AC has a frequency, your request does not.
AC can have a frequency that is so low that you can see what it is driving moving slowly up and down, or it can have an extremely high microwave radio frequency.
If the efficiency is only 50% then for 12VAC at 3A output, either the 12V input must be higher and/or the 3A input current must be higher to produce the wasted 36W of heat.
A sinewave of 12V RMS has an output that is 34V peak-to-peak so a voltage boosting circuit must be used and a current boosting circuit must boost the current of 3A RMS which has peaks of 4.3A.
12V x 3A= 36W. What is it for? 12V DC is used in a car. A modern bridged class-D car radio can produce a sine like audio frequency output of 8.5V RMS into a 2 ohm speaker producing 36W.