Index Of Intro To Sealed Enclosures

Introduction | The Two Types | AS & IB History | Terms To Know
What Is Q? | Utilizing Qtcs | Important Conclusions | Table of Qtc Calculations

Introduction
A sealed enclosure is the simplest loudspeaker enclosures to design and build. If you are new to building loudspeaker enclsoures you probably want to make your first design a closed box one. This ease of design and construction by no means make this type of enclosure merely a low end design. Many audiophile grade lowspeakers are sealed designs. The analouge of the sealed enclosure's electrical and pneumatic properties is that of a second order crossover. If you don't know what that is or haven't read what it is on my site that, it means that below a sealed enclosure's "cutt-off" frequency it's magnitude response decreases by 12dB/octave. For example if a sealed enclosure as a cut-off, or -3dB point of 40Hz and our reference SPL is 90dB, at 20Hz the SPL will be 75dB. (It's 82dB because you have to remember that the -3dB point at 40Hz puts us already at 87dB then subtract 12 from that and you get 75dB).

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The Two Types!
There are two basic types of sealed boxes. The first if the infinite baffle (IB) design and the second is the acoutic suspension design (AS). What these two terms actually mean, I dunno... just joking, anyways.... The two different designs are defined as such because of the volume of air present in the enclosure. For the IB design, the volume of air within the box has a higher compliance than the the speaker to be used in the enclosure. The design becomes an AS design when the opposite is true, hence, the box has a lower compliance than the speaker. Keep in mind that the IB design will yield larger volume boxes. (If you are an experianced builder or know about the alpha parameter an AS design has an alpha value larger then 3. And for anyone who doesn't know what alpha is don't worry I will get to it also, I didn't forget to lable it with units it doesn't have any.)

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Short AS and IB History
The IB design was very populart starting from the very beginging of loudspeaker design (1926?) up until the early 1950s. But after 1949 when the AS design was patented by Harry Olson and his associate J. Preston things began to change. Edgar Vulcher also deserves mention because he was an early advocate for AS designs and also during 1954 he published a series of artilces in Audio magazine that declared that the AS was the ultimate design. But one of the most recognized engineers is Richard Small for his work done in 1972. Small gave us on of the most definitive works done in closed box design.

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Terms to Know Before Proceeding
Here is a list of terms you should know before reading on, or jumping right to making a box!

f3 Minus three decibel half-power frequenc (designates the beginning of lowend rolloff).
fs Resonance frequency of driver.
fc Resonance frequency of the closed box system.
Q Ratio of reactance to resistance (seriers circuit), or resistance to reactance (parallel circuit).
Qts Total Q of driver (usually you're talking about a woofer here), considering all driver resistances (mechanical and eletrical).
Qtc Total Q of speaker system at fc, taking all driver resistances in to account.
Vas Volume of air having the same acoustic compliance as the driver's suspension system.
Vab Volume of air having the same acoustic compliance as the enclosure.
Xmax Peak linear displacement of driver cone.
Sd Effective surface area of the driver's cone.
Vd Peak displacement volume of driver cone.
Vb Net interal volume of enclosure.
alpha Compliance ratio. (Alpha as in the greek letter)
n0 Reference effiecieny (Greek letter eta).
Cas Acoustic compliance of driver suspension.
Cab Acoustic compliance of the air in the enclosure.
(All definitions taken from source 2,The Loudspeaker Handbook, Dickason)
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What is Q? No, not the guy in Bond Films....
The reason we talk about Driver and Enclosure Q in a sealed system is because the entire point of fitting a specific volume of air to a particular speaker is so that we may control the response of the combination. That's why we sometimes refer to them as loudspeaker systems.In the case of driver Q and enclosure response, Q describes to an extent the resonant magnifaction in speaker boxes. Q also describes to what degree which electrical, mechanical and pneumatic circuits of the woofer/box combination interact to control resonance.

Understanding and Utilizing Different Qtcs
The term Qtc is a very important value to consider when initially designing a sealed enclosure. The value of Qtc will determine the "sound" of the bass, the bass extention (f3), box volume and where/if the peak dB response will occur, along with a host of other things. All of these values can be calculated quite easily with a scientific calculator.

On a sidenote today the design of the actual enclosure for the woofer in a loudspeaker system has become quite insignificant. Computers can do a better job of calculating losses and can compentsate for things which would be basically impossible to do on a calculator. Today the focus is placed much more on crossovers and control polar response of the high end because of the humans relatively low ability to place low frequency sounds in a sound field.

Although different Qtcs will give different responses, a sealed enclosure is analougs to a 12dB/Octave highpass filter. This is a nice shallow rolloff compared to that of 24dB/Octave on vented enclosures. There are a few specific values of Qtc that have certain characteristics which you should be familar with.


Qtc = 0.5
Critically Damped - transient perfect

Qtc = 1/(3).5 = .577
Bessel Response (D2) - max flat delay

Qtc = 1/(2).5 = .707
Buttworth Response (B2) - max flat amplitude response with minimum cutoff

Qtc >= 1/(2).5 (>= .707)
Chebychev (elliptical - C2) Equal Ripple response - max power handling and max efficency, degraded transients

Although those were only a few values of Qtc you may choose any of the numbers in between. You could choose a Qtc of 10 but the results would be quite disappointing, the resulting cabinent would be very very boomy and it's transient (remember transients are very important, transient repsonse dictates how fast the driver will respond to the input signal [music, or test tones]). Choose a Qtc much below .707 and most find the results to sound too "taut" and overdamped. The graph below (figure 1) shows you what a couple of different Qtcs would look like.

figure 1

As you can see the Qtc of 10 has a huge peak at 50 Hz. This attributed to it's increased efficeny, and it's predictable reponse peak. Also with the Qtc of .7 the line is quite even then begins to rolloff at the predictated 12dB/Octave.

Normally a Qtc > 1.2 should be considered undesirable. Also a Qtc of 1 has "warmth" to it but no real kick. Qtc = .9 has pretty nice "kick" to it but still is quite "smooth". It is hard to describe what exactly these all sound like so my best suggestion is to buy an experimental woofer and build a bunch of different boxes with different Qtcs, listen to them and then determine which sound you like the most.

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Important Conclusions
Here are a few tables and more writing to help you get an idea of what characteristics each Qtc has.

One very important thing, which may be very evident to everyone but me is to remember that decreasing Qtc having values up to .707 will have larger boxes, better transients, and a lower f3. Qtcs which are below .707 have these characteristics: Still better transients, higher f3 and still larger boxes.

A few of the other things which may be calculated are fgmax which is given as a ratio with box resonance, fc there is also fxmax which is the frequency at which maximum cone displacement will occur, this is also given as a ratio to fc. The table below shows that these calculations are the same for each Qtc, the only governing number is box resonance. The table 1 below summarizes.

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Qtc Peak dB fgmax/fc fxmax/fc
.5 0 - -
.577 0 - -
.707 0 - -
.8 .213 2.138 0.468
.9 .678 .1616 0.619
1.0 1.249 1.414 0.707
1.1 1.833 1.305 0.766
1.2 2.412 1.238 0.808
1.3 2.974 1.192 0.839
1.4 3.515 1.159 0.863
1.5 4.033 1.134 0.882


Table 1

You can find the formulas necassary to calculate these numbers out for any Qtcs on the closed box design page.
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