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TPS40000: Voltage mode buck compensation

Mike McDonald
Prodigy 140 points
Part Number: TPS40000

Hello:

In the TI whitepaper document: ``Switch-mode power converter compensation made easy``, under the section for compenstating a voltage-mode buck there is an equaiton (89) for selecting the midband gain (Avm = Wc/Wo*Avc), I was trying to work out the origin of this formula but was unable. It may be very simple and I am missing something so if someone could explain I`d be grateful. Thanks.

  • 0
    TI__Mastermind 23815 points
    Hi,

    Ok i will try to find the author

    Thanks
    -Arief
  • 0 in reply to Arief Hernadi
    TI__Mastermind 23815 points

    Hi,

    As it seems it is not that simple to derive the equation as shown on the article. The merit behind this equation is that when you put your zero at the same location of the double pole of the LC filter, then the bode plot of the overall loop response will be -20dB/decade instead of -40dB/decade. Therefore using this one pole approximation, the equation shows the ratio between wo and wc is going to be proportional to the ratio between Avm and Avc.

    Thanks and i hope that helps.

    -Arief

  • 0 in reply to Arief Hernadi
    Prodigy 140 points

    Hi Arief,

    I derived the formula: You are correct if one assumes the inverted zero and zero of the compensator are equal to the complex conjugate poles of the output filter (Wo) then, the combined transfer function of the power stage and compensator is given by:

    Avm*Avc*(1+wo/s)/(1+s/wo)

    For this TF to have a zero crossover at wc it must be equal to 1 when s=wc:

    Avm*Avc*(1+wo/wc)/(1+wc/wo) = 1

    Solving this for Avm gives the formula in  the whitepaper:

    Avm = wc/wo*Avc

    That's the answer I was seeking, thanks. 

    I really appreciate TI putting this information out, it's very helpful. Thanks

    mike