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TPS560430-Q1: PCM control equation deduction problem

user4803816
Prodigy 40 points
Part Number: TPS560430-Q1

From the application report "Loop Response Considerations in Peak Current Mode Buck Converter Design", the Gdi‘s expression from equation 2 simplified to equation 3, Gdi=Vin/s*L, the reason is "The internal loop compensation is designed so that the crossover frequency is much higher than the corner frequency, 1/(2π√LCO). For crossover frequency and higher frequency, Equation 2 can be simplified"as Equation 3. "

My question is i could not understand the simplification procedure well, as why we just care about the crossover frequency or higher frequency? Why the frequency range below crossover frequency is not important?

Thank you

  • 0
    TI__Mastermind 27470 points

    Hi 

    because in the low frequency, Ipeak=Icomp,so the inductor looks like a constant current source, the output load will be the major pole equal to 1/2*PI*Ro*Co.

    only when the frequency is high, the inductor will be consider as another pole appeared in the system. so at this time 2*Pi*f is very large which can be consider to Vin/sL

    Thanks

  • 0 in reply to Daniel Li14
    Prodigy 40 points

    Hi

    Thank you for your reply, I also noticed that you are one of the authors., i really appreciate your work and would like to further study the report.

    For your first statement, i think which can explain the output impedance's equation(1);


    But for your second statement, "only when the frequency is high, the inductor will be consider as another pole appeared in the system",

    i still can not understand well, can you explain in more detail or can you share some dedicated material could help explain?

    (I can only observe a pole when an equation has been written down, but before that, i could not recognize somewhere will appear a pole when frequency changes.)

    Thanks

  • 0 in reply to user4803816
    TI__Mastermind 27470 points

    HI 

    Gdi=(1+s*Co*Ro)/(Ro+s*L+s^2*L*Co*Ro) when f is lager 1+s*Co*Ro~=s*Co*Ro; Ro+S*L+s^2*L*Co*Ro~=s^2*L*Co*Ro

    so Gdi=Vin*s*Co*Ro/s^2*Co*Ro=Vin/s*L it means in high frequency, Gdi is ~=Vin/s*L

    you can refere below article for PCM modeling 

    http://www.ti.com/lit/an/snva555/snva555.pdf