# RE:

```Original poster: "Breneman, Chris" <brenemanc@xxxxxxxxxxxxxx>

Hi Chris,

```
The leakage inductance of the NST (as seen by its output) forms a series resonant circuit with the tank capacitance (Cp) that it is charging. The TC primary inductance is negligible compared to this leakage inductance and can be ignored. For NSTs. the winding resistance (in series with the leakage inductance) is also small enough to be ignored. Therefore, it is easy to measure the leakage inductance by measuring the NST's output impedance:
```
Zo = Vs_rms_open_circuit / Is_rms_short_circuit

```
If you don't make the measurement, the nameplate data is good enough. Because of the small winding resistance, it can be assumed that all the output impedance is due to the leakage inductance.
```
XL = Zo

```
The series LC circuit, therefore, has a series impedance of XL - XC. The minus sign is a result of the math of complex numbers. The following are the inductive and capacitive reactances of the series circuit:
```
XC = 1/(2*pi*freq*Cp)
XL = 2*pi*freq*Ls  = Zo

If you let XC = XL and solve for C you get:

Cp (at resonance) = Cres = 1 / (2*pi*freq*Zo)  or restated for nf:

```
Cres = 10^9 / (2*pi*freq*Zo) where freq is the line freq.
```

```
The multiplier (1.6) for a static gap is based on simulation that results in around 120 bps when the main gap is set for Vs_peak_open_circuit.
```
```
The multiplier (2.8) for a SRSG that operates at 120 bps is also based on simulation. The reason why this multiplier is higher is due to the ability of the SRSG to fire after peak voltage of the charging wave form. This sounds counter intuitive, but delaying firing until after peak allows some of the energy in the tank cap to back flow into the leakage inductance for the next and opposite firing. Other words, we sacrifice some energy from this firing cycle to get a head start on the next one. The result is a larger Vs_peak the next time around and a larger Vfire than if we were to time the firing for just Vs_peak. The main benefit of a SRSG is the ability to charge a larger Cp to our maximum voltage than what we could do with a static gap.
```
Gerry R

---------------------------------------------------

```
Thanks a lot Mike and Gerry, that's exactly what I wanted to know. But now I'm curious as to the derivation of that formula and the different LTR multipliers for the different types of spark gaps.
```
Thanks,
Chris

________________________________

From: Tesla list [mailto:tesla@xxxxxxxxxx]
Sent: Fri 1/5/2007 10:50 PM
To: tesla@xxxxxxxxxx
Subject: RE:

Original poster: Mike <megavolts61@xxxxxxxxx>

Hi Chris,
If you match the impedance of your NST  ( which
equals  12000/.03)   by using the equation:

C = 1/(2*pi*f*Xc)    you will have C =
1/(2*3014159*60*12000/.03)  and get 6.63nF.   If you use this,  you
can cause a resonant rise of voltage in your NST and possibly fry
it.   The value of 10nF,  or 0.01uF   will ensure your cap can take
all the energy from the transformer safely for the transformer.  If
you use both of the caps you were talking about  (.1uF and .03uF) in
series,  you'd still have .02uF.   You can make that work.   you will
just have a lower gap voltage and unless you have a LOT of turns on
your secondary,  it could prove harder to tune.   Still not that big a deal.
Mike

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```