Just I had a electrical burning smell coming into car. After research I found out it was my alternator. The smell is from a bad diode. If you have this problem you can confirm it is the alternator by taking it to AutoZone. And a word of advise, they are a bitch to change.
The alternator is better to replace than to repair. I found it costs me almost the same to replace than to repair in South Africa. You can safely replace it with the J2 Elantra 2.0 alternator. It also depends if you're running any amplifiers in the car or not. In that case I would replace the battery at the same time because those two components seem to have the same lifetime.
Search Hyundai Tiburon Questions
Hyundai Tiburon Experts