In the book, Power Electronics, by Need Mohan at the end of chapter 7, it is this image:
Relating the output power and the power that the transistor is handling, I want to reproduce this plot for the buck, boost and the buck-boost converters, but I don't quite understand how to write down the equations.
I understand the boundary values at D = 0, D = 1 for the buck and the boost since the transistor is either on or off during the whole period, But I'm not sure why the relations is completely linear.
In the book, fundamentals of power electronics by Robert Erickson there is table regarding this subject
In this case, there are no plots, and obviously, the plots of this equations will be different that the ones in the above image.
Both, the images and the table give some kind of intuition that if possible it's better to use the buck or the boost converter instead the buck-boost.
I believe that both, buck and boost converters are more efficient than the buck-boost but is still hard for me to made that claim without more information. There is other book or article which covers this subject more in-depth?