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I have determined the transfer function of my converter operating in closed loop configuration. Nevertheless I saw on the web that the transfer function is not the same if my converter follows a PFC. This refers to the Extra theorem element and the Middlebrook theory. A correction factor must be applied to the transfer function of the original converter to obtain the transfer function of the converter with the PFC. It depends of the output impedance of the PFC and the input impedance of the converter. I would like to know if it is possible to find the output impedance of a PFC. It seems possible to find to me the output impedance of a boost with the PWM average switch model but it seems to me difficult to find the output impedance of a PFC as the PWM average switch model is not defined and must be complicated to find as it depends on two loops? Isn't it? So do you have an idea to approximate the transfer function of my converter with a PFC "attached" to it?

Have a nice day and thank you for all you ve done :)

winny
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Jess
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  • The output of the PFC is such that for a certain variation of current, the voltage is constant. If the current increases, the resistance decreases; if the current decreases, the resistance increases. So it's a basic resistance. The input of your converter will have a negative incremental resistance, if it's a loop regulated SMPS. But the PFC could be modelled by a simple voltage source. – a concerned citizen Feb 16 '21 at 15:09
  • I do not think so ... But I may be wrong. Supose a boost converter, at s = infini, the ouput impedance delta(Vout)/delta(Iout) is nulled as the output capacitor is short circuited. If there is no ESR on the capacitor. Your point is I think true at s = 0 but I am not looking for the transfer function at s = 0. By using the average PWM switch on LTspice, I think it is possible to simulate the output impedance of a boost. But for a PFC i do not know a model for this... – Jess Feb 16 '21 at 18:05
  • That's true, but that doesn't stop you from adding a series resistance and a capacitor. At any rate, I was being cheap with the example, so for a more detailed analysis, Basso's book may help since (IIRC) it has an example of an averaged model for a PFC. – a concerned citizen Feb 16 '21 at 20:02
  • You re right ! I will take a look on it. I am a bit confused to see that the average model is the same than the one used for an other converter as the method used for the regulation is not the same in a PFC and for a current mode controller or a voltage mode controller. I may do not understand – Jess Feb 17 '21 at 09:53
  • Well, he would be better suited to make a comment, but the only differences between a "regular" boost converter and a boost PFC is the control law. They're both boost and both are (most often) current controlled, it's just that the PFC follows the shape of the input rectified voltage. Otherwise, their output voltage is regulated to meet the same requirements: keep the voltage even if the current varies. – a concerned citizen Feb 17 '21 at 11:04
  • You re right. But the PWM average switch depends on the control law, isn't it ? I will try to give a bounty to the question when it will be availaible. – Jess Feb 17 '21 at 12:32
  • Oh, if you meant in terms of modelling the PFC, sure, the control differs, but the principle is the same as in a boost converter. You can't just take an averaged model for a boost converter and use it as if it were a PFC; you do need to modify its control law. I was talking about what is seen from the outside, since that seemed to be what interests you (the output resistance to be used as input for your converter). – a concerned citizen Feb 17 '21 at 12:39
  • Well, I do not still get it ... I think the output impedance of the PFC depends on the control laws ? I will start a bouty tommorow :) – Jess Feb 17 '21 at 16:20
  • Have you seen [this link](https://www.onsemi.com/blog/innovation-forum/derive-transfer-function-of-pfc-stage/)? It's basically what I said (but with control). Here's a [quick hack](https://i.stack.imgur.com/5OarG.png). Why did you have to add the bounty? Now your points will be lost whether there's an answer or not. Well, if no one answers, I'll give you your points back. – a concerned citizen Feb 18 '21 at 09:56
  • The Zo impedance of the PFC appears to be just a capacitor with a negative series resistance that matches the average load – Tony Stewart EE75 Feb 21 '21 at 08:15
  • @aconcernedcitizen Thank you for all your replies. I didn't get all what you said, and I hope someone could help me to show me the direction in order to modelize the output impedance in order to see the impact on the regulation of the converter that follows. I will check the link :) – Jess Feb 21 '21 at 10:48
  • Thank you for the points ;) But that's not a problem if i loose some points :) – Jess Feb 21 '21 at 10:49
  • Your link seems to be amazing ! – Jess Feb 21 '21 at 10:50
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    https://www.nxp.com/docs/en/application-note/AN5257.pdf – Tony Stewart EE75 Feb 21 '21 at 13:40
  • Thank you ! I will take a look on your link ;) – Jess Feb 21 '21 at 18:52

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