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Registered Member #1875
Joined: Sun Dec 21 2008, 06:36PM
Location:
Posts: 635
So lately I've been trying to figure out how to relate capacitor ratings to what's really going on in a SGTC.
To figure out the peak current experienced in the primary circuit, I've come up with the following:
Take a capacitor bank of 120nF charged to 14400V in a circuit with Fres= 40kHz.
I = (dv/dt)*C
so Imax = (dv/dt max) *C
dv/dt max occurs at t = 0 (well, just after, but effectively and mathematically, t=0)
so taking the equation as V = (14400)*sin(40000x)
dV/dt = 14400*40000*cos(40000x)
at x = 0, dV/dt max = 576*10^6 V/s = 576V/uS
Imax = 576 (V/uS) * .120 (uF) = 69.12 A.
Please tell me where I went wrong, as I know that peak currents are supposed to be quite high, and I haven't even factored in losses like the spark gap!
69A from a big ol' 120nF, 14.4kV capacitor? Is it because my math is wrong or because my Fres is so low? Thanks!
Though 14400*69.12 does suggest close to a megawatt of power, so I don't know!
I feel like there should be a pi or something in the math...
[EDIT] should it be V = (14400)*sin(40000(2pi)x) so that would make dV/dt max = 1152piV/uS = 3617.28V/uS
( sqrt = square root ). Vmax = initial charging voltage (14400 V). C = MMC capacitance (120 nF) L = inductance of primary coil; must be 132 µH in the example to obtain Fres=40 kHz.
Probably most MMCs would not be rated to the currents if a sinusoidal oscillation with that current would exist continuously. But the current gets quickly smaller after firing. Probably the RMS current (averaged over the time between two firing events) would be better suitable if you want to see whether it's OK for the MMC.
Registered Member #2481
Joined: Mon Nov 23 2009, 03:07PM
Location: ITALY
Posts: 134
monokel wrote ...
Probably the RMS current (averaged over the time between two firing events) would be better suitable if you want to see whether it's OK for the MMC.
That is not exact...
Bot the rms and the peak current have to meet the maximum ratings. Usually, cap datasheets specifyy the maximum dV/dt (which tells you indirectly the maximum peak current) and the maximum rms current.
Bot the rms and the peak current have to meet the maximum ratings. Usually, cap datasheets specifyy the maximum dV/dt (which tells you indirectly the maximum peak current) and the maximum rms current.
But if you take good capacitors the maximum dV/dt will absolutely be no problem. For example consider a MMC with WIMA FKP-1 220 nF, 1250 V DC. http://www.wima.com/DE/WIMA_FKP_1.pdf
To get an allowed DC voltage of 15000 V DC you have to connect 12 of them in series (and, of course, some of these series connections parallel to get the desired capacitance). In the example of ScotchTapeLord the correct dv/dt (max) is 3619 V / µs. You have to divide by 12 to get the dv/dt of each WIMA cap, thus 3619 / 12 = 302 V / µs. Each WIMA cap is rated for a maximal dv/dt of 11000 V / µs, this is 36 times of the actual dv/dt.
Of course in smaller TCs with higher Fres the dv/dt will be higher. But these WIMA FKP-1 caps will be suitable regarding dv/dt up to Fres of 1 MHz.
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SGTC Primary Peak Current Calculation
