Selection of the output capacitor

The following three factors are important when selecting the output capacitor.

Of course the voltage and ripple current applied to a capacitor must be below the maximum ratings for the capacitor. The ESR is an important parameter that determines the output ripple voltage associated with the inductor current, and must be studied carefully.

The ripple current of an output capacitor is a sawtooth wave, as indicated by ICO in the waveform diagram above; its effective value can be represented by the following equation.

The output ripple voltage is represented by the following equation as the composite waveform resulting from the ripple component ΔILof the inductor current IL in the above diagram, and the voltage occurring due to the capacitance, ESR, and ESL of the output capacitor.

When illustrated as waveforms, we obtain the following.

The ripple component ΔIL of the inductor current generated by switching causes a ripple voltage that is simply proportional to the ESR, and the ESL generates a square-wave voltage. The electrostatic capacitance component is combined with these to result in the final output ripple voltage waveform, shown at the bottom.

When representing the output ripple voltage, the following equation is used. Because the phases of the ripple due to the capacitor and the ripple due to the ESR are shifted, the two cannot simply be added together, but the following equation is often used to estimate the worst case value of the ripple voltage.

From this equation we see that in order to reduce the output ripple voltage, we should lower the ESR, increase the capacitance of the output capacitor, raise the switching frequency and reduce IL to the minimum necessary level.

In recent years, there appears to be a trend toward increased use of multilayer ceramic capacitors as output capacitors. Ceramic capacitors have extremely low ESR and ESL values, and so observed ripples originate almost entirely in the capacitance of the capacitor.

From: https://micro.rohm.com/en/techweb/knowledge/dcdc/dcdc_pwm/dcdc_pwm02/2366