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The duty cycle D is the fraction of each switching period that the main switch is ON, and it directly sets the ideal (lossless, continuous-conduction-mode) voltage conversion ratio of a switch-mode converter. Each topology has its own D-to-ratio relationship because of how the inductor charges and discharges relative to the switch state.
| Topology | Duty Cycle Formula | Voltage Range |
|---|---|---|
| Buck (step-down) | D = Vout/Vin | Vout < Vin |
| Boost (step-up) | D = 1−Vin/Vout | Vout > Vin |
| Buck-Boost (inverting) | D = |Vout|/(Vin+|Vout|) | Any ratio, output inverted |
| Switch on-time | Ton = D/f = D×Tsw | — |
These are ideal formulas assuming continuous conduction mode (CCM), zero component losses, and 100% efficiency. Real converters need a slightly higher duty cycle than ideal to compensate for switch/diode voltage drops and conduction losses — the ideal value from this calculator is the starting point for compensator and PWM controller design.
The fraction of each switching period that the main power switch (MOSFET) is turned on, expressed as D=Ton/Tsw, ranging from 0 to 1 (0% to 100%).
Each topology stores and releases inductor energy differently relative to the switch state (buck connects the inductor to Vin only when the switch is on; boost stores energy in the inductor while the switch is on and releases it to the output when off), leading to different volt-second balance equations and thus different D-to-ratio relationships.
CCM means the inductor current never falls to zero during the switching cycle. These duty cycle formulas assume CCM and zero losses; in discontinuous conduction mode (DCM, typically at light load) the actual duty cycle needed differs from the ideal formula.
Real switches and diodes have voltage drops, and inductors/traces have resistance; these losses reduce the effective voltage delivered to the output, so the actual duty cycle must be somewhat higher than ideal to reach the target output voltage.
Approaching D=1 (100%) is not practical in any real converter — PWM controllers reserve a minimum off-time for control/gate-drive circuitry, so practical maximum duty cycle is typically capped around 90–95%.
The inverting buck-boost topology produces a negative output whose magnitude is set independently of polarity; using the magnitude in the ratio D=|Vout|/(Vin+|Vout|) correctly gives D=0.5 when |Vout|=Vin (unity magnitude inversion).
On-time is inversely proportional to frequency for a fixed duty cycle (Ton=D/f); doubling the switching frequency halves the on-time needed for the same D.
Yes, whenever Vout exceeds half of Vin (e.g. 12V→7V gives D=58%); there is no inherent 50% limit for a buck converter, unlike some resonant or half-bridge topologies.
Yes, the ideal CCM duty cycle formulas are the same for synchronous (using a low-side FET instead of a diode) and non-synchronous (diode) converters — synchronous rectification mainly improves efficiency, not the ideal duty ratio.
The converter's small-signal transfer function (and thus loop stability/bandwidth) depends on the operating duty cycle, especially for boost and buck-boost topologies where D directly affects the location of the right-half-plane zero.
For buck, M=D; for boost, M=1/(1−D); for buck-boost, M=−D/(1−D) (negative denoting inversion) — each is simply the inverse rearrangement of the duty cycle formula.
For a buck converter, D increases as Vin falls (to hold Vout constant); for boost, D also increases as Vin falls further below the fixed Vout — both need headroom in the PWM controller's duty cycle range to handle the full battery discharge curve.
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