### Capacitor impedance

The capacitor ESR has 2 roles. It affects negatively the output voltage AC ripple. It affects positively the loop because of adding a zero in voltage mode control. In case of 2 parallel capacitors one ceramic C with ESR = r and one tantalum C0 with ESR = r0

Output capacitance total impedance =

The total impedance shows 2 zeros and 1 poles:

One zero at very high frequency = 796MHz

One zero at lower frequency = 31KHz if C0 = 47uF and r0 = 0.11Ω

One pole between the 2 zeros frequency at = 14MHz if C = 0.1uF and r = 2mΩ

It shows the dominant zero is still due to C0 and its ESR because the pole and zero due to ceramic capacitor are at very high frequency relative to circuit bandwidth < 100KHz. We can conclude that there is no influence of the ceramic capacitor in term of loop study.

By neglecting the very high frequencies pole and zero , the total capacitor impedance is .

There is no problem if the ESR is 10% higher or lower because the gain and phase will not be much affected. In this example the gain difference is 20log1.1 = 0.83db and the phase difference is Arctan1.1 - 45º = 3º