I'm testing a Switch Mode Power Supply that is not outputting the required voltage. It's only two prong, hot and neutral, and I wanted to get clarification on the best way to approach measuring the hot and cold sides respectively with my oscilloscope. The usage of the circuit is to charge a +12V battery. Just so it's clear, I'm an instrument technician by trade so I'm familiar with the dangers of mains voltage, 120VAC in my case, but I'm a few years out of school so I'm rusty on the usage of my scope.
First question is this: Even with a two pronged mains input, is an isolation transformer still needed?
When probing the hot side of the transformer, if isolated, can I use the common lead on my probe or will I need a differential probe since there's no ground and the reference will be neutral mains or the negative output of the full wave bridge rectifier?
Lastly, in this instance would I be able to use the "Bat-" as my ground reference for the cold side with my common lead on my probe?
Thank you everyone for your time and please let me know if I wasn't clear enough about something.
This is the SMPS that I'm testing at the moment, which is used as a +12V battery charger: -