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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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