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Design Theories: PR - Passive Radiator

PR - Passive Radiator
Basic Theory
A passive radiator is used in conjunction with an active driver and its purpose is to replace the port or vent of a typical 4th order enclosure. A passive radiator is sometimes referred to as a drone cone. A passive radiator (PR) enclosure is most similar to a vented enclosure in that they acoustically behave very much the same. Response characteristics include: there is a notch at the Fp of the passive radiator (resonant frequency of PR) and the typical cut-off rate below fB is 36 dB/octave. The resonant frequency of the PR is intentionally altered by the designer in order to achieve the proper fB of the enclosure. In other words, it is used to tune the box to the desired frequency and for optimum performance. This is done my adding or removing calculated amounts of mass from the cone of the PR. More mass = lower tuning. Less mass = higher tuning. The increases mass also helps to lower the Fp of the PR which in turn moves the undesired notch out of the passband resulting in improved transient response. In theory, the Vd (volume displaced by PR) should be at least 2 times the Vd of the driver it is being used with. Yet in practice, a good rule of thumb to go by is to have anywhere from 3-4 times as much displacement in the PR. This is to ensure the longevity of the PR's by preventing excessive continual over-excursion.
Advantages
Simplicity of tuning. By merely adding and removing small amounts of mass, the tuning frequency of the enclosure may be changed up or down by as much as 15 Hz or as little as 0.1 Hz. Precision tuning is very possible. Ability to tune small enclosures to very low frequencies without the loss of volume due to internal ports taking up enormous amounts of precious space. No port noise or any kind of air-turbulence of air speed levels to worry about. Pipe resonances and port standing waves are non-existent because there are no ports or vents in this system. Better driver stability below fB due to increased damping on the driver below fB. This is because of specific compliance characteristics of the PR which help to keep the driver under better control at subsonic frequencies.
Disadvantages
Steepest of all cut-off rates with a roll-off 36 dB/octave below fB. Given the same size volume and tuning frequency of its vented counterpart, the PR alignment would result in a slightly higher f3. The expense of of PR's can be quite high when compared to a simple piece of PVC pipe. Especially when 2 or more PR's is needed, which is usually the case when using high-power, high-excursion drivers.
Best Applications
Best suited just about anywhere a regular vented enclosure would be used. May be used in applications where a smaller box is desired while wanting to maintain a 4th order alignment. It was once believed that the PR alignment can be made half the volume of the same vented alignment and still be designed to have the same tuning frequency and achieve the same frequency response. Though this theory has been argued. Passive Radiator alignments in most cases will require a comparable box volume and tuning as 4th order vented alignment in order to achieve similar results.
   
Source: www.danmarx.org