Overview of inverted and passive radiator speakers

So far, our description of speakers has been "closed" speakers. This is a box with no outward opening, and the only device that can emit sound waves is the speaker unit. We already know that the cabinet will move the resonant frequency and Q of the woofer upward. For its part, a closed box is considered to have no natural resonance of its own. At least in the ideal case, whether it has resonance problems or not will depend on the details of the production.

Do we want the cabinet to consciously resonate? If we do this, what is its effect on sound? The answer to the first question is yes. This is the role of inverted (open-ended) and passive radiator cabinets, and their impact on low-frequency response can be very significant.

Overview of inverted and passive radiator speakers
An inverted tube (also called a wind tube) is an opening on the inner wall of the box to allow air to enter and exit. As long as the size of the opening is moderate, it will not affect the ability of the cabinet to eliminate the useless sound waves emitted from the rear of the woofer, nor will it affect the compliance of the air in the cabinet. The inverter tube is usually composed of a tube, which is installed in a round hole. The size of the inverter tube is calculated to make the box resonate at a desired frequency, and the inverter tube generates its own sound wave at this frequency. The left side of the figure above shows a schematic diagram of an inverted speaker.

A passive radiator is like a woofer without a motor. They used to be called "passive cones" and can be made by removing the magnetic circuit components from the woofer. Because it has no magnetic circuit, the diaphragm can move freely. The quality of the diaphragm of the passive radiator and the compliance of the elastic wave make it resonate much like a unit. The actual effect is very similar to an open box. The resonant frequency of the box can be changed by adjusting the quality of the diaphragm.

Using openings or passive radiators, it is possible to adjust the resonance of the cabinet to a frequency, which will extend the low frequency response of the speaker. The typical response curve is as follows:

Overview of inverted and passive radiator speakers
The curve in the figure above was generated with a different speaker unit. The total Q value of the speaker unit used here is equal to 0.38, so it is more suitable for various cabinet types. The green curve is the largest flat closed cabinet design. This is for comparison. Note that its -3 dB point is about 50 Hz. Note: The low-frequency limit of the speaker's frequency response is usually specified as the point where the response drops by 3dB. This is also known as the "half power frequency", because increasing the sound pressure level by 3dB requires twice the power (this is explained in the article "What is the sound"). So a reduction of 3dB is equivalent to halving the power.

The red curve is created by placing the same unit in a maximum flat inverted box. Two things are obvious. First, the open box extends the low frequency response below the airtight box. It moves the -3 dB point to 30hz. Second, the low-frequency response rolls off much faster than the closed box (open box has a drop rate of 24 dB per octave, which is twice the drop rate of 12 dB per octave for a closed box).

How does the inverter tube work? The air in the inverter tube is like a piston, vibrating with the movement of the speaker diaphragm. However, the sound waves in some tubes lag behind the sound waves of the woofer, causing a phase shift. Above the resonant frequency of the woofer, that is, the frequency at which the speaker moves forward, the sound waves of the duct and the sound waves of the woofer are in the same phase, so they reinforce each other. At the resonant frequency of the speaker, the air duct also damps the woofer, so that the movement of the diaphragm is very small, and the air velocity is maximized in the air duct. Below the resonant frequency of the speaker, the phase of the air duct sound waves will quickly move 180°, making them out of sync with the sound waves of the woofer. This does two things: First, the sound waves of the woofer and the air duct begin to interfere with each other and cancel each other out under the resonance of the speaker. This produces a fast low-frequency cut-off frequency, which prevents excessive displacement of the woofer. Second, it "offloads" the woofer, which may make it prone to excessive excursions at ultra-low frequencies (despite having a fast cut-off rate).

The blue curve is generated by placing the same unit in a passive radiator box with the largest flatness. Generally speaking, the function of a passive radiator is very similar to that of an inverter, except that the passive radiator has a suspension, so it has compliance and deflection restrictions that a wind pipe does not have. However, if the compliance and deflection limits of the passive radiator are large, it will behave very close to a duct. The passive radiator cuts the frequency below the resonance frequency of the speaker, resulting in a fast low-frequency cut-off similar to an open box, reducing woofer damping at ultra-low frequencies (although its compliance prevents it from reducing woofer damping).

If a passive radiator is very similar to an air duct, why is there a huge gap in the frequency response of about 16-17 Hz in the above example? This is a distinguishing feature of many but not all passive radiator boxes. It occurs at the resonance frequency of the passive radiator and is the result of the phase inconsistency of the passive radiator. However, if we further plot the response curve, we will see that it ends up with a cutoff rate close to 24 dB per octave, similar to an open box. In other words, it is possible to adjust the passive radiator box to be different from the open box, and use the compliance and resonance of the passive radiator to make a slower cut-off speed, more similar to a closed box. However, the latter design often requires a passive radiator with high damping, which is not very well implemented.
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