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SM72445: Input capacitance calculation for SM72445 / AN-2124

Part Number: SM72445

Hi TI-Team,

I'm working on a design with SM72445 and I found your document AN-2124 Power Circuit design for the buck boost topology.
I checked the calculations and I think I found a mistake.
The input capacitance of the boost part is given by C_in = \Delta Q_BST / \Delta V_in (beeing the electric charge and the ripple voltage on the input). Furthermore the electric charge is  calculated with \Delta Q_BST = D_BST * V_mpp / (8 * f_s^2 * L) ( beeing the boost duty cycle, the in put MPP-voltage, the switching frequenz and the inductance used).
The document concludes with C_in = V_out - V_mpp / (8 * f_s^2 * L * \Delta V_in).
Ich think the wrong duty cycle was used and it should rather be C_in = (V_out-V_mpp) * V_mpp / (V_out * 8 * f_s^2 * \Delta V_mpp * L)

Am I missing something here?

All the best,
Frieder

  • Hi Freider,

    Thank you for the post. Let me study this and get back to you tomorrow.

    Thanks,
    Youhao Xi, Applications Engineering
  • Hi Frieder,

    I took a look, and Yes, you are correct that there is an error in the equation. Your derivation is correct, but it is only applicable to the Boost mode. For Cin selection, it should consider the buck mode, which is actually the worst case for the input current ripple voltage calculations, because the input capacitor will see the switched current pulses, namely the chopped inductor current pulses. Therefore,

    Delta_Q = Io x Dbuck /Fsw

    Io = Impp x Vmpp /Vo

    Dbuck = Vo /Vmpp

    Delta_Q = Impp /Fsw

    Therefore, Cin >= Impp /(Fsw x Delta_Vin)

    Where Impp is the Impp max power point current.

    Similarly, the output capacitor should be chosen by evaluating the chopped inductor current pulse that flows into the Cout, which yields the following:


    Cout >= Impp x Vo /(Fsw x Vmpp x Delta_Vo)


    Hope this helps.

    Best Regards,
    Youhao Xi, Applications Engineering
  • Hi again,

    thank you for clearing the first question.

    I also did the calculations of the chopped input and output currents to determine Cout and Cin.
    I get to another result though.
    Concerning Cin of the buck mode I think it should be:

    Delta_Q = Impp x Dbuck /fsw

    Because its the input current that the capacitor has to take in that switching period.
    which would lead to:

    Cin = Impp * (1-Dbuck) / (Delta_Vin * Fsw) = Impp * (Vmpp - Vo) / (Vmpp * Delta_Vin * Fsw)

    The output capacitor however has to provide the output current in boost operation, so:

    Delta_Q = Io x Dboost /fsw

    and therefore:

    Cout = Io * Dboost / (Delta_Vin * Fsw) = Io * (Vo - Vmpp) / (Delta_Vin * Fsw * Vo)

    Thank you for your support!
    Frieder
  • Hi Frieder,

    It is not correct to use Impp x Dbuck/fsw to calculate the Delta_Q. Immp is the average current. The Delta Q is calculated with Io x Dbuck /fsw, where Io is the output current which is also the inductor dc current in the buck mode. It is the chopped inductor current, not the input current.

    Similarly, for the boost, the output capacitor sees the chopped inductor current, not the load current.

    Thanks,
    Youhao Xi, Applications Engineering

  • Hi Youhao Xi,

    sorry for keeping this up. But I think it's still not correct.
    You are right that the first formula I gave was not correct, it was I typo. I continued with the correct formula. Because it should be

    Delta_Q = Impp x (1-Dbuck) /fsw

    When the highside switch is open (during 1-Dbuck) than the only way the Input current has, is going into Cin. There is no other way.
    What am I getting wrong?
    Also the inductor current ist never chopped, is it?
  • Hi Frieder,
    Yes your are right. There was a typo in my previous msg. Sorry for the confusion.

    Thanks,
    Youhao