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[FAQ] How efficiency influences duty cycle in non-isolated DC/DC Converters?

Wenhao Wu
Genius 9046 points

A lot of engineers are using DC/DC converters for their power systems, in order to bring stable and clean power supply. As efficiency cannot be 100%, it must influence DC/DC converter's work in some way. This E2E FAQ will present how efficiency is influencing duty cycle D and bring origins of duty cycle calculation equations in TI's DC/DC converter datasheets.

  • 0
    TI__Genius 9046 points

    The relationship of efficiency η and duty cycle derives from Conservation of energy law:

    VIN*IIN*η=VOUT*IOUT

    Where:

    VIN: input voltage

    VOUT: output voltage

    IOUT: output current

    ŋ: efficiency

    Boost converter:

    For Boost converter, input current's average current equals to inductor's current average. We have:

    IL=IIN

    Inductor's average current has relationship to output current as:

    IL*(1-D)=IOUT

    Therefore, substitute above equations to Conservation of energy law, we have:

    VIN*IL*η=VOUT*IL*(1-D)

    Remove IL from equation, we build relationship between efficiency η and duty cycle D for boost converter:

    D=(VOUT-VIN*η)/VOUT

    Similarly, we have Buck converter and buck-boost converter's relationship

    Buck converter:

    D=VOUT/(VIN*η)

    Buck-boost converter:

    D=VOUT/(VIN*η+VOUT)

    Summary below:

    As what can be seen, the duty always increase as efficiency goes lower. This means the converter is trying to draw more energy from input side.

    Best Regards,

    Wenhao Wu

    Application Engineer, BCS