convert 2.5VAC to 5V DC wave
I recommend you AC couple the signal to the ADC. This will create a high-pass effect, which, hopefully, will be acceptable.






simulate this circuit &ndash; Schematic created using CircuitLab

The high-pass frequency is controlled by R1, R2 and C1. You have to use the parallel combination of R1 and R2 (5k) for the RC calculation. In this case, the cutoff frequency of the high-pass filter is around 3 Hz. So 50 Hz will pass with very little attenuation.

Another thing to consider is that the source of the 50 Hz signal will see this as a 5k load. I do not know if that will be a problem because you have not mentioned where the 50 Hz signal is coming from. Assuming it can supply 1mA pp without sagging, there should be no problem.

You could make R1 and R2 larger (47k, or 100k) but then the effect of the 10 uA max leakage current might become a problem. I chose 10k to make sure that effect would be negligible.

Addendum about Mains Power:

Mains voltage is not well regulated. I would suggest you attenuate the signal further before sending it to the ADC, or add robust over-voltage protection to the ADC input. Also, for safety, make sure your step-down transformer provides good isolation. You should also probably have a fuse on the secondary side of the transformer. I am not an expert on mains powered equipment, but there are many safety hazards associated with it.