Following this answer I looked into the datasheet of the OKI-78SR-5/1.5-W36-C and see the following:

In general the requirement is clear for me: resistance at the start event must not be too low for regulator to go to shortage protection state and fail starting.

I am not sure how to calculate the ESR for the circuit which is going to be powered by the regulator. The circuit is having one 10TPB220ML, three 10TPB47M, and quite a set of GRM21BR61C106KE15L and CC0805KRX7R9BB104.

Bigger caps have ESR listed at 100 kHz (page 2), and direct computation gives 0.016 Ohms. Then looking at the GRM21BR61C106KE15L ESR graph (page 2) I see that its ESR at 500 kHz (operating frequency of the converter) is well below 0.01 Ohms.

Thus logically one GRM21 cap at the output is enough to trigger max 300 uF condition per datasheet.

This sounds really strange for me as I think I assume and calculate something wrong. Regulator's datasheet does not list conditions ESR to be measured in, so I am stuck.

The only reasonable thought I have regarding MLCC is that when device starts, its "frequency" is zero, thus 10 Ohms ESR applies, and thus I need 1000 caps to trigger 330 uF condition for regulator, and ESR does not matter for regulator when it starts and gets up to its nominal output voltage level (as ESR is applicable to the high frequency noise component, and not to the full swing voltage).

What do I miss here?

• Suppose you have 10 uH inductor, 10 volt input, want 3.3 volt output, and have 1 Farad output capacitance. What will happen? ohhhh We need to know the Load Current ---- 1 amp. Now how to design that? Does the 1 Farad matter? – analogsystemsrf Sep 25 '19 at 9:19
• You actually care about the ESR of the cap within the loop bandwidth of the converter. Although the switching frequency is 500kHz, the loop crossover frequency will be well below this (usually no higher than switching frequency / 4). Granted this device is still below 0.01 ohm at that frequency but it is an important point. – Peter Smith Sep 25 '19 at 14:47
• What is the "direct computation" that gets you from a spec that says a cap has (for example) 40 mohms ESR to "0.016 ohms"? – The Photon Sep 25 '19 at 15:51
• @ThePhoton parallel connection of the resistors. Capacitors are connected in parallel, thus ESR must also be subject to parallel connection. Am I wrong here? – Anonymous Sep 25 '19 at 15:58
• The ESR / max capacitance relates to the frequency of the output zero of the converter (1 / (2 x pi x C x ESR)) – Peter Smith Sep 25 '19 at 16:19

It's hard to guess what is going on inside the black box, but I think you are right in the first sentence; the concern is to keep out of overcurrent protection.

I believe this is a buck converter. We don't know what the high-side FET is but the concern is that the voltage across this FET is not significant so that it does not dissipate any power. Because the "on" resistance varies between devices, I believe this type of regulator current limits by measuring the voltage directly across the high-side FET when it is in the "on" state. To keep this a low value, we must avoid high peak currents. The device will truncate each pulse and count a fault each time the FET voltage exceeds the limit before the PWM period is complete, and go into shutdown if a small number of consecutive pulses register this fault condition, stay off for a while, and then restart (hiccup).

Although your GRM21BR61C106KE15L (10 uF) has a low ESR, it has a relatively high reactance at 500 kHz of .03 ohms. The capacitance dominates the impedance, and you can ignore the real (ESR) component when determining the current contribution from the applied voltage.

For the 3300 uF capacitor specified in the data sheet, the reactance of the capacitive component is about .0001 ohm, so the specified ESR of the data sheet of 0.01 ohms dominates. From this I would conclude that the impedance seen at the output from all of your capacitors' impedances in parallel should not be less than .01 ohms. I think your decoupling capacitance distributed around your circuit is less of an issue, because the trace resistance and inductance will come into play.

ESR (equivalent series resistance) isn't the same as impedance, although it is frequency dependent in ceramic caps. ESR represents the real part of the overall impedance, which may also contain capacitance or inductance. The overall impedance includes capacitive and inductive effects, dominated by capacitance below the part's resonance.

You can reasonably accurately calculate the capacitance from the impedance (not ESR), but the frequency is a part of that calculation. So the fact that the impedance changes over frequency doesn't mean the capacitance does (although the capacitance does increase just below resonance, then becomes overall inductive at higher frequencies).

So although you may trigger the maximum 300uF requirement, this capacitor will never be even close to 300uF. If you put more than 300uF total on this line, your larger caps will need to have a higher ESR.

This spec isn't so much to limit inrush current as it is to guarantee stability. If you find yourself using large capacitors with low ESR, a small resistor in series will do the trick.

• 10TPB220ML (40 mOhm) in parallel with three 10TPB47M (70 mOhm) in parallel with 7 x 10 uF MLCCs will be 431 uF. I still can not get what is the issue here, and how to comply to this datasheet requirement properly (e.g. replace 7805 with this converter). Furthermore, datasheet states that we must use low ESR caps (but putting 11 uF [<< 300 uF] at the output). There must be some further knowledge regarding the subject... – Anonymous Sep 25 '19 at 14:31
• @Anonymous, you could remove some capacitors to get below 300 uF. – The Photon Sep 25 '19 at 15:52