Parallel Capacitors-Theoretical Question

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.

Kirkus, please elaborate on the statement that 6uF & 7uF caps together will be better than one 13uF. Isn't there a benefit to having two less solder joints in the filter?
Thanks,
Jay

Hi Jay . . . the most basic model of a real-world capacitor is an ideal capacitor in series with both an inductor and a resistor. For a high-quality film cap, the inductance comes from the leads and the fact that it's impossible to acheive a perfect "non-inductive" wind to the film/foil itself. Series resistance comes from the leads and the (usually crimped) connection from the leads to the foil. Virtally all of these non-ideal properties increase with the physical size of the capacitor, especially inductance. Larger caps also tend to be more suceptible to crosstalk from nearby inductors.

For electrolytics there are additional losses and parasitic properties from the electrolytes, which can be signal-modulated and heat-modulated. And while these properties do get better with physically larger capacitors, doubling the number tends to make much larger improvements than merely increasing the physical size, and it does so without incrasing inductance. And if there is significant ripple current (causing heat), two caps will disipate the heat much better than one, given the greater surface area.

Compared to all of this, any solder-joint of reasonable workmanship is but a tiny grain of sand on the beach. The biggest vulnerability would be for i.e. a production wave-soldered PC board, which frequently has "thermal" pads of significant resistance . . . but even in this case, paralleling two smaller caps would mean less weight (hence less vibration stress) on each connection, and the resistance of the board traces and thermal pads would be in parallel. So, still an improvement.

Thanks, Kirkus :)

the most basic model of a real-world capacitor is an ideal capacitor in series with both an inductor and a resistor

Excellent point. If caps are in parallel than total parasite resistance and inductive impedance would be halved if used two caps of the same value and same manufacturer.