Theory of LTR Discussion from the Tesla List

Updated: 5-17-11

LTR Calcs

Q. 5-1-4 TL. What exactly is the LTR value of a cap? I understand for a static gap system it is pi/2 * the resonant cap size, but why. Also why should we use it?

Q. 4/30/2004, How do you compute the LTR cap value for a given transformer with a static gap? SRSG? I see that the Geek Group website has a table for a given range of NST sizes but what I'm after is the formula(s) to determine the recommended LTR cap value for a given transformer. I know how to determine the resonate cap value for a given neon but how do I arrive at LTR? I realize that the very nature of this thread suggests that the optimum LTR value might be up in the air. Daniel.

A. Terry F. Hi Daniel, Let me see if I can remember ;-)). Originally, LTR values were computed with long hard MicroSim simulations:

- http://hot-streamer.com/TeslaCoils/Misc/NSTStudy/NSTStudy.htm

The equations for MMC also were known:- http://hot-streamer.com/TeslaCoils/MMCInfo/MMCPower4.html

These were combined into the program here:- http://hot-streamer.com/TeslaCoils/programs/Mmccalc2.zip

A modern Excel version is here:- http://hot-streamer.com/temp/MMCcalc2.xls

These two programs were used by Mark Broker to make the GeekGroup chart that everyone goes by now. Eventually the equations were justified:- http://www.pupman.com/listarchives/2002/April/msg00038.html

Cheers, Terry.

Date: Fri, 11 Nov 2005 10:42:43 -0700 - Subject: Theory of LTROriginal poster: "Bob (R.A.) Jones"

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

Date: Mon, 14 Nov 2005 11:01:01 -0700 - Subject: Re: Theory of LTROriginal poster: "Dmitry (father dest)"

> Original poster: "Bob (R.A.) Jones"

> Hi all, I recently tried a different direction on the theoretical the optimum primary C (Cp) for a given inductive ballast (L)

is it only for nst using case? coz i for example choose the ballast for the Cp and the current i need, not vice-versa.

-----

The solution to no primary hits lay in getting rid of the primary! This is no joke either. 20-06-96 (c) Richard Hull, TCBOR

Date: Mon, 14 Nov 2005 11:05:44 -0700 - Subject: Re: Theory of LTROriginal poster: "Bob (R.A.) Jones"

Hi all,

I am reasonable confident I got it right. Here is the latest. It much simpler to consider the equivalent circuit of the SG and Cp as series Requ and Cp, where Cp is unchanged and Requ is the product of the impedance of Cp at the supply frequency, the sin of the firing angle relative to the charging current and the ratio of fundamental to peak of a square wave. The power dissipated in R per cycle is the bang energy. Note that the harmonics of the square wave are ignored but this produces only an approximately 5% error in firing voltage because of the amplitudes of the harmonics and the high impedance (relative to the supply frequency) of the L at their frequency.

It relatively simply (using AC circuit theory) predicts the optimum firing angle, C value for max bang size, bang size and PF in the synchronous SG case. It theoretically confirms the experimental and circuit simulation results that an LTR C has the biggest bang energy.

Robert (R. A.) Jones

Date: Mon, 14 Nov 2005 12:33:59 -0700 - Subject: Re: Theory of LTROriginal poster: "Bob (R.A.) Jones" <a1accounting

Hi Richard,

The equivalent circuit is just for the SG and C. I used it with an NST to determine the C for the biggest bang.

But its equally applicable to any ballast including inductive and inductive/resistive combination or primary ballast. It just requires that you can define the ballast impedance (constant impedance) so you can put that impedance in series with the equivalent circuit and do the ac analysis on it. The theory is applicable to a sync gap. But as a static gap has similar parameters in a LTR, STR sense you can use it for that as well.

Robert (R. A.) Jones

Date: Mon, 14 Nov 2005 21:37:26 -0700 - Subject: Re: Theory of LTROriginal poster: "Gerry Reynolds" <gerryreynolds

Hi Bob,

How did your results compare to the "standard" 2.8*Cres recommendation for LTR value when using SRSG (at 120pps).

Gerry R.

Date: Mon, 14 Nov 2005 21:48:41 -0700 - Subject: Re: Theory of LTROriginal poster: Harvey Norris

--- Tesla list wrote:

> It just requires that you can define the ballast

> impedance (constant

> impedance) so you can put that impedance in series

> with the equivalent

> circuit and do the ac analysis on it.

Of quite great interest also is the ability of a field regulated alternator to supply power. In a certain way the field regulated alternator, ( as a control factor measure) also represents a "ballasted" supply when hooked to the pole pig transformer. In fact at lower regulation values it may be safe to short out the stator outputs to determine how much availability of amperage that source can supply. Suppose the short reveals a 10 AMP supply at the specified open circuit voltage. Now suppose that we then use a capacitive reactance that should deliver the same 10 AMPS at the noted open circuit voltage. If fact what happens is that excess of 10 amps is drawn under those conditions, because the chosen capacitive reactance begins series resonating with the internal Z(int) value of the stator windings. Thus in actuality the method of using a short to the supply to determine maximum available amperage from the same supply is invalid; when using matched opposite reactance values.The objection that when NST's are used in this same kind of reactance matching; where that objection to overvolting the NST transformer is countered by using Larger The Resonant: LTR cap values as a load, would seem to be ruled unnecessary in the case of a well insulated pole pig to achieve the same objective. It may well be that "identical to resonant cap loads" or ITR values could then be successively employed with pole pigs themselves powered by the (properly) field regulated alternator. If we look at the Z(int) value of the pole pig itself being a perfect reflector that would cause its capacitive secondary load to achieve its same primary consumptive value as the secondary predictions would make; this is a serious error.

Predictions mean nothing when practical real world demonstrations show different results. The inductive reactance of an open secondary pole pig primary amperage measurement is SUPPOSED to be a linear relationship with regard to frequency input. The quantity of inductive reactance present in the pole pig primary measured by open secondary measurement at 60 hz is Supposed to be linear/ whereby 8 times the frequency input that should result in 8 times the measured inductive reactance is entirely untrue. Likewise the same linear supposition for large inductive reactive loads being linear is likewise entirely untrue. The relationship is quite more unlinear then people would assume by book learning.

But assumptions themselves can be deceiving. If a 30 ma rated short NST is driven at 8 times the pole pig imparted frequency by a smaller voltage inputed alternator, the shorted NST output THEN does show the same linear relationship, in that formerely at 60 hz I shows 30 ma on short, with 120 volt input/ but now it shows 30 ma/8 currents at short.( with the same 120 volt input @ 480 hz) In contrast however the same (resonant)capacity chosen as the pole pig load may provide a significant voltage rise.

These things may sound confusing however certain non- linearities are present when assuming X(L) to be a constant linear increased value with increase of frequency input. There is far more here to the eye then would initially appear.

Sincerely HDN

- 5-22-11

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