Hello.

I've learn that it is better to have different value capacitors between power and GND to countermeasure various frequency range.

But...as you know, parallel connection of capacitances results in equivalent one capacitance of series-sum, so two capacitors actually plays as single bigger one.

Mathematically, I don't see the reason to use two capacitors instead of one single bigger one.

Can somebody clarify this confusion?

 

parallel connection of capacitances results in equivalent one capacitance of series-sum

Hi,
This is incorrect, its a parallel sum if the two capacitors are connected in parallel.
E

 

a capacitor has an impedance depending on the frequency applied.
using different caps example 10uF and 100nF will each be a load for different frequencies.

 

You place capacitors in parallel to increase total capacitance not series. Smaller caps in parallel will typically have a lower ESR than one big cap.

 

Mathematically, I don't see the reason to use two capacitors instead of one single bigger one.

Can somebody clarify this confusion?

Mathmatically, you are correct - it doesn't make sense to put two capacitors in parallel instead of one larger cap. Unfortunately, we live in the real world and not the mathmatical world. Since every real capacitor is a series combination of R-L-C, all caps behave differently at various frequencies. If you are concerned about the higher frequencies, you would add a 100 to 1000pF decoupling cap IN ADDITION to your 10uF decoupling cap.

For instance, if you are worried about a 250 MHz signal on your decoupled line, a 10 uF would have little effect on that freq. Why? The SRF (Self Resonant Frequency) of the 10uF is around 1 MHz (assuming a 2 nH lead inductance). At 250 MHz, the 10uF looks inductive, so would have little effect at that freq. The 100pF capacitor has a SRF of around 500 MHz (assuming a 1 nH lead inductance), so would effectively decouple the 250 MHz signal on the line.

If you have a specific frequency that you need to suppress, you would ideally select a decoupling capacitor that had a SRF as close to the problem freq as you can, because at the SRF, the cap looks like a very small series resistor to ground.

This is why you can often see different decoupling caps in parallel on a power line, or any line that needs protection.