If you think you're doing it faster than 45 minutes, then you're just cooking them. I did this for a couple years. Things got busy and I kept having to rush dinner, so I'd cook the onions on a higher heat and keep stirring them. And when they're done they still look caramelized, but caramelization isn't about color; it's about bringing out the natural sweetness in the onions.

Then one evening I bothered to take the time, let them simmer on low for an hour, and then I remembered what caramelized onions taste like.

Which is why I always say: if it takes less than 45 minutes, you're just cooking them.

As for my method, I start with a yellow onion, not a sweet onion. Sweet onions are cheating. I either dice them, mince them, or cut them into long strips. And yeah, I'll keep them on longer if there's less surface area. I start the pan with a pat of butter, a bit of oil, or both. Then I turn it on high because I'm allowed to be impatient for this part. Once it's sizzling, I add the onions, drop the stove to a one or a two, and cover it. I'll stir them once or twice, and if they're drying out I'll add a splash of water. Forty-five minutes is the minimum. After that I'll keep it on low until I'm ready to add them to the main dish. The longer they're on low, the sweeter and more complex the flavor gets.