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If you do manage to find a transformer which has a 6000:1 ratio and it is 100% efficient youl'll only have 1/6000th of the current at the output. What are you intending to drive with the 12V ac?
And in reality you'll have way less!!
Yes it is possible to step This up.
you will have to use an OPamp with Dual supply with Low offset and use the required Amplification, ofcourse you will require an external power supply to power it.
Dont ever think that you will be able to use a stepup transformer to do this job. it is not possible to build an ideal transformer, even with a superconducting wire you will be able to reduce the winding resistance but you cannot remove the interwinding capacitance. even if you can build a very special transformer, your 2 mv source should be able to deliver the magnetising current.
The new "giant magnetoresistance" based technology may provide a direct solution for your problem.
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