How a buck converter is sized
A buck converter chops its input and smooths the result with an inductor and a capacitor. The duty cycle sets the output voltage, the inductor sets the ripple current, and the output capacitor absorbs that ripple. Ripple is largest at maximum input voltage, so that's where the inductor is sized.
- Duty cycle:
D = Vout / (Vin·η) - Inductor:
L = Vout·(Vin,max − Vout) / (Vin,max·fsw·ΔI) - Output capacitance:
C ≥ ΔI / (8·fsw·ΔVout) - Capacitor ESR:
ESR ≤ ΔVout / ΔI
Worked example: 12 V to 5 V at 3 A
With 10.8–13.2 V in, 500 kHz switching and 30% ripple, the inductor works out to 6.9 µH. The next standard value, 8.2 µH, gives 0.76 A of ripple and a 3.38 A peak. For 20 mV of output ripple the capacitor needs at least 9.5 µF with no more than 26 mΩ of ESR.
Good to know
- Choose an inductor whose saturation current is comfortably above the peak current, and above the controller's current limit if it can reach it.
- Ceramic X5R and X7R capacitors can lose 30–70% of their capacitance at their working DC voltage. Check the derating curve.
- Higher switching frequency means smaller parts but more switching loss. A ripple of 20–40% of the load current is the usual compromise.
- Pro adds input-capacitor sizing, RMS currents, the light-load DCM boundary and ripple across the input range.