Re: How do you measure couplin

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

Original poster: Peter Lawrence <Peter.Lawrence-at-Sun.COM> 

Antonio,
         is there an exact mathematical formula for the voltage and current in
the primary verses time in a TC (a hypothetical one with no losses) (ie a
losely coupled dual resonator).

I'm guessing its proportinal to either sin(C*t)+sin(D*t) or sin(C*t)*sin(D*t)
for suitable constants C,D that depend on Fres and K...

thanks,
-Pete Lawrence.



 >Resent-date: Thu, 18 Sep 2003 20:23:52 -0600
 >Date: Thu, 18 Sep 2003 20:20:53 -0600
 >Resent-from: tesla-at-pupman-dot-com
 >From: Tesla list <tesla-at-pupman-dot-com>
 >Subject: Re: How do you measure couplin
 >Resent-sender: tesla-request-at-pupman-dot-com
 >X-Sender: teslalist-at-twfpowerelectronics-dot-com
 >To: tesla-at-pupman-dot-com
 >Resent-message-id: <c3kPK.A.lSE.chma_-at-poodle>
 >MIME-version: 1.0
 >X-Loop: tesla-at-pupman-dot-com
 >X-DCC-neonova-Metrics: dick.jymis-dot-com 1127; Body=2 Fuz1=2 Fuz2=2
 >X-Mailing-List: <tesla-at-pupman-dot-com> archive/latest/14849
 >Original-recipient: rfc822;Peter.Lawrence-at-Sun.COM
 >
 >Original poster: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br>
 >
 >Tesla list wrote:
 >
 > > Original poster: Peter Lawrence <Peter.Lawrence-at-Sun.COM>
 >
 > > a coil operating in 9:10 mode has a K of ~0.10497 from one of your
 > > formulas: k=(b^2-a^2)/(b^2+a^2), and takes b/2 cycles => 5 to the
 > > "first notch".
 >
 >This is correct. 5 full cycles in the primary voltage until the
 >first notch, or 10 full cycles in a complete beat. The interpretation
 >of cycles in this case, where there ate two frequencies in the waveform,
 >is "interval between two peaks of the same polarity". But this is
 >also 10 cycles of the higher frequency.
 >The time must be this, because the two oscillations start with the
 >same polarity and the same amplitude. The first notch occurs when they
 >add destructively, at 5 cycles of the higher frequency and 4.5 cycles
 >of the lower frequency. Note that this formula only makes sense
 >when there is complete energy transfer (b and a integers with odd
 >difference).
 >
 > > someone else recently posted a formula that says the number of 
oscillations
 > > it takes for the energy to transfer from the primary to the secondary is
 > > sqrt(1-k^2)/k, which for 0.10497 computes to ~9.42, which is about double
 > > the b/2 that you state.
 >
 >The correct formula would be:
 >Number of full cycles until first notch=(k+1+sqrt(1-k^2))/(4*k).
 >I just substituted a=b-1 and found b/2. This relation is valid for
 >a=b-1, but this is the usual case. It's possible to have a=b-3,
 >for example, but this results in a "false" first notch at 2.5 cycles,
 >without complete energy transfer, before the true complete energy
 >transfer at 5 cycles.
 >
 > > I can see how it is real easy to lose track of whether you're counting
 > > full cycles or half cycles, whether you're measuring cycles relative 
to Fa,
 > > Fb, or Fres, and I'm sure there are other simple things to 
accidentally drop
 > > out of a description of how to use a formula.
 >
 >Another formula, more basic: If the two resonance frequencies are
 >a*f0 and b*f0, the energy transfer takes 1/(2*f0) seconds.
 >
 >Antonio Carlos M. de Queiroz
 >
 >