Re: TESLA COIL REVISED

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

Original poster: Paul Nicholson <paul-at-abelian.demon.co.uk> 

Hi Jaro, All,

Further to the wealth of correct advice already given in this
thread:

The reason that secondary coil Q factor is not too important
in TCs is that

a) Other losses tend to dominate: mainly primary drive (gap or FET
    resistance), ground circuit resistance, and load resistance;

b) The TC is usually fairly heavily loaded so that the loaded Q is
    much less than the unloaded Q and efficiency is high as a result.

It is important to distinguish between two quite different modes of
operation of the TC:

1) The cap discharge type, in which the primary cap acts as a power
compression circuit;

2) The CW drive, in which there is no power compression and energy
is stored/accumulated in the resonant secondary.

(In both cases a kind of 'resonant rise' is involved, but the term
is too vague to be of much use in discussion).

In case (1) the output voltage is at most sqrt(Lp/Ls) or sqrt(Cp/Cs)
times the input voltage, and is reduced only a little by poor Q
factor due to (a) and (b) above.  Transfer of the compressed power
through the TC is very quick - only taking a few or several RF
cycles, and as a result there is time only for a few percent of the
input energy to dissipate in the secondary coil loss.  Increasing
secondary Q from say 50 to 500 would only make a few percent
increase in output voltage.  As the Q factor approaches infinity,
the output tends, not to infinity, but to Vin * sqrt(Cp/Cs), etc,
because only a finite quantity of energy is injected into the coil
with each cap discharge.

In case (2) the output voltage is at most Vin * Q, where Vin is
the equivalent CW voltage applied to the secondary base.  The Q in
this formula involves all the circuit loss resistances, not just
those of the secondary.  Unlike type (1), the energy accumulation in
the secondary takes typically many tens to a few hundred RF cycles,
and as a result secondary Q factor becomes more important, but is
still not the dominant loss.

For example, my CW TC secondary is about 90mH, with an AC
resistance of around 43 ohms (accounting for proximity and skin
losses - the DC res is only 7 ohms).  At the operating Fres of
91.5kHz the Q factor of the coil alone might in theory be
2 * pi * 91500 * 0.09/43 which is around 1200.  In practice the
measured values are nearer 200, suggesting a total loss resistance
of 2*pi*91500*0.09/200, which comes out to around 250 ohms. The
coil itself is only accounting for around 20% of the total losses.

In the CW case if the resonator Q tended to infinity, so would the
output voltage, because with CW drive, an infinite amount of energy
is available (in principle you can wait as long as you like while
more and more input power steadily accumulates in the resonator).
In practice, stored energy rises until it is leaking into the losses
at the same rate at which input power is supplied.  When this steady
state is achieved (after maybe a few hundred RF cycles) the output
is steady at a peak voltage of sqrt(Q*Pin/(pi*F*Cs)).

If the coil is well matched to the intended load, the load
resistance itself will dominate the operating Q, so that coil
resistance and other loss resistances are small in comparison. The
efficiency is then high and further reduction of coil resistance
only makes a marginal improvement in efficiency and output voltage.

For example, roughly, if I was to double the inductance of my coil,
or reduce its resistance by a half, I would only gain another 10%
on the output voltage.

So, resonator Q factor is only important in the CW case, because
the energy storage quality of the resonator is what counts
in that mode of operation.  But you must consider total loss
(including the output load) in determining the Q, and not just go
by the coil resistance.

Yes, you can make coils with few turns resonate with very high Q
at very high frequencies.  Q values of several hundred are possible
with silver plated coils inside silver plated cavities.  They give
hot and bright but short discharges, due to the high frequency
involved, not the small coil size.

With cap discharge TCs, the dominant losses are those of the
primary spark-gap and primary proximity loss.  Ground circuit
resistance comes a close third, secondary coil resistance trails in
at fourth place.  Despite these losses a well designed TC can
deliver over 60% of its bang energy to the output discharge. (Figure
comes from measurements on Terry's OLTC).

Naive reasoning (eg focusing too much on secondary inductance and
resistance) may lead the experimenter to try high frequencies
with few secondary turns.  But the other losses increase dramatically
as operating frequency is increased, so unless you have an
application which requires some particular high frequency, better
results overall are obtained with lower frequencies (35-300kHz) and
fairly high secondary turn counts (500-3000).  The low frequency
of modern TCs encourages long but not so bright discharges, which
seems to be the preferred fashion these days.

The point is, the operating frequency is a matter of taste, not
physics.  Go for a HF coil if you like, but don't expect long
streamers or high efficiency.  Examples are available in the ham
radio literature, eg base loading coils for short vertical antennas.

Jaro wrote:
 > you don't have to take my word for it ... here's what Tesla
 > had to say...

I'm afraid that quotes from Tesla don't carry much weight. A century
later we know a lot more about Tesla coils than Tesla ever did.  You
should study modern research, and beware the pseudo-scientific
drivel that lurks around the topic.  You've come to the right place
here on this list for reliable and up to date info.
--
Paul Nicholson
--