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Re: MMC currents (was Re: pole pig beginner)

Original poster: "Gerry  Reynolds" <gerryreynolds@xxxxxxxxxxxxx>

Hi Aaron.

See comments interspersed.

Original poster: "J. Aaron Holmes" <jaholmes@xxxxxxxxxxxxxxxxxx>

Not so according to JavaMMC
 I've been going through this same exercise for a
PT-based coil I'm scraping together, and actually
meant to ask about this.

Indeed, peak current appears to grow in proportion to
the square root of total C.

Peak current is given by [ Vfire / sqrt (Lp/Cp) ] where Vfire is the voltage that the spark gap fires at. So for a given resonant frequency as you double C the L must be halved and the impedance of the primary will be halved and the peak current will double. The current per string will remain the same. Of course, if you change the resonant frequency this is not so.

So, if you double C by
doubling the number of strings in your MMC, the peak
current *per string* goes down.  However, most folks
seem to worry about Irms, *not* Ipeak, when it comes
to frying capacitors in MMCs.  The kicker appears to
be this:  If you double the total C of your MMC by
doubling the number of strings, JavaMMC reports that
Irms ***per string*** is also doubled!  Ouch!!  Can
somebody (Bart?) explain how this RMS calculation is

I dont know about Java MMC as I havent used it but I believe there may either be an error or the assumptions are different. Given a constant Vfire, constant BPS, constant resonant frequency, and a constant energy transfer time (constant k), as you double the Cp strings and halve the Lp, the total rms current will double but the rms current per string will stay the same. Of course, for a SRSG, doubling the Cp will change the Vfire. For a static SG, doubling the Cp will approximately halve the BPS. If you do lower the resonant frequency with the same coupling, the energy transfer time should increase proportionally. Anyway, the RF current thru the cap during the bang will ring down as the secondary rings up. If you make a simplifying things by assuming this current doesnt ring down but remains constant for the duration of the energy transfer time, you can overestimate the RMS current thru the MMC by using the following relationship:

Irms = Ipeak (given by the above calculation) / sqrt (2)

This current only exist during the energy transfer time so the average RMS current needs to be time weighted by the following:

Irms_ave = Irms * energy transfer time * BPS

Since the actual RMS current rings down during the energy transfer time, the actual Irms_ave will be less than predicted above (the error is on the safe side).

So, Irms ***per string*** appears to scale in
proportion to total C.  The next really interesting
thing JavaMMC reports is that Irms scales in
proportion to the *square root* of BPS (spark gap
break rate).

NO, the RMS current will be proportional to BPS

Since the coil power is given by:

P = BPS * 0.5 * C * V^2

If you hold V constant, then you've got a couple of
choices left for increasing your coil power.  If you
doubled your power by doubling C, you also double your
Irms ***per string***, which seems really bad!!  If
you double your power by doubling BPS, your Irms
***per string*** only goes up about 40% as opposed to

I believe these results are in error. I think it is useful to think of the problem using symetry. If you double the power and double the strings, each string will process the same power. If you double the power, the power source should be able to charge double the capacitance in the same time, so V will remain the same and BPS will remain the same.

Considering those figures alone, it would seem
as though increasing BPS is the better choice.  Of
course, I've heard folks suggest that break rate only
gets you so far, but perhaps going from 120 to 240 is
better than going from .03uF to .06uF?

Let's see.  From JavaMMC:

If you use 3 strings of 15 "Geek Group" caps (good for
13A RMS, supposedly) to get .03uF, run 15kVAC at
120BPS, then your Irms per string is 7.34A.  That's
good.  If you double C by using *6* strings for .06uF,
Irms per string *doubles* to 14.67A.  That's not so
good.  If instead you had doubled the break rate to
240BPS for the same "coil power", your Irms per string
would have increased only to 10.38A.  Still under the
max.  Seems "better".

If these are the 942C20P15K caps, they are good for 13.5 amps rms and 432 amps peak. Three strings of them would give you a MMC thats good for 40.5 amps rms and 1296 amps peak.

All this seems to suggest to me that increasing your
total C is not a very MMC friendly thing to do
(despite an intuition that tells me that more of
<thing> in parallel means less current per <thing>)
and that increasing V and BPS are the cooler ways
(literally) to get more power.  Is that correct,
though?  I fully admit to not understanding how
JavaMMC gets its Irms figure, and would really like to

Aaron, N7OE

--- Tesla list <tesla@xxxxxxxxxx> wrote:

> Original poster: "Gerry  Reynolds"
> <gerryreynolds@xxxxxxxxxxxxx>
> Hi Ben,
> Just design your MMC so the Ipeak, Irms, and Vdc
> specs are not
> violated. The bigger PIG will require more
> capacitance meaning more
> strings in parallel.  Thus the current capacity of
> the MMC goes up as
> the number of strings is increased.
> Gerry R.