How to build a sealed subwoofer box – Practical example

Why choose a sealed box?

In terms of difficulty, learning how to build a sealed subwoofer box, is the easiest. Sealed enclosures have many advantages. If you are an audiophile and don’t particularly care for loud volumes, you will appreciate the linearity and the low end extension of a closed box. The transient response of sealed enclosures are considered to be the best, if made correctly. Also, compared to other types of enclosures, it requires less volume, so no bulky boxes. It takes the least amount of effort to design and build a sealed subwoofer box, and the tolerance for error is high. So, if you got some minor design / build errors, it won’t affect the sound that much. On the negative side, it does have reduced efficiency and power handling.

Choosing your speaker

Before we learn how to build a sealed subwoofer box, we need to choose our speaker wisely. When choosing your speaker, you should have a look at the f_s and Q_es values. The resonant frequency should be as low as possible, and the electrical Q should be as high as possible. Actually, the ratio between these 2 values is what you are looking for, and it’s called the Efficiency Bandwidth Product (EBP)

• EBP = F_s / Q_es
  • If EBP is around 50 or less, then the woofer is suited for sealed.
  • If EBP > 100 then the woofer will perform better in a bass reflex.
  • If EBP is between 50 and 100, then it’s good for either closed or bass reflex enclosures.

The woofer chosen for our project is the Scanspeak 26w/8534g00 and you can find all the specs of the driver here : 26w-8534g00.

For our particular driver f_s = 23 Hz and Q_es = 0.42. This means that the EBP = 23 / 0.42 = 54.7. In conclusion, it’s a good candidate for our acoustic suspension enclosure.

Designing a sealed box

Designing a closed enclosure doesn’t require a lot of effort. The only thing you need to calculate is the net volume of the enclosure, which doesn’t include the volume displaced by the driver, bracing, etc. Get to know what kind of response you want from your subwoofer, and then you calculate the volume. To establish the frequency response you want, you will need to calculate the Q_tc of the box. Depending on the value of Q_tc, the woofer-enclosure system will exhibit a different response.

• Q_tc = 0.5 : Perfect transients, but low efficiency (over damped).
• 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 (under damped).

Q_tc values also correspond with names :

• Linkwitz-Riley – Q_tc = 0.5
• Bessel – Q_tc = 0.577
• Butterworth – Q_tc = 0.707
• Chebyshev – Q_tc > 1

To calculate Q_tc, the volume of the box (V_c), and resonant frequency of the box (f_c), use these formulas :

• Q_tc = Q_ts * (V_as / V_c + 1)^1/2 
• V_c = V_as / [(Q_tc / Q_ts)² -1]
• f_c = f_s * (V_as / V_c +1)^1/2

The design for our speaker

After I made a complete break-in of the speaker, I measured the Thiele / Small parameters and they were a bit off, compared to the quoted values on the spreadsheet. We are going to use the measured values which are :

• f_s = 24.9 Hz
• Q_ts = 0.45
• V_as = 139 l

For these parameters, we are going to model the response curve of each value of Q_tc and see how they compare. I already decided that I am going with a Butterworth response, but it’s nice to see how different values of Q_tc stack up, for our particular speaker.

Since we chose the Qtc of 0.707, we are going for a maximally flat Butterworth response. Having this information, we can start to answer the question: how to build a sealed subwoofer box? We can use the above formulas to calculate the volume of the box, and the resonant frequency of the box.

• V_c = 139 / [(0.707 / 0.45)² -1] = 94.66 L
• f_c = 24.9 * (139 / 94.66 +1)^1/2 = 39.12 Hz

How to build a sealed subwoofer box

Here are some tips on how to build a sealed subwoofer box. If space permits, I always recommend using a golden ratio for the dimensions of the box. I’m using the one suggested by Ben Kok, which is 1 : 1.12 : 1.41. Using that ratio, I managed the following external dimensions (using 18 mm thick MDF) : 592 x 420 x 470 mm which translates into 92.67 liters of internal volume.

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Now we have to add the volume dislocated by the magnet structure of the driver, but I’m not going to do that. I got a lower volume than 94.66 liters, and taking the magnet assembly into consideration the volume is even lower. However, that is not going to matter, because the box will be stuffed with sound damping material which will effectively increase the volume of the box, by altering the sound velocity inside the box. And, as always, it ain’t that serious when it comes to sealed enclosures, few liters extra or missing.

Here are some pictures with the build :

Apply sufficient silicone sealant on every joint. You can see this in the picture with the inside of the box. This is very important for a closed enclosure, to be as air tight as possible. The woofer is of a measly 80 W of power, so I didn’t consider any bracing.

Stuffing

If you want to know how to build a sealed subwoofer box the proper way, you know that after you finished assembling the box, you are not done yet. As with all the sealed enclosures, using sound damping material on the inside of the box is always a good thing. Sometimes only the walls are lined with such material, but most of the times the whole box is stuffed. I used Visaton loudspeaker wool (Amazon affiliate paid link) for the walls first, and then I continued to fill the box, till the wool got close to the magnet of the speaker.

Before I started to fill the box with sound damping material, I used a large amount of silicone on the terminal plug so I don’t have any air leaks.

Measurement

Let’s start with the impedance chart of the enclosure :

From the impedance chart, we can tell the resonant frequency of the system, which is at the impedance peak. The resonant frequency is 38.36 Hz. Very close to the 39.12 Hz we previously calculated. The difference comes from the stuffing inside the box. It is pretty unpredictable, but you can correct it afterwards. You can always remove some of it, if you so desire.

How much volume did we gain by stuffing the box?

By knowing the resonant frequency, we can now calculate the effective volume of the box. Just out of curiosity, to see how much volume did we gained by using damping material.

The internal volume of the box was 92.67 liters and the volume displaced by the speaker is not given in the spec sheet, but I’m guessing a little above 1 liter. So, let’s say the enclosure has a net volume of 91.5 liters.

Using the formulas from the beginning of the article, we can replace the new resonant frequency of the box (f_c) and the rest of values remain the same(V_as and f_s), except the volume of the box (V_c) which we are trying to find out. Using the new values V_c = 101.21 liters. So, by stuffing the box we gained an additional 10 liters of effective volume.

Frequency response and Q_tc

Using the new volume we can calculate the new Q_tc, because it has slightly changed. As a result, if you do the math, the new Q_tc = 0.69. Which is not much of a difference from the 0.7 we were aiming for. That’s the beauty of sealed enclosures, you can make slight errors and still be on track.

Let’s take a look at the frequency response :

The graph displays till 200 Hz, because it’s a subwoofer and the higher frequencies are of no interest. It is amazing how the modeled frequency response resembles so much the measured frequency response. It plays linear down to 100 Hz and then it starts to very slowly roll-off. We wanted a subwoofer with a linear frequency response and a large response bandwidth.

Conclusion

I’m sure you found a lot of tips and tricks on how to build a sealed subwoofer box. The stuffing not only increases the effective volume of the box, but has other useful functions, like : absorbing back waves, minimizing standing waves etc. The gain in perceived volume was about 10%, but the impact on Q_tc was minimal. That’s why I always encourage an amateur DIY-er to start with a sealed enclosure, because it requires minimal amount of effort and has a high tolerance for design and build errors.

References

1. Loudspeaker Design Cookbook 7th Edition by Vance Dickason (Audio Amateur Pubns, 2005). (Amazon affiliate paid link)
2. How to Build Speaker Enclosures by Alexis Badmaieff and Don Davis (Howard W. Sams  & Co, 1966). (Amazon affiliate paid link)
3. Image source : link.