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Re: Primary Qs

Tesla List wrote:
> 
> >From MALCOLM-at-directorate.wnp.ac.nzMon Sep 30 22:40:12 1996
> Date: Tue, 1 Oct 1996 16:03:18 +1200
> From: Malcolm Watts <MALCOLM-at-directorate.wnp.ac.nz>
> To: tesla-at-pupman-dot-com
> Subject: Re: Primary Qs
> 
> All,
>        I'd better add a note to the measurements (with the CP cap)
> that I've just posted. I used the logarithmic decrement to calculate
> Q but it is obviously wrong where a linear decrement is concerned
> as Mark Barton has pointed out to me. My thoughts :
>      The thing we have to look for is a change in amplitude per cycle
> to make any real meaning of this, in other words, the slope of the
> decrementing waveform.
>      Thinkin' out loud: If you adjust the scope timebase so that the
> cycles from different circuit configurations (different frequencies)
> are plonked one on top of the other, we're looking for differences
> in amplitude degradation in defining the Q's. I came up with a linear
> equation that I'll throw open for comment :
> 
>     Q = n*A0/(A0-An)  where A0 is the amplitude of some cycle,
>                       An is the amplitude of some succeeding cycle n
> and n is the number of cycles over which A0-An is measured. Since Q
> is defined as energy retained/energy lost per cycle, and energy is
> proportional to V^2, this may need some modification, perhaps :
> 
> Q = n*A0^2/(A0^2 - An^2) ??
> 
>      Thoughts on this one please. I need help (hopefully not
> psychiatric :)
> 
> Malcolm

Malcolm,

Excellent insight! In previous measurements of my primary, I hadn't
noticed that the decrement was linear instead of exponential - back to
taking some more measurements!

Your bottom formula is very close, needing only a factor or 2*Pi as a
multiplier (per Terman, in a footnote discussing series RLC circuits in
"Radio Engineering", Third Edition, McGraw-Hill Book Co, Inc, 1947, pp.
39-40): 
  
  Q = 2*Pi*(Energy stored in circuit)/(Energy lost during one cycle).

Your formula would become:
  
  Q = 2*Pi*n*A0^2/(A0^2-An^2)  (approximately)

If you are correct, the gap's resistance is inversely proportional to
the current (Rgap = x/Igap from your other post), and the gap resistance
is apparently rising with decrementing current in a manner which
_approximates_ a constant power loss/cycle. Even if this is non-linear,
the "average" Q over the measurement interval should be computable with
your formula. This looks like better news re: gap efficiency!

Keep up the excellent work! 

Safe coilin' to ya!

-- Bert --