LTR Coils and Cap Sizing

[Terry Fritz <twftesla-at-uswest-dot-net>]

Hi All,

	Let me try and explain some of the LTR stuff for those that have not
followed all this over the years.

There are three "sweet spots" or optimal values of capacitors for a given
transformer voltage and current (NSTs or current limited transformers).
These values allow the maximum power to be drawn from the transformer.

The first is the old resonant value of capacitor.  The transformer acts like
it is being current limited by an inductor.  There is a specific value of
capacitance that will cancel the current limiting inductance of the
transformer.  Thus, it can basically run without much current limiting.
That value is:

C = I / (2 x pi x F x V)

Where:

C = the resonant capacitance value in Farads
I = The transformers current rating in amps RMS
pi = 3.14159...
F = The line frequency (50 or 60 Hz)
V = The transformers rated voltage (volts RMS)

There is one big problem with running at the resonant values.  If the gap
does not fire and the safety gaps don't fire, the voltage will ring up to
incredibly high values (like 80,000 volts!).  Resonant systems need
something to drain the system of energy.  If the gaps fail to fire for any
reason, something WILL blow up!  There is a law of nature that says the
thing you cherish most will be the part that blows :-)  Rotary gaps are
often not recommended on these systems since the gaps my fail to align at
some critical moment and the voltage my skyrocket and blow something.
However, if you have a very good static gap in parallel with the rotary and
it is properly set to fire just above the transformers maximum voltage (like
a safety gap), it will be fine.  The problem is you HAVE to do it all right
the first time!  Also, if things are not all set just right, the static gap
may fire a lot and the natural response is to widen the static gap until it
does not fire.  That "will" stop it from firing, but it will probably stop
everything from firing permanently!!  In general, it is not recommended
using rotary gaps with resonant systems unless you really know what you are
doing.  Just too much can go wrong.  Static gaps are far safer since they
will fire at anytime the voltage reaches the firing voltage.  However, you
should ALWAYS have safety gaps too.  Resonant systems also tend to have a
fairly high break rate which places greater stress on the capacitors and can
cause gap heating and flaming problems (this probably wastes power too).  Of
course, NEVER "readjust" safety gaps!!  I hear all too often of that being
the last adjustment before the transformer died...  If the safety gaps are
firing, something else is wrong.

Resonant systems performance can also be "improved" dramatically by
increasing the gap width (and thus raising the firing voltage).  However,
that is a sure way to blow the system up, but those longer sparks are a
giant temptation that draws people in :-))

Resonant systems are easy to make and the cap values are easy to calculate.
They also tend to use smaller caps which are easier to make if you are using
beer bottles or other tight budget capacitors.  Many beginners use resonant
systems for this reason but they also can go through a lot of transformers
until they understand everything.  If you use resonant capacitance values,
ALWAYS use safety gaps!!


The next "magic value" is the "LTR" or "Larger Than Resonant" value.  Here,
we increase the capacitor size until the transformer will just barely charge
the cap to full voltage in 1/120th of a second.  With just the cap and
transformer, the voltage simply cannot get above the transformer's rated
voltage because the capacitor is just too large for the transformer to
charge any higher in the time given.  This eliminates the skyrocketing
voltage problem of the resonant systems.  The system will now run at 120 BPS
which is slower than the resonant systems but the larger cap size stores
more energy to make up for the lower firing rate.  In fact, it seems like
performance is a bit better due to the streamers "liking" 120 BPS more than
higher break rates.  These systems like rotary gaps but static gaps work
fine too. 

There is no easy formula for finding the exact "best" size cap.  However,
multiplying the resonant value by 1.5 gets very close and is good enough so:

Cltr = Cres x 1.5


The last value is a variant of the LTR.  If one carefully sets a sync rotary
gap to fire at 3.5mS after to AC zero voltage crossing, the energy stored in
the inductance of the transformer can be more efficiently pulled out of the
transformer to charge "really big" cap values.  This is commonly referred to
as the "inductive kick effect".  Much like breaking a current circuit of a
large inductor to get a big voltage spike.  The energy in the inductor can
be transferred to the cap by careful value selection and gap timing.  If the
gap stops firing in these systems, the capacitor voltage will actually drop
substantially, as odd as that sounds.  You have to turn up the voltage
considerably just to get the firing started too.  The advantage here is that
you can charge very large caps to full voltage.  My 15/60 coil has a 28nF
cap and my 9/30 coil uses 24nF.  Very large values for these transformers
but they still charge to the transformer's rated voltage at 120 BPS.  The
current is a bit higher than the transformer's rating (~1.5X) but this is
not a problem since the tranny is at room temperature and all.  These are
the most efficient NST systems of all.  They are also the most technically
complex, but not excessively so.  Interestingly, these systems were born
from computer modeling and optimization rather than actual trail and error
testing.  They were running on computers before the hardware was actually
proven to work.  Sort of a "triumph" of Tesla coil computer modeling!!  I
always like to point that out to those that don't quite agree with us that
"build" our coils with a keyboard ;-)))

The cap size for these systems are given by:

C = 0.92 x ( Vo x Io - L ) / ( BPS x Vo^2 )

Where:

C = Capacitor value in Farads
Vo = Transformer RMS output voltage (volts)
Io = Transformer RMS output current (amps)
L = known system loss (protection filter) (watts)*
BPS = Breaks Per Second

*For filters like I use:

Lr = (BPS x Cr x Vf^2) / 4 + 2 x Ir^2 x Rr 

Where:

Lr = Power lost in filter (watts)
BPS = Breaks Per Second
Cr = Capacitance per leg (Farads)
Vf = Actual firing voltage (transformer rating x 1.414)
If = Actual Transformer current (transformer rating x 1.5 for inductive kick
LTR coils)
Rr = Resistance value per leg.

Note that 1/2 Lr is the power dissipated in each protection resistor.  They
are always larger to get voltage stand off and to keep the temperature lower
than the 350C!! they "normally" like to run at.  I also highly recommend to
use full protection filters and transformer fusing for these systems.  There
is a lot of power and stored energy and they can "go nuclear"...


So, with a given NST, these are the three options.  I do not recommend
resonant systems.  The LTR system is just as simple and the extra time
making a bit larger cap will be saved in hunting down replacement NSTs...
Inductive kick LTR coils require rotary sync gaps and MMCs or other stable
and precise value capacitors.  However a standard LTR coil can easily be
expanded to an inductive kick coil with the addition of a sync gap and more
capacitance.

Cheers,

	Terry