Why does boost voltage rise as D increases?

In CCM the inductor is charged for fraction D of the period and transfers energy to the output for (1−D). The volt-second balance yields V_out/V_in = 1/(1−D), so larger D means a smaller off-interval and higher voltage gain—until nonidealities and DCM invalidate the ideal formula.

When is V_out ≈ D·V_in wrong for a buck?

That average holds in ideal CCM. In discontinuous conduction mode, with large ESR, or with significant diode/switch drops, the ratio departs from D. A misconception is that duty cycle alone always sets the ratio regardless of load current and inductance.

What does the ripple cartoon represent?

It sketches the triangular inductor-current and capacitor-voltage ripple expected from the switching period under CCM averaging—not a full SPICE transient. Use it to build intuition that higher frequency or larger L/C reduces ripple amplitude for a given power level.

DC–DC Buck / Boost

Ideal CCM averages: buck V_out ≈ D·V_in, boost V_out ≈ V_in/(1−D); schematic + ripple cartoon.

About this model

Ideal continuous-conduction-mode (CCM) averages for two classic DC–DC stages: the buck converter gives V_out ≈ D·V_in, while the boost gives V_out ≈ V_in/(1−D), with D the switch duty cycle between 0 and 1. The schematic and ripple cartoon show inductor current and capacitor voltage ripple trends under the averaged switching model. Assumptions: ideal switches and diodes, CCM (inductor current never reaches zero within a cycle), neglected ESR and switching losses, and quasi-steady averaged voltages across the period. You can vary D and input voltage conceptually through the ideal relations and compare buck step-down versus boost step-up behavior together with qualitative ripple size.

Who it's for: Intermediate power electronics, mechatronics, and embedded systems courses introducing switched-mode supplies.

Key terms

buck converter
boost converter
duty cycle
CCM
DC–DC conversion
inductor ripple

How it works

Ideal continuous-conduction average models: buck Vₒᵤₜ ≈ D·Vᵢₙ, boost Vₒᵤₜ ≈ Vᵢₙ/(1−D). Real converters add switch drops, inductor resistance, and discontinuous conduction at light load.

Key equations

Buck: Vₒᵤₜ/Vᵢₙ = D

Boost: Vₒᵤₜ/Vᵢₙ = 1/(1−D)

Frequently asked questions

Why does boost voltage rise as D increases?: In CCM the inductor is charged for fraction D of the period and transfers energy to the output for (1−D). The volt-second balance yields V_out/V_in = 1/(1−D), so larger D means a smaller off-interval and higher voltage gain—until nonidealities and DCM invalidate the ideal formula.
When is V_out ≈ D·V_in wrong for a buck?: That average holds in ideal CCM. In discontinuous conduction mode, with large ESR, or with significant diode/switch drops, the ratio departs from D. A misconception is that duty cycle alone always sets the ratio regardless of load current and inductance.
What does the ripple cartoon represent?: It sketches the triangular inductor-current and capacitor-voltage ripple expected from the switching period under CCM averaging—not a full SPICE transient. Use it to build intuition that higher frequency or larger L/C reduces ripple amplitude for a given power level.

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