# RE: calcs: Parallel R to equiv series R affect on MMC perf

```Hi Nick,
I've been so busy with work and robotics afterward (FIRST national
competition).
I agree with what you say for the higher freq AC case.

The equalizing resistors do become effective as the charging source
approaches DC. The finite Rvalue moderates any variance in the dielectric
resistance (T ohms +- G ohm ?)
It should be easy to calculate at what frequency reactance is no longer
effective in equalizing individual Cap voltages for the case where charging
is max'ing out and they are not due to discharge for a TBD time.
Some assumptions need to be made
or measurements of the variance of the dielectric of a lot of Caps would be
nice.

I believe those using DC (especially at very low BPS)
must be more concerned about equalizing series string Caps.

A quick charge rate will initially provide equal charge as a function
of capacitance (reactance from ramp up time) but after charging the
DC relationship dominates and 10M becomes significant relative to
the much higher dielectric resistance.

Regards, Dale

-----Original Message-----
From: Tesla List [mailto:tesla-at-pupman-dot-com]
Sent: Saturday, January 29, 2000 7:08 AM
To: tesla-at-pupman-dot-com
Subject: Re: calcs: Parallel R to equiv series R affect on MMC perf
Original Poster: "Megavolt Nick" <tesla-at-fieldfamily.prontoserve.co.uk>

Hi All,
for the 'equalising' resistors you want to analyze it as a
capacitative and resistive divider parallel connected.  My point was that
enough charge cannot flow through the 10meg resisitors to substantially
change the capacitor voltages, therefore the equalising effect is almost
nil.  The resistance is so large that it doesn't figure very much in the Q
calcs - it will have a small inverse sine damping effect, but not much with
the total in a string being 100meg.

Regards
Nick Field

> Original Poster: Dale Hall <Dale.Hall-at-trw-dot-com>
>
> Hi Nick & ALL,
> The series equivalent R of resistance paralleled with a Cap (or L)
>
> Rseq = X^2 / R
>
> for .056uF (Xc=14.2ohms) paralled by 10 meg at 200kHz:
>
> (1/(6.28*200e-3*.056e-6))^2 / 10e6 = .00002 (.02 milli) ohm each
>
> 10 in series = .0002 (.2 milliohm) (assume 1 string)
>
> increasing series equivalent resistance lowers Q
>
> Q = X/R  142/.0002 = 710,000 (yeah right, ! so dielectric is likely limit)
>
> so influence of paralleled R is not significant for these values.
>
> Rarc (and to lesser degree Rdc) of Lpri will be greater system factor:
>
> assume Rarc ~= 2ohms
>
> Resonant Q = (XL=Xc)/Rseries_eq = 142 / ~2ohms ~= 71
>
> note: a single R across series Cap string will not discharge the caps.
>       (no DC path, just redistributes the charge a little)
>
> Nicks I believe refers to one bleeder R for each stage (~10)
> in multi parallel strings (~3).
>
> Regards, Dale
>
> -----Original Message-----
> From: Tesla List [mailto:tesla-at-pupman-dot-com]
> Sent: Thursday, January 27, 2000 6:51 AM
> To: tesla-at-pupman-dot-com
> Subject: Re: Yet Another MMC question
>
> Original Poster: "Megavolt Nick" <tesla-at-fieldfamily.prontoserve.co.uk>
>
> Hi Jim,
>            It depends.....
> The mmc bleed resistors do not change the performance of the cap in tc
> service, but they do help to prevent operator injury through a charge
> remaining on the caps after the coil has been switched off.  If you're not

> likely to touch the caps between runs, then don't bother. You could also
> just put a single set of resisitors across the whole lot rather than
across
> each cap.
>
> Regards  Nick Field
>
> > I about to assemble a small MMC  (10 x 2).
> > I noticed that most builders put a bleeder resistor across each cap.
> > << Jim

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