Ordinarily, the energy stored by the output capacitors combined with the control loop response prescribe to maintain the integrity of the output voltage within the dynamic (transient) tolerance specifications. The usual boundaries restricting the output capacitors in power management applications are driven by finite available PCB area, component footprint and profile, and cost. As the load step amplitude and slew rate increase, the capacitor parasitics – equivalent series resistance (ESR) and equivalent series inductance (ESL) – take greater precedence in shaping the load transient response of the regulator.

The output capacitor, C_OUT, filters the inductor ripple current and provides a reservoir of charge for step-load transient events. Typically, ceramic capacitors provide extremely low ESR to reduce the output voltage ripple and noise spikes, while tantalum and polymer electrolytic capacitors provide a large bulk capacitance in a relatively compact footprint for transient loading events.

Based on the static specification of peak-to-peak output voltage ripple denoted by ΔV_OUT, choose an output capacitance that is higher than that given by Equation 13.

Equation 13.

Figure 8-1 conceptually illustrates the relevant current waveforms during both load-on and load-off transitions. As shown, the slew rate of the inductor current represent a large-signal constraint as the inductor current ramps to match the new load-current level following a load transient. This slew-rate limiting exacerbates the deficit of charge in the output capacitor, which must be replenished as rapidly as possible during and after a load-on transient. Similarly, during and after a load-off transient, the slew rate limiting of the inductor current adds to the surplus of charge in the output capacitor that must be depleted as quickly as possible.

Figure 8-1 Load Transient Response Representation Showing C_OUT Charge Surplus or Deficit

In a typical regulator application of 48V input to low output voltage (for example, 12V), the load-off transient represents the worst case in terms of output voltage transient deviation. With that voltage conversion ratio, the steady-state duty cycle is approximately 25% and the large-signal inductor current slew rate when the duty cycle collapses to zero is approximately –V_OUT/L. Compared to a load-on transient, the inductor current takes much longer to transition to the required level. The surplus of charge in the output capacitor causes the output voltage to significantly overshoot. In fact, to deplete this excess charge from the output capacitor as quickly as possible, the inductor current must ramp below the nominal level following the load step. In this scenario, a large output capacitance can be advantageously employed to absorb the excess charge and minimize the voltage overshoot.

Equation 13 calculates the output capacitance to meet the dynamic specification of output voltage overshoot during such a load-off transient (denoted as ΔV_OVERSHOOT with step reduction in output current given by ΔI_OUT).

Equation 14.

The capacitor manufacturer data sheet provides the ESR and ESL, either explicitly as specifications or implicitly in the impedance versus frequency curve. Depending on the type, size, and construction, electrolytic capacitors have significant ESR, 10mΩ and above, and relatively high ESL, 10nH to 20nH. PCB traces contribute some parasitic resistance and inductance as well. Ceramic output capacitors, have low ESR and ESL contributions at the switching frequency, and the capacitive impedance dominates. However, depending on the package and voltage rating of the ceramic capacitor, the effective capacitance can drop quite significantly with applied DC voltage and operating temperature.

Ignoring the ESR term in Equation 13 gives a quick estimation of the minimum ceramic capacitance necessary to meet the output ripple specification. Four 22μF, 25V, X7R capacitors in 1210 footprint are a common choice for a 12V output. Use Equation 14 to determine if additional capacitance is necessary to meet the load-off transient overshoot specification.

A composite implementation of ceramic and electrolytic capacitors highlights the rationale for paralleling capacitors of dissimilar chemistries yet complementary performance. The frequency response of each capacitor is accretive in that each capacitor provides desirable performance over a certain part of the applicable frequency range. While the ceramic provides excellent mid- and high-frequency decoupling characteristics with low ESR and ESL to minimize the switching frequency output ripple, the electrolytic device with large bulk capacitance provides low-frequency energy storage to cope with lower frequency load-transient demands.