"Big Three"
How do you "know" it's because the alternator is not charging the battery fast enough ? So your system is truly drawing so much power that not only does the battery have to fill back up the alternator for peak transients, but is used so heavily that the voltage drops so low as to turn the system off ? If that is the case, then not only will you need a HUGE alternator to keep up with the demand, but your battery is toast as well from all of the discharge, recharge cycling it's been going through.
Upgrading some wires is not going to cure this problem, if the problem truly is because of too much current draw from the alternator. What amps do you have that are using this much power ?
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I agree with Mike - the cabling is not your problem. Certainly it won't hurt to do the upgrade but it definitely won't solve your current problem (pun intended). The big clue is that it only happens at low rpm. That means that the cables are quite capable of handling the charging at higher engine speeds. Cable resistance doesn't change with engine speed but alternator output does. The problem is that your alternator isn't putting out enough current at low engine speed. Upgrading the cables won't change that - only upgrading the alternator will.
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my buddies 97 TA on stock alternator, with big 3
is running 2 BP1200.1 amps and a 4 channel. The substage is 2400watts rms alone, so way more then your car is pulling and he is fine
2400 watts is about 170 amps of current... those amps are definately struggling to make power.





