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I'd like to preface this by saying that I have bachelor's degrees in electrical engineering and computer engineering, and I have experience designing, building, and testing DC power supplies and board-level analog and digital circuits. I'd like to fill in some blanks and resolve some misconceptions regarding "voltage stabilizers".
A typical car battery may hold on the order of 50 amp-hours, or 180,000 coulombs of charge. At 12.6 volts, that's equivalent to around a whopping 14,000 farads. By comparison, let's be really optimistic and say that a "voltage stabilizer" contains 100,000 microfarads (say, fifty 2000 uF electrolytic caps), or 0.1 farads. Putting that in parallel with your battery increases its capacitance by 0.0007%. My point is that compared to the relatively huge capacity of your battery, the capacitance of a "voltage stabilizer" is practically nothing.
Various sources I've found online put the internal resistance of a typical car battery on the order of 0.01 ohms. In other words, car battery will only drop about a volt during a brief 100 amp drain. A typical alternator can provide up to 70 amps at full load, such as while powering accessories and recharging the battery. Alternator noise depends on engine speed, but is typically in the audible range, in the hundreds or thousands of hertz. Head- and taillights together draw around 10 amps of pure DC, and your audio system might draw as much as a couple dozen amps, again with frequencies in the audio range.
With such high amperage, relatively low frequency currents coming out of the alternator, into the accessories, and in or out of the battery, the "voltage stabilizer" doesn't have a chance of noticeably impacting the car's electrical system voltage. It's orders of magnitude too small.
An important question that nobody seems to ask is, what specific problem are "voltage stabilizers" meant to solve? Noisy power to the ECU? To the audio system? If these were actual problems, a much better solution would involve one or more LC circuits (pi filters, as mentioned earlier) and/or an active semiconductor voltage regulator in series with the supplies to these components. A relatively microscopic capacitor in parallel with the entire electrical system won't cut it. Chances are good that the ECU already has a semiconductor-regulated supply, but I haven't dissected mine, so I can't say for certain. However, both devices were designed to be powered by an alternator, and both have their own internal power filtering.
In summary, my expert opinion: it's a waste of money. Any benefit one might experience will be due to the placebo effect or simple experimental variation. This I can say without owning or testing a "voltage stabilizer", as the principles by which it is supposed to work are well understood, and have been known and studied for over 200 years.
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