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PV Audio
11-20-2009, 02:17 PM
Having seen that some people are still struggling with the fact that not every subwoofer on the market needs to go into a certain type of enclosure, I figured that I’d take some time and briefly go over WHY every subwoofer does not need to go into a certain enclosure. I'll try to write this in as simple a method as possible without confusing anyone with jargon that isn't necessary. I’ll divide this into five parts: sealed, ported, infinite baffle, transmission line and horns. Let’s start with sealed enclosures, shall we? :)

What is a sealed enclosure? It’s a closed space behind the woofer which acts as an airspring. As the speaker moves throughout space, the air behind the cone becomes pressurized. This same pressure is what keeps the speaker linear and controlled. The sealed enclosure will typically have a greater transient response and lower group delay than a ported enclosure, but that is merely a rule of thumb and I won’t say that it’s always true. Now, what should you look for in a sealed enclosure? Well, many systems in the world have what is called a Quality Factor, or Q factor for short. This Q factor determines a lot of things: how long a bell will ring after being struck, how long it takes for a charge inside an inductor or capacitor to become neutral and for us, how well a speaker can be controlled by itself and in an enclosure. Using the sealed enclosure as an example, the smaller the box, typically the higher the Q. :eek:

Why? A higher Q (>.5) means that the system is called UNDERDAMPED. What is under damped? That means that it takes a lot longer for something to return to its baseline condition. Hey, that’s kind of hard to grasp, how about an example? Sure thing! Think about the bell I mentioned earlier: if you strike a bell and touch it, what happens? It stops ringing, obviously. Now, let’s assume that the bell is flawless, is radiating in free space with no air or heat or anything to stop it. This bell would therefore continue to ring forever, which means that it has an infinite Q. The higher the Q, the “freer” that something is to oscillations above its equilibrium state. For a circuit, that means that it takes a long time after an impulse is sent to it for it to return to equilibrium, for a speaker, it means the same thing! If you take a speaker with a high Q (called Qts which is a combination of the mechanical and electrical Q factors which I’ll talk about later) and play a tone into it, the more ability that it has to oscillate freely. Since for us that means that the speaker will become uncontrolled easily, you need the control of the sealed enclosure for it to work best. :(

The sealed enclosure itself ALSO has a Q which you need to look at. As I said, the smaller the enclosure, the higher the Q. Why? Because as the airspace drops, the speaker must pressurize a smaller amount of air which thusly means the pressure in the box rises. That means that it takes longer for the speaker to return to equilibrium as it has to dissipate that pressure for longer. In the end, that corresponds to a very peaky response because the sound will go from baseline to a gain over baseline, to under baseline to over baseline over and over until the system reaches equilibrium. It’s that simple! The higher the system Q, the more tendency for the sound to be peaky or boomy at certain frequencies near the roll off point since the frequency response is not flat at all frequencies. :crap:

If you make a larger enclosure, then the frequency response becomes flatter to a point where the speaker will actually end up rolling off TOO early. This is just as bad as a peaky response because it can cause what many of you know as bottoming out. What happens is that because there is not enough pressure in the box to keep that high Qts cone under control, then the speaker behaves like it’s just sitting outside an enclosure or in what’s called infinite baffle (I’ll tackle that later). This is BAD for speakers not made for IB applications because it leads to over excursion and subsequently mechanical damage to the speaker. While many speaker companies use various methods to stop bottoming out from happening (special tricks to the ends of the voice coil such that as the speaker is going to clear the magnetic gap which causes excursion, the motor essentially has nothing left to charge up and the cone can’t go any further), if you push it hard enough, it will happen! :D

So, how do you tell how large to make the enclosure? Well my friends, you need a few parameters: the Fs of the speaker, the Qts, the Vas, Xmax, Sd and Vd. If you don't fully understand any of those, just ask, because they aren't as simple as you might think (Xmax is not just simply how far the cone can move linearly, it's helpful to know why that's its linear limit ;) ). ONce you ahve those, you're going to want to either use a design program or if you're like me and trust tried and true mathematics, you'll use a sealed enclosure design table. These are are tables with numerous values for the desired SYSTEM Q or Qtc that you want. Some useful Qtc values are:

Butterworth: 1/sqrt(2) = .707 (flat magnitude response)
Bessel: 1/sqrt(3) = .577 (flat group delay)
Chebyshev: > .707 (maximum power handling and efficiency, bad transient response)
Transient perfect: .5 (critically damped, right on the limit of usefulness for high Q drivers) :cool:

So let's say that you want a Butterworth Q of .707 which has a flat magnitude response. You go to the table, then along the left side of the table, you'll find numerous Qts values for the speaker. Once you find the Qts for your speaker, it's time to choose a value called "alpha". All that alpha is is (Qtc^2)/Qts - 1. Take your alpha value and now you're good to go! THe Vb, or net air space, is the Vas of the speaker divided by alpha, or Vas/alpha. That's it! While there are numerous other things needed to design specific parts to your sealed enclosure, knowing how to pick the correct volume is probably the most important. That's all for sealed, and if you want some more specifics, then let me know! :)

-Dave

altoncustomtech
11-20-2009, 06:55 PM
I can see this is going to be a GREAT thread.... while alot of this information can be found in many good books on the subject, it seems alot of people don't care enough to read them....

Fantastic explanation PV, carry on!

michaellane
11-20-2009, 07:01 PM
you never replied back to my other pm...hope it didnt get lost...

PV Audio
11-20-2009, 07:16 PM
It probably did, people have been PMing me a lot about my design competition. Send it again please? My bad, man. :(

PV Audio
11-20-2009, 07:17 PM
I can see this is going to be a GREAT thread.... while alot of this information can be found in many good books on the subject, it seems alot of people don't care enough to read them....

Fantastic explanation PV, carry on!
Ported will be done in about 20 minutes :)

PV Audio
11-20-2009, 07:37 PM
Ported Enclosures

Ahh yes, the bread and butter of the car audio world for reasons most do not understand. Believe it or not, throwing any speaker into a ported enclosure will NOT necessarily make it perform better. To determine what speaker is suited for a ported enclosure, you'll need to be looking at the Qts again. This time, we're going for OVERDAMPED speakers, or speakers with Qts values below .5. Why? Well, these speakers don't tend to oscillate freely and potentially out of control like under damped speakers do, so by placing them in a sealed enclosure, you're essentially doing the woofer's job for it. That is horribly inefficient and a waste of time. Instead, people use ported enclosures to gain some extra output since the speaker can handle it without hurting itself. :)

The main precaution surrounding ported enclosures is the fact that you need to design the enclosure around the driver, NOT the other way around. Going out and getting a pre fabricated enclosure is one of the worst things that you can do to a subwoofer. It won't necessarily sound poor, but there is no way it's suited for that specific speaker. How do you know what is suited for your speaker? Good question! You're going to need those tables I talked about earlier, except this time, instead of looking for a Qtc value that you like, you're going to look for a Ql value, or a loss Quality. Ported boxes have losses that you need to take into account. The average loss value is 7, and while this isn't very practical for most people it's the best method: construct the enclosure with QL of 7 in mind, then tune it to the frequency that you calculate (later). Afterwards, try to measure the box for losses and if you're pretty close to neutral, then you're good to go! If not, then here's the rule of thumb: if you have LESS LOSS or a HIGHER Ql, then decrease the Vb. If you have MORE LOSS or a LOWER Ql, then increase the size of the box. Think about it like this: you build a container to hold a cup of water. The higher the quality of the container, the less water that will be draining out. The lower the quality, the more water you'll need to put in and thus you'll need a larger container. ;)

Now, I know most of you guys are like pffft, I'm not wasting time on that, I'm just going to plug some numbers into a computer and get what I want. Not so fast, slick. You need to understand why your computer is giving you the given values. Your Vb is equal to the Vas/alpha. Alpha in this case CAN be derived, but that formula is going to take too long to derive, so just assume that it's a constant between around .1 and 4 for a normal Ql = 7 enclosure. Your tuning frequency is equal to the driver's Fs * H, where H is the tuning ratio for your given alignment. Now assuming that you have all of this, you can calculate your theoretical port length which is easier to see via a website:

http://www.diysubwoofers.org/misc/portcal.htm

I realized about halfway through this that it's quite difficult to have a short theoretical basis on ported enclosures because the science is pretty hairy and you need at least a moderate understanding of physics to fully grasp the concepts. Seeing as most people just want a good enclosure, the quick and dirty steps are to use the tuning and minimum diameter formulas to find those respective parameters, then find the volume that you want by the Vas/alpha formula by looking up alpha in a design table, or calling the manufacturer and asking them. They'll know exactly what it should be and can help you if you need anything else. :)

I know this post wasn't very helpful, which is why I added the last part. It's very difficult to go into the theory without you seeing the design tables, and it's even MORE difficult to understand if you want the formulae behind the design tables because they are far too long to write out in one-line text :crap:

I'll make the next post a bit better :)

lambofgood91
11-20-2009, 07:46 PM
Are you going to cover 4th/6th order bandpasses? :D

tez4life
11-20-2009, 07:52 PM
Very nice guide, worded quite well. Im sure this will be very helpful to alot of fourm members, including myself :) Thanks.

michaellane
11-20-2009, 07:55 PM
It probably did, people have been PMing me a lot about my design competition. Send it again please? My bad, man. :(

its kool ima eat then pm you. its just a simple aero port tunning question. prolly take you 25 seconds :)

PV Audio
11-20-2009, 08:02 PM
Are you going to cover 4th/6th order bandpasses? :D
No sir. I would rather leave that to someone like 80INCHES or Immacomputer who actually know how to design bandpass enclosures to their maximum possible performance. I don't. :)

altoncustomtech
11-20-2009, 10:16 PM
Are you going to cover 4th/6th order bandpasses? :D


No sir. I would rather leave that to someone like 80INCHES or Immacomputer who actually know how to design bandpass enclosures to their maximum possible performance. I don't. :)


Bandpass enclosures are like fuzzy logic..... hard to understand without a degree in it.... lol..... but seriously if someone knew how to explain them well I'd be all ears.... I've built a couple but it was only by manufacturer's specs.... they turned out good tho, sounded like bandpass boxes... lol

lambofgood91
11-20-2009, 10:22 PM
Bandpass enclosures are like fuzzy logic..... hard to understand without a degree in it.... lol..... but seriously if someone knew how to explain them well I'd be all ears.... I've built a couple but it was only by manufacturer's specs.... they turned out good tho, sounded like bandpass boxes... lol

Indeed. I'm trying to learn more about them myself ;)

plugitin
11-20-2009, 10:28 PM
i agree with the bandpass suggestions...i would love to learn more about them.

slam
11-20-2009, 10:32 PM
Tapped horn enclosures are the shizzzz :fyi:

PV Audio
11-21-2009, 01:55 AM
I'll get to infinite baffle tomorrow. That should be the shortest section since it's technically under sealed enclosures.

marcotheclepto
11-21-2009, 02:15 AM
excelent write up ill definately be hanging around for the IB and t line as well as the horns :)

PV Audio
11-23-2009, 12:00 PM
Transmission line theory will be coming up today. I have to finish writing about Linkwitz-Riley crossovers for my lab paper first though :crap:

Johnny Law.Lulz
11-23-2009, 12:02 PM
Great write up. I sent you a PM but havnt heard back :laugh:

IDSkoT
11-23-2009, 12:11 PM
Transmission line theory will be coming up today. I have to finish writing about Linkwitz-Riley crossovers for my lab paper first though :crap:

In for T-lines.

michaellane
11-23-2009, 12:13 PM
title of the PM is hey man

PV Audio
11-23-2009, 12:14 PM
Great write up. I sent you a PM but havnt heard back :laugh:I saw it, its up next actually. People kept asking me how they did on my little competition and i got like 10 PMs :crap:

marcotheclepto
11-23-2009, 12:26 PM
haha, did anyone else try for the optional portion?

PV Audio
11-23-2009, 12:27 PM
No :laugh:

marcotheclepto
11-23-2009, 12:30 PM
so i win? hahaha

PV Audio
11-23-2009, 12:37 PM
so i win? hahaha
:eyebrow:

marcotheclepto
11-23-2009, 12:38 PM
:eyebrow:

:P i kid. idk im bored this morning off work... about to go out to eat.... all we have is pancakes here.

PV Audio
11-23-2009, 12:44 PM
:laugh: I'm like, I know my man ain't serious, you can't win a competition with no one to compete with.

RJesus
11-23-2009, 01:39 PM
transmission line and horns should be next.

galacticmonkey
11-23-2009, 01:43 PM
Cliffs?

PV Audio
11-23-2009, 02:01 PM
Cliffs?I can make your toes curl :naughty:

PV Audio
11-24-2009, 12:56 AM
This took some time!

Transmission Lines

NOTE: There are typically two types of TL enclosures: ones for us, and ones for others. The ones for us are what you typically see on here and involve output at the exit of the line. The other type is designed such that there is no output at the exit and functions simply to completely eliminate box resonance by fully damping any waves from the rear of the speaker. That models roughly as the ideal sealed enclosure and isn't intended to produce extra bass, but is perhaps the smoothest sounding enclosure you can have. The design theory is the same, although this write up concerns the first type.

Also note that I use terms like tube or pipe. That doesn't mean that a TL is supposed to by a cylinder because it doesn't have to be.

Alright, down to one of the more unique enclosure types out there. It seems like everyone here wants to know about the magical being that is the transmission line. They think that it's something so revolutionary or so technical that there's no way that they'd ever be able to build one, let alone design one themselves. Think again. :)

The best way to start this discussion is to talk about a ported box. As I didn't say previously in the ported box section since it wasn't really necessary, a woofer moving on a baffle emits two waves: the front wave and the back wave. Picking whichever reference point you want, the two waves are 100% out of phase with one another. Scientifically, this means that they are 180 degrees out of phase with one another. What is phase? All that phase is is a displacement of a wave from a reference point. What does that mean? Well, lets take a look at a picture, shall we?

http://upload.wikimedia.org/wikipedia/commons/thumb/3/38/Sine_cosine_plot.svg/800px-Sine_cosine_plot.svg.png

The sine wave and the cosine wave are 90 degrees out of phase with one another. If you've forgotten or never learned, angles in units of "pi" are called radians. 2*pi radians is equal to 360 degrees, so 90 degress is equal to 1/4 of 360, so it's pi/2 radians. Why is that important? Look at 0 radians for the cosine wave, then look at pi/2 radians for the sine wave. What do you see? If you start looking at the sine wave at pi/2, then they're the same wave! Interesting, you might say, but not terribly important. Hold on there, that's the entire point behind transmission lines. Let's look at two waves, which will represent the front and back waves of your speaker:

http://www.4815162342.org.uk/e014b2.gif

As you can see, these two waves are 180 degrees out of phase, or pi radians out of phase. How do we know that? Assume that each intersection on the plot with the x axis is 90 degrees or pi/2 radians. Therefore, if you go to the second intersection for the red curve, you'll notice it's identical to the green curve starting at zero. Another way to look at fully out of phase waves is that they are simply the negative of one another. Simple eh? :cool:

Now let's look at another picture that I'll explain below:
http://upload.wikimedia.org/wikipedia/commons/7/7d/Standing_wave_2.gif

This image is for what's called a standing wave but I'm just going to use it to illustrate my point. Look at the two waves in the background: when the black wave is zero, the two waves are 180 degrees out of phase. When the black wave is at its maximum, the two waves are 0 degrees out of phase, or completely in phase. When your speaker moves, it produces two waves: one like the red one, one like the blue one. These waves CANNOT be allowed to mix in their immediate phase shape. Ever wonder why when you play a speaker free air, all you can hear is the cone movement and not any sound? That's the two waves having completely destructive interference and canceling out because they are completely out of phase.

Back to the ported enclosure: what does it do? It attempts to take that back wave and pull it in phase with the front of the cone's wave to give you a summed output. Usually, however, the waves are not fully in phase with one another as the wave has not had sufficient time to become 180 degrees out of phase with itself. That presents a problem: you can get more output, but as frequency drops, the rolloff of the speaker is very sharp, 24db/octave in fact. For you crossover nuts, that's a 4th order slope! Why? The reasons I said above: as frequency goes down, the waves do not have sufficient time to become in phase and end up cancelling out more than adding. That's where the transmission line comes in. :thumbsup:

When you put a speaker in a transmission line enclosure, the wave emitted from the "port" is supposed to be exactly in phase with the front wave. The enclosures are sometimes called phase inverters for that very reason. The classical transmission line is an enclosure that has a tube length 1/2 as long as the wavelength of the driver's resonant frequency, or Fs. Why? Well, once the driver reaches Fs, which is the frequency at which the impedance of the speaker is maximum due to the electrical impedance being purely resistive and more importantly, the fact that the speaker's moving mass is precisely balanced with the restoring force of the suspension, the speaker begins to drop off in frequency response. Why? Well, Fs is the inverse relationship of suspension compliance and moving mass. That means that as the frequency gets lower, the suspension cannot provide sufficient damping to the speaker. If you can't somehow add mass to the cone or increase the suspension's compliance, the speaker's ability to reproduce those frequencies goes into the tank due to purely mechanical reasons. :crap:

Anyway, enough on Fs, and back to the theory: the resonant frequency, as I stated, is effectively the bottom end of the speaker's frequency response. As I said before, vented boxes end up rolling off sharply due to low frequency cancellation. If you could somehow make it such that the waves are in phase once the speaker gets to its resonant frequency, you could have outstanding bass performance across the speaker's entire bandwidth! Well, there you go: by having a tube the length 1/2 of the wavelength of the resonant frequency, once that wave leaves the tube, it combines with the wave on the front and gives you a healthy boost in output, thus giving you outstanding bass at frequencies that a ported box simply cannot reproduce and with a smoothness that rivals a sealed enclosure. :eek:

Well, wait up a second, how long IS a wavelength (speed of sound/frequency)? Well...quite long. Let's take a Fi.Q18. If we pick the Dual 2 ohm, which has a Fs of 23.8Hz, we calculate that it has a resonant frequency wavelength of, get this: 343/23.8 of 13.6 meters, or for us Americans, 1125/23.8 or 47.27 FEET. Since we need to shift the wave 180 degrees, we halve that and get over 25 feet. Yes, that tube needs to be well over 2x the length of your car. That isn't feasible, even for a home audio environment. :verymad:

So, why do we use a quarter-wave design? Well, as we'll see in a moment, 1/4 is the best compromise between tube length and size. That means our Fi.Q would only need a tube length of about 11.8 feet, which is still long, yes, but far more manageable. But wait, if it's only 1/4 of the wave length, then that means that all we're doing is shifting the back wave by 90 degrees! Quite right, quite right. That, my friends, is where line stuffing comes in. When you build a 1/4 transmission line, you need to stuff the line with enough material such that it slows down the speed of the wave and gives it plenty of time to invert its phase completely. The amount of stuffing that you use is entirely dependent on the material and the length of the line. If your target is for a 36Hz fs, thus a line length of 94", you want to use about .5 pounds of poly fill per cubic feet. The amount of stuffing increases as line length shortens. Typically, stuffing consensus is just the opposite of a consensus, as some sources say to stuff heaviest at the woofer end and lightest at the exit, while some texts, such as the Loudspeaker Design Cookbook state to stuff heaviest at the exit and lightest near the woofer which results in a constant resistive load throughout the whole length. You can even leave about 15 to 20 percent of the end of the line completely undamped so you can play with how much you might need to get the best bass response.

The other reason to use stuffing is to reduce distortion caused by high frequency sounds. As sound passes through the fibrous medium that is your stuffing, two things happen: first, when the frequency is low, the fibers and the sound waves couple together to slightly attenuate the magnitude of the output, but more importantly, to slow down the speed of sound which is what we're after. Second, when the frequency is higher, the wave and the fibers do not couple at all, and instead the sound is merely attenuated from the output. This is the reasoning why TLs tend to have exceptionally smooth bass characteristics because the line damping knocks out high frequency harmonics that have no business being passed through the line. ;)

Continued BELOW

PV Audio
11-24-2009, 12:57 AM
Continued from ABOVE

The final considerations are the pipe diameter and where to put the woofer. In this case, you want the cross sectional area of the tube to be the radiating area, or Sd of your speaker. Why? Well, all that we're doing is taking whatever is coming off of the back wave, shifting its phase, and combining it with the front wave out front. You don't want anything bigger or smaller, as all you're trying to do is simulate having the backwave be another speaker that is in phase with what you already have. You can, if you want, taper from beginning to end starting with 1.5-2x Sd at the start and ending with Sd at the exit. You can also load the speaker with a slight chamber before it enters the tube, but that's up to you. What that does is creates an effective 1st order filter that again knocks down upper harmonic sounds as well. It's suggested by George Augspurger, a phenom in the field of TL design when he worked for JBL, that the volume of the chamber should only be about 1/3 of the total line volume. Most of these changes are either rules of thumbs or are subjective to the listener. To keep it simple, keep it uniform. :D

For the location of the speaker in the tube, you've got a couple of choices. You can usually offset the speaker about 1/5 to 1/3 from the beginning of the tube if you want. The further away you move the speaker from the opening, however, the higher the rolloff frequency of the system. At 1/5 offset, that means you lose 20% of your bandwidth. While that might be desirable in some cases where the speaker has notorious breakup modes or simply poorly damped low frequency behavior, it usually isn't and you should put the cone at the beginning of the tube. ;)

Well, that's about it! There's a fair bit more to TL theory than this, such as how to fold the tube, flaring it, tapering it, variations of the two, damping materials, stuffing density, and loads of other stuff that you really don't need to know to start designing your own TL. I hope this cleared TLs up! :)

-Dave

IDSkoT
11-24-2009, 01:11 AM
Good write-up. Unfortunately, and this of course is not your fault, I knew all of this. :crap:

I might throw a SI BM in a TL. What do you suggest in terms of parameters for TL? As in, what would you recommend in terms of a good Fs / Sd for a driver. Or just give me links.

BTW, here are T/S for the SI BM:

12 inch
Re (coils in series) 7.8
Fs 28.3
Le 3.4
Qms 3.55
Qes 0.38
Qts 0.34
Cms 158
Mms (grams) 128
Vas (liters) 83.6
Sd (cm^2) 480
BL 21.9
SPL (1W/1M) 88


EDIT:: Also, where did you derive 1125 from?

PV Audio
11-24-2009, 01:17 AM
Good write-up. Unfortunately, and this of course is not your fault, I knew all of this. :crap:

I might throw a SI BM in a TL. What do you suggest in terms of parameters for TL? As in, what would you recommend in terms of a good Fs / Sd for a driver. Or just give me links.That wasn't for people who already know this, silly. :laugh:

What I would do is to use a TL alignment table or spreadsheet. Look at the bottom here:

http://www.quarter-wave.com/TLs/TL_Theory.html

:)

Oh, and 1125 is the speed of sound in feet/sec. The 343 number is the speed of sound in meters/sec.

IDSkoT
11-24-2009, 01:22 AM
That wasn't for people who already know this, silly. :laugh:

What I would do is to use a TL alignment table or spreadsheet. Look at the bottom here:

http://www.quarter-wave.com/TLs/TL_Theory.html

:)

Oh, and 1125 is the speed of sound in feet/sec. The 343 number is the speed of sound in meters/sec.

Okay. Thank you. And I confused the speed of sound with the speed of light. D'oh. FAILSAUCE. I was like, "Certainly the speed of sound is more than 1125 feet / second!"

PV Audio
11-24-2009, 12:54 PM
I'll have the horn write up done probably today. :)

PV Audio
12-01-2009, 05:44 PM
Horns and IB are still coming, school > audio unfortunately :(

supermaxx123
01-14-2010, 01:21 PM
Great Thread!!

tRiGgEr
01-14-2010, 06:02 PM
Someone post his box build pictures!!!!

jmanpc
01-14-2010, 06:29 PM
This just makes me want to make a half-wave transmission line for like an 8" woofer and throw it in my car, just to mess with peoples' heads.

supermaxx123
01-14-2010, 11:44 PM
This just makes me want to make a half-wave transmission line for like an 8" woofer and throw it in my car, just to mess with peoples' heads.

Do it, it would be so long!