Buck converter duty cycle

The switch chops the input into pulses and the inductor and capacitor average them out; the output is simply the input times the fraction of time the switch is on.

D = Vout / Vin (ideal buck, continuous conduction)

Ideal converter in continuous conduction, no switch or diode losses. Real duty cycles run a few percent higher, and most ICs limit the maximum duty and the minimum on-time. Inductor and output capacitor sizing come from the datasheet’s application notes.