Buck-Boost Duty Cycle

Formula

Description

The inverting buck-boost converter can produce an output voltage that is either higher or lower than the input, with inverted polarity. The duty cycle determines the output voltage magnitude. At D = 0.5, Vout = Vin. For D < 0.5, the converter acts like a buck (Vout < Vin). For D > 0.5, it acts like a boost (Vout > Vin). This topology is used when the input voltage range straddles the desired output voltage, such as single-cell Li-ion (2.7-4.2 V) powering a 3.3 V rail. The SEPIC and Ćuk converters share this same duty cycle relationship.

Variables

• D — Duty cycle (ratio 0 to 1)
• V_out — Output voltage magnitude (V)
• V_in — Input voltage (V)

Practical Notes

This is the ideal (lossless) relationship. Real converters have higher duty cycles due to switch, diode, and inductor losses. The formula assumes continuous conduction mode (CCM). In discontinuous conduction mode (DCM), the relationship changes and depends on load current. The same formula applies to SEPIC and Ćuk converter topologies.