Re: Recycled: Measuring Coupling Coefficients

From: 	Malcolm Watts[SMTP:MALCOLM-at-directorate.wnp.ac.nz]
Sent: 	Sunday, December 07, 1997 2:24 PM
To: 	tesla-at-pupman-dot-com
Subject: 	Re: Recycled: Measuring Coupling Coefficients

Hello All,
            I had a think about my post on this subject over the 
weekend and realized that I had included a false piece of 
information, namely that transfer time = infinity at critical 
coupling. That is clearly untrue. Aside from that, I'm happy with 
what I said. However, I can differentiate between k and kc 
considerably more lucidly:

    k  relates to shared flux linkages between the coils and is the 
sole arbiter of rate of energy transfer. Transfer time varies from 
infinity (k=0) to zero (k=1).

   kc  relates to aggregate resistive losses in the system. It just 
so happens that if kc matches k the system is critically coupled. The 
balance is loss/time vs transfer time. 

In a good 2 coil system, we want to transfer energy far faster than 
the rate it is lost at (unless it is being lost in a secondary 
discharge in which case the rate of transfer defines the rate of 
loss). If this happens, you can see that kc must have changed to be 
equal to k. That implies that the Q of one or both coils has changed. 
Q for a tuned circuit embodies any loading it is subjected to and in 
the case of kc defined as 1/SQRT(Qp.Qs), it is pretty obvious that 
Qs has dropped due to the loss of energy from it to output sparks.
So as the secondary becomes loaded, kc *rises* in value until it = k
beyond which it cannot go. The way around this is to get all the 
energy into the secondary before a discharge issues in which case one
does *far* better than critical coupling.

Hope this is easier to follow.