LDO regulator stability with bypass capacitor

Question

I'm working on a dac which use a Te7022 as usb receiver, it will be powered by the mic5205 LDO so I search for articles about stability with LDO and got this: http://www.ti.com/lit/an/snva167a/snva167a.pdf. It's quite easy to understand until section 7 "Additional Poles From Ceramic “Bypass” Capacitors". I think the author forgot to include the Esr of the bypass capacitor in the equation.A single 0.1uf X7R capacitor will often have an esr about 20mohm so 10 capacitors in parallel is effectively about 3mohm and it's also parallel with the tantalum so isn't Rout in the equation 3mohm instead of 0.43ohm?

Answer 1

MIC5205 using 1nF bypass cap can be modelled by a 0.01R resistor in series with an inductor of value 0.6 ... 1.5 µH (it depends on DC current).

Using these parameters, you can simulate its stability with the ESR of your tantalum caps. Set the transition from regulator to cap below 40 kHz to avoid the regulators' second pole.

Answer 2

It is the capacitance in series with the ESR (not just the ESR) of the bypass capacitors that are in parallel with Rout. The app note has ignored the series ESR of the ceramic capacitors combined because it is quite small comparing to Rout.

Another way to look at this is, for this analysis around the unity gain frequency of 600kHz, a 10uF tantalum looks more like a resistor. A bunch of ceramic bypass capacitors looks like a pure capacitor. One way to see how good or bad are these approximations is to calculate the impedance of the capacitance at frequencies of concern and compare them to the ESRs.