Duty cycle of a step-down (buck) chopper Select the correct definition of duty cycle for an ideal step-down chopper switching with period T and on-time Ton. Also infer its relation to the output/input voltage ratio.

Introduction / Context:The duty cycle of a chopper determines the average output voltage. In a buck (step-down) converter, the control variable is the fraction of time the switch stays on within each switching period.

Given Data / Assumptions:

• Ideal components (no drops, no ripple for average relation).
• Switching period T with on-time Ton and off-time Toff.

Concept / Approach:By volt-second balance on the inductor in steady state, the average output voltage equals the input voltage multiplied by the duty cycle. Hence, duty cycle is defined as Ton/T and directly scales the output.

Step-by-Step Solution:Define D = Ton / T.Apply inductor volt-second balance: average inductor voltage over one period is zero.During on: V_L ≈ Vin − Vout; during off: V_L ≈ −Vout.Set D*(Vin − Vout) + (1 − D)*(−Vout) = 0 → Vout = D * Vin.

Verification / Alternative check:Simulation or measured average output of a PWM buck confirms proportionality to D for continuous conduction.

Why Other Options Are Wrong:Toff/T: That is 1 − D, not D.Vin/Vout or inverse powers: Dimensional/physical mismatch.f_s/Vout: Nonsense dimensionally (Hz/Volt).

Common Pitfalls:Confusing duty cycle with conduction ratio in discontinuous mode (where Vout relation deviates), or ignoring non-ideal drops that slightly reduce Vout.

Final Answer:D = Ton / T (and ideally Vout/Vin = D)