The Subwoofer DIY Page v1.1
DUMAX Parameters
last updated: 08 January, 2009
Read almost any advertisement for a subwoofer driver in your typical car audio magazine, and you'll see headings like "600 watts power handling!", or "56 oz. magnet!".  Unfortunately, these "specifications" really tell us NOTHING about how that driver is actually going to perform.

There IS a particular set of parameters that DO give us a fair idea of how the driver will perform.  Referred to as the Thiele/Small (or "T/S") parameters, these numbers describe the particular characteristics of the driver, and can be used to determine its output capabilities and box requirements, in the process removing an enormous amount of guesswork involved in subwoofer design and construction.

The basic T/S parameters are as follows:

Small-Signal Parameters
Fs = resonance frequency of the driver.
Qes = Electrical Q of the driver at Fs. 
Qms = Mechanical Q of the driver at Fs.
Qts = Total Q of the driver at Fs. 
Re = DC resistance of the driver's voice coil. .
Vas = Equivalent air compliance. 

 

Large-Signal Parameters
Pe = Thermal capacity of the driver, in Watts. 
Sd = Effective surface area of the driver. 
Xmax = Linear (one-way) travel of the cone. 

The "small signal" parameters are typically used by designers to determine optimum box size and tuning (i.e. "alignment") for a particular driver.  The "large signal" parameters are normally used to estimate the output capability of the driver in the chosen alignment.

Traditionally, the measurement of large-signal T/S parameter Xmax has been based solely on the length of the voice coil and the length of the gap, therefore ignoring any non-linearities introduced by the driver's suspension, and also ignoring any compensatory effects introduced by same and/or the driver's magnetic structure.   This traditional "Xmax" parameter could therefore be used only as a ROUGH estimate of the driver's linear excursion potential.

What was needed was a new definition for Xmax, one that has a direct relationship to the driver's output potential.

In its Nov/Dec 1995 issue, Car Stereo Review included two articles on David Clark's DUMAX device - a driver measurement system that can, among other things, measure how far a driver's cone can travel while still working in a linear fashion.   The DUMAX system actually measures TWO excursion parameters that define the driver's linear operation.  These are as follows:

Xmag = Excursion limit due to the magnetic limitations of the driver's motor.  Xmag is defined as the displacement at which the BL product has fallen to 70% of its value at the cone's rest position.
Xsus = Excursion limit due to the driver's suspension.  Xsus is defined as the point at which the compliance of the suspension has decreased to 25% of the value at the cone's rest position.

From these two figures, Xmax is then derived as follows:

Xmax = The shorter of the Xmag and Xsus values, in each direction of cone travel.

Note that very often Xmag and Xsus are NOT the same for each direction of cone travel.  Therefore, an "average" Xmax figure is usually derived from the Xmax for forward travel and Xmax for reverse travel.

Example:
Given:
   Xmag (forward) = 14 mm
   Xmag (reverse) = 8 mm
   Xsus (forward) = 14 mm
   Xsus (reverse) = 14 mm

Then:
   Xmax (forward) = min(14,8) = 8 mm
   Xmax (reverse) = min(14,14) = 14 mm
   Xmax (average) = (14+8)/2 = 11 mm

It should be clear to see the advantages that the DUMAX measurement of Xmax brings to loudspeaker design and construction. Not only can we now determine the optimum alignment for a particular driver using the "traditional" T/S parameters, but we can also quite accurately determine the system's linear output capability as well, along with the power required to make the most use of the driver's excursion range.

A final note: it has recently become quite fashionable to prominently feature a driver's Xmax capability in subwoofer advertisements.  Please note that Xmax is only ONE of a number of parameters that have an effect on the overall response!  Do NOT make the mistake of choosing a driver solely on its Xmax rating - you may end up with a disappointing system.

Driver Measurements

Brian Steele 

References:

  • "To the Max"- David Clark
    Car Stereo Review (Nov/Dec 1995)
    Hachette Filipacchi Magazines

  • "Just Do It" - Tom Nousaine
    Car Stereo Review (Nov/Dec 1995)
    Hachette Filipacchi Magazines