Re: Racing Spark Prediction

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: Paul Nicholson <paul@xxxxxxxxxxxxxxxxxxx>

Hi All,

Just a few more comments on the effect of coupling, as
seen in a frequency sweep.

Imagine you have a dual resonant TC with a signal generator
feeding the primary, a scope probe on the secondary topload,
with the sig gen set to sweep mode and the scope in xy mode
with the x axis driven from the sweep.

Start out with very low coupling to obtain a single small
peak on the scope.  As the coupling is increased, the peak
will rise in amplitude, eventually reaching a maximum
height.  This point of maximum amplitude response is called
critical coupling:-

 k_crit = ((Qp * Qs)^2 + Qp^2 + Qs^2 + 1)^(-0.25)

where Qp, Qs are primary and secondary Q factors, and the
formula assumes the uncoupled Fpri = Fsec.   For example if
pri and sec have Q=30, k_crit comes out to be 0.033,
and if Q=100, k_crit is 0.01, so quite small couplings
compared to normal TCs.

Further increase in coupling causes the height of the peak
to fall and the top of the peak starts to become noticeably
flattened.   At some point the center of the flat peak
starts to form a dip.  This is transitional coupling:-

 k_trans = sqrt( 0.5 * ((1/Qp)^2 + (1/Qs)^2))

k_trans is usually higher than k_crit.   But if by some
unlikely coincidence you happen to have Qp = Qs = Q, say,
then

 k_crit = 1/(Q^2 + 1)
 k_trans = 1/Q^2

so they are virtually equal for coils with reasonable Q.

Normally, one or other coil with have a higher Q than the
other (it doesn't matter which) and then k_crit is smaller
than k_trans.

Things that could upset the sweep measurement:-
a) Secondary Q limited by scope probe loading: 1Meg applied to
   a resonator of say Zo = 50k would limit the Q to about 20.
b) Primary Q limited by sig gen output Z. The generator must
   be padded to very low Z - with a primary Zo (surge impedance)
   of say 20 ohms, a 1 ohm pad will limit the Q to about 20.
c) Sweep rate: if the sweep rate is high, the effective bandwidth
   of the sweep signal itself may be greater than Fres/Q and
   the response peaks will be blurred into broader humps.  High
   Q coils need slow sweep rates.

Above k_trans we are into the realms of normal TC coupling
coefficients, where k might be 5 or 10 times k_trans. The beat
period 1/(F_high - F_low) becomes short compared to the decay
time - we get several complete beats before the energy decays
and the two humps of the frequency response become very distinct.

Gerry wrote:
> I could be wrong but I have a suspicion that DC's critical
> coupling is not the same as your transitional coupling.  Im
> thinking he is intending the use of "critical coupling" to mean
> the coupling below which we shouldn't experience  racing sparks.

Maybe.  His procedure for avoiding racing arcs is obviously
effective in practice, but we don't know why.

> I dont know if he has swept his coils and found no double hump.

D.C. wrote:
> we always check our coeff. of coupling right to the peak where
> it starts to split and then reduce it a bit in our initial
> design work.

> A signal generator is used having it's frequency swept in
> synchronism with the time base of the oscope.  The double hump
> is clearly visible when the primary to overcoupled to the sec
> coil.  Back off this point until the double hump disappears and
> you have set the optimum coupling point for your coil.

It was the above that caught my attention - the procedure would
produce a very low coupling equal to k_trans or less.  His coils
work so there must be something not right with the sweeping or
our understanding.

Perhaps D.C. will elaborate.
--
Paul Nicholson
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