The Fake Coin

You have twelve coins. You know that one is fake. The only thing that distinguishes the fake coin from the real ones is that its weight is imperceptibly different. You have a perfectly balanced scale. The scale only tells you which side weighs more. What is the smallest number of times you need to use the scale to find the fake coin?

Use only twelve coins you have and nothing more, like other weights. Don’t cut the coins, don’t make any marks on the scale, etc.

These are modern coins, so the fake coin is not necessarily lighter.

Presume the worst scenario, and don't hope that you will pick the right coin on the first attempt.