Calculating LTR

Hazmatt_(The Underdog), Mon Sept 11 2006, 12:59AM

I'm taking a look at all the details in greater scrutiny then what I probably should be, but the issue is I want to know that what I am doing is efficient. I am also trying to expand and improve SGTC's with a wealth of information glossed over by most Coiler's.

Insted of using a correction factor, I want to know what is the reasoning behind LTR, and I have some answers for all of you, but this will mean a lot of work on your part to solve your particular problem.

Here we have the extracted equavilent circuit of a 9000VAC 120mA NST as the source for a nasty Tesla Coil I am designing for C.S.U.L.B. This system needs to be efficient and effective because of portability, power, cost, and other factors.

As you can see from the system I have performed the load/unloaded tests to find all the related characteristics from the transformer. The details for this can be found on our local Wiki.

In playing with the transformer we find the resonant charging defined from Z = E/I.

9000 VAC / 120mA = 75000

And to find the resonant Capacitor value we have simply

Z = 1/(2piFZ) = 35.4nF at 60Hz.

This is a good start, but not our LTR value. So what exactly is a proper LTR value?

Let us consider only the inductive component of the Transformer now as something critical. This value can be seen on the schematic as 61H. This is the extracted inductance of the transformer during power on. It is not the measured static inductance of the core. These two inductances vary greatly. If you attempted to measure the inductance of the secondary windings you would find that the inductance of this transformer is ~200H per coil, no where near the 61H powered-on.

So let us consider the reactive component: XL = 2piFL = 23000

And the Resistive component = 17000

Taking the magnitude of the two gives us our Zbranch equavilent of 28600, but lets consider it to be 28000 to be conservative.

Subtracting our Z from XL gives us: 75000-28000 = 47000 = Z'

Now Z' is our impedance of our system that the transformer should be matched to the capacitor. Lets see what the value is

C = 1/2piFZ' = 51nF Wow! our LTR Value.

Now lets go to simulation to see how this matches up and see if our predictions are true.



You can see in the graph that the power distribution is pretty accurate and gives a region of 1100W in the capacitor. This is critical because a correction factor may not approximate the actual inductances and losses inherent in a given transformer.

To do this analysis on a transformer requires a Wattmeter. I bought one from Extech for about $200 USD. Simply loading the transformer is not good enough because you need the power factor for the analysis. The clamp-on wattmeter gives you power factor.