Re: Explanation of K

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

Original poster: "Antonio Carlos M. de Queiroz by way of Terry Fritz <twftesla-at-qwest-dot-net>" <acmq-at-compuland-dot-com.br>

Tesla list wrote:
> 
> Original poster: "Jason Petrou by way of Terry Fritz
<twftesla-at-qwest-dot-net>" <jasonp-at-btinternet-dot-com>

> Basically the coupling (K) determines the rate of voltage rise in the
> secondary coil. A low coupling will mean a relatively slow voltage rise and
> poor energy transfer, because the primary rings for longer and wastes more
> energy. A very high coupling will mean a fast energy transfer, but a great
> potential difference in the secondary. The fast rising difference between
> the top and the bottom of the coil causes the racing arcs. The trick is to
> couple as tightly as possible without racing arcs.

Allow me to disagree with the last two phrases. If you look at the
waveforms deduced from the lumped model, there is no significant
difference
in rising time, dv/dt, di/dt, etc., anywhere in the system when the 
coupling is high. "Racing sparks" can't be caused by this, at least 
not directly.

Returning to the original question, when two coils are not too distant,
it the current varies in one of them, the magnetic field generated
affects
the other coil too, inducing a voltage across it. This voltage (v2) is
proportional to the rate of change of the current (i1), by a 
proportionality constant called "mutual inductance" (M):
v2=M*di1/dt
If you try to interchange the coils, you will see that M doesn't change.
For serious physical reasons, M can't be greater than the square root
of the product of the inductances of the two coils (L1,L2):
M<sqrt(L1*L2)
The coupling coefficient is just the adimensional ratio:
k=M/sqrt(L1*L2)
It measures how close to the maximum possible M is, varying between
0 to 1.
In a Tesla coil, k controls in how many oscillations the energy transfer
takes place, as described in the previous answer.

Antonio Carlos M. de Queiroz