## How do isobaric subs work?

An isobaric subwoofer box design sounds like something that only an experienced engineer can grasp. In reality, it’s really rather simple, after you understand how it works. The term isobaric is made by two parts : iso = equal and baric = pressure. Therefore, isobaric stands for “equal pressure” or “constant pressure“. The main idea of the design is that you have 2 identical speakers, and 1 small chamber between them. As the speakers move, they do it at the same time and in the same direction. As a result, the pressure in the small chamber remains constant. We shall see how this affects the parameters, and what are the pros and cons of an isobaric subwoofer box design.

### Back to the roots

Before we get to explain how the isobaric design works, we need some basic understanding on Thiele / Small parameters. Even if you don’t have this know-how, you can still understand the conclusion. However, if you want to dig deeper into the subject, you need to be familiar with the T/S parameters and how their values are affected by the isobaric subwoofer box design.

I will try to clarify things along the way, if it get’s too confusing. Anyway, the isobaric setup implies using 2 speakers. First of all, let’s see which parameters change when using 2 speakers in a standard configuration. Then, we can move to the isobaric configuration.

### Standard dual speaker configuration

When you plan to use 2 identical speakers in the same enclosure, some parameters change, and most notably, some retain their original value. Depending on how you wire the speakers, in series or in parallel, some parameters change in different ways.

Parameters that change when adding another speaker in series :

• Sd doubles (cone surface area).
• Re doubles (the DC resistance and the impedance as a result).
• Vas doubles (the equivalent compliance in liters. This translates in a bigger box).
• Pe doubles (the power limit).
• Le doubles (the inductance of the voice coil).

Parameters that change when adding another speaker in parallel :

• Sd doubles (cone surface area).
• Re halves (the DC resistance and the impedance as a result).
• Vas doubles (the equivalent compliance in liters).
• Pe doubles (the power limit).
• Le halves(the inductance of the voice coil).
• +6 dB more efficiency.

Judging by the information above, we can draw several conclusions. If your amplifier is up to the task (lower impedance loads), wiring in parallel is the obvious choice, as we get an extra boost in efficiency. The rest of the parameters are pretty much common sense : doubling the cone area, more power handling (2 speakers … duh), and an enclosure twice as large (2x Vas).

### Parameters that retain their original value

When judging a speaker by its parameters, the first thing you look at is at the Fs (resonant frequency), Qts (total damping) and Vas. We already know that Vas doubles its value when adding a secondary speaker, but what about the resonant frequency and Qts?

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Fs and Qts do not change their value regardless how many (identical) speakers you add. It’s easy to clarify. The resonant frequency depends on the driver’s moving mass and compliance. As a result, halving or doubling the impedance will not a affect Fs. On the other hand, the Q value is dependent on the shape of the impedance curve near resonance. While adding another speaker will increase or decrease the magnitude of the impedance curve, the shape will remain the same. In conclusion, Qts will remain unchanged.

### Isobaric subwoofer box design

In the isobaric configuration, only one speaker is radiating sound. The other one is coupled to the first one by a small sealed chamber. This is the chamber where the pressure remains constant, as the speakers move in the same direction, at the same time. The main advantage for doing this setup is that you need only half the volume, compared to only 1 speaker.

When you wire the 2 speakers together, you have the same 2 choices : series or parallel. The most popular choice is parallel, so we are going to focus only on that. Parameters that change :

• Vas is halved.
• No is reduced by -3 dB (efficiency).
• Re is halved.
• Le is halved.
• +3 db efficiency for wiring in parallel.

While the efficiency is down -3 dB, we gain an additional +3 dB from wiring in parallel. Just 3, not 6, because only 1 speaker is radiating sound. When wiring the speaker in parallel the isobaric subwoofer box design has no efficiency loss or gain.

### Why is Vas halved?

The answer to this question lies in the formula for Vas  :

Vas = 1.4 * 105 *Sd2 * Cms

In conclusion, altering the cone area of the driver (Sd) or the compliance (Cms), will result in a different Vas. Even though there are 2 speakers, only one is contributing to sound radiation, so the piston size is the same. This means we need to look at the compliance (Cms). Because the 2 speakers are interconnected by the sealed tunnel between them, their suspension systems are coupled. As a result, combining the 2 suspensions, makes for a twice as rigid speaker. In other words, half the compliance. Halving the compliance will directly result in halving the Vas.

### Does the resonant frequency (Fs) remain the same?

In short, yes it does. But the compliance is half the original value, surely this means that the resonant frequency has changed. While your observation is correct, you must see the whole picture to understand why the Fs remains unchanged. Fs is dependent on the moving mass and the compliance :

Fs = 0.5π * √(1/(Cms * Mms))

We already know that compliance is half the original value. The small sealed tunnel between the speakers is joining the drivers into one standalone system. As a result, we need to add their moving masses together. So you can see that the product : (Cms * Mms) becomes (1/2 * Cms * 2 * Mms). Which is exactly the same thing. In conclusion, the resonant frequency doesn’t change.

### Conclusion

The  compound isobaric design is not very popular these days. It was widely spread several decades ago, when speakers used to have a huge Vas value. In the present, speakers are more optimized and many don’t require big enclosures. However, some companies (like Bose) use the isobaric subwoofer box design technique, for a small footprint but big on sound. The advantages and disadvantages are few and straightforward :