I'm currently designing a buck converter using the AP64501. This issue/question is not specific to that buck however. I have a python script that I wrote that uses the formula's in TI's appnote: AN-1197 Selecting Inductors for Buck Converters. As per their example, you either need to be given the specs for r, or directly given the r value. As per ROHM's appnote: Inductor Calculation for Buck Converter IC (and many other places) r should be around 0.2 -> 0.5.
In CCM mode, valid ranges for r are 0 -> 2 (source)
My design that is using the AP64501 is:
Using the TI appnote, if I use these values (as well as calculating v_sw and v_catch from the rds of both FETs, and an r of 0.3) I get an inductance value of 83.22uH, which is of course not ideal. If instead I use an output current of 5A (which is what the buck is rated for), I get 3.33uH, which is basically the exact value that the AP64501 datasheet uses. So I can confirm that these equations are valid for this converter at the max rated current for the buck.
The only way to have the inductance be near the 3.3uH recommended at 200mA is to increase the value of r to like 7.5, which isn't valid.
So what am I missing with respect to the r and converters at lower currents like this. Also, If I set the inductance to be 3.3uH for the rest of the equations to solve for inductor currents, energy, etc., since I fudged on the inductance, are these values even valid anymore?