Capacitors. The math behind the myth!

[SterTheDer]

Common misconceptions about Capacitors, and the math to back them up.

The single BIGGEST misconception about audio.

"The rule of thumb is to put in 1 Farad of capacitance for every 1,000 watts RMS of total system power... The larger the cap, the faster it gets ready for the amp's next big hit."~ Crutchfield.com

Before I deconstruct this myth, lets cover the basics.

What is a capacitor?

Simply put, a capacitor is an electrical device that stores a voltage potential. It stores power in the same way that a cup holds water.

In this analogy, Capacitor voltage = Cup water level

and Capacitance = volume of container.

For the capacitor to do anything, it requires a voltage drop. For water to be used, the water level in the cup must be lowered.

The water (Volume) will flow from the point of highest elevation to the lowest.

Current flows from the point of highest Voltage.

Whatever has the highest voltage in an electrical system will supply the rest of the system.

(Water flows downhill!)

This means that it is IMPOSSIBLE for ANY NUMBER of batteries to be of ANY USE if your current draw does not exceed the limits of your alternator.

The cars alternator will supply ALL the current/power at about 14.8v

(The alternator has the highest voltage at this point)

Voltage drops below 14.8v when the current draw is greater than the alternator output.

How much this voltage drops is dependent upon the alternator and current draw.

Voltage will continue to drop until it reaches 12.8volts.

The cars battery/ies will supply all the necessary current below 12.8v

(Here, the alternator voltage output drops to the level of the batteries, and the batteries will supply the current needed)

If the current draw continues, the batteries will eventually be depleted, as indicated by a voltage below 11 volts.

(the chemical reaction in the batteries is exhausted, and the batteries can no longer support the load)

Voltage of 10.8v or lower indicates that you have completely drained all the reserve capacity of your battery.

(Probably should turn it down now and let things recharge)

Now that we have this understood (you took notes right?);

Consider this scenario: Stock electrical. Aftermarket audio system where the amp draws more current than the alternator can supply.

System drops voltage from 14.8 volts to 12.8v. After some time the voltage drops to 10.8v.

MATH:

E = (1/2)* C * V^2

Joules(Watt-seconds) = (1/2) * Capacitance (Farads) * Voltage^2

1 farad capacitor:

E= (1/2) * 1 * 14.8^2

E = ~109.52 Joules of energy.

This is how many Watt-Seconds the 1farad capacitor can supply from 14.8 volts down to 0 volts.

to figure out how much power would be supplied to the system, we calculate the difference in stored power across our voltage drop.

1 Farad capacitor:

14.8v = ~109.52 Joules. <- Vehicle charging voltage. The ideal maximum voltage your car will see.

12.8v = ~81.92 Joules <- Battery voltage. The maximum voltage your batteries can supply.

10.8v = ~58.32 Joules <- Critical battery voltage. This low of a drop indicates depleted batteries.

Now, we calculate the voltage drop and receive the amount of power the capacitor contributed to the system!

(Drop from 14.8v -12.8 ) 27.6 watt-seconds.

(Drop from 12.8v-10.8 ) 23.6 watt-seconds.

(Drop from 14.8-10.8 ) 51.2 watt-seconds.

This means that if you added a 1 farad capacitor to this car audio system, the cap would supply a whopping 27.6 WATTS for 1 second before the batteries became the current source. WOW!

a 10 farad cap would supply 276 Watts.(meh..)

a 100 farad cap would supply 2,760 watts.(that is a lot of power eh?)

It seems like a 10 farad capacitor or greater might be a worthy investment after all?

JUST WAIT.

This power, Joules, Is a measure of watts/second. This means that over time the cap really flounders.

that same 100 farad cap would only supply 1,380 watts for two seconds (not bad)

690 watts for 4 seconds... (eh)

345 watts for 8 seconds... (um)

172 watts for 16 seconds... (boo)

and less than 80 watts for 30 seconds

To really be effective with a capacitor, we need to get stupid ridiculous.

a mammoth 1,000 farad capacitor would supply 27,600 watts... for one second. (Holy smokes!)

that 1,000 farad cap would only supply 13,800 watts for two seconds (not bad)

6,900 watts for 4 seconds...

3,450 watts for 8 seconds...

1,725 watts for 16 seconds...

Hopefully you see how incredibly useless a 1 farad capacitor would be in this situation?

Now, back to the misconception, 1 farad for 1000 RMS...

how much power does 1000watts (RMS) take?

Heh, in an ideal world with 100% efficient amplifiers, 1000 watts would take exactly 1000watts of power.

Based on our calculations, we would need approximately 37farads to supply this metaphorical amp for one single second...

But wait a minute! Did someone say “What about the alternator?!?” yes, we must discus that!

The alternator, as stated, supplies the power above 12.8volts. In most cars, the alternator produces somewhere around 100amps, give or take. (My 97 Camry has a 40/80 amp alternator)

This seems like a lot, but it is needed to power the car itself, the lights, electronics, and engine.

Budget that the car will take at least half of your alternators capacity, in my case ~40 amps.

This leaves you with ~40 amps for aftermarket amplifiers, or (14.8*40 + 592 watts)

so, I can easily deliver around 600 watts to my system, ANYTHING over this amount will cause my voltage to drop, eventually to 12.8v.

The capacitor will help supply current to whatever is above the limit of the alternator. In my case, if I had for example a 700w amplifier, I would need to supply 100w from somewhere to keep my system above 12.8v. In this case a 10farad capacitor would work quite well! It would fill in the gap for 2.7 seconds. When playing music, this would fit perfectly.

When we get into large systems, 1Kw, 2400rms, 4000w systems... a capacitor just isn’t feasible.

Therefor I can say that the myth of 1f per 1kw is bullshit and false!
( can you imagine.. Steve Mead.. with stock alt,stock battery, and a 30farad cap? LOL!)

Now, a departure into the opposite side, those arguing that “While using a cap much larger than recommended will not damage an audio system, it is not recommended because of the unnecessary strain it puts on the vehicles electrical system.” -SonicElectroinix

The myth that capacitors add additional strain to your system.

In theory, yes.. yes they do.

But really.. look again at the math!

It takes roughly the same power to charge a cap as it does to drain it, meaning that the electrical load for charging that 1 farad capacitor from 12.8 volts to 14.8 takes a whopping 27.6 WATTS for 1 second WOW!

a 10 farad cap would take 276 Watts.( 276w/14.8v =~ 20 amps)

We can clearly see that the capacitor doesn’t take much to charge, meaning that if your system is close to the alternators capabilities (As in the 700rms system example) that a 10farad capacitor wouldn’t hinder the system much! (It would charge back up in between peak current draw, IE with the beat of the music)

To take this further, it becomes apparent that if you have a system with a large cap bank and small charging system, say my setup with 40 amps and 1000 farads, it would take me (27,600/14.8 = 1,864 amps. 1864/40 = ~46 seconds) If I drained my cap to battery voltage, and then shut off my amps completely, it would take 46 seconds to charge my capacitors. You can see that a large cap can be harmful!

In conclusion, a capacitor can be a wonderful way to extract additional performance out of a system that is drawing slightly more power than your alternator can handle, but only when the capacitor has around 5-10 farads.

Unfortunately the price range for such a capacitor puts it out of the range of consideration because much more viable options are available.

A better option instead of investing in a capacitor is to upgrade your main battery. Straight up replace your lead-acid battery with a performance AGM car audio battery. Why would you do that when the alternator does all the work above 12.8 anyway? The high performance battery does not draw as much current as the lead acid does, meaning less strain on the alternator and more power available to your amplifiers. In addition, if/when the voltage drops to 12.8v the high performance battery will supply more current than its Lead acid counterpart. Your new battery will also offer better cold weather performance, will look wicked cool, and will recharge faster.

For those who have, or are planning, a really large system, and are planning on spending several hundred on batteries.. consider upgrading your alternator instead/ in addition. You must increase your current generating capabilities in order to power your setup. An alternator also weighs much less than batteries, and doesn’t need to charge.

I hope you have learned something from reading this article, please let me know what you think!

(PS, i am still figuring things out on SMD forums, If this post belongs somewhere else i would be happy to move it)

[Smoove]

There are several threads about this already. And the Tony D has has done some testing using the AD-1 to show some results.

And seeing you are new. Welcome to the group.

[SterTheDer]

There are several threads about this already. And the Tony D has has done some testing using the AD-1 to show some results.

And seeing you are new. Welcome to the group.

Thanks.

I know there are several threads, each with many valuable pieces of information and experience, I think that their should be a dedicated post just to the math side of things, to count out oppions and miss-information.

(In my own search for answers it is difficult to find many clear and consise threads that explain just HOW a capacitor works in a system, without bias or oppinion.)

(In addition, finding such threads [in my findings, witch are limited] the information i find is presented in the form of answers to users questions regarding capacitors)

(case in point http://www.stevemeadedesigns.com/board/topic/181966-why-dont-more-people-use-caps/?hl=%2Bcapacitor#entry2698529

Wonderfull post by SnowDrifter, but no math to back it up, giving little real detail for anyone who is truely interested in integrating capacitors)

Thank you, i am glad to be here

[Smoove]

Not sure if your familiar with the AD-1 or Tony D. But here is another thread on the subject. Hopefully it helps clear up some of your questions.

http://www.stevemeadedesigns.com/board/topic/167043-ad-1-amplifier-dyno-answers-question-do-caps-work/

[SterTheDer]

Not sure if your familiar with the AD-1 or Tony D. But here is another thread on the subject. Hopefully it helps clear up some of your questions.

http://www.stevemeadedesigns.com/board/topic/167043-ad-1-amplifier-dyno-answers-question-do-caps-work/

I wouldn't say "Familliar", i could pass a test on the AD-1 (well.. maybe...), but not Tony D.I have seen that video and it was a welcome addition to my knowledgebase

But again, it doesnt give any math behind it for someone looking for math. (I know what the AD-1 is and what it does)

"that same 100 farad cap would only supply 1,380 watts for two seconds (not bad)

690 watts for 4 seconds... (eh)

345 watts for 8 seconds... (um)

172 watts for 16 seconds... (boo)

and less than 80 watts for 30 seconds"

Results are great, and i am ever so thankfull for what Tony D did to show some limitations of the cap, but i feel that understanding WHY it doesnt work is just as, if not more, important than just having the results

[Krakin]

Math,

DC: http://www.ibiblio.org/kuphaldt/electricCircuits/DC/DC_13.html

AC: http://www.ibiblio.org/kuphaldt/electricCircuits/AC/AC_8.html

[Smoove]

So here an example of caps being used

http://www.stevemeadedesigns.com/board/topic/14953-rockford-t15k-the-proto-pics-and-short-story-more-pics/

And here is another example of caps being used.

http://www.stevemeadedesigns.com/board/topic/134094-the-black-nasty-6-hdc4-15s-6-q1-3500d1s-162s-on-music/page-79

Getting your electrical up par is always the first goal. If your electrical bites, a cap won't make up the difference.

[SterTheDer]

So here an example of caps being used

http://www.stevemeadedesigns.com/board/topic/14953-rockford-t15k-the-proto-pics-and-short-story-more-pics/

And here is another example of caps being used.

http://www.stevemeadedesigns.com/board/topic/134094-the-black-nasty-6-hdc4-15s-6-q1-3500d1s-162s-on-music/page-79

Getting your electrical up par is always the first goal. If your electrical bites, a cap won't make up the difference.

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ THIS! ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

That is exactly what capacitors look like when used properly

Thank you both for adding those awesome references to this thread!

[Krakin]

This is really fun to mess around with to simulate circuits.

http://www.falstad.com/circuit/

I can't remember exactly how to model a speaker on there, but someone else might know how.

[alaskanzx5]

To say caps don't work is false. Caps do work and have a place i'm car audio. They are not a fox soul for voltage drop but with a strong electrical a cap bank can help stiffen voltage and help sustain voltage for longer time periods. A 1"farad bank can be made for around $400-500 and with a nice ho alt can power a fairly decent size system. Right now a battery is cheaper but as technology advances and the price to manufacture caps drop so will the price of caps. The biggest issue with caps is people usually only know about the cheap ones that shops try to push out the door with a fancy volt meter on it. A real cap that will benefit a system are the carbon caps/Supercaps/ultra caps.