In the Lab
Part 1 of this objective measurement section consists of large signal analysis using the very expensive (about $50,000 including all the software) but enormously effective Klippel analyzer followed by the LEAP 5 analysis. Utilizing the Klippel analyzer (on loan from Klippel GmbH), Pat Turmire, CA&E reviewer and CEO of Redrock Acoustics, performed the large signal analysis on the Critical Mass 12" subwoofer and provided the Bl (X) curve shown in Figure 2. The black Bl curve shows the motor strength of the woofer as it moves in both directions outward from center rest position. The lighter curve is a type of displacement curve and if both curves were identical, the motor system's motion in and out of the frame would be perfectly symmetrical. When a woofer is totally linear ("linear" indicates that the woofer motion tracks the input signal exactly with zero distortion), the Bl curve should be centered on the 0mm point (where the cone is positioned when there is no signal) and symmetrically decrease Bl (as the number of turns in the gap decreases with outward motion) with the same slope in either direction of voice coil travel. When a woofer exhibits a forward or rearward offset, it may indicate that the magnetic and mechanical systems are not absolutely optimal. If the motor strength decreases more rapidly in one direction (usually the outward direction) than in the other, the result is increased levels of distortion at high operating levels. It is not uncommon, however, for a woofer voice coil to be deliberately offset a few millimeters in order to keep the motor more linear in the 90-110dB SPL range, which exactly describes the situation with the Critical Mass sub.
The UL12 Bl (x) curve shows the woofer voice coil is offset by a fairly trivial 1.5mm rearward (inward) from its rest position. This Bl curve is a very symmetrical broad shallow slope plateau with nearly equal slopes in either direction. The displacement at operating SPL near Xmax is nearly 0mm, so this is about as good as it gets. Bl can decrease to approximately 70% of its small signal value and the driver will still function in a satisfactory manner, only with an elevated level of distortion (about 20%). The 70% of maximum Bl displacement limit for the UL12 is 36.8mm, 4.8mm more than the physical Xmax of 32mm.
This subwoofer's Kms(x), or Stiffness of Suspension, curve (see Fig. 3) likewise exhibits very good symmetry in both directions of travel. The offset is a negligible 0.5mm rearward at the rest position. The compliance limit for the suspension when it drops to 50% of its rest value is greater than 36mm. Both "limit" numbers, Bl and compliance, represent the level at which distortion climbs to 20%, which is a realistic criteria for subwoofers given the ear's lack of sensitivity to distortion at low frequencies.
Next I produced the T/S (Thiele/Small) parameters for the UL12 subwoofer. Utilizing my normal speaker geek test protocol, I employed a LinearX LMS (Loudspeaker Measurement System) analyzer and VIBox (VI for voltage/current) for measuring dynamic impedance (impedance at different voltage levels). Testing is accomplished through a series of voltage and current sweeps that are later converted to multiple voltage impedance curves. With the driver clamped to a rigid test stand, measurements were made at 1V, 3V, 6V, 10V, 20V, 30V and 40V (the 40V curves were later discarded as too non-linear for LEAP 5 to curve fit properly). Instead of using the standard added mass (delta mass) or test box method (delta compliance) to find the Vas (volume of air equal to the driver compliance) of this driver, the measured weight of the cone body (with 50% of the surround and 50% of the spider removed) was used instead as this method is considerably more accurate. The group of multi-voltage impedance curves was uploaded into the LEAP 5 CAD program and the Transducer Model Derivation utility used to create the T/S parameters shown in the Data Chart. These numbers were then used to generate the computer box simulation numbers also located in the Data Chart.