JAJSSU1 データシート

JAJSSU1 September 2024 LMR51425-Q1 , LMR51435-Q1

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8.2.2.5 Output Capacitor Selection

The device is designed to be used with a wide variety of LC filters. Minimize the output capacitance to keep cost and size down. The output capacitor or capacitors, C_OUT, must be chosen with care because capacitor or capacitors directly affects the steady state output voltage ripple, loop stability, and output voltage overshoot and undershoot during load current transient. The output voltage ripple is essentially composed of two parts. One part is caused by the inductor ripple current flowing through the Equivalent Series Resistance (ESR) of the output capacitors:

Equation 11.

∆ V_{O U T_E S R} = ∆ i_{L} \times E S R = K_{I N D} {\times I}_{O U T} \times E S R

The other part is caused by the inductor current ripple charging and discharging the output capacitors:

Equation 12.

∆ V_{O U T_C} = \frac{∆ i_{L}}{8 \times f_{S W} \times C_{O U T}} = \frac{K_{I N D} {\times I}_{O U T}}{8 \times f_{S W} \times C_{O U T}}

The two components of the voltage ripple are not in-phase, therefore, the actual peak-to-peak ripple is less than the sum of the two peaks.

Output capacitance is usually limited by transient performance specifications if the system requires tight voltage regulation with presence of large current steps and fast slew rates. When a large load step occurs, output capacitors provide the required charge before the inductor current can slew to an appropriate level. The control loop of the converter usually requires eight or more clock cycles to regulate the inductor current equal to the new load level during this time. The output capacitance must be large enough to supply the current difference for 6 clock cycles to maintain the output voltage within the specified range. The following equation shows the minimum output capacitance needed for a specified V_OUT overshoot and undershoot.

Equation 13.

C_{O U T} > \frac{1}{2} \times \frac{6 \times (I_{O H} - I_{O L})}{f_{S W} \times ∆ V_{O U T_S H O O T}}

where

K_IND = Ripple ratio of the inductor current (Δi_L / I_OUT)
I_OL = Low level output current during load transient
I_OH = High level output current during load transient
V_{OUT_SHOOT} = Target output voltage overshoot or undershoot

For this design example, the target output ripple is 25mV. Assuming ΔV_{OUT_ESR} = ΔV_{OUT_C} = 25mV, choose K_IND = 0.45. Equation 11 yields ESR no larger than 15.9mΩ and Equation 12 yields C_OUT no smaller than 17.9µF. For the target overshoot and undershoot limitation of this design, ΔV_{OUT_SHOOT} is 250mV. The C_OUT can be calculated to be no less than 47.7µF by Equation 13. In summary, the most stringent criteria for the output capacitor is 47.7µF. Considering derating, two 22µF, 16V, X7R ceramic capacitor with 10mΩ ESR is used.

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8.2.2.5 Output Capacitor Selection