Before you go hacking the plug off make SURE the plug does not contain the voltage dropping circuitry! Measure the voltage on the output side of the plug, if it's less than 12 volts then the plug is the dropping device. If you feed 12 volts to a 6-9 volt device, well, smoke is the usual result

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Your noise problem is most likely caused by a difference in grounds(commonly known as ground loops) used in the audio system. Experiment with grounding the components together with a jumper wire. Example: Ground the frame of the head unit and the frame of the Nomad to a common ground. If that doesn't work you might try an isolator between the head unit input and the Nomad output to break the ground loop. Any good stereo shop carries these. They can also help you solve the problem for a fee

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Alternator noise is a whine that increases in volume and frequency when the RPM's go up. In line filters can help cure this but don't count on it completely disappearing! A constant hum is usually a ground loop issue or a poor ground. I think the isolator would cure your problem since it doesn't happen on battery power.