Use a different bracket
An articulating arm on a single stud is a bad idea. Maybe if it's mounted very well in a wood stud with four 1/4 inch lag screws, maybe. Definitely not on a metal stud and not on plywood. With the arm swung over to one side and some human weight tugging on it, the leverage on the bolts is very high, and it's neither vertical shear nor pullout, but twisting the bolts sideways across the stud in a direction that studs were not meant to experience any force at all.
Buy a new bracket. Preferably not articulating. But regardless, one where the base of the mount is horizontal, at least 33 inches wide so you can mount on three studs, or if you'll use plywood as a sub-base and the wood is on three studs, your bracket should be at least 18 inches wide to reduce the leverage of an articulating arm.
Block out the studs
Some say the correct approach for an articulating mount is to open the wall, add wood studs floor to ceiling and wood blocking across them. I don't know if that's overkill but it's worth mentioning. I can't find any of those answers now but maybe someone will in comments.
Mount to the studs
This question discusses how to properly use a toggle bolt to mount to metal studs (my answer) and suggests in a couple of answers that sheet metal screws are even better, and how to choose and use them properly (answer from @StayOnTarget).
If you buy a bracket with a base that spans three studs with two screws in each you'll do pretty well, although I still would be wary of an articulating mount. The big variable is people grabbing the TV and tugging it in random directions with a ton of leverage.
Mount via wood
If you insist on using a smaller bracket, then you can simulate a larger one with a piece of plywood as you suggest. Mount the wood to three studs, two screws each, and the bracket to the wood.
Mount the bracket to the wood with nuts and bolts, big washers on both sides of the wood, and drill holes in the wallboard to accommodate the hardware sticking out the back of the wood. If you do it this way, the weak point will be the wood mounted to the metal studs.