Modeling vibration in Speakers with Passive Radiators

Subwoofers with passive radiators may have significant vibration. This Simscape model calculates performance including vibration.

For several decades, the low frequency response of woofers and subwoofers has been expanded with tuned ports. The theory and analysis methods are well covered elsewhere. The more recent development of passive radiators enables more compact subwoofer systems. The passive radiator has a design similar to that of a speaker, but with no electrical drive coil.

A system model for a speaker with a single passive radiator is shown here. The cone is driven on its back side by the pressure in the enclosure, and it radiates sound from its front side to the far field. The front side of the passive radiator has a radiation impedance and a block that calculates the far field radiation from its velocity. The far field pressure from the speaker and passive radiator are added to give the total output. The “scope” output collects the separate pressures from the speaker and radiator as well as their sum.

The mechanical components at the center of this figure allow the total vibration force to be calculated. This model shows the case where the passive radiator is mounted on the same side of the enclosure as the speaker. In that case, the vibration forces from the two radiators add in phase. The author has heard anecdotal evidence that this case can create a significant vibration problem at the resonance frequency of the passive radiator.

A better design with reduced vibration uses two passive radiators mounted on opposite sides of the box so that their vibration forces act in opposition. Examples of commercial products of this design are easy to find by searching the internet with the search phrase “dual passive radiator subwoofer.” At the time this is being written, that search found these: link1 link2 link3. A system model for the dual passive radiator subwoofer is shown below. Note that the mechanical domain connected to the moving coil speaker is independent from that for the passive radiators because its axis is perpendicular to the passives. The mechanical domain for the passive radiators includes a “lever” component to reverse the direction of the force for one of the radiators. Data for the “lever”component is defined to have a force ratio equal to negative unity.