I just put in a 10" woofer with a small amp. I have a Powermaster 130amp alternator (1 wire setup hooked up directly to the battery not the factory plug)

The alternator always charges around 4-6 volts then I rev it up a bit and it jumps up to 12 volts and no issues.. Now with the monster cable ran directly to the solenoid, the radio comes on fine when I first start the car but when ki rev it up to charge at 12 volts it shuts the radio down.