Why does my radio rapidly turn off and on only when sitting at a stop light?

What is your question?

My radio will turn off and on rapidly when I'm sitting with the car in gear at a stop light. This normally only happens when the AC is on. If I turn the AC off then the radio plays fine. It's just an aftermarket head unit, no subs or amps. When I accelerate from the stop light, then the radio plays fine, even with the AC on. I checked all my connections to my stereo and they are fine, I had the same problem with a different head unit and replaced with a new one, and am still having the same problem. Any ideas would be greatly appreciated....p.s. I had the battery and alternator tested, and they are both good