# Re: [TCML] MOT Measurements

```Hi All,

```
Regarding resonant rise here with these shunted transformers, I realize now where the confusion is. If you remember, Ted's 600W test MOT was found to be resonant at 2.25uF. The inductance was assumed to then be 4.5H:
```Xc = 1/(2 * pi * F * C) = 1/(6.28 * 50 * 2.25uF) = 1414.7 ohms.
Since Xc=Xl at resonance, L = Xl/(2 * pi * F) = 1414.7/(6.28 * 50 ) = 4.5H.

```
Seems logical, yes? The problem here is that this L is "not" the secondary inductance, but the leakage inductance of the MOT which the capacitor is resonant with (so yes Ted, your data was very helpful). The self inductances of the transformer are very different. They can be used to find the leakage inductance (and thus identify Cres).
```
Here's a series of equations for predicting an accurate Cres:
------------------------------------------------------------
w = angular freq = 2 * pi * F = 377
Cres = 1/(w * XLleak)
XLleak = w * Lleak
Lleak = L2 * (1-k^2)
```
k = sqrt[1-(Ioc/Isc)] where Ioc is the open circuit current and Isc is the short circuit current.
```L2 = L1 * Lratio
Lratio = turns ratio^2
turns ratio = Vout/Vin (open circuit  with low voltage to L1)
L1 = XL1/w
XL1 = Vin/Ioc where Ioc is the open circuit current of L1.

```
Let me walk through this. I obviously need to measure primary current with the secondary open and again with the secondary shorted. I also need to measure the secondary voltage at a low input voltage. Here are my measurements for 60.2V input.
```
Vin = 60.2V
L1 primary current with secondary open = Ios = 0.43A
L1 primary current with secondary shorted = Isc = 10.63A
---------------------------------------------------------
For turns ratio: Vin = 10.14 and measured Vout = 182V
---------------------------------------------------------
XL1 = L1 reactance = Vin/Ioc = 60.2 / 0.43 = 140 ohms
L1 = L1 inductance = XL1/w = 140 / 377 = 0.37136H
Turns Ratio = Vout/Vin = 182 / 10.14 = 18
Lratio = turns ratio^2 = 18^2 = 324
L2 = L2 inductance = L1 * Lratio = 0.3714 * 324 = 120.32H
k = sqrt[1 - (Ioc/Isc)] = sqrt[1 - (0.43/10.63)] = 0.9796
Lleak = Leakage Inductance = L2 * (1-k^2) = 120.32 * (1-0.9796^2) = 4.859H
XLleak = Leakage Reactance = w * Lleak = 377 * 4.859 = 1831.8 ohms
Cres = 1/(w * XLleak) = 1/(377 * 1831.8) = 1.45uF

I previously listed Cres at Vin, so let me use the above method and compare.

Microsim     Above method
Vin       Cres(uF)     Cres(uF)
------    --------     --------
10.14      1.39         1.39
20.00      1.34         1.35
30.20      1.37         1.36
40.20      1.32         1.35
50.10      1.35         1.38
60.20      1.47         1.45
70.20      1.57         1.57
80.00      1.72         1.70
90.10      2.20         2.18
100.00     2.34         2.37
110.10     2.68         2.68
120.20     2.83         2.93

```
Good correlation. The low inductance as viewed from an impedance standpoint at the transformer for Cres is not the secondary inductance, but the leakage inductance predominantly. I performed the same routine for a modified 12/60 NST, and the numbers came out just as close.
```
```
For an unmodified NST (shunts in tact), I expect Cres to be somewhat near what we would expect (maybe), but Cres will change depending on magnetizing current and current through the magnetic shunts. The shunts have inductance with the AC cycle, and as current is increased, the leakage inductance is increased. The result is a rather significant changing reactance dependent ultimately on the input voltage, and thus Cres will not be a constant throughout a voltage range (such as driving an NST with a variac). The impedance of a shunted transformer is not constant with varying input voltages (which is counterintuitive to non-shunted power transformers).
```
Best regards,
Bart

tesla wrote:
```
```Greetings again team, thanks all for comments on this interesting thread

```
I had a practical look tonight into the resonance effects of a MOT . I had been assuming that the thread was concerned with finding out what resonant rise would occur and at what capacitance of a single MOT without any primary ballasting in that cct.
```
METHOD
I used a normal 600 watt MOT with magnetic shunts in place.
```
I incremented the secondary load by 150nF steps up to 2.475uF and measured the voltage across the secondary. The source driving the MOT was a large Variac i.e. a voltage source and a very low source impedance.
```
The results were interesting.

```
With sufficient primary excitation to cause over well 10 amps of primary current at resonance the resonance was very slippery changing with excitation as saturation effects altered the inductance. It was possible to find excitation values where you could watch the whole system "pull" into resonance slowly At lower excitation resonance was stable and occurred at 2.25uF above that capacitance the voltage magnification dropped off very quickly. I did not measure the primary voltage but it was quite low of the order of 60 volts. The voltmeter was a digital panel meter version of Peter Terren's "High Voltage Meter" on his Tesla down-under site (a great site)
```
Some of the data points were

Load 0.6uF Secondary voltage out 398
Load 2.25uF Secondary voltage out 1352 (at or close to resonance)
Load 2.4uF Secondary  voltage out 513

```
The inductance seen by these capacitors is thus 4.5Hy in this configuration. Whether this is leakage L or transformed L from the primary side by N^2 or all of the above it seems to me that is the inductance the practical external load has to deal with when deciding what capacitive load will actually cause resonance.
```
```
Hope this is useful data, full data can be sent to anybody who would like it
```
Best
Ted L in NZ
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