NST power rating -- another perspective

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

Original poster: "Gerry Reynolds" <gerryreynolds-at-earthlink-dot-net> 

A different perspective:

I have a 4500 Vrms 22ma transformer (100VA).  The primary resistance is 
17W.  The secondary resistance is 22.1KW.

The issue of power transfer, I believe, can better be understood by 
starting from a simple model and progressing from there.  I will thevenize 
the transformer to start.

First the turns ratio is 4500/120 or 37.5.  The open circuit output voltage 
is 4500 Vrms and the short circuit output current is 22ma.  The thevenin 
output impedance is 4500Vrms/22ma or 205KW.  I will transform the primary 
resistance to the secondary 17W * n^^2 or 23.9KW and add this to the 
secondary resistance of 22.1KW for a total thevenin resistance of 
46KW.  The primary leakage flux has already been accounted for by the short 
circuit current measurement.  Next, I will decompose the 205KW into its 
reactive and resistive component. Xl will be 200KW (or 530 heneries) and Rs 
is 46KW.  Therefore, the simplified NST model will be:

     Vs = 4500 Vrms
     Ls = 530
     Rs = 46KW

The next step is to add a linear load (a pure ideal C with no esr).  I will 
not (at this time) add a sparkgap nor a load resister.  I will pick C to 
resonate with Ls at 60 hertz.  Xc and Xl will cancel and the current will 
be limited only by Rs.  The output current will be 4500V/46KW or ~100ma 
(note much greater than the 22ma rating).  Question: what is the power 
across C.  Answer:  Zero real power, it is all reactive power.  At peak 
voltage, there is zero current.  At zero voltage, there is peak 
current.  If one were to calculate the instantaneous power vs time, it 
would go positive and negative and the average power would be zero. Now, 
lets get maximum real power transfer.

Realizing in a linear circuit, the only time one can get real power is with 
resistance (I^^2 R). The maximum real power transfer will be with Rl 
matched to Rs.  If we add Rl (=Rs) in series with C, the reactances will 
again cancel and the power transfered into Rl will be 1/2 * V^^2 / (Rs + 
Rl).  For this case, the power into Rl is 110 watts (higher that the VA 
rating of the transformer because we are running at resonance - not what it 
was spec'd for).

Now comes the complexity.  We add an ideal sparkgap that we can control 
"the when" and "how long" it fires.  We remove Rl and neglect the TC 
primary inductance for charging purposes.  The only components for this 
consideration is Vs, Ls, Rs, C, and the sparkgap (standard topology).  The 
TC primary in reality, will control the discharge rate of C and affect the 
energy transfer time.

This is a non linear circuit that often results in a lot of confusion 
(myself included so don't fret).  First, we realize that a charging 
interval (at 60 Hz) is 8.3ms, so we will fire the ideal sparkgap every 
8.3ms when Vc reaches peak.  For my coil, the energy transfer time is 18us 
(to 1st primary notch) and we realize this is much less than a percent of 
the charging time.  Lets assume all of the 1/2 CV^^2 energy goes thru the 
sparkgap and into the secondary never to be seen again.  Otherwords, lets 
open the sparkgap 18us after it fires.  Now we have a pseudo linear circiut 
that would normally not have any real power delivered (remember we removed 
the R in the load) but now we are removing real energy at a rate of 1/2 
CV^^2 times the break rate (BPS).  This real energy transfer rate is REAL 
POWER and has to be replaced by the charging circuit.  The hard question is 
how much is this REAL POWER, how do you optimize for it, and what other 
constraints do you need to consider (like not overvolting the transformer 
at resonance).  I'm still learning the answer to this but believe the best 
way is by simulation.  I DO believe the real metrix for spark length is the 
REAL POWER transfered thru the sparkgap and not the VA rating for the 
transformer (at least NST types).  This REAL POWER will certainly be 
porportional to VA (everything else being the effectively the same), will 
vary with Cp, the sparkgap setting, and the resultant BPS (static 
gaps).  It will probably be very close to the POWER measured in the line 
cord using a WATT meter (I^^2 R loses in the transformer would need to be 
factored out).  The actual line cord VA could be significantly larger than 
the VA rating of the transformer and will ultimately depend on your chosen 
operating point.

Hope this adds some clarity to a very muddy subject.

Gerry R
Ft Collins, CO