# 4th order bandpass calculator – With box design example

## How to build a 4th order bandpass subwoofer box in 7 steps?

The 4th order bandpass box design is not recommended for the first time builder. You need some experience before you get into these complicated designs. Actually, if you are a good listener and/or are savvy with enclosure design software, you shouldn’t have much of a hassle when making this kind of project. The problem is, even if you conceive a good 4th order bandpass design, but have slight building errors, the result will be sub-par. Now that you are all encouraged, let’s learn more about these bandpass enclosures.

**What is a 4th order bandpass box ?**

The term bandpass is also used in passive crossovers. Usually used for midrange drivers, to filter low frequencies and high frequencies at the same time, only to let the frequencies between the crossover points pass.How is this passive filter example relevant to the bandpass speaker enclosure ? It is, because when you look at the frequency response of a bandpass subwoofer, it looks exactly like the frequency response of a speaker with a bandpass filter on it. Imagine the frequency response of sealed or bass reflex enclosure. For the very low frequencies, when the resonant frequency is reached, the response starts to roll-off. Now, for the higher frequencies, the response will naturally start to roll-off, at different points, depending on the speaker. Because of the size of the woofer, it will be impossible for it to play high frequencies at some point, so it naturally rolls-off.

However, the 4th order bandpass design acts differently. It is composed by two chambers : a rear sealed chamber and a front vented chamber. You can think of it like a normal closed box system, but the vented chamber in front of the speaker acts like an acoustic filter, a low pass filter to be more precise, so higher frequencies are filtered depending on how it is designed. Because of this filtering, the frequency response bandwidth is quite narrow. You can make it broader, but you will sacrifice efficiency. Or you can make it even more narrower and increase efficiency by a lot. This seems appealing for those who want to play a narrow frequency range at very high volumes (like car audio SPL competitions). Sealed and bass reflex can make this kind of trade-off also, but bandpass has a better “yield”.

**How to make a bandpass box ?**

Further on, I will explain how to design your box without any design software. Your pen and paper will be the actual 4th order bandpass calculator. This will get a bit technical, but I’m sure you will figure it out. Before you start off your project, you should first select a woofer. Anything that will work well in a sealed box, will work well in 4th order bandpass design as well. If you want to crunch numbers when choosing your speaker, you can divide f_{s} / Q_{es} , and the smaller the number, the better (lower than 60). This means a good bandpass speaker will have a low f_{s}, or high Q_{es}, or both.

First of all, let’s define some terms, so we can speak the same language :

- f
_{B}– Tuning frequency of the port in the vented chamber. - R – The radius of the port in centimeters.
- L
_{v}– Length of the port in centimeters. - f
_{L}– f_{3}of the low frequency roll-off. - f
_{H}– f_{3}of the high frequency roll-off. - Q
_{bp}– Q of the sealed rear chamber. - V
_{f}– Volume of the front chamber (the acoustic filter chamber) in liters. - V
_{r}– Volume of the rear chamber (the sealed chamber) in liters. - S – Passband ripple (How many ±db does the frequency response deviate from linear frequency response).
- V
_{t}– Total volume (V_{f}+V_{r}) in liters.

As you can see from the graph above, f_{L} and f_{H} are positioned -3 db after the response starts to roll-off (for low and high frequencies). The passband ripple measures the amount of variation from linear response. High amount of ripple will result in peaks / dips in the frequency response. Judging from our graph the ripple looks like around ±0.5 db.

### 4th order bandpass calculator in 7 steps

We are going to explain, step by step, what are you supposed to do in designing a great sounding box. To make things more clear, we are going to use a real life woofer, and design a bandpass subwoofer box for it. The woofer I chose is the **JL 10TW3-D4** . There is no particular reason for my pick, other than it has good specs for a sealed enclosure, which means it will be good for bandpass as well.

### How to design loudspeakers - video courses

I’m going to list the Thiele / Small parameters of the JL woofer for convenience :

- F
_{s}= 32.3 Hz. - Q
_{es}= 0.656 . - Q
_{ms}= 11.35. - V
_{as}= 19.82 L. - Q
_{ts}= 0.62. - X
_{max}= 15.2 mm.

### Step 1 : Know what do you want

You have to understand that there is no perfect bandpass enclosure for each kind of woofer. You have to make compromises between linear frequency response, how wide the frequency response is, and efficiency. General rule of thumb is that the louder it is, the narrower the frequency response is. Depending on what you want to achieve, you will have to find a balance between these 3 aspects, so that you will end up with a 4th order bandpass design that suits your needs.

### Step 2 : Determine how linear the frequency response should be

Remember, at the beginning of the article, we talked about some parameters that are relevant to this project. One of them is S, which is the passband ripple. This ripple, describes how many ±db, the frequency response will digress from linear response. In a perfect world the ripple would be ±0 db, which is achievable. However, that is at the expense of the other 2 characteristics we need to take care of, in the later steps.

There are 3 values of S, which give an acceptable amount of ripple, and have the following characteristics :

- Best transients for S = 0.7, and 0 db ripple.
- S = 0.6 , somewhat degraded transients , ±0.35 db ripple.
- S = 0.5 , worse transients than S = 0.6 , ±

Picking a certain value for S, will narrow your possibilities for the other factors we need to figure out. Another guideline which is useful when choosing S, is that if you go for a bigger value (0.7), the frequency response will be narrower. On the other hand, a lower value S (0.5), would translate into a wider frequency response. So, choose the ripple you like, but keep this in mind when doing so.

Here is a table with the values of S, and the values of the frequency response and sensitivity, corresponding to that certain S value. Get familiar with this table, as we will need it for the next step as well.

**For our woofer we will choose S = 0.6.**

### Step 3 : Determine the desired frequency response bandwidth and sensitivity

Now you have to determine the values of f_{L} and f_{H}. This means you will determine the – 3 db points, when the response starts to roll-off, for both low frequency and high frequency roll-offs. This will effectively set your frequency response bandwidth between the two values. You figured out the value of S, at the 2nd step, now you will chose the values of f_{L} and f_{H}, corresponding to that S. After that, the value of the sensitivity is chosen for you. If you choose a certain value for the sensitivity, then the values of f_{L} and f_{H} are chosen for you. This is the balance I talked about, that you need to make, to find the sweet spot.

To find the values of f_{L} and f_{H} you have to do the following :

- f
_{L}= F_{s}/ Q_{ts}* (f_{L}factor) - f
_{H}= F_{s}/ Q_{ts}* (f_{H}factor)

**Now let’s do some number crunching for our woofer :**

**I’m choosing the sensitivity to +5 db because I want a loud bandpass enclosure.****This means that the start and end of the frequency response are chosen for me.****f**_{L}= 32.3 / 0.62 * 0.7317 = 38 Hz.**f**_{H}= 32.3 / 0.62 * 1.6877 = 88 Hz.

**So, we have figured out that the frequency response will be from 38 Hz to 88 Hz, with a +5 db boost and **±**0.35 db ripple.**

### Step 4 : Calculate the volume of the front enclosure

Calculate the front chamber volume using the following formula:

**V _{f} = (2S * Q_{ts})^{2} * V_{as}**

**V**_{f}= (2 * 0.6 * 0.62)^{2}* 19.82 = 11 L

### Step 5 : Calculate the volume of the rear enclosure

Calculate the rear chamber volume using the following formula:

**V _{r} = V_{as} / ((Q_{bp} / Q_{ts})^{2} – 1)**

**Vr = 19.82 / ((1.1113 / 0.62)**^{2}– 1) = 19.82 / (3.21 – 1) = 9 L

### Step 6 : Calculate the tuning frequency of the front chamber

Calculate the tuning frequency using the following formula:

**f _{b} = Q_{bp} * ( F_{s} / Q_{ts})**

**f**_{b}= 1.1113 * ( 32.3 / 0.62) = 1.1113 * 52.1 = 58 Hz

### Step 7 : Calculate the dimensions of the port

The radius of the **port** (R), should be as large as possible, to minimize port non-linearity. Understand that making the port bigger, will mean that the length of the port will be longer. This means there are certain limitations to how large you can go.

**For our project I’m choosing a port radius of 5 cm (10 cm in diameter).****R = 5 cm.**

Calculate the port length using the following formula:

**L _{v} = ((94250 * R^{2}) / (f_{b}^{2} * V_{f})) – (1.595 * R)**

**L**_{v}= ((94250 * 5^{2}) / (58^{2 }* 11)) – (1.595 * 5) = (2356250 / 37004) – 7.98 = 63.68 – 7.98 = 55.7 cm

### Results for our 4th order bandpass calculator

Now we have finished making a 4th order bandpass design box for our 10″ JL woofer, and the dimensions are as follows :

**Front chamber = 11 L.****Rear chamber = 9 L.****Port diameter = 10 cm.****Port length = 55.7 cm.**

Please bear in mind, that these are the net volumes. This means that you will have to add the volume displaced by the speaker, to the volume of the rear chamber. Also the volume displaced by the port needs to be added to the volume of the front chamber. Add any other elements to the total volume (like bracing).

### How to design loudspeakers - video courses

The frequency response will look like the following graph :

### Variations of 4th order bandpass enclosure

In the example above, we used just one speaker, and made a 4th order bandpass design. If we use 2 speakers, we can place them in different positions so that we end up with different variations of bandpass enclosures. Here are some variations of the 4th order bandpass enclosure:

**Single driver bandpass**subwoofer box.**Dual driver**push / pull bandpass enclosure.- Push / pull compound bandpass box design.
- Triple chamber bandpass subwoofer box.
- Push / pull triple chamber bandpass box design.

For the dual driver push / pull variation, calculate the volume of the front and rear chamber, for each individual driver, and then add them up. For the triple chamber bandpass subwoofer box, the rear chambers are separated, and therefore calculate them normally. The 2 drivers are sharing the center chamber. So calculate the volume of the front chamber for each driver individually, and add them up, to get the volume of the center chamber. When there is a push / pull configuration, remember to connect one of the drivers out of phase electrically (reverse polarity).

### Conclusion on bandpass box design

The 4th order bandpass box design is definitely an interesting solution. If you do not need a wide frequency response, and want a boost in output, you should seriously consider it. However, the enclosure can get quite big, and you don’t have direct access to the speaker. As a result, if you need to replace the speaker, you have to tore open the enclosure. The design and build difficulty can be a let down for the inexperienced builder, but if done properly, the 4th order bandpass design can be quite impressive.

*References*

- Loudspeaker Design Cookbook 7th Edition by Vance Dickason (Audio Amateur Pubns, 2005).
- Introduction to Loudspeaker Design: Second Edition by John L. Murphy (True Audio, 2014).
- Image source : link.

## 135 comments

Nice write up

Thank you for breaking this down in easy to follow directions. I have always wanted to know how they were figured. Thanks to you, I will be building my first one today to enclose a JL Audio 13.5 shallow mount ironically enough. Thank you again!

prejudice compliments for the explanation. very clear the only past that I do not understand is this f L = F s / Q ts * (f L Factor)

f H = F s / Q tof H factor fl and fh factor have fixed values or has taken them from the woofer parameters. I have an audio jl 12w7

The values of fL Factor and fH Factor can be found in the alignments table, which can be found at step 2. Qts and Fs are woofer parameters and can be found in your 12W7 parameter spread sheet.

Let’s say you choose the ripple S=6 and the sensitivity of +3 dB. Then, the fL=0.6217 and fH=1.5778. You have the liberty to choose other values for fL and fH (from the alignments table), but then the sensitivity will be different.

Grazie mille per la spiegazione

these are the characteristics of my driver. S factor which I could use to have a good system

FS 27,2

Qes 0,514

Sgq 7,807

Qts 0,482

Vas 66,0 lt

Xmax 29mm

No 0,25%

(1w/1m) 86,2 db spl

Sd 0,0542 mq

That is a choice that you have to make, there is no perfect choice, it depends on your application. I would go for a +3 dB sensitivity and when you choose S, consider the following :

lower value S means : higher ripple, wider frequency bandwidth, worse transients, smaller box

higher value S means : low or no ripple, narrow frequency bandwidth, better transients, bigger box.

If you have a hard time choosing you can go for S=0.6 which is the middle point.

Grazie ancora

from the calculations I got back chamber volume 20.483 liters 22.080 liters anterior chamber diameter pipe length 10cm led 1901.420 cm. Now as I understand it should add to the rear volume the volume occupied by the driver, and front volume that occupied by the conduit?

The volumes are correct. The pipe is 10 cm in diameter and 38.7 cm in length. And yes, those are net volumes. You have to add the volumes displaced by anything (driver, pipe, bracing etc)

The length I 19 not 38. But if I put a tube with blunt ends I have to calculate as if it all straight?

I have made the calculation again, and even used a modeling software and it’s 38 cm. Check your calculations. If by blunt you mean flared, then the total length (38 cm) is the length of the straight pipe + half of the length of the flare.

Ho eseguito la formula sopra riportata. Quindi 38 cm da metá svasatura interna a metá svasatura esterna? Scusa tutte queste domande ma non vorrei fare dei danni

Corretta 🙂

La formula che ho eseguito è questa L v = ((94250 * R 2 ) / (f b 2 * V f )) – (1.595 * R)

E quindi L v = ((94250 * 25) / (3123,580* 22,080)) – (1.595 * 5)=26,189

La Fb=55,889

Vf=22,080

Yes, you are right. I somehow used the Qbp from S=0.7 and got an Fb of 47.9. But, taking a closer look now, you are correct. The length is 26 cm

Is there some preferenced distance between the speaker and the port? The configuration of the two (on the same side of the box, on in one side and one in the other, ecc..) is going to change some parameter of the system??

All things being equal, port placement shouldn’t affect functionality. You just have to take into consideration that the back end of the port (the one which is inside the box) should be a certain distance from the nearest panel. This distance must be equal or greater to the diameter of the port.

help please , I can’t count the chamber and port , I don’t understand the subwoofer machete M15 D2 here the data of Thiele small SPL – 88.28 dB. vas-75.36 L. FS-34.10 Hz . BL-16.70 qts-0.63. I love when low bass.

For S=0.6 and a sensitivity of +4 dB you get the following :

Rear sealed chamber : 42.5 L

Front vented chamber : 43 L

Port diameter : 150 mm

Port length : 300 mm

For S=0.7 and a sensitivity of +3 dB (this will go very low, but the enclosure is big) :

Rear sealed chamber : 92.4 L

Front vented chamber : 58.6 L

Port diameter : 150 mm

Port length : 350 mm

thank you very much for your help !

Un’ultima domanda per determinare la lunghezza del condotto devo tener conto del diametro interno effettivo o di quello esterno perché internamente misura 9,6 cm ed esternamente 10 cm. Mille grazie

the internal diameter

Ok grazie mille proverò a realizzare questo progetto e ti farò sapere grazie ancora

Buongiorno! Volevo Avere un consiglio per la Realizzazione del box mio passa banda avrei Pensato di Mettere Sulla parte anteriore per Poter VEDERE il conducente del plexiglass vorrei Sapere di che spessore?Le altre Pareti Sono in MDF da 30 mm

Please stop speaking in Italian. I never used plexiglass before, so I can’t tell you how thick it should be. However 30 mm MDF is really thick. Totally overkill in my opinion. Don’t get me wrong, the thicker the better. But the enclosure will be very heavy. Most definitely you won’t be able to lift it alone.

Buon giorno! Volevo avere un consiglio per la realizzazione del mio box passa banda avrei pensato di mettere sulla parte anteriore per poter vedere il driver del plexiglass vorrei sapere di che spessore le pareti sono in MDF da 30 mm

I try with plywood 28 mm.

I am building a fourth order bandpass enclosure for 412 inch subwoofers and I am wondering if I will be able to do this with a space that is 36 x 37 x 15 please get back to me with answer or if you may even have a Nother suggestion if I could do a six order Banpass enclosure with 3 12s instead in that space

That’s a really big box. Calculate the volume for 1 speaker and multiply that by how many speakers you have. That’s your overall volume. My guess, it will surely work for 3 speaker, but you have to check for 4.

I have these factors:

Fs 30

Qes 0.53

Qms 7.07

Vas 67.8

Qts 0.49

Xmax 10

And with S:0.6 and -2dB i got Lv < 0, could you help me with that or am i doing something wrong

fL = 30 / 0.49 * 0.4052 = 24.8 Hz

fH = 30 / 0.49 * 1.3612 = 83.3 Hz

Vf = (2 * 0.6 * 0.49)^2 * 67.8 = 0.34 * 67.8 = 23.05 L

Vr = 67.8 / ((0.7427 / 0.49)^2 – 1) = 67.8 / (2.29 – 1) = 67.8 / 1.29 = 52.55 L

fb = 0.7427 * (30 / 0.49) = 45.5 Hz

I suspect you have a 12″ woofer so a 15 cm diameter port would be nice. R= 15 / 2 = 7.5 cm

Lv = ((94250 * 56.25) / (2070.25 * 23.05)) – (1.595 * 7.5) = 5301562.5 / 47719.26 – 11.96 = 111.1 – 11.96 = 99.14 cm

That’s going to be pretty hard to implement. Let’s try with a 10 cm diameter port R = 5 cm

Lv = ((94250 * 25) / (2070.25 * 23.05)) – (1.595*5) = 2356250 / 47719.26 – 7.97 = 49.37 – 7.97 = 41.4 cm

Good luck!

The numbers that I came up leave my Vf more then half as small as my Vr. Most 4th I see the sealed cabinet is smaller then the ported cabinet. I was wondering if I’m doing this right. Looking for a very flat response for sound quality for home stereo.

S=0.5 0db

Fs=33

Vas=1.39

Xmax=8.128mm

Qes =1.058

Qts=0.825

Qms=3.751

83.3db

Your driver has a very high Qts and it’s not the most fortunate pick for BP4. If you use S=0.7 you will see that you will get negative numbers which indicate that the alignment is not possible for your driver.

Bună seara, și felicitări din nou pentru toate marile sfaturile pe care le dau noi, cititorilor. pentru că am de gând să realizeze a patra comanda mea și a vrut să știe cum să calculeze volumul tubului reflex pentru a putea adăuga la volumul caseta. și conducta de formă circulară

Thank you for this write up! You’ve made it very easy to understand banpass box design

hi.can i ask u a question?

i got a sub with these parameters

Fs 43

Qes 0.5

Qms 5.3

Vas 12.15

Qts 0.46

Xmax 22mm

i want to use 12th of this sub in a 6th order box if u can please help me.

thank you

There isn’t much documentation out there for 6th order bandpass. Bose has a patent on the design and unfortunately it’s not available. You can find software to model the 6th order bandpass response, and you could make one for personal use, without any legal issues. However, the design has a very thin tolerance for error, and since you are vaguely asking for help, I’m advising you to chose another enclosure design.

hello

what’s you suggestion about regarding ti subwoofer parameters?

what’s you idea about 4th order

please advise us one technically channel virtual network and website or Email or another connection way.

best regards

Hi!

I’m calculating a 4th Bandpass Triple Chamber for Dayton Audio RSS210HF. I’m calculating a single woofer first to add the Vf values later. But I have some questions regarding the ports…

I want the frequency range to be really low, as the mid range is taken care of by other speakers. The woofers are supposedly able to handle the low frequencies quite alright. Low sensitivity is not going to be an issue, as the amp powering them will provide more than enough, so I went for 0,35dB ripple and -3dB sensitivity to get the frequency range where I want it, Fl 19,2 Hz & Fh 69 Hz.

However, I’m confused by the port. Using a 6 inch port will give a length of 340 (!) centimetres, and a 4 inch port will give a length of 148 cm, which isn’t possible to fit.

Also, how do I calculate more ports since I’m building a triple chamber with twice the volume of the front chamber Vf? I assume that two equal 4″ or 6″ ports won’t result in the same Vf as a single one?

Vf 11 litres

Vr 42,3 litres

Fb 37Hz

Lv 340cm/148cm ????

Link to woofer… http://www.daytonaudio.com/index.php/rss210hf-4-8-reference-hf-subwoofer-4-ohm.html)

Specs

Fs 29,6

Qts 0,57

Qes 0,69

Qms 3,25

VAS 23,71

Thanks

Looks like you already calculated the front and rear chamber volumes. In a triple chamber, the rear volume is the same (each speaker with its own chamber). And the front chamber is shared by the 2 drivers, and it has to be double the volume of Vf.

Unfortunately you calculated the port correctly. You can’t do nothing about that. The problem is that the Vf is only 11 liters. As the volume of the ported chamber get’s larger, it will demand a shorter port. Only thing you can do is go for a smaller diameter port. Going for 2 ports is not a solution. For ex : If 1 port of 4″ diameter needs to be 148 cm long, 2 ports of 4″ need to 300 cm EACH. So you can understand that makes things even worse.

Try to choose another alignment, where the ported box is bigger, or go for a smaller port (but you risk unwanted wind noise).

Hello,

I want to build band-pass enclosure as specified above with RCF L15S800 and i calculated Vf= 16,6 L which is 0.016 m3 and Vp=10,2 L which is 0.01 m3. I wonder isnt this a bit too little volume for 15″ transducer ?

I wait for Your help…

Your calculations look correct. Your driver has a very high Fs for a 15″ woofer. Very high sensitivity also. It’s probably designed for outdoor use, to be very loud. Because of this, it doesn’t go very deep in bass. Since it’s not playing the very low notes, it doesn’t demand a big enclosure.

Thanks a lot Marius 🙂

I’m obviously really thick as I don’t get any of that!

Is there anyone here can help me design a 4th order box as I don’t have a scoobie what any of those calculations mean??

thanks

can someone help me what a three chamber for 2 8″ kicker C8 old school model.

I have a Rockford fosgate 12″t2. With a fosgate 1200rd amp, rms 1347 watts @ 1ohm. Would a 4th order box rock my Toyota t100?

Yes it would :). Probably you should go for bass reflex though. You have enough power and it’s easier to make.

Any secrets of the bass reflex or a helpful site?

Check out these 2 articles :

http://audiojudgement.com/bass-reflex-speaker-design/

http://audiojudgement.com/bass-reflex-alignments-explained/

I will read them! Thank you ! God Bless you.

Maybe one of you could help me out:

I am trying to design a small(ish) sub to fit under the sofa. In order to see what woofer could fit the bill, I have been trying a couple different ones.

With a Monacor SP-202PA (Q_ts= 1.1; V_as= 12 L; Q_es = 2.25, f_s= 68) I am getting a usable design even with S=0.7.

The problem is that I am getting a negative rear volume.

V_r = V_as /( (Q_bp/Q_ts)^2 )-1

V_r = V_as/ ( (0.8489/1.1)^2 )-1

Q_bp/Q_as is smaller than 1, so its square must also be. Subtract 1 and you end up with a negative coefficent to scale V_as.

I’m missing something very obviuos, ain’t I?

Your driver has a Qts of 1.1 which is very high. It is suitable for infinite baffle, and not much else. If you want a small enclosure you should take a look at sealed enclosures. You should definitely forget band pass.

Yeah, you’re probably right.

The damping on that particular chassis is terrible. The other ones that gave negative volumes are also very non-compliant drivers, so the math is obviously teeling me to keep my hands off cheap rubbish like that. :o)

How do you choose the S value?

I dont quite understand that.

A higher S number will translate into better transient response and better linearity. However, the response bandwidth will be narrower. (and vice-versa)

The PS48 subwoofer of bose (bass module from a Lifestyle V35 for exemple) comprises 3 event on the from face. With type of isobaric construction is it exactely ?

Because there is a small cavity inside the subwoofer box where the 2 speaker are mounted, but the cavity is not completely closed.

The box also presents two other opening, one on the upper part of the box (seems to be attached to the upper speaker) and a second at the lower part of the box (seems to be attached to the second speaker). What is the utility and functionning of all theses 3 openings ?

Thanks for explanations.

Can’t really tell for sure from pictures. But my guess it’s a 6th order bandpass enclosure (because bose has the patent on the design) and the extra cavity on the inside is an isobaric setup to reduce the volume of the box.

Thanks a lot for your reply.

On an isobaric construction the internal cavity is generally totally closed. But this is not the case here with the ps48 sub.

Do you know the reason ?

Do you think is it possible to design a sub similar to a PS48 from BOSE perfectely adapted to Home Theater use ?

Note that the particularity of this “bass-medium” enclosure from bose, it to work upto 260 hz ! (On the upper part of bandpass).

If you say that the inside cavity is open it does rise a lot of questions for me too. You kinda expect this from bose. This is their philosophy : very cheap speakers, but over-engineered enclosures and a lot of digital processing. If you try to copy the design, not knowing how it works, you will most likely end up with something that you won’t be proud about. The fact that it goes so high in frequency response means one of 2 things : the lower part of bandpass is high as well (not hitting the very low notes) or it does go low in frequency but has poor efficiency rating (not impressive in volume department).

I need some help. I can’t figure out the Qbp of my woofer. It’s a DDX-15D2. I have my front enclosure volume as 13.308L

I cannot tell you that. Qbp doesn’t depend on the speaker. It depends on how linear you want the frequency response (S), frequency response bandwidth (fH and fL), and efficiency of the enclosure. These are parameters that you choose (more or less) however you want. Read the article again and pay more attention.

So when designing the triple chamber how does port size work? Do we just double it in size as we do the volume of the box?

No. You just double the volume of the chamber (so Vf is now double). Set a diameter for the port as you would normally (go for a larger diameter now so you don’t end up with chuffing noise). Then, calculate the length of the port using the Lv equation (difference is now that Vf is larger so the length will be different).

I want to do a double 18” fourth order bandpass. I want both drivers to share the rear chamber in parallel. What do I do for calculating Vf and Vr?

I would like both magnets housed in the sealed chamber

It’s just like having one speaker but with double the Vas value. The rest of the parameters (which are relevant to this enclosure) remain the same (Fs, Qts).

Hi, I have TWO of these subwoofers going into a 4th order bandpass box, both magnets in the ported side with their own separate sealed enclosures. I am looking at around 1.2 cubic feet per sealed chamber, and around 5.5 cubic feet on the ported side. My enclosure should be around 32″ wide, 30″ long, and 14″ tall. Using these specs, I am trying to figure out the port size for this. I will be building a rectangle shaped port, but not sure how big to build it. I want a musical box and don’t mind losing some output in exchange. Any ideas on port size and length? Hoping for about an 8-10″ port, not sure how long to go though.

Woofer Size 10″

F(s) 37.68 Hz

R(e) 7.06 Ohms

Q(ms) 5.231

Q(es) 0.536

Q(ts) 0.486

V(as) 9.340 liters (0.330^ft)

L(e) 8.74 mH

M(ms) 282.10 grams

C(ms) 0.09 mm/N

Sensitivity 81.59 1W/1m

BL 29.67

RMS Power 1200W

Peak Power 2400W

Displacement .07^ft”

Replying to my own comment, it looks like if I go an inch taller, to 15″, it gives me a 1.25 cubic foot sealed area per side if I go 9″ deep. That gives me a 5.5 cubic foot ported area at right around 20″ deep. If I did my math correctly, a 10″ wide by 8″ tall rectangle port should be 9.45″ long to be tuned at 48Hz. It seems like everyone says that’s a happy medium tuning area for a musical box. Any comments, questions, concerns would be greatly appreciated.

Sealed area: 32″ wide X 15″ tall X 9″ deep for 2.5 cubic feet giving me 1.25 cubic feet per chamber.

Ported area: 32″ wide X 15″ tall X 20″ deep for 5.56 cubic feet

Port size: 10″ wide X 8″ tall X 9.5″ long for 48Hz tuning

First of all, those dimensions that you quoted will guarantee you a misaligned enclosure, that will sound awful. Secondly, I would advise you to choose an easier to make enclosure. Bandpass enclosures are difficult to design and to make. And have all sorts of inconveniences (like if you want to take the speaker out, you have to destroy the box). I’m not saying you should not try to make a bandpass enclosure, but you seem to not have much experience. As a result, I invite you to look at sealed or bass reflex enclosures.

I have zero experience in building a 4th order bandpass box, but have lots of experience building sealed and ported. That’s why I’m asking all the questions, I don’t want another sealed or ported enclosure.

So working on designing a 4th order for my side by side and have some questions. I was playing with 2 Rockford p2 12s as I’m not sure exactly what I’m going to run but something around that. They have qts of .54, fs of 27.2, and vas of 81.5 liters.I did an s value of .6 with a +3db output. The problem I run into is then I get 2.4cuft for the front chamber(before any displacement) and 2cuft for the rear(before displacement). One this seems really small, I have 11 cubes I can use, and two isn’t the ratio supposed to be 2:1 or 3:1? These are the formulas I used

I actually did the calculations myself with the numbers that you mentioned. I got Vf = 2.41 cuft , Vr = 2.43 cuft, tuned at 50 Hz. Frequency range 31 – 80 Hz, +3 dB efficiency. There is no rule like this chamber should be this size compared to the other. These calculations reflect the 4th order bandpass alignments. You can make the box whatever volume you want, but you will need a box modelling software to see if the frequency response will suit you. 5 cubic feet box is not a small box in my standards. Going for a larger volume will make it louder but reduce the frequency response bandwidth. If you really want to use all of the available space, my advice is to go for bass relfex. Less things that can go wrong.

hi there – and thanks for a informative site.

At the moment I’m working on a 4th order bandpass woofer for my home cinema. I want the freq. range to be say 20-70 Hz. It’s gonna be a flat formation 300 mm in hight inside and 1000 mm in width, but I still want a 15″ speaker. And there’s gonna be two 6″ ports. The woofer is going to be a podium for the 2nd row of seatings. I want it so make an ‘atmosferic’ sub, in order to feel the helicoper noice etc.

But it seems very difficult to get any decent 15″‘er with Fs/Qes that goes below 60, or even 100.

So any suggestions of a good speaker, or is that 60 value different with a 15″ speaker?

Thanks and all the best

Óla Jákup

I don’t understand why you are having such a hard time finding a 15″ woofer that will go that low. Usually they have a low resonant frequency. My guess is that you are looking at pro audio drivers, which have a higher Fs, but high power handling. Check out normal hi fi drivers.

how would this convert to a triple chamber design

trying for skar sdr-12 D4(i know but they are payed for)

fs 32hz

qts0.5

vas 43.3

hoping for s 0.7 0db to +3db depends on space

ok i finished the page and answered my question

ok going with a radius of 10 cm which is 20cm round,which would be 7.874 inch i get 24.54cm long which is 9.66inch ,how can i slot port this?

Make a slot port with the same area of the circular port. PI * R^2 = 3.14 * 10^2 = 314 cm2 (for example 35 x 9 will result this area). And the length is exactly the same as the circular port.

I’m looking for a total 4 ohm load, which driver would work better in a 4th order enclosure, one of these?

https://www.parts-express.com/dayton-audio-um8-22-8-ultimax-dvc-subwoofer-2-ohms-per-coil–295-508

or two of these face-to-face in an isobaric arangement?

https://www.parts-express.com/dayton-audio-rss210hf-4-8-reference-hf-subwoofer-4-ohm–295-456

Well, the 2nd option is either 2 ohm or 8 ohm, since you have two 4 ohm drivers. The first driver (Ultimax) seems like a good choice anyway.

I think I maybe linked to one of the wrong drivers.

However, How about if either one was edequately powered, would two of the RSS210hf drivers in an isobaric 4th order bandpass arangement work better or worse than 1 um8-22-8 ultimax in a single driver 4th order enclosure?

The whole point of going isobaric is to cut the enclosure size in half. However, you have to make room for an additional driver. Also, a smaller enclosure demands a longer port to keep the same resonant frequency. If you add all of these up, you don’t get much of a volume benefit, while paying for an additional driver. Isobaric is nice for very specific applications. Haven’t made any number crunching but my guess would be that it’s not worth it. Go for the single ultimax.

You are right, I gain a tiny bit of power handling having two drivers, the increased cost of the additional drivers, and the absolute inability of being able to fit the port inside for the desired Fb. if the port goes outside then it looks like a submarine. The enclosure volume actually becomes so small that two drivers won’t fit face-to-face.

I NEED HELP,MASSIVE AUDIO,TOROX 124 I HAVE CAME UP WITH 3 DIFFRENT FIGURES AND I DONT KNOW WHY.S.7 0DB. FS 36.4 QES .67 QMS 4.2 VAS 23.5 QTS .57 3 CHAMBER BOX. I HAVE 1.05 FRONT 1.44 REAR,AND THIS PORT I HAVE A -4.ORR IS IT FRONT 1.5 REAR .695 4 INCH PORT 12.20 IN LONG ALL CUBIC FOOT PLEASE LET ME KNOW.bethington@gmail.com

For a +3 dB box with S7, I got 0.73 cu ft front, 1.37 cu ft rear chamber. Tuning frequency 46 Hz. 4″ diameter port of 8.4″ in length.

is that front shared by both or individual? im going for 3 chamber and that doesn’t leave much room for the port. im not questioning your ability im just making sure i get it right

Ah, I thought you had a single speaker. Good thing you asked. In that case, each speaker has its own sealed cabinet of 0.73 cu ft and the ported enclosure has to have 2.74 cu ft of volume. Since you have 2 speakers, go for a 6″ diameter port, of 8.42″ in length. Remember, the quoted volumes are net volumes. You need to add everything that takes up space (volume displaced by speaker, by port, braces etc).

Thanks for the information you rock.

How would one go to work if you want to do 8×15 in a 4th ?? 4 on the left and 4 on the right with ported chamber in the middle all inverted to the ported chamber . Each sealed section would be around 15cm x 90cm x 105cm = 2.5cft and the ported chamber will be 60cm x 90cm x 105cm = 15.6cft can always do away with ported and add 1.2cft to sealed??

You probably want to do hair tricks and stuff. So, sound quality is not important. Just use all of your available space. You forgot to mention port size, but any window-like opening will do.

I’d like to build a 4th order box and have a small single 10” sub with a (FS 30.4, Qts .55, Qes .64, Qms 4.22, Vas 1.34 ft3 ) just trying to hook my son up with a great sounding box . I had a 3 chamber as a youngster and it pounded any help is appreciated.

OK. Here are some numbers : Rear chamber : 0.67 ft3 , Front chamber 0.79 ft3. The front chamber is tuned at 52 Hz, so this means you can go for a 3″ diameter port and 6″ long, or a 4″ diameter port and 11.7″ long. If you have the available space the bigger port will have less air turbulence. The volumes are net volumes and do not include the volume displaced by the speaker, port, braces etc (you have to add them up).

Thanks for the info I appreciate it?

Hi i want to make a 4th order bandpass (triple chamber) box with two rockford p3d4-12. with

Fs:27.7 hz

Vas:57.7 l

Qts:0.52

Qes:0.57

Qms:5.60

can you help me please?. I want the box from 33hz to 80hz. i do all the math but at the end on the port length i got a massive number.

Tank you

Sealed chamber 69 liters. Ported chamber 60 liters, tuned to 45 Hz. Port diameter 150 mm (5″) and length of 320 mm. Response from 30 Hz to 68 Hz.

Skar Audio ZVX-8 D2 – 8″ SPL Car Subwoofer

Dual 4 Ohm Voice Coil Configuration

Peak Power: 1,100 Watts

RMS Power: 900 Watts

Competition Grade Pressed Paper Cone

Stitched High Roll Foam Surround

Massive Triple Stacked Magnet

2.5″ High Temperature Copper Voice Coil

Motor Weight: 156 oz

Frequency Response: 40 – 500 Hz

Sensitivity: 80.4 dB

Fs: 41.8 Hz

Re: 4.0 Ohms

Qms: 3.6

Qes: 1.25

Qts: 0.76

Nref: .07 %

Cms: 0.02 mm/N

Bl: 15.5 n/a

Vas: 14.2 L

Mms: 132 gr

Sd: 188 cm^2

Xmax: 14 mm

I would like to do a triple chamber bandpass 2 drivers both in there own sealed chamber with the magnetic to the inside. If u wouldn’t mind could u please give me a recommendation ofor box dimensions and port size length? Thanks in advance

Sealed chambers : 20.33 liters each. The middle chamber 40.67 liters tuned to 54.5 Hz. Using a 4″ port, that would be 25.65 cm long.

So ive just started looking over this. Very well written.

Im currently doing a blow through on my f150.

My question since i have ample space. I was planning to do a

Band pass box. Can you do 3 subs in a bandpass set up.

Cutting the blowthrough out and then putting plexi glass where the cut out is to seal the front enclosure and (kerfing) the ports under the enclosers and into ports directed into the cab itself.

Is this possible or am i just a dreamer.

I don’t really understand what you are describing exactly. But, you can put how many woofers in a bandpass box as you like. Secondly, you can route the port to where you want, given that the length of the port corresponds to the resonant frequency you want. Extending it too much, will decrease the resonant frequency of the box, which may or may not be a good thing.

I am wanting to build a 3 chamber box. I have 2 jl audio 12s. Can you help me do the dimensions.

Yea, I can help, Which JL woofers are we talking about?

12w1v3-4

This is what I came up with. Front C 27.80

Rear C 7.12L

Port dia. 10cm

Port len. 17.22cm

If this is correct the rear chamber would only be .25 cubic feet???

I don’t know which parameters have you chosen, but for S=0.6 and +3 dB you get the following :

Vf = 27.57 l

Vr = 26.20 l

Port dia = 10 cm

Port length = 24.2 cm

If I go isobaric with two woofers, what do I change in the formula to get proper result?

Adding 2 woofers in isobaric configuration will effectively halve the Vas value. So, even though you will have 2 speakers, consider you have only one, with the same specs, only difference is that Vas is half the value of one speaker.

Some electrical parameters change as well, but for box building purposes you should only take into consideration that Vas is now (0.5 * Vas).

This is excellent burn the only thing I’m having a genuine issue with is port diameter calculations. The formula

Lv = ((94250 * R2) / (fb2 * Vf)) – (1.595 * R)

Is yielding a port length 129.35 cm with a radius of 10 cm. That’s 50.75 inches and I have 2 subs so multiply by 2 that’s 100 inches of port? I’m so lost and I’m just trying to learn how to do this. I’m trying to design and build an enclosure for 2 13jlw7s for a truck blow through. I really some help please.

Well, it’s not uncommon to get really long port lengths if you have a very low tuning frequency or very small box, or very large port size(not your the case). Also, if you have 2 woofers you don’t just multiply by 2. Anyway, let me give you a box example for your woofers. Having 2 of these woofers will demand a very large box (somewhere around 300 liters). But let’s make a compromise so we can make the box a little more manageable (not tune it so low, but have a decent volume).

I would suggest a 120 liter box tuned at 30 Hz, which means one 6″ port and 382 mm in length.

Hello, I attempted to use the formulas here to create a box for my Dayton Audio UM15-22 15″ Ultimax DVC Subwoofer 2 ohms Per Coil

Here are the product specs and ts parameters:

Product Specifications

Nominal Diameter15″

Power Handling (RMS)800 Watts

Power Handling (max)1600 Watts

Impedance2+2 ohms

Frequency Response15 to 1,000 Hz

Sensitivity86.5 dB 2.83V/1m

Voice Coil Diameter2.5″

Thiele-Small Parameters

(Fs)19.5 Hz

(Re)3.4 ohms

(Le)1.31 mH

(Qms)2.40

(Qes)0.59

(Qts)0.47

(Vas)7.92 ft.3

(Cms)0.24 mm/N

(BL)15.4 Tm

(Mms)279.4g

(Xmax)19 mm

(Sd)814.6 cm²

The issue I am having is that the enclosure volumes are too small to even accommodate the driver.

Mounting Information

Overall Outside Diameter15.28″

Baffle Cutout Diameter13.78″

Depth7.55″

Bolt Circle Diameter14.65″

# Mounting Holes8

I retrieved all the information information out of this link:

https://www.parts-express.com/dayton-audio-um15-22-15-ultimax-dvc-subwoofer-2-ohms-per-coil–295-514?gclid=EAIaIQobChMIjKmklLqM4gIVB1qGCh1xUQN0EAAYASAAEgI6evD_BwE

I selected a S value of 0.6 at 2db.

This enclosure is going in the trunk of a 2019 Lexus GS 350. I wanted a bandpass so that I can run the port through the rear arm rest. The arm rest is roughly 6″ x 11″.

I’ve heard other bandpass enclosures built this way and they sound great. But the volumes I get from the formulas here don’t quite make sense. Maybe my math is wrong. Any help would be great.

The alternate sub would be the 10″ version of the same sub that can also be found in that same site.

I already did the math for S=0.6 and +2 dB and the numbers are as follows :

Sealed chamber 76 liters. Ported chamber 71 liters tuned at 39 Hz (6″ port 14.75″ long).

My guess is that for Vas you used 7.92 (cu ft) instead of 224.3 (liters). Always check the units.

Thank you so much. By the way, amazing write up on the 6th order bandpass for the 10″ W6. That graph looked awesome and your box build was great. Ok back to this now. I think 5.18 cu.ft is definitely too large for me. I’m still in need of a trunk space after this is installed. So I will be crunching these numbers for the 10 in version of the sub. Might even consider a 6th order for an 8 inch. Do you have a write up that shows how to manually calculate a 6th order the way you explain the 4th order here?

Nope. You need to model it with software. You won’t find any alignments numbers (like with BP4) because BP6 is patented by Bose and BP6 enclosure cannot be made commercially, unless you pay patent royalties to Bose.

Hi I am trying to spec a 4th order blow through but lost with the calculations, in your calculation where did you get the 3.21 from for the rear chamber . I am using a single HCCA 124 black coil. I want to have a port or 2 pointing through my armrest. I am not sure if it will work but willing to try it ( I actually have 4 of the HCCA 124 but limited to trunk space. Your help would be very grateful .

If you look closely, you will find that 3.21 comes from (Qbp/Qts)^2. It’s written just before. Qbp you will find it in the table at the beginning of the article. And Qts is the total speaker Q found in T/S parameters list of the speaker.

Ok Thanks for you reply but i am still lost at this is it possible for you to calculate it for me.

HCCA124 single and Double

your help would be appreciated

Hello

You woofer is not that friendly when it comes to BP4 enclosures. Mainly because it results in a small enclosure and you are going to have a hard time fitting the woofers and a long port. The one example which I see kinda doable is this one :

Sealed chamber : 11.28 liters , ported chamber : 11.92 liters. Port 100 mm diameter and 457 mm in length. These are net volumes so you have to add the volume displaced by the speaker (if you place the magnet inside the sealed chamber then the volume is 11.28 + the volume displaced by the speaker). Also make sure to add the volume displaced by the port (if you place the port or part of the port outside the enclosure then you don’t add that to the overall volume). The minus here is that the 4″ port seems kind of small for this kind of woofer and might exhibit port noise. But placing a larger one will demand a too long length to be viable.

Thanks for your post. I have a situation where at an S value of 0.5. I am seeing some negative values for my rear chamber volume. I ran your number through my spreadsheet and got 8.95711. Which you had listed as 9, so I believe my formulas have been input correctly. I read the comments and see others have gotten negative values. I was going to try for a sensitivity of -3 db which gives me a vol of 29.396 L, -6, -7, -8 db are all negative. Am I OK to use -3 db as my sensitivity, so long as my volume is positive?

The number I am using are:

Vas:9.127 Qts:0.735 Qbp values correspond to an S of .5

You have to understand that these are alignments. This means that for specific numbers, you get very specific results. Sometimes, a speaker is unfit for these specific alignments. For example, it will have a ripple of 3 dB. You don’t see that in the table. But you could potentially build that enclosure.

You follow these alignments if you want those specific results. Your speaker has a very high Qts number and it will be unfit for certain alignments. Basically, if you see a negative number, your speaker is not good for that particular alignment. But you can make a box with your custom frequency response by using box modeling software. Just to give you a hint, if you want to follow these alignments, if the Qbp you choose is smaller than the Qts of the speaker, then it’s no good.

Hi i want to make a 4th order bandpass box with one 12″ rockford fosgate sub t112d4

Fs:33 hz

Vas:34.8 l

Qts:0.55

Qes:0.63

Qms:4.46

can you help me please?. I want the box from 33hz to 80hz.

Thank you

So you need 15.15 liters ported chamber, tuned to 59 Hz. This means a 10 cm diameter port of 36 cm in length. The sealed chamber needs to be 15.5 Liters. The response is +3 dB and the frequency bandwidth is 37 – 94 Hz.

These are net volumes so add the volume displaced by the speaker/port.

Hi i had a look at the manufacturers recommendations for the Rockford fosgate t112d4 and they recommend 1.25ft (35.39lt) for a sealed enclosure and 1.75ft (49.55lt) for a ported enclosure so

15.15l for the ported and 15.5l sealed seams to be quiet a small enclosure

Well, first of all, those are the volume for either sealed or reflex. I gave you the volumes for a 4th order bandpass which has a sealed and a reflex chamber. So the total enclosure will be roughly 31 liters (quite a bit more when you add the speaker and port displacement. Their recommendation for sealed is good but for bass reflex it translates into a +5dB peak which I don’t fully agree with. The bandpass enclosure I gave you, has a more conservative +3 dB but with a more linear response.

Your article was awesome and really taught me a lot. But I’m still struggling on the total volume and the port dimensions. My subwoofer has these specs

Qes-.422

Fs-23

Qms-96

Vas-226.14

Qts-.404

Xmax-13.5

I chose a s of .7 and a +3db

Which gives me a frequency response of 32hz-73hz.

And my volumes came out as Vf-72L or 2.5 cubes and Vr-66L or 2.3 cubes

Does this all sound good for a ext cab truck enclosure, and I always thought bandpass boxes where built as a 2-1 or 2-1. But my volumes are almost identical. If you think I should switch my S or my db choice please tell me. I want a stupid loud box but still able to hit lows. Thank you

Your article was awesome and really taught me a lot. But I’m still struggling on the total volume and the port dimensions. My subwoofer has these specs

Qes-.422

Fs-23

Qms-96

Vas-226.14

Qts-.404

Xmax-13.5

I chose a s of .7 and a +3db

Which gives me a frequency response of 32hz-73hz.

And my volumes came out as Vf-72L being 2.5 cubes and Vr-66L being 2.3 cubes. Am I on track or way off ?

Sorry for the late reply. I did the calculation and your are spot on. Good job!

Hi Marius,

First off, thanks so much for this awesome tutorial! Very informative and well put-together.

If you don’t mind, I’d like you to double-check my calculations, as the results I’m coming up with have my volumes looking a little smaller than I expected.

Sub: JL 12W6v2-D4

Fs = 25Hz

Qes = 0.48

Qts = 0.45

Qms = 7.1

Vas = 79.9L

Xmax = 17mm one-way

I went for an S value of 0.7 for flatter response and +4db gain. Here are the values I calculated:

Fl = 33.8Hz

Fh = 73.83Hz

Vf = 31.7L

Vr = 23L

Fb = 52.9Hz

For the port I am planning on using 6″ concrete tube, and I came up with 49.5cm for the length. I’m just concerned that my calculations are off as the air space seems low to me. The recommended sealed enclosure for this sub is 35.4L, so it seems like this box would be starving it for air space. Would appreciate any input.

Thanks!

I made an excel spreadsheet to easily calculate the alignments. Here are the numbers :

Sealed chamber 28.54 Liters

Ported chamber 31.71 Liters

Tuning frequency 48.7 Hz

Frequency range 34 – 74 Hz

Port diameter 150 mm

Port length 584 mm

Thanks so much! Not sure where my math went wrong… Making an excel sheet is a great idea.

Take care

Brandon

🙁 ughhh I really hate sucking at math.. I have read read and re read this article and all I hear is my brain saying dumb ass you should have paid more attention in school…. I really need help though I have a JL W7, 8 and would love to make a LOUD head turning box… Any suggestions would be greatly appreciated!!!

Nice woofer. You are talking about the 8″, right? Here are the numbers

Sealed chamber 8.49 Liters

Ported chamber 12.77 Liters

Tuning frequency 61.5 Hz

Frequency range 44 – 86 Hz

Port diameter 100 mm

Port length 408 mm

Remember that those are the net volumes. Depending into which chamber you place the back of speaker, you have to add the volume displaced by the speaker (which is 1.7 liters). Also, you have to add the volume displaced by the port. If you find the port too big to fit into such a small enclosure, try a 75 mm diameter port with only 215 mm in length (might exhibit port chuffing at high volumes because of the lower diameter).

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