Capacitors in parallel are the same as resistors in series.
Parallel Capacitors-Theoretical Question
I want to replace the capacitors in my speaker's crossover networks. My Large Advent's came stock with 13uf NPE's which I would like to replace with PIO caps. Unfortunately, PIO caps are unavailable in that value. What's the best way to get to 13uf, (12uf + 1uf) or (6uf + 7uf)?
This is a purely theoretical question and I realize either method would probably sound the same, but I'm wondering if there is a reason why one method would be preferred over the other. Are there phase, impedance or other issues associated with either method. I realize of course that I could simply use 12uf or 15uf and probably never notice anything given that the original 13uf NPE had a 20% tolerance, but in theory, what's the best way and why?
This is a purely theoretical question and I realize either method would probably sound the same, but I'm wondering if there is a reason why one method would be preferred over the other. Are there phase, impedance or other issues associated with either method. I realize of course that I could simply use 12uf or 15uf and probably never notice anything given that the original 13uf NPE had a 20% tolerance, but in theory, what's the best way and why?
- ...
- 21 posts total
03-22-11: PaulsaxHi Paul, You ask a good question, as usual. If the two tolerances are the same in percentage terms, then as I stated the tolerance of the parallel combination will be that same percentage. That can be seen by calculating the worst case values. For example, if a 10uF 10% capacitor is paralleled with a 5uF 10% capacitor, the minimum possible value of the combination is 9uF + 4.5uF = 13.5uF. The maximum possible value of the combination is 11uF + 5.5uF = 16.5uF. In both cases the deviation from the nominal value of the combination (15uF), is 1.5uF, or 10%. My statistics courses are now a (very) distant memory, but I believe that combining inaccuracies on an rss (root sum square) basis such as you described would be applicable to standard deviation and related calculations, that involve the PROBABILITY that a combined inaccuracy will fall within limits that are NARROWER than the worst-case limits. That in turn would typically involve situations where tolerances are being combined that act on the same nominal value, not on nominal values that sum together. Best regards, -- Al |
Speaking theoretically, the most predictable performance will be from two capacitors of the same manufacturer and series, and close in value - that is, the 6uF and the 7uF together. This is because their residual inductance and ESR will also be close as well . . . which will give improved characteristics (over a single 13uF capacitor) without the possibility of a secondary HF resonances as can happen when an electrolytic is bypassed with a high-Q film cap. As far as tolerance goes, Al is correct for the worst-case scenario - two 10% tolerance components in parallel have a maximum deviation of 10%. But in reality the tolerance does indeed get better the more components are placed in parallel, the extent of how much is dependent on their probability density function: http://en.wikipedia.org/wiki/Probability_density_function The "normal" or Gaussian function can be used to derive an approximate tolerance, but some manufacturers will actually have documentation that specifies this. Frequently the required testing and documentation for these sorts of things is what comprises the difference between mil-spec and standard components, and is what drives up the cost of the former. |
- 21 posts total