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Re: [TCML] cap rms current
Alright, So
I took information from The green monster coil. and ran it threw java TC to export a few parameters.
I then modeled a pulse in the form of cos(w*t)*cos(w2*t)*e^(-t/tau)
Where
w is the angular resonant frequency,
w2 is an envelope frequency defined as being 4* the energy transfer time Java tc produces,
and
tau being a decay constant being defined via a multiple of the energy transfer time Java tc produces, where the decay is mostly complete by at least 5*the energy transfer time, then the constant would be .37*5*energy transfer time.
5 is the maximum time assuming a 3 notch quench. and the over all time constant is still just an approximation.
The 858.6 is the peak current posed by java tc.
Here is something to copy into wolfram alpha to see the wave form, if you wish
"
Plot[ 858.6*cos(58000*2*pi*t)*cos((1/(4*5.636e-5))*2*pi*t)*e^(-t/(5.636e-5*5*.37)), {t, 0, .0003}, {y,-900,900}]
"
I then took that equation squared the whole thing and integrated it over a time scale slightly larger than the time length of my decay, in this case .0004 seconds. This is in accordance with the formula for a root mean square.
I divided by the time interval 1 second, and then multiplied by the beats per second of the spark gap. 350 max was posed for the green monster.
Here is the code for wolfram alpha again
"
sqrt( 350 * integral (858.6*cos(58000*2*pi*t)*cos((1/(4*5.636e-5))*2*pi*t)*e^(-t/(5.636e-5*5*.37)))^2 dt from t=0 to t=.0004)
"
So by this analysis, discounting capacitor charging, and assuming a complete charge already on the capacitor.
The rms current comes out to be between 40 and 60 Amps depending on what tau constant I use for what notch value.
What does everyone think? A reasonable assessment ?
Also important to note, I did this analysis for the worst possible case, that means max bps, and max input power. so 20Kva for the green monster.
Thanks,
John "Jay" Howson IV
"Why thank you, I will be happy to take those electrons off your hands."
----- Original Message -----
From: "Carl Noggle" <cn@xxxxx>
To: "Tesla Coil Mailing List" <tesla@xxxxxxxxxx>
Sent: Wednesday, February 1, 2012 11:10:30 AM
Subject: Re: [TCML] cap rms current
These Maxwell caps are bulletproof. I bought a 0.05uF, 50kV cap about
20 years ago knowing that it had a leak around the top terminals, and it
finally gave up the ghost about two weeks ago, after much service in my
TC, 1800 watts from three 9/60s in parallel. I got a nonleaking one at
the same time and it is still going strong.
> trying to start/move the thread
>
> Jay,
>
> I have a cat # 31885, .1 ufd, 75 kV rated Maxwell
> that I believe is also rated at a "mere" 25 amps RMS,
> but I run my Green Monster coil (10 kVA pig fed
> and overdriven up to 20 kVA) with it as the sole
> primary cap and I have never been able to notice
> any external warmth on it above ambient temp,
> even after several minutes of non-stop 15 kVA +
> running.
>
> David Rieben
>
>
> ---
>
> Assuming your pig is 14.4kV, at 15kVA it's roughly 1 Amp RMS "into the
> coil"
>
> Now, the question comes up of "what's the effective RMS current in the
> cap". I like to back of the envelope these kinds of things by doing
> an energy balance kind of computation.
>
> Let's, say, for argument that your coil runs at 100kHz, and takes
> about 10 cycles to go from "break" to "quench", or, call it 100
> microseconds.
>
> So, during a 8.3 millisecond half cycle, the cap is "charging" at 1
> amp (from the pig) for most of it, and then, for 0.1 millisecond it is
> discharging ALL that stored energy.
>
> That is, in round numbers, it spends 99% of the time charging and 1%
> of the time discharging.
>
> We know that energy goes as the square of either voltage or current,
> so the RMS current during discharge is going to be 1/10th of the RMS
> current during charging (since we already know that the energy flow
> ratio is 100:1)
>
> therefore, I would assume that you're running an effective RMS current
> of somewhere between 10-15 Amps, well within the rating of your
> Maxwell cap.
>
>
> Somewhere back in the archives, there's a better calculation of this.
> I integrated a variety of damped sinusoids (linear and exponential
> decrement). It would be pretty easy for someone to set up an excel
> spreadsheet and do it by numerical integration, as well.
> _______________________________________________
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