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Duty Cycle (D)

The ratio of the ON time (TonT_{on}) to the total switching period (TsT_s). It governs the average output voltage (Vout or VavgV_{out} \text{ or } V_{avg}) in many converters: VoutDVinV_{out} \approx D \cdot V_{in}.
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The statement of the theorem

Let TsT_s be the total switching period and TonT_{on} be the duration during which the switch is ON. The duty cycle DD is defined as the dimensionless ratio:\nD=TonTs such that 0 and D are constrained by 0 and 1D = \frac{T_{on}}{T_s} \text{ such that } 0 \text{ and } D \text{ are constrained by } 0 \text{ and } 1