Q1: "I removed a Sony XRCA600X from a 1993 Peugeot 405. It was working fine in the previous vehicle it was in. Now it won't hold its memory. If I switch off the ignition and then turn it back on it works fine, but if I leave the ignition off for a couple of minutes it loses its memory. Is there a fault in the head unit or is there a special way of programming these?"
A1: It sounds like you've connected the head unit's constant power lead to switched twelve volts. The constant wire is what supplies power to the head unit's memory while the car is off. The head unit will keep the memory for a few moments after the power is turned off because it is running off the residual voltage in the internal capacitors. As they discharge the head unit loses it's memory. Check your connections and make sure you connect the constant power lead to a constant +12 volt source.
Q2: "I have a Sony CD player and normal aftermarket speakers (no subs as of yet). When I turn the car to just accessory position and turn the radio up to a loud volume, (not too loud, but loud) the cd power kicks off. It will try to come back on but if I don't turn it down it will just do the same thing right away. Also, not sure if this pertains to this issue or not, but the head unit lights dim quite a bit when the little bit of bass hits. There is no amp in the car right now, I'm waiting for the wiring and box to come in the mail!"
A2: Though it is unusual it sounds like your head unit is drawing enough power to cause a voltage drop in your system. That makes me suspect that your battery is in need of replacement. Usually that only happens with amplifier in the system. I'd definitely get that checked out before your amp comes in as the problem will only get worse. Most auto parts stores will check your battery for free.
Q3: "What is the safe way to connect two amps together to use both their power in two subwoofers?"
A3: You have to wire one amp to each subwoofer. You can't combine the power of two amplifiers together to drive one (or more) speakers. Doing that will damage your amplifiers. It is possible to run a subwoofer with multiple amplifiers if the subwoofer has multiple voice coils but that's unusual and not necessary in most cases.
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