RE: K formula?

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

Original poster: "Malcolm Watts by way of Terry Fritz <teslalist-at-qwest-dot-net>" <m.j.watts-at-massey.ac.nz>

Hi John,

On 29 Jul 2003, at 11:59, Tesla list wrote:

 > Original poster: "John H. Couture by way of Terry Fritz 
<teslalist-at-qwest-dot-net>" <couturejh-at-mgte-dot-com>
 >
 >
 > There is another method of finding the K Factor. This is a much simpler
 > method and you have a better chance of getting it right.
 > Or do you?
 >
 > Find the resonant frequency first
 >     Fr = F1 + (F2 - F1)/2
 >        = 193.42 + (216.1 - 193.42)/2
 >        = 193.42 + 11.34
 >        = 204.76
 >
 >      K = (F2 - F1)/Fr
 >        = (216.1 - 193.42)/204.76
 >        = 0.110763
 >
 > Note that this gives you a slightly different K Factor. The other K factor
 > is 0.1104. Which is correct? Rounding off numbers or avoid squaring numbers
 > when possible?

The other one is correct. The one you've used is an approximation
whose answers get more inaccurate as k increases. The reason this is
so is the built-in assumption that F2 and F1 are equidistant from Fo
which they are not. In fact, as k -> 1, the upper frequency ->
infinity and the lower to SQRT(2)xFr.

Malcolm
<snip>