratio of 
>Length/Diameter,
>d is the diameter in inches, and sqrt(f) is the square-root of the
>frequency in megahertz.
>
>Some approximate values for A:
>  A=102 when L/D=1
>  A=120 when L/D=2
>  A=130 when L/D=3
>  A=135 when L/D=4
>  A=137 when L/D=5
>
>I tried using this formula with a number of different theoretical
>coils.  In each case, I calculated a Q value which was about 2.7 times
>higher than that obtained from the TESLAC program.  I don't know if
>TESLAC derates the Q by a fixed factor to account for empirical 
>losses,
>or if the difference is due to something else.
>
>The ITT book does state that the above formula is only good when the
>thickness of the wire is > 2.5 times the skin depth of the current. 
>Also, the formula assumes the winding density is between 40% and 80%.  
>I
>believe typical secondaries are more nearly at about 95% winding 
>density
>(i.e. closewound).  Perhaps these items account for the difference.
>
>Does anyone have a (reliable :-) formula for the Q of a solonoid given
>the typical dimensions and winding density of a Tesla coil secondary?
>
>	Steve Falco
>	sfalco-at-worldnet.att-dot-net
>
>
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    Steve,

  TESLAC calculates coil Q by first determining the RF (not DC!!)
resistance
of the wire used in the winding, and then dividing that value into the
calculated
reactance of the winding at the coils self resonant frequency. This is
the 
classical method of Q calculation for series resonance. Then the Q value
optained is "derated" in a attemp to compensate for the coil form,
coupling to
the primary and such other things that reduce the effective Q of the
coil.
 TESLAC calculation of Q is NOT absolute, and no other programs
calculation
is either, they are best used in comparisons between one coil design and
another.  The main thing I've found in high Q coils is LOTS of inductance
and
coil diameter,  it rather seems that any wire size that will allow 800 to
1000
turns close wound at a H/D ration of 2.5 to 3.5 to 1 will result in a
pretty decent
secondary coil in a standard tesla coil.

			Mark Graalman






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