Buck Converter Duty Cycle
Solve duty cycle, output voltage, inductor ripple, and CCM boundary for a synchronous or diode buck.
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The engineering
In continuous conduction the buck's duty cycle is just the voltage ratio Vout/Vin — the switch is on for that fraction of each period, and the inductor volt-second balance handles the rest. Adding a diode or switch drop nudges the required duty slightly higher, which is why this card lets you enter Vd.
The ripple term is where you size the inductor: ΔiL scales with (Vin−Vout)·D and inversely with L·f. A common target is 20–40% ripple relative to full load. If the load current drops below ΔiL/2, the inductor current hits zero each cycle and the converter falls into discontinuous mode, where the simple duty ratio no longer holds.
Sanity check: at 12 V in, 3.3 V out you expect ~27.5% duty — if your bench measurement is wildly off, suspect a low switch node from excessive dead-time or a converter that has slipped into DCM at light load.
Where this math comes from
Switching regulators grew out of aerospace and computer power needs in the 1960s, when linear regulators simply burned too much heat at the currents digital logic demanded. The buck topology — a switch, a catch diode, an inductor, and a cap — became the workhorse step-down, and the volt-second balance argument that gives D = Vout/Vin was known to power engineers well before it was formalized in textbooks.
The modern averaged-model treatment that this card leans on was crystallized by Robert Erickson, whose Fundamentals of Power Electronics turned the inductor volt-second and capacitor charge-balance methods into the standard teaching tools for CCM/DCM analysis. His steady-state ripple and boundary-current expressions are exactly what a designer reaches for when sizing an inductor.
- 1959General/aerospace power groupsSwitching step-down regulators adopted to cut heat versus linear designs.
- 1976R. D. Middlebrook & Slobodan ĆukState-space averaging formalizes converter small-signal and steady-state models.
- 1997Robert W. EricksonFundamentals of Power Electronics standardizes volt-second balance and CCM/DCM boundary analysis.
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