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a large cap can be deep cycled for a very long time though. Even the best batteries hate deep cycles.
You have a maximum amperage that the system is capable of producing from the alternator. If ever the current draw exceeds the charging capability of the alternator, OR exceeds the current output of the voltage regulator, you have a problem. This is usually noted by a drop in the supply voltage, causing the customary dip in teh lights on bass hits.
Capacitor is very good if you exceed the current draw ONLY on bass hits. This would mean matching your car's capabilities. If you exceed them ridiculously, then nothing short of an alternator capable of keeping up with the system current draw will help.
By the way, one of my university lecturers has a patent on the super cap. Capacitor the size of a grape rated to about 5~10V with a capacitance of 55 farad (That is NOT a typo). So if people are making smaller capacitors, believe me its possible. I do however believe that many shops would sell a "Capacitor" without actually rating it, which is a rip. Caveat Emptor (Latin, means buyer beware)
As for class D, they are very kewl amps, run off nice big power mosfets. The only thing i would say about it due to the amplification technique, they're sound quality and faithful reproduction is sacrificed in order to achieve good amplification. Push pull amps (AB) are much cleaner, but as you mentioned are only usually 50% efficient. (Theoretical maximum is 75%). Class A are even more faithful again, but then they have a max efficiency of something like 25%. Class D are what is used in broadcast stations nowadays, any new radio trasnmitters are usually class D.
To be honest, if you bought some 0 Gauge wire, and wired up where the cap SHOULD go, walk into the hifi shop, and say, lemme plug it in, if my lights stop dimming, i'll buy the capacitor. That would be my advice to anyone with an unintentional light show! Whats a bit of wire gonna cost you? really?
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