current control PWM switch model?

As I tried to derive the transfer function of the boost converter(peak current mode control) in CCM and DCM as Vout(s)/Verr(s) using the CC-PWM switch model accordingly to the book of Pr.Christophe Basso, I am currently facing some issues regarding the PWM switch model in Current mode. because in the Voltage mode I can derive the equations however when it comes to the current mode I cannot really derive it as I am completely confused about the PWM switch itself how is it derived. If I want to structure my questions, I will start first by showing you the model on the picture of the Pr.Christophe Basso ;

and now the transfer function I want to get in: and:

my questions are: as he derived his PWM switch model; I am wondering where is the term Verr and instead I find the term Vc which I don#t understand how he derived it? How do I replace the Vap and Vcp here, it seems to me for example in boost converter I have to use just the average value?

in the reference given, I checked the Dissertation Of Dr.Cuk but I found out that he was using state space machine and I want to learn to do it in PWM switch model for current control mode.

I have uploaded the small signal PWM switch model for boost converter as below best regards, Yaakov

• It it just me or is this too much name dropping? "Pr.Christophe Basso" twice and "Dissertation Of Dr.Cuk". Also, please start your sentences with capital letter. Voltage and current are spelled with lowercase letters unless the start of a sentence. – winny Mar 21 '18 at 13:16
• Sorry for that, I am new to StackExchange and it is in my learning curve. I dropped the names as they are my reference's work and want to give more details. – Yaakov Mar 21 '18 at 15:21

In these expressions, $V_c$ and $V_{err}$ refer to the same variable, the control voltage delivered by the error amplifier. Small-signal variables like $v_{ac}$ for instance have to be replaced by the right value depending on the PWM switch wiring diagram. For instance, in a buck CM, terminal c would be the node going to the inductor while terminal a would go to $V_{in}$. As $v_{ap} = v_{in}$ and $v_{in}$ is 0 V in this ac analysis, then the controlled source featuring $v_{ap}$ is also 0 in ac, simplifying the circuit by open-circuiting it. You have the example of a derivation in my APEC 2014 seminar using the PWM switch in a buck converter as shown below:
• The extra capacitor $C_s$ is added to model subharmonic oscillations with double poles located at $\frac{F_{sw}}{2}$. The dummy voltage source in series with terminal c is there to measure the current leaving the terminal. – Verbal Kint Mar 21 '18 at 19:34