Theory of LTR

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Original poster: "Bob (R.A.) Jones" <a1accounting@xxxxxxxxxxxxx>

Hi all,

I recently tried a different direction on the theoretical the optimum
primary C (Cp) for a given inductive ballast (L)
The maths is not finished but the direction appears productive. Here is the
short word version of it, minus many of the assumptions, for those into the
theory stuff.
First in a sync gap operating at the same break rate as twice the supply
frequency.
The Cp and its repeated discharge is equivalent to a square wave signal in
series with Cp but without the SG.
The amplitude of the square wave is equal to the voltage on Cp at the point
of discharge and has the same phase as the discharge but opposite polarity.
Considering only the fundamental of the square wave, the square wave  lags
the voltage on  Cp but with the opposite polarity so equivalently it leads
the voltage.
Hence the combination of Cp and squarewave generator has an impedance (at
the supply frequency) equal to a smaller C (Cequ) in parallel with a R.
(Requ)
The energy dissipated in Requ is equal to the bang energy.
Therefore maximum dissipation in Requ will be when the impedance of Cequ is
equal to the impedance of the ballast inductor. i.e. resonant.
As Cequ is smaller than Cp, Cp must be increased until its equivalent Cequ
is resonant with L to obtain the maximum power in Requ which is the maximum
bang size.

I am guessing but it will be similar with a static gap. The repeated
discharge of Cp advances Cp voltage relative to its charge current so again
the equivalent impedance (at the supply frequency) is equal to a smaller
capacitor and so the actual C must be made large to obtain the maximum bang
size.
The above may also explain why the maximum bang size is obtained when the
current in L is not zero. ie when the real current is a maximum there must
still be some reactive current.

Robert (R. A.) Jones
A1 Accounting, Inc., Fl
407 649 6400