I'm trying to build a 3.3V power supply using a AP1501-33 switching voltage regulator. In the datasheet for the regulator there are two capacitors with no suggested values. How does one go about choosing/calculating the values of Cin and Cout?

 

220 uf should get you 50 mv or less of ripple. If you cant even less, use more capacitance. With a 3 am load, use a low equivalent series resistance (ESR) capacitor.

You may need to put a few in parallel to get the ESR and therefore ripple down to an acceptable level.

 

10uF multilayer ceramic seems to be popular, used in multiples for larger output currents.
You will also need some smaller ceramic caps in parallel to deal with the higher frequencies.

 

The evaluation board is an excellent place to check. I am surprised it is not in the datasheet though.

 

I was wondering if there were equations that would allow for choosing capacitors for different input voltages. For example the 12 Vdc input is going to come from half wave rectified 24 Vac. So, I think that Cin should be bigger to account for the varying input voltage, but I don't know by how much. Are these things usually figured out experimentally?

 

The input capacitor for a buck handles the discontinuous current. You will find numerous examples of how to calculate buck output caps, but rarely input caps.

However, TI has a good design note on the subject:
https://www.ti.com/lit/an/slyt670/s...25095&ref_url=https%3A%2F%2Fwww.google.com%2F

 

You can also pick up a copy of Switch Mode Power Supplies by Christophe Basso. He actually takes the time to derive formulas.

https://electronics.stackexchange.c...tage-and-output-ripple-voltage-for-capacitors