I need a 1:1 isolation transformer and was curious if that could be achieved by using two similar 12v transformers with the secondary’s connected to each other?

 

Yes. But it would not finish up being exactly 1 : 1. It would probably be something like 1: 0.9 which would probably be OK if it is just for safety when repairing things.

 

But it would not finish up being exactly 1 : 1. It would probably be something like 1: 0.9

Why do you say that?
If the output is unloaded, then with identical transformers, it should be very close to 1:1.

The voltage will decrease with load, of course, and the load should probably be no more than about 50% of the transformer VA rating for a tolerable voltage drop.

 

The transforner would be designed to give the rated output voltage at the rated load. To do that the transformer would have to be designed to give a slightly higher open circuit voltage so that the voltage drop caused by winding resistance and leakage inductance would drop the open circuit voltage to the required full load voltage. So for example if the input voltage was 240 volts and the output voltage (Open circuit.) was 12 volts then the ratio would be 20 : 1.

But to allow for say a 1 volt drop due to losses at full load the ratio would have to be adjusted to give 13 volts off load which would be a ratio of 240 : 13. So when the two transformers were used back to back the first transformer would be outputting 12 volts at full load.

The second transformer has a ratio of 13 : 240 (As it is used in reverse.) so (12 x 240)/13 = 221.5 volts. You would than also have resistive losses in the second transformer which would cause a further drop in the output voltage when it's 240 volt winding is loaded.

 

You appear to be unduly complicating the calculations.

If the transformers are identical, the unloaded output voltage will essentially equal the input voltage regardless of their turns ratio.

So the main voltage drop of concern would be due to the load current through the winding resistances.

This means the percentage voltage drop for a given load would be twice that of one transformer.

That's why I recommended loading the transformers no more than 50% of their VA rating.