Crystal Ring

The Crystal Ring is an optional upgrade from the game Sonic Adventure and its remake Sonic Adventure: Director's Cut, which becomes available after Sonic gets the Light Speed Shoes. It is a bracelet that allows Sonic to halve the time it takes to charge the Light Speed Dash and the Light Speed Attack. This upgrade is optional, but can come in very handy.

Using the Crystal Ring changes Sonic's aura when charging up his techniques from blue to turquoise.

Location
The Crystal Ring is found behind a door inside the hotel in the Station Square Adventure Stage and can only be accessed via the Light Speed Dash, which can only be done by obtaining the Light Speed Shoes.

First, Sonic has to climb the stairs on the left side of the hotel entrance. On top of it there are two buttons; one to open a door on the other side of the lobby, but only briefly, and the other creates a trail of rings leading to it. Use the Light Speed Dash immediately on the trail of ring to pass through the door in time and the Crystal Ring can be found behind it.

Trivia

 * Since Sonic Adventure is the only game where the Light Speed Dash requires charging by spin dash (having been switched to a single button-press onwards), this may explain why this upgrade has not appeared since.