Bass reflex speaker design – easy explanation
What is a bass reflex subwoofer?
A bass reflex speaker is just like a normal closed box speaker, but in addition, has a an open tunnel, or port, which allows air to circulate freely in and out of the box. This vent helps increase the efficiency of the woofer, with substantial contribution on the low frequencies. This type of enclosure is very popular and is the pick of the range when stacked against a sealed enclosure. It’s like a sweet spot, if you will, for woofer enclosures. It gives the best balance between efficiency, low end extension and build difficulty. While building a bass reflex enclosure is pretty straight forward, designing it will take a bit more effort and the end result doesn’t tolerate designing errors, like a sealed enclosure does.
Why choose a bass reflex speaker design?
Here are some pros :
- +3 db efficiency compared to the equivalent volume sealed enclosure.
- Lower cutoff frequency. Normally after reaching the resonance frequency of the driver, the response will start to go down hill, but that is when the port starts to put in some work and extends the frequency response.
- Lower distortion at resonance frequency. At this point, the port does most of the work. The speaker barely moves when the resonance frequency of the box is reached. This means less distortion and more power handling.
There are some bad points for a bass reflex speaker as well. After resonance frequency is achieved, the response is degraded with a steep roll-off of 24 db / octave. The vent, if not designed correctly or at high sound levels, can get noisy, as the air escapes the port. Transient response is not as good as sealed equivalent.
How does bass reflex work ?
We know that the whole point of an enclosure is to separate the waves created by the back of the speaker from the ones generated by the front. Because these waves are out of phase, when they meet, they will cancel each other out. You can make an analogy with math, positive numbers are in phase and negative numbers are out of phase. And just like in math : – x + x = 0.
But wait a minute! If I use a port, doesn’t that mean that the back waves travel through the port and reach the front waves and achieve cancellation ? That is a very good question, because at first glance, that looks like a valid theory. In reality, something else happens. The port acts like a Helmholtz resonator, and back waves reverse phase and come out the port in phase with the front waves. Because of this, not only it does not cancel the front waves, it reinforces them ( +x +x = 2x ). This is where the +3 db efficiency comes from.
This effect only happens when reaching the resonance frequency of the port. Above this point (higher frequencies), the mass of air inside the port is too great to respond to the speaker movement, and it acts like a perfectly sealed enclosure. Below this point, the port acts just like a hole in a sealed box . The back waves do not reverse phase and come out of the port, only to cancel the front waves. That is why the bass reflex speaker has such a steep roll-off (24 db / octave) below the resonance frequency point.
Achieving a desired fB (resonant frequency)
To achieve a desired resonant frequency of the box, now you have to take into account the dimensions of the port as well. The air inside the port has its own mass and resonates according to the movement of the air “spring” inside the box (see the closed box article for more information about this “spring”). The internal volume of the box and the internal volume of the port are key to defining the resonance frequency.
- Altering the size of the box :
- Making the box bigger => lowering the resonant frequency
- Making the box smaller => increasing the resonant frequency
- For a given port diameter, altering the length of the port :
- Making the port longer => lowering the resonant frequency
- Making the port shorter => increasing the resonant frequency
Remember, when choosing the dimensions of the port to achieve a certain resonant frequency, there are 2 things that matter : the mass of the air inside the port and the compliance. If the port needs to have 2 L of volume, you don’t just pick any dimensions for radius and length just to hit that target volume. Compliance needs to be taken into account. If the port is wide, it’s more compliant, because air moves with less restriction. This means that the port needs to be made long enough to meet the desired compliance. In a reverse fashion, a small port is less compliant and doesn’t need to be long. So, the radius and length of the port are interconnected and must be matched correctly to reach the desired result. You can see this relation, between length and radius, in the visual graph just below.
The most common used shapes for a bass reflex port is either cylindrical or rectangular. Rectangular ports are made using pieces of the material you are using to make the box, but most often circular ports are used. These are made by various materials (mainly plastic), but if your local audio store is out of bass reflex ports, you can successfully use PVC pipe for example. For the ongoing discussion about these vents, we are going to focus on the cylindrical one, as it is more popular.
The port dimensions plays a major factor into deciding the resonating frequency (fB) of the box. I’m not going to write the formula for calculating the fB of the box, because you are going to use specialized software for this.
- But I am going to mention that (for a given speaker) the tuned frequency of the box (fB) will depend on 3 factors :
- Length of the port
- Radius of the port
- Volume of the box (VB)
Choosing port dimensions
The dimensions of the port are somewhat at your choosing. For example : if you want to achieve a certain fB using a certain volume of the box, you can alter the length of the port as you choose, but you will have to change the radius of the port accordingly, so that the first 2 values (fB and VB) remain constant. Even though it looks like you have the freedom to choose the dimensions you like, in reality there are certain factors you need to take into account seriously.
The diameter of the port needs to have a minimum value. When the frequency reaches the resonance value (fB), the port radiates almost all of the acoustical power (the speaker moves very little and the port does most of the work) and because of this, the vent needs to have a minimum volume displacement in order to prevent power compression.
Mr. Thiele and Mr. Small have come up with their own formula of deciding which is the minimum diameter required for the port. Depending on who you fancy more, you will end up with a different result. But in reality this has little relevance because you are always going to aim for a bigger port. Making the port bigger in diameter means that you have to make the port longer to keep the same resonance frequency, so you can understand that there are some limitations on how big can you go. Vents operate in a nonlinear fashion no matter the dimensions you choose, but going for a larger one, will almost certainly end up with less nonlinear performance. Bigger diameter means that there is less air turbulence as well and will translate in less port noise at high volumes.
Diameter to length correlation
- Port diameter 2″ (5 cm) => Length of 2.3″ (5.8 cm)
- Port diameter 3″ (7.5 cm) => Length of 6.2″ (15.5 cm)
- Port diameter 4″ (10 cm) => Length of 12.3″ (30.8 cm)
- Port diameter 6″ (15 cm) => Length of 30″ (75 cm)
These numbers are just to make a point. A random woofer and box volume was used to generate them. Please don’t use them for your project.
As you can see, going too high with the diameter can yield impressive lengths for the bass reflex port. Longer ports tend to resonate themselves and that does introduce some minor frequency response alterations. You shouldn’t worry too much about this and think about how smaller vents are way worse.
Recommended minimum size
A bass reflex speaker should be matched in size with its port. Here are some recommendations on minimum vent size compared to speaker size :
- 1″ vent => 4″ speaker
- 2″ vent => 4″ or 5″ speaker (6″ max)
- 3″ vent => 6″ speaker (8″ max)
- 4″ vent => 8″ or 10″ speaker (12″ max)
- 6″ vent => 12″ or 15″ speaker
As the diameter goes up, the length of the port goes up, so if you are using big woofers and need a longer vent, you can use one of these solutions
- Use a 90° elbow to redirect the vent up or down. This way you don’t have to make the enclosure really deep to accommodate the long vent.
- Use multiple ports. To find the combined diameter of 2 ports use the formula : dt=(d12+d22)1/2. So if you have two 5″ ports, it will equal to one 7.07″ port.
Another way to increase the linearity of the vent is to use a flared port. Having a flare at both ends of the vent reduces distortion and minimizes the noise the air makes when it rushes out the port. At high volume levels, it is said that a flared port reduces noise for about 5 db, which is significant. Some companies, like B&W, have gone even further and made the flare of the port like a golf ball texture. They call it flowport and reduces air turbulence even further
Additional factors to consider
Subsonic filtering. Below the resonant frequency of the box-port assembly, the vent acts just like a hole in a sealed box. As a result, the compliance of the box is really high and the speaker moves unrestricted. In the absence of the internal air “spring”, the woofer is not damped anymore and can reach impressive excursions, over the quoted Xmax, if push too hard. To counter this, passive or active filtering should be made so no damage can occur on the woofer.
Damping material. Like with sealed enclosures, damping material can be used to reduce panel resonances and standing waves. Unlike the sealed enclosure, you don’t stuff the box with damping material, because you will obstruct the port. Just place 1-2″ absorbent material on the the walls of the enclosure (on one of each opposite sides or all of the walls).
The bass reflex speaker design, while not difficult to build, will take a bit more time to design. Anyway, we will cover more about designing the bass reflex box in a future article, because we only mentioned the basic principles (check out the bass reflex alignments). This should not discourage you to try something more challenging. Building and designing a sealed enclosure is pretty straight forward and you should definitely start with one of those. Ported boxes are not so tolerant to design and build errors. So, when you are ready to take a step forward, and think that the advantages of a bass reflex subwoofer are something you want, you should definitely give it a try.
- Loudspeaker Design Cookbook 7th Edition by Vance Dickason (Audio Amateur Pubns, 2005).
- The Audio Expert: Everything You Need to Know About Audio by Ethan Winer (Focal Press, 2012).
- Image source : link.