RE: Balance resistors

>Message-ID: <199605310310.VAA09901-at-poodle.pupman-dot-com>
>Date: Thu, 30 May 1996 21:10:11 -0600
>From: Tesla List <tesla-at-poodle.pupman-dot-com>
>> It is important 
>>when series capacitors are hooked up to use about 50megs of resistance 
>>across each cap to help divide the voltage equally.
>I had been thinking about this one myself recently. It is almost standard
>practice in in H.V. supplys when placing two or more caps in series to
>increase the working voltage balancing resistors are placed in parallel
>across the caps to enshure an even voltage distribution across them all.
>They also act as bleed resistors to prevent the caps holding a high voltage
>after the power is removed.
>What i was wondering was is it worth applying to my 15 section series cap.
>and what would the effect be on the 'Q' of the capacitor?
>Would the 50megs still be a correct value on this cap?
>Ian Hopley ---->  i_hopley-at-wintermute.co.uk
>Scotland          Callsign  M M 1 A B A

   I loved doing these questions in school!

   On the job and for my hobbies, whenever I designed and built any
   high-voltage power supplies, if I had to put capacitors in series I
   always put large equalizing resistors across them to make sure the
   DC voltage was distributed correctly.  Needless to say, I tried to
   avoid having to do this.  But in the Tesla world, I think it's

   Incidentally, when putting solid-state diodes in series to increase
   their peak-inverse-voltage rating, say, in a bridge-rectifier
   circuit, not only should you put an equalizing resistor across each
   diodes, but you also should put small-value equalizing *capacitor*
   across each diode.  If the diodes are all the same, then all
   resistors must be equal and all capacitors must be equal.  In
   really odd cases where the PIV ratings of the diodes were unequal,
   one can tailor the resistors and capacitors accordingly.  (A diode
   with half the PIV rating would get *half* the number of ohms and
   *twice* the capacitance across it.)  However this is only
   "emergency" engineering practise and not "good" engineering
   practice to use unequal-PIV -rating diodes.  The resistors evenly
   apportion out any large DC or low-frequency inverse voltages, and
   the capacitors equally apportion out any inverse spike voltages
   which  from the power line you can *count* on happening.  Of
   course, the resistors and the capacitors *themselves* had to have a
   sufficient voltage rating to be able to stand this service.  Yes,
   resistors not only have ratings in ohms and watts, but resistors
   also have *voltage* ratings based on what quick voltage spike will
   cause the resistor to break down internally or across its surface. 
   So these equalizing resistors may themselves have to be a series of
   other identical resistors!  Each capacitor should have a greater
   voltage rating than the diode it's protecting, say twice the value.
   For a 600-volt primary power circuit, you'll be pretty safe, I think,
   if each capacitor is rated at 5kV, since the caps will be inseries and
   typical power-line spikes are usually limited to a factor of 10 in my

   For your capacitors, the Basic calculation:

   In your case, theoretically on a perfect capacitor, the resistors'
   effect on the Q of the capacitors themselves depends on Xc, the
   reactance of the capacitors, and R, the value of the resistors. 
   For resistors in *parallel* with capacitors, at resonance the Q is
   close enough to R divided by Xc.  Xc = 1 / (2*PI*F*C) . 
   Capacitance is in Farads and Frequency is in Hertz.  Xc and R are
   both in ohms, so "Q" is a dimensionless number. If all the
   capacitors in series are equal and all the resistors are equal,
   then the Q of each section will be the same, as would the Q be if
   you calculated all the capacitors as 1 capacitor and all the
   resistors as 1 resistor.  That is in your case (C of one cap) / 15 
   and (R across 1 cap) * 15.  The "15" cancels in the Q calculation.

   Practical consideration:

   But this to some extent depends on the "Q" of the capacitor to
   start with.  No capacitor is perfect, all have some power
   dissipation from the heating of the dielectric material.  This can
   be thought of as an internal series resistance in each capacitor,
   and the value of this resistance can be calculated from the heat
   dissipated and the reactive power flowing in the capacitor.  Once
   you know the value of that resistor, it can be converted to an
   equivalent parallel resistor and then "tossed outside" as it were,
   in parallel with your resistor.  The way you toss a series
   resistance outside is by using the alternate formula for "Q" which
   is Xc / series resistance.

   We have been talking about perfect resistors.  Unfortunately, most
   resistors have *inductance* which can form parasitic resonances
   with your capacitors.  For RF circuits, one should always try to
   use non-inductive (bulk composite material) resistors.  Whereas
   they are more accurate than composite bulk-material resistors,
   popular film resistors and wire-wound resistors should not be used
   unless their inductance is considered.  And remember that resistors
   can break down internally, invisibly, and develop tracks.  Always
   measure the resistance of your resistors individually to make sure
   they will balance the voltage across your capacitors.  Also, with
   some materials, resistance is itself a function of voltage and so
   you should also measure the resistance of your resistors at an
   appropriate high voltage just to be sure.  This takes a special
   test setup.  We had this problem at the Van De Graaff lab.  Don't
   burn them out ;-)  Stable high-voltage resistors are no easy
   engineering feat.  And always keep safety first!  Did that safety
   FAQ ever get written ??

   All the best,

 Fred W. Bach ,    Operations Group        | Internet: music-at-triumf.ca
 TRIUMF (TRI-University Meson Facility)    | Voice:  604-222-1047 loc 6327/7333
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 University of British Columbia, Vancouver, B.C., CANADA   V6T 2A3
 "Accuracy is important. Details can mean the difference between life & death."
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