How to convert PS3/360 Sticks back down to PS2 console

Hello, how are you?

With the high numbers of people playing SF4 and the PS3/360 generation of video games, it makes it difficult to anyone to play PS2 generation games with the Arcade Stick.

In example I am trying to host a Capcom vs SNK 2 tournament, but the problem is everybody uses PS3 USB plugs. Is there some sort of adapter I can use to convert a PS3/360 signal into a PS2 signal?

So this isn't a thread about converting PS2 to PS3.
This is a thread about converting PS3 (and 360) down to PS2.

Any help would be appreciated, need tips asap!