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I was running 1200 watts on a 105A alt and the dimming was terrible, even after the big 3 and a yellow top under the hood. I upgraded to a 200A alt and the dimming **** near subsided. After I threw the stock batt back under the hood and the yellow top in the trunk I don't have problems at all. But to say 1300 watts would run off of a 105 alt is a bit ridiculous. I know for a fact you need more power than that. By the time I upgraded my alt the inside of the old one was burnt to hell and about to just die totally. I would recommend getting the bigger alt. Even if the dimming isn't horrible, your probably doing a shit load of damage to your alt and it's just gunna die on you sooner rather than later.
so with that said I would say leave the yellow top under the hood and put the money towards a new bigger alt. Check out KnuKonceptz, I can vouch for them, their alts are nice.