# Bass reflex alignments explained – Step by step

## What are the ported box alignments ?

The bass reflex alignments are like a description on how the box will sound like. A good analogy would be with the sealed boxes. If you haven’t read the article, I encourage you to do so, as it will make more sense. But I will briefly explain it anyway. To calculate the volume of a sealed box, you first need to make up your mind which Q_{tc} you want. Q_{tc} is a factor of Q_{es}, Q_{ms} and the Q of the box. Since Q_{es} and Q_{ms} are speaker qualities, and are fixed, only the Q of the box can be altered, by modifying the volume of the box. In a reverse fashion, by knowing which Q_{tc} you want, and considering that Q_{es} and Q_{ms} are given by the speaker manufacturer, you can calculate the volume of the box.

### Sealed vs bass reflex alignments

Here are the sound characteristics corresponding to different values of Q_{tc} for sealed boxes :

- Q
_{tc}= 0.5 : Perfect transients, but low efficiency. - Q
_{tc}= 0.707 : This is the number most people try to reach for, as it gives good transients and flat response with minimum cutoff. - 0.7 < Q
_{tc}< 1.2 : Better efficiency, somewhat degraded transients, steeper roll off. - Q
_{tc}> 1.2 : High efficiency, bad transients, bad frequency response.

Since, the ported enclosure is more complex than the sealed box, it is not as easy as choosing a value of Q_{tc}. Instead, there are several well known bass reflex alignments, from which you can choose from. I made the analogy with the sealed enclosure, because it is easier to understand, but for bass reflex, the process is much more complex. Making slight variations for Q in a sealed box, will result in a minor alteration of the response. However, for bass reflex, can cause notable increases or decreases in the bass region, which are referred to as “misalignments”. Ported boxes have much steeper roll-off, and if confronted with misalignment issues, can cause serious transient ringing.

So, to determine to volume of the box and the size of the vent, you first need to choose a certain alignment. Because different drivers have different parameters, and therefore different drawbacks, you need to choose an alignment that compliments your driver, so that you will get, more or less, a flat response.

### Types of bass reflex alignments

There are two basic categories for bass reflex alignments, one of which extends into two other categories :

**Assisted.****Unassisted.****Flat.****Non-flat.**

**Assisted alignments**

involve an active electronic filter equalization, to achieve the desired response. This type of alignment is not particularly popular and we shall not focus on it. Instead, we shall concentrate our attention to the unassisted bass reflex alignments, which do not need extra electronic devices to achieve a predicted response. Because of this simpler design, it is more widespread.

**Unassisted flat alignments**

generally requires values of Q_{ts} lower than 0.4, and are divided into 6 categories :

**SBB**– is characterized by a large box, low tuning frequency (longer vent) and good transient response (which puts the term boom-box out of place)._{4}or Super Forth-Order Boom Box**SC**– about the same enclosure size and f_{4}or Forth-Order Sub-Chebyshev_{3}as the SBB_{4}, but with different tuning frequency. Somewhat degraded transients compared to SBB_{4}.**QB**– is the most popular vented alignment, because it yields a smaller box and a lower f_{3}or Third-Order Quasi-Butterworth_{3}. However, the transient response is not as good as SBB_{4}or SC_{4}.**B**._{4}or Forth-Order Butterworth**BE**._{4}or Forth-Order Bessel**IB**._{4}or Butterworth Inter-Order

**The last three bass reflex alignments are called discrete alignments**, because they exist for only one single value of Q_{ts}. These are quite difficult to obtain, because the box losses affects the value of the alignment. Out of the three discrete alignments, BE_{4} has the best transient response.

**Unassisted non-flat alignments**

are generated using a higher value for Q_{ts}. These bass reflex alignments tend to have an inferior transient response and frequency response. For this reason, they are not suited for high-end audio applications. However, if the negative parts are not an issue, the non-flat alignments can reach lower values of f_{3}. These alignments are split into 3 categories :

**C**– can be useful for low values of ripple (less than 1 db)._{4}or Forth-Order Chebyshev**BB**– has a peak in response close to roll-off, similar to high Q_{4}or Forth-Order Boom Box_{tc}sealed boxes (1.2 or higher).**SQB**– is a high value Q_{3}or Super Third-Order Quasi-Butterworth_{ts}extension of the QB_{3}alignment.

### Box losses

Before we explain the bass reflex alignments, we need to talk about box losses first. When you are manufacturing a box, you have to take into account that there will some air leakage, or other factors that will change the result. All of these factors combined describe the box losses. You will encounter three main types of losses :

- Air leakage – Q
_{L}. - Absorption from damping material – Q
_{A}. - Vent losses – Q
_{P}.

Total losses (Q_{B}) is the sum of all 3, which add together in the following fashion :

**1/Q _{B} = 1/Q_{L} + 1/Q_{A} + 1/Q_{P}**

In a real world scenario, where the **sound dampening material **would be absent, or 1″ of wall lining, Q_{A} would be minimal. Also, considering that the port is not obstructed, Q_{P} is negligible as well. So, when we are talking about box losses, we are talking about box leakage, which is Q_{L}. As a result, different amounts of Q_{L}, will affect the frequency response in a different way.

### Adjusting box losses

When constructing a box, you will have to take account the box losses, or more to the point, the leakage (Q_{L}). So, before you start your build, consider that the box will have a normal amount of leakage, which is Q_{L} = 7. After you have completed the box, you will have to measure the box losses and see if the value is close to 7. If indeed Q_{L} is around 7, then you can congratulate yourself. Otherwise, you will have to take corrective measures.

Discovering that Q_{L} is lower, means you will have to make the box bigger. This usually means that you will have to make the box all over again. If Q_{L} is higher, then you will have to make the box smaller. This is done pretty easy, by placing solid objects (rectangular pieces of wood) inside the box, to make the net volume lower. If you are afraid of the low Q_{L} result, you can over-volume the box, and after you measured the box losses, you can reduce the volume by the appropriate amount.

### How to measure box losses?

You cannot predict how much losses you will have for a predefined enclosure. As a result, only after the box is complete, you can see how lossy it is. To measure the box losses, you will have to make some measurements for the speaker and the enclosure. After you get those values, there are several calculations that you will need to do. Since it is pretty difficult to write all of those formulas, I prefer to add an excel spreadsheet, where you input the needed values and Q_{L} is calculated for you.

Excel spreadsheet for calculating Q_{L} : Calculate QL

Explanation of terms inside the spreadsheet regarding the enclosure :

- f
_{b}– resonant frequency of the box. - f
_{H}and f_{L}– The impedance curve of the enclosure will show 2 peaks. Note the frequencies that correspond to those 2 peaks. f_{H}represents the value for the bigger peak and f_{L}the value for the smaller peak. - R
_{0}– the impedance at f_{b}.

### How to calculate box size using bass reflex alignments ?

First of all, get acquainted with this table in excel format : alignments table. Now follow these steps :

- Choose the alignment you would like, and go to the appropriate table.
- Then go to the Q
_{L}= 7 column, since it’s the typical loss figure. - Find out the Q
_{ts}of your driver, by measuring it, or look for it in the tech sheet. - If Q
_{ts}is lower than 0.4, you will end up with a flat alignment. If it’s higher than 0.4, the alignment will be non-flat. You can also tell by the peak-db or ripple-db from the table (if it’s 0, it is flat). On the same row with your Q_{ts}value, you will have : H (tuning ratio) , α (the system compliance or box volume ration) , f_{3}/f_{s}(the f_{3}ratio). - Find out the V
_{as}and f_{s}of your speaker, by either measuring it or by looking it up in the tech sheet. - Calculate the volume of the box : V
_{b}= V_{as}/ α . - Calculate the tuning frequency : f
_{b}= H * f_{s}. - If you want to calculate the f
_{3}, you can do that by taking the f_{3}ratio value from the table and multiplying it by f_{s}. Calculate f_{3}= (f_{3}/f_{s}) * f_{s}. - Choose a diameter for the port. The bigger the better. Half of the diameter is the radius (R).
- Calculate the length of the port : L
_{v}= [(14630000 * R^{2}) / (f_{b}^{2}* V_{b})] – (1.463 * R) . Length and radius are in inches and volume in cubic inches.

**Let’s do a real world example, for an 8″ woofer with the following specs :**

Q_{ts} = 0.52 ; f_{s} = 47 Hz ; V_{as} = 7.86 L

- Alignment chosen : SQB
_{3}(since Q_{ts}has a high value, it’s a non-flat alignment). - Looking in the middle column where Q
_{L}= 7 . - Q
_{ts}= 0.52 . - H = 0.8116 ; α = 0.1971 ; f
_{3}/f_{s}= 0.6835 . - f
_{s}= 47 Hz ; V_{as}= 7.86 L . - V
_{b}= 7.86 / 0.1971 = 39.88 L (2433.63 cubic inches) . - f
_{b}= 0.8116 * 47 = 38.14 Hz . - f
_{3}= 0.6835 * 47 = 32.12 Hz . - Choosing the diameter to be 4″. This means R = 2″
- L
_{v}= [(14630000 * 4) / (1454.66 * 2433.63)] – (1.463 * 2) = (58520000 / 3540103.24) – 2.93 = 16.53 – 2.93 = 13.6″

**So for our 8″ woofer we got :**

- SQB
_{3}alignment. - Volume of the box 39.88 L .
- Tuning frequency 38.14 Hz .
- f
_{3}= 32.12 Hz . **Port**diameter 4″ .- Port length 13.6″ .

### Conclusion

Similar to Q_{tc} from sealed boxes, the bass reflex alignments work in a similar fashion. It’s like choosing your response curve before you even made the box. Unlike the closed enclosure, bass reflex has an additional element (the vent) and it’s not as simple as choosing a Q_{tc} value. Driver Q_{ts} is an important variable in this equation and will determine whether the alignment will be flat or non-flat.

*References*

- Loudspeaker Design Cookbook 7th Edition by Vance Dickason (Audio Amateur Pubns, 2005).
- Image source : link.

## 22 comments

This is a great article thanks for the information, could you point out how you calculated the allignment table or point me to the source i want to develop a program using Octave also a source to calculate the assisted allignment table would be great. Anyways the excel spreadsheet is the great source

You can find the alignment table in the Loudspeaker design cookbook , which I highly recommend.

I can’t understanding this “Discovering that QL is lower, means you will have to make the box bigger. If QL is higher, then you will have to make the box smaller.”

Let me give you a practical example. I’m just using random numbers to make a point.

If you calculate the box for QL = 7 to be 20 L.

After you made the box, and measure QL and find out it’s 15, then the box is less leaky (more air tight). This means it doesn’t need to be as big. So to get the same response, as you calculated before, the box needs to be smaller (Let’s say 18 liters).

In conclusion a box with QL=7 and V=20L will have the same response as a box with QL=15 and V=18L. Again I’m just using random numbers to make a point.

A box which is less leaky has a smaller footprint than a box with normal losses, considering they achieve the same frequency response. The inverse is also true. If QL = 5 then the volume needs to be higher than 20L to achieve the same frequency response.

It’s not uncommon to make a box with QL of 15 if you use silicone sealant on the inside joints of the box.

Please point me to a article/link to “assisted” LF extension be it sealed or ported

I have ample power & PEQs. No knowledge source to tap into.

Thanks, tony

If you are talking about electronically assisted designs, you can go ahead and search on google for “Linkwitz transform circuit”. I’m sure you will find many articles to clear things up. Sadly, I haven’t wrote about this subject.

The LT circuit is for sealed boxes.

If you are interested in assisted bass reflex boxes, then you might want to check Speaker Builder 1/82 article by Dr. Bullock on sixth-order alignments. You might be lucky and find a pdf somewhere online. If not, you can buy Bullock’s book which contains this article.

Hi

It is great article!

My question can be a little weird but

If we put the port outside of the box,Can we use same alignment table??

I will use it For my calculation..

Thanks..

It doesn’t matter if you place it inside or outside the box. If you place it inside, you have to make the box bigger to compensate for the volume displaced by the port. Remember, these calculations will yield the net volume of the box. Then, you have to add everything you place inside the box (port, volume displaced by speaker, bracing, crossovers etc).

If you place the port on the outside, it’s basically the same thing. Only difference is that you don’t account the port for the overall volume of the box.

Thanks.

I want to be more specific with one more question:

I am trying to build supravox baffles compenses enclosure suitable with my Drivers..

And I need a confirmation..

Bass reflex enclosure compliance Cab=Vb/p*c^2.

Is this equation universal For all bass reflex??

Yes that equation holds true for all bass reflex enclosures.

Dear Marius Tanasescu,

I like reading this work, it demonstrates a very clear way of putting it down in words and equations. Thanks for making this available.

There is a thing puzzling me still, and I am not sure how to make this up from the written information:

Imagine one wants to make a small box volume, so smaller than “6. Calculate the volume of the box : Vb = Vas / α “. Can this be compensated for by altering the bass reflex port?

If yes, can the port length be calculated by using the smaller (desired) box volume in the equation “10. Calculate the length of the port : Lv = [(14630000 * R2) / (fb2 * Vb)] – (1.463 * R) .” Or must additional measures be taken for the calculation?

How far could this “limit” be pushed (if possible in the first place)? 10% less? 20%?

Any feedback welcome,

JvanderHoeven

You can calculate the port length using that formula, yes. Problem is that as you keep decreasing the volume of the box (Vb), the port will demand a very long length. And since the box is small, you don’t have any room to fit such a long port. If you want to make a small enclosure, sealed would be a better bet.

Hi Marius,

Great article, thanks for the information!

You had mentioned “Choose a diameter for the port. The bigger the better.” May I know why bigger is better? Thanks

Hello Bernard

Ideally a port should be as large as the speaker diameter, but that will translate into a very long length, and it’s not possible. As you go lower in diameter, you run into power compression issues and unwanted port noise (chuffing) at higher volumes. As a rule of thumb, go for a large diameter while the length remains reasonable.

I see.. thank you very much

Hi Marius,

Using the provide formula in this article, if I decided to use two ports in stead of one port (consider the area of the 2 ports opening is the same as one), should I use the same port length for both ports?

Thank you again.

Yes, you have to use that length for both ports. I know, it gets kinda difficult when choosing ports with larger area, but it’s the way to go, when possible.

Hi

I already asked but I want to ask again to. be sure.

Bass reflex enclosure compliance Cab=Vb/p*c^2.

Is this eq. also true if I use ‘funnel’ like shaped port?

I mean that is it true for ‘changing cross sectional area’ ports..

The compliance of the air inside the box is independent of the size and shape of the port. So, to answer your question specifically : yes, the equation is true for tapered ports.

Thank you very much..

Dear Marius Tanasescu,

Could you help me with the following: How should one use the formulas (how should one approach box design) in case two smaller woofers are preferred over using one larger one? By doing so one can make, for example, the box frontside less wide (resulting in a “slimmer” box). Such designs are rather common to my impression, using two woofers and one bass-reflex-pipe. How should the calculations be started? Just by doubling the Vas, or is it more complex/very different? Any suggestion welcome.

If the speakers are identical, resonant frequency and Qts remain the same. Like you said, you have to double the Vas value, and take your calculations from there.