There are a couple of issues being discussed, and they are not all the same thing......
Extra batteries will extend the playing time of the system with the engine off (TRUE)
An extra battery on an isolator will not extend the playing time with the engine off, but at least once you kill the "stereo" battery you can still start the vehicle. (TRUE)
However, here's where things get a little non-intuitive:
If you ran two batteries in parallel (no isolator), you would actually have LESS power available to run the stereo when the engine was running!!! The alternator now needs to maintain the charge on TWO loads instead of one, so you are really going in the wrong direction if a solid power source was the goal.
On a seperate note, capacitors are used because they discharge MUCH more quickly than a normal car battery....and most music is about QUICK transients...not sustained low freqency sinewaves. Yes, even a capacitor will eventually be depleted by sustained bass notes, but it does offer a significant improvement in the stability of the power being delivered to the amps.
Here's a clip from the rec.audio.car FAQ:
2.9 What is a "stiffening capacitor", and how does it work? [JSC]
Stiffening Capacitor (note capitals) is a trademark of Autosound 2000. However, "stiffening capacitor" (note lowercase), as a generic term, refers to a large capacitor (several thousand microfarads or greater) placed in parallel with an amplifier. The purpose of doing so is to provide a sort of reserve power source from which the amplifier can rapidly draw power when it needs it (such as during a deep bass note). The electrical theory is that when the amplifier attempts to draw a large amount of current, not only will the battery be relatively slow to respond, but the voltage at the amplifier will be a little lower than the voltage at the battery itself (this is called line drop). A capacitor at the amplifier which is charged to the battery voltage will try to stabilize the voltage level at the amplifier, dumping current into the amplifier. Another way to think about it is that a capacitor in parallel with a load acts as a low pass filter See section 3.10 What is a crossover? Why would I need one? [JSC], and the voltage level dropping at the amplifier will appear as an AC waveform superimposed upon a DC "wave". The capacitor, then, will try to filter out this AC wave, leaving the pure DC which the amplifier requires.
2.10 Should I install one in my car? If so, how big should it be, and where do I get one? [JSC]
If you have a problem with dimming headlights when you have your music turned up and the bass starts to hit and the engine is running and you don't want to upgrade your alternator, or if the transient response of your amplifier is unacceptable to you, a stiffening capacitor could help you out. The commonly accepted "formula" for determining the proper size capacitor to use is 1F/kW (one farad per kilowatt). For example, a system running at 300W would need a 0.3F (or 300,000uF) capacitor.
To install the capacitor, you should not simply attach it to your power and ground wires near your amplifier, as it will draw very large amounts of current from your battery and could blow fuses (or over charge). Instead, you should insert a small-value power resistor (25 ohm, 1/2 watt) or a 12VDC test lamp in between the power lead and the capacitor, and then charge it. If you use a lamp in series with the cap, when the lamp goes out, the capacitor is done charging. When it is done charging, carefully remove the capacitor's leads from the charging circuit, being certain not to touch the two leads together. You may then permanently install the capacitor by wiring it in parallel with your amplifier (be careful not to short the leads!). Large caps are currently available from some audio dealers, such as Phoenix Gold. You could also try electronics shops or mail-order houses.
2.11 What about adding a new battery? Or upgrading the amplifier? [IDB]
Generally, adding a second battery is great if you want to listen to your stereo with the car turned off (and be able to start it again later!). As far as simply upgrading your current battery to a larger model, you may find that this will help solve the problem because batteries like the Optima 800 offer a larger number of cold cranking amps. However, the "response time" between when a battery kicks in a large amount of extra current and how long it takes a capacitor is vastly different.
Although a battery may be able to respond in tenths of a second, bass notes are often much shorter and need current immediately -- which capacitors can supply. The difference between the two is that while the capacitor can supply a large amount of current immediately, their voltage quickly drops making them ineffective -- but by this time, usually the bass note has passed, and the capacitor has done its job of "stiffening" the supply voltage.
Upgrading your alternator becomes a concern when you need a large amount of current from it frequently. If you are always listening to your stereo at a fairly high volume (assume your amp is drawing 20A), and then you use the A/C and a few other misc. accessories in your car, you can get to the point when the alternator can no longer provide enough current to effectively supply the car and charge the main battery. So, the main battery is always supplementing the alternator's current supply, and slowly (but surely) dies a relatively quick death.
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