Parallel Capacitors-Theoretical Question

I was really trying to get away from experimentation, it gets too costly. I realized that after rolling op-amps into my phono preamp recently. Before I knew it, I had spent nearly $300.
Capacitors are a bit more complex I think. There are more issues than their face value that can affect them. For example, Mundorf interleaves their capacitor's windings to cancel inductance. After I read that, I wasn't sure what might happen with 2 caps in parallel. Would they induce each other and do strange things at a particular frequency? There's also ESR to consider.
Although I realize many designers make their component choices from an economic standpoint, I still respect those choices as being the best available at the time to get the job done. After all, isn't engineering the art of compromise? That's why I wanted to keep the 13uf value, or get as close to it without causing other problems. It would therefore seem that a good 12 uf capacitor would be the place to start, maybe add 1uf to see how it changes things, and maybe add a bypass 0.1mf after that.
Thanks for your help guys. If anybody's interested in the final result, contact my email and leave me a message.

Capacitors in parallel are the same as resistors in series.

Al shouldn't the tolerances for cap add in quadrature? (0.1^2 + 0.1^2)^0.5 = 0.14 or 14%?

kind of ticky tack, sorry. I'm more curious and electronics are not my field.

03-22-11: Paulsax
Shouldn't the tolerances for cap add in quadrature? (0.1^2 + 0.1^2)^0.5 = 0.14 or 14%?

Hi 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.