The following article talks about the theory and application of installing the right subwoofer capacitor to improve the performance of your bass system. It discusses some of the concepts and calculations of subwoofer capacitors and gives my recommendations on how to choose the right size capacitor for your audio system.

Article:

Here’s a little secret about audio and power ratings that most people don’t know….
The maximum RMS power you can deliver to a resistive load is equal to V*V / R

Where V = your power supply regulated voltage (of 12 to 14 volts in a car audio system)
and R is the resistive load of your subwoofer which ranges from 1 ohm to 8 ohms for different car subs and configurations.

And thus there are 2 ways to get more peak power out of your subwoofer setup…

1- Get an amplifier that has a built in power supply with a step up DC to DC converter, for example boosting the internal supply voltage of the amplifier from 12-14volts to 24-28volts using a capacitor ladder or voltage doubler circuit.

2- Speakers are not entirely resistive load they are more of an inductive load (combined of a resistive part and an inductor coil). At the same time the amplifier is not a pure power source and has its own internal resistance and a capacitive nature as it stores and delivers power to the subwoofers. By studying and exploiting these characteristics of subwoofers and amplifiers it becomes possible to momentarily deliver a voltage spike between the amplifier and subwoofer giving it a higher momentary peak power. This is where the term PMPO (peak momentary power output) comes from and in the more educational circles is referred to as an ILS rating “If Lightning Strikes the amplifier, it may deliver 3000 watts to a 2 ohm load for a very short duration of time effectively consuming all of the energy inside the amplifier to overdrive the subwoofer for that short duration of time”

Anyhow, both the methods mentioned above of delivering more power to an unchanged load rely on the concept of power storage and momentary power delivery…. If we can charge an ignition coil using 14 volts for 1 minute, and then use that same amount of charge to deliver 24,000 volts to the spark plug for 10 milli seconds to ignite the mixture inside the engine, then similarly, we can charge our amplifier circuitry using 14 volt power and then deliver a momentary 200 to 300 volts (inductive load spikes on 14 volt fuel injectors with tiny solenoid coils can be as high as 60 volts and so on a larger coil such as a subwoofer voice coil higher voltage spikes are not out of the ordinary), then we can over extend our subwoofer’s performance and power delivery.

This is where a good audio capacitor comes into the question… An audio capacitor keeps a good amount of power stored near the amplifier, this doesn’t really affect RMS audio performance that much so long as the alternator charging system is capable of delivering a steady 14 volts to the amplifier at the back of the car. However, when it comes the time to reach deep into the amplifier to deliver our peak momentary power output of 3000 watts into a single channel (or however much your amplifier is rated for per channel) then having a capacitor bank charged and ready to delivery such power is critical. What’s even more important, and what makes a capacitor shine over having a second battery installed in the trunk of the car, is that a high quality capacitor, has a really low series resistance built into it. This extremely low E.S.R (equivalent series resistance) that is characteristic of a good audio capacitor allows the capacitor to deliver it’s stored power to the amplifier (and thus to the subwoofers) almost instantaneously. This is even more important when you think about a 125hz audio signal that need power to be charged and delivered in the amplifier 125 times per second.

Here’s a great example of a power audio subwoofer capacitor. The boss audio Cap10 capacitor here has an 10 Farad rating, a digital control circuit, and a voltage indicator, with an ultra low E.S.R. of less than 0.002 ohms.

A 10 Farad capacitor running at 14 volts can store up to 140 Coulombs of charge or 980 Joules.
When we look at the fastest possible ‘bass’ frequency of 250hz then we have a wavelength with a duration of 4ms.
If we deliver half of our charge energy of 980 Joules to our subwoofer in 4ms, and keep the capacitor running at 50% (i.e. it is charging and discharging at the equal rate of 4ms which is the most we can take without draining it) then the maximum power we can deliver with such a capacitor without draining it (for the next coming bass hit) will be:

Peak power (Watts = Joules / Second) = (980/2) / (0.004) = 122,000 Watts !

Hrm, so why do we need such a large capacitor for a 1000 to 4000 watt system ?

The reason we need such a large capacitor, is that although capacitors can discharge power very rapidly, they take a long time to charge up. For example our 10 Farad Boss Audio Cap 10 , connected to the battery power through a low resistance 2 ohm power cable, will draw 7 amps of power for 100 seconds just to reach full charge… if we use higher resistance lower quality power wires, this charge time will grow even more.

So we have to use a larger capacitor bank because we have to find a balance between the capacitor charge and discharge characteristic as follows.

Say we have a 3000 Watt sound system wired up to the Cap 10. That 3000 Watt system for a slow 250hz bass hit will consume 12 Joules of energy in those 4 milli seconds.
E=0.5CVV and so V= sqrt ( 2E/C)
We started with 980 Joules of eneregy at a fully charged 14 volts.
We delivered 12 of those 980 Joules to our 3000 watt system in 4 milli seconds.
Our new Energy level is 968 Joules and our new voltage is 13.9 volts.

Let’s redo this calculation with a 1 Farad capacitor and a 3000 watt system
1 Farad gives us an energy of 98 Joules at 14 volts.
To reach that level of charge it takes the capacitor 10 seconds of total charge time (which makes sense since it’s 1/10th the capacitance, it takes 1/10th the charge time).
But look at what happens when we deliver 12 joules to our 3000 watt system in 4 milli seconds?
Our new energy level is 86 Joules and our new voltage is 13.1 volts

Now you see from this comparison that the 10 Farad cap is still fully charged after the first 3000 watt bass hit, on the other hand our 1 Farad cap has lost 1 volt which it has to replenish.
How long does it take the 1 Farad to re-charge again ? The answer is about 5 seconds. So, a couple of consecutive 3000 watt bass hits and your 1 Farad cap becomes a drain on your system rather than a power source, whereas the larger 10 Farad still has a stable 13.x volt power supply to your amplifier.

Let’s go one step further and try to scientifically answer the question: How big a cap do I need for my system ?

The following is calculated as a minimum subwoofer capacitor required to maintain a voltage of 13.8 to 14.0 volts for the power level indicated….

Now this is the first time I crunch these numbers but it’s very interesting to look at things this way.

Another great feature of the Boss Cap10 is that it has built in digital circuitry to do 2 things:

1- Monitor your running voltage level and warn you if your voltage dips below a safe level.
2- To monitor the charging and discharging of the capacitor. A charged directional electronlytic capacitor can be dangerous without proper monitoring circuitry.

Reverse the polarity of the wiring on a bare electrolytic capacitor, charge it for 3 seconds and watch it explode (I’ve seen this mistake first hand in my EE250 laboratory back when I was in college). Reverse the polarity on a 10F capacitor and you’re asking for trouble.

Then again, fully charge a 10F capacitor and then accidentally short it, and watch the flames. As we stated before these caps have an ultra low ESR (equivalent series resistance) and so if you short a 14 volt capacitor that has an internal resistance of 0.002 ohms then the peak current it can deliver is 7000 amps. You really don’t want to be the fire starter.

So to be able to deliver to you a powerful, effective, and SAFE product Boss Audio has included an charging and discharging circuit monitor to shutdown against reverse polarity wiring and protect against short circuits and thermal overload protection. Totally awesome.

Note: Read more about the Boss Cap 10 Subwoofer Capacitor, deliver more peak power to your system, and save 150 dollars off of MSRP.

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