Control to Output transfer function of Buck converter.

[cupoftea]

Hi
TN-203 App note on page 8, Fig 6, gives the control to output transfer function for a Current Mode CCM Buck...

https://www.microsemi.com/document-portal/doc_view/124786-voltage-mode-current-mode-and-hysteretic-control

...This expressions doesnt incude the Duty Cycle or Switching period.
In App Note AN4716....(Page 8)

https://www.nxp.com/docs/en/application-note/AN4716.pdf

..it shows their expression for control_to_output of a Current Mode CCM buck....it does include Tsw and D.
So which is more accurate?

 

[Easy peasy]

For the U - semi - the plant response is for CCM ( pk curr mode control ) - the duty cycle does not impact the graph - except at light loads where the gain rises - and this is more of a load thing.

the reason the duty cycle does not matter so much is that for a simple buck, Vout = D. Vin, but the ckt response does not change depending on whether D is 35% or 75% - you get the same response to a small perturbation in D, or to Vin, or to load - this is true for some other toplogies in ( strictly ) DCM or CCM too.

at the boundary of DCM / CCM there will be a change in the plant response

--- Updated Apr 22, 2024 ---

If you are talking about the DC gain of the power stage - then yes you must include D - for a buck the max gain is of course 1.

--- Updated Apr 22, 2024 ---

Note the subscript dc on the following ( NXP )

the careful reader always reads best.

 

[cupoftea]

Thanks, thats very interesting, and as can be seen from the two App notes in the top post, they are both equations for control_to_output transfer function of a CCM current mode Buck,
One includes D, and one does not. Are you saying this doesnt matter?

I get what you are saying about the D not being needed, but then why does the nxp app note include it.?

 

[Easy peasy]

Hopefully it is sort of obvious that the term for DC gain has no terms that are freq dependent ( although in the real world - dead time comes into play at HF ) - this is why the plant response in the U-semi paper does not include a Duty Cycle term.

The DC gain does vary with Duty Cycle, but for a fixed operating point, the duty Cycle is fixed, as is the load and the Vin - the plant response is always measured at small signal at a fixed point - you can of course plot a whole lot of curves - for differing loads and duty cycles and Vin - but this often does not help with clarity ( even if it is done in the real world with a real converter as part of due diligence testing ).

Step response, especially larger steps - reveal things that a low level Bode plot cannot - which is why load stepping is so important for psu testing.

 

[cupoftea]

Thanks, yes indeed, DC only. In fact the two expressions both come up with the same Bode plots. However, they are different to the Bode plots produced by the ti.com Webbench...the x'over freq is only around 60% of what Webbench gives it. The phase margin is also only about half of what webbench gives it.

 

[Easy peasy]

I cannot comment on the accuracy or otherwise of web-bench