Buck converter inductor calculation doesn't agree with typical application schematic

Question

Im trying to play around with some buck converters and have found one that I might want to make a circuit with. The IC I want to use is the the TPS53125 in QFN package. It's a dual output buck converter IC which takes between 4.5 V and 24 V.

Data sheet

When I use equation 3 from the datasheet to find the suggested inductor value for regulating 1.8 V with a max input of 24V and a output correct of 4 A I end up with the value of 4 uH for the inductor.

Working:

4uH is somewhere in the range that I would expect and sounds correct.

My problem is that in the example circuit above they use a 1.5 uH inductor although they try to regulate 1.8 V at a max of 4 A which should use a 4 uH inductor if you follow equation 3, but instead they use 1.5 uH:

So now I'm very unsure who is wrong? Is the diagram using an inductor value which doesn't conform to the equation or is my calculation faulty?

Answer 1

TI provides the sample design targeting 12V Vin. From the datasheet:

This explains the discrepancy between formulas (that assume 24V Vin) and the value of inductor in the example design. They should however mention this fact in their schematics, which boldly says "4.5V to 24 V", and you can try to advise them to correct the schematics.

However, I think the conversion from 24V to 1.8V is unwise, it will suffer in terms of efficiency.

CORRECTION: It is true that 12V V in doesn't change much the result. However, the whole selection of inductor uses just 30% ripple current at max load, and the datasheet has another note:

Note:The calculation above shall serve as a general reference. To further improve transient response, the output inductance could be reduced further. This needs to be considered along with the selection of the output capacitor.

So if you (I mean quality of your output capacitor) can afford 75% current swing in the inductor, then all numbers will align.

I would say this: don't confuse yourself with formulas too much, all simplified formulas are derived under many assumptions, which may or may not be exactly true. Always use the manufacturer's reference design as the main guidance. They build it, thoroughly characterized it, and sell it. More, if you want to avoid surprises, follow their recommended (tested!!!) layouts, and get their particular inductor from their BOM - not all inductors are made equal.