Re: Primary Cap rms current not a function of frequency

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Robert Jones" <alwynj48-at-earthlink-dot-net> 

Hi Terry,

Comments within the text.


 > Original poster: Terry Fritz <teslalist-at-twfpowerelectronics-dot-com>
 >
 > Hi Bob,
 >
 > >break rates.
 > >
 > >I was surprised to discover a simple equation for the primary rms
current.
 > >Assuming no R or SG losses, quench at a notch, assuming magic k's
 > >and  ignoring charge current the rms primary current in amperes is given
by:
 > >
 > >Irms=pi x V x C x (break rate) x (number of primary cycles to quench)
 > >where V is the charge voltage and C the capacitance in F
 > >
 > >For a standard MMC cap of 0.15uF it is   0.113A rms per number of primary
 > >cycles per 2000V of charge per 120Hz break rate. (0.094A rms for those in
 > >50Hz flicker land using 100Hz break rates)
 > >
 > >The value above means the rms current rating of 13.5Arms of the cap will
 > >not be exceeded unless the coupling is very low or the break rate much
 > >higher than 120Hz. In any case the current rating may be at 85C.
 > >
 > >WoW I think this means you can have break rates of 1000Hz  with out
frying
 > >the caps with 1st notch quench I should add.
 >
 > In general, the RMS current is proportional to the BPS rate given the same
 > primary cap size and firing voltage.  But I am not quite sure what you
 > conditions are here.

  I am refereing to any cap in the primary of a coil that is charged to a
particular voltage. When the sg fires I assume the voltage is a cosine
modulated cosine wave and the amplitude is constant ie no losses. I assumme
quench occurs at a notch and break out is after the quench. Both assumptions
ensure a worse case current.

The derivation is simple. The peak current is given by 2 x pi x C x f x V,
the rms is 1/2 of that.  Then you must multiply it by the duration which is
the number of cycles  x the poeriod which is cycles/f. where f is the
primary frquency without the secondary. The 2s and f cancel.  Then multiply
by the break rate. QED
The more difficult part is proving that f is the correct frquency to use.
The 1/2 factor rms to peak can proved mathematicaly.  Note the trig id
cos(a-b)+ cos(a+b) = 2xcas(a)xcos(b).

  > >
 > >How close to or over rated can the  maximum allowed peak current and dvt
 > >of the cap spec be pushed  for reasonable (in home TC service) life given
 > >the rms current is not a limiting factor.
 >
 > In general, the cap makers give a margin of SQRT(2)X  (twice the
 > heating).

I don't think I understand that statement can you expand on it.

 >>But they DO have bad days...  I would not exceed RMS current or
 >> dV/dT ratings.  We certainly know that exceeding those ratings can
 >> completely destroy the whole cap.

For the 0.15uf/2000Vdc caps from dV/dt=i/C the max dV/dt rating is the same
as the max peak current rating. So if either are not to be exceeded the
frequency of operation for a 2,000V max cap voltage must be lower than
230KHz.. I was suprised how low that is.

 >
 >Comments please.
 >
 >I still need to double check the above  but I thought I would bounce it of
 >the group first.

 >>It would certainly be a new and cool equation!!  Hope it works out!!

I have checked it again. It appears to be correct. There is a problem with
the definition of cycles. A better description would be peaks. It means the
number of fundemetal cycles which may be a 1/4 or o1/2 less than the number
of peaks you observe on a scope. Perhaps a better form for the equation
would use k. I will work on that.

Bob