Passive Radiator Technology
A passive radiator (drone cone) can be used instead of a port, which is commonly used in bass reflex applications. Together with an active driver, it works according to the Helmholtz resonator principle. If a passive radiator is used, we still have quite the same response like a vented enclosure: We make use of one simple resonance at the tuning frequency. The acoustically behavior is quite similar, although there are relevant differences in practice.
The passive radiator represents basically a port with the same diameter like the membrane, the adjustable mass of the cone equals the mass of the vibrating air of the vent. Such a port tube, however, would be too long and voluminous for most cabinets.
The moving mass of the passive radiator can be tuned by the designer in order to achieve the desired tuning frequency of the resonator. The higher the moving mass, the lower the tuning frequency and vice versa. By applying proper moving mass, the tuning frequency can easily be set very low, even in small enclosures. In this way, effective radiation down to 20 Hz can be achieved without the need for very large cabinets and long ports. Additionally, no volume is wasted on the port.
With a passive radiator there is no source of port noise and far less air turbulence, and no pipe resonances and standing waves modulate the music signal. The modulation problem gets more important, when the active driver in the system covers a wide frequency range like a mid-bass driver. Because of its wide spectrum, it is more sensitive to inter-modulation distortion, caused by port resonances and standing waves. These are typically located in the midrange, and mix with the music signal. The consequence is, that a distorted and time delayed version of the active drivers´ response is present at the port. As a passive radiator consists of acoustically rigid materials and is consequently “closed” for frequencies above the tuning frequency, no inter-modulation products appear.
See the frequency response at the mouth of a bass-reflex port, when a midrange driver is used:
A lot of the midrange signal gets through the port, and the correlation between the drop in the midrange driver FFT around 550Hz and the peak in the port response is clear.
Below the tuning frequency, the active driver is under better control, compared to a vented system. The compliance of the passive radiator prevents ultra-large excursion in the anti-phase region, seen in a vented situation acting “open” below the resonant frequency.
For a good working setup, you need more piston area of the passive radiator, than you chose for the active driver. This is because the resonance of the passive radiator in a typical system is lower by a factor of sqrt 3 than the resonance of the active driver. At these two resonances, the largest excursions appear. As the resonance of the passive radiator is much lower in frequency, but at a similar sound pressure as the active driver, the passive system needs to move a lot more air (2 – 4 times more, depending on the alignment). So, the effective area of the passive radiator should at least be twice of the active driver.
You can easily see the situation by comparing the following two graphs:
5mm excursion at 35Hz of the active driver vs. 12mm excursion at 23Hz of the passive driver
A typical alignment with a Q of 0.6 was used for this comparison.
In the datasheets of our passive radiators, you find a diagram about how to chose the right extra mass for a given enclosure volume and your desired tuning frequency. For explanation, the P280 diagram is shown here:
The area around the graph illustrates, that the resonance frequency of the passive radiator is not a constant. It varies with the excursion, because all spiders available today have a progressive characteristic. But of course, we are working on this...
In the datasheets of our passive radiators, the stated resonance frequency Fs is measured at an excursion of 3mm. This gives a more realistic basis for calculating the resulting tuning frequency in your application. The graphs are consequently calculated this way.
If you like, you can calculate the resulting tuning frequency for a given extra mass and enclosure volume.
At first, the resulting compliance in the box has to be calculated:
Cmsr = 1 / [ (1/Cms) + 1/( (Vb/Vas) x Cms) ] (1)
with Cmsr: resulting compliance
Cms: compliance of the passive radiator
Vas: equivalent volume of the passive radiator
Vb: desired enclosure volume
Then, we can insert the Cmsr into the second equation to get the resonance frequency:
Fres = sqrt [ 1 / (Cmsr x Mres x 4 pi^2) ] (2)
with Mres: Mms + extra mass
In case you choose two passive radiators for one enclosure, you just have to halve the Vb
of your desired enclosure volume for calculation or use of our diagram.