How do the Delta Mass and Delta Compliance Vas Tests work?
The mechanical resonance point of a driver is essentially nothing more than the mechanical interaction of two basic
properties, mass (Mms) and spring stiffness (Kms) where Fms=sqrt(Kms/Mms)/2*pi.
The inverse of Kms is compliance: Cms=1/Kms. Since 'spring stiffness' is more meaningful to most lay persons than
spring compliance, the equations shown use Kms.
Looking at the equation for Fms, we can see that a single measurement of Fms will only reveal the ratio of Kms/Mms.
Therefore, it is not surprising to find that both the delta mass (easy nickel) and delta compliance (test box)
methods for measuring Vas seek to modify one or the other parameter and therefore shift the driver resonance.
In either case, a shift in resonance and a some math reveals Mms and Kms. As an example, consider that if a driver
is put into a test box, the air spring 'stiffness' of the box will add to the overall stiffness shifting the
resonance frequency up. Using Fbs and Kbs as the modified box resonance and box air stiffness respectively, we can
set up and solve the following equations. (A similar derivation is used for the delta mass method):
1) Fms = sqrt(Kms/Mms)/2*pi from Q and Fms test
2) Fbs = sqrt((Kms+Kbs)/Mms)/2*pi from Vas delta compliance 'box test'
Dividing 1 into 2, we then get
3a) Fms/Fbs = sqrt(Kms/(Kms+Kbs)) square both sides
3b) (Fms/Fbs)^2 = Kms/(Kms+Kbs) multiply both sides by (Kms+Kbs)
3c) (Kms+Kbs)*(Fms/Fbs)^2 = Kms Move all instances of Kms to one side
3d) Kms*(Fms/Fbs)^2 + Kbs*(Fms/Fbs)^2 = Kms
3e) Kbs*(Fms/Fbs)^2 = Kms - Kms*(Fms/Fbs)^2
3f) Kbs*(Fms/Fbs)^2 = Kms*(1 -(Fms/Fbs)^2)
3g) Kms =Kbs*(Fms/Fbs)^2/(1 -(Fms/Fbs)^2) finally, multiply top and bottom by Fbs^2
4) Kms =Kbs*Fms^2/(Fbs^2-Fms^2) The equation we see most often!
Probably not too surprisingly, the delta mass method lowers Fs, while the delta compliance method increases Fs. And,
on what kind of driver is being tested, each method will have strengths or weaknesses that will argue for
its use. If we
tabulate these strengths and weaknesses we may be able to derive some conclusions:
Delta Mms Method
Delta Cms Method
- Test simplicity - Very simple and fast
- Test Mass accuracy - Reasonably good using 'nickel' or other standard weight
- Test mass buzzing - Test is restricted to lower frequencies or drive levels
- Suspension droop - Using a clay mass with a horizontally mounted driver is a solution
- Fms accuracy - The lower Fs point requires a very good testing device
- Test simplicity - Takes time to build a suitable test box
- Box leakage or loss - A sturdy low loss box and a good driver seal are required
- Box volume accuracy - Internal damping will make the box appear larger - measure carefully!
- Fs measurement accuracy - A higher Fs helps, but accuracy is needed
At the end of a Q/Fs test, the Woofer Tester software computes the effect of Le on the phase and impedance curve. Later, during
during the Vas test, this allows it to recompute the effect of Le on the zero phase point. With this, the Mms and Kms values can
also be corrected resulting in a close correlation of measured and simulated phase and impedance plots. The Woofer Tester is the
only speaker testing product that performs this calculation!
Given the complexity of building suitable test boxes, it is not surprising that the delta mass method is quite popular when it comes
to testing large woofers with low resonance points. Smaller drivers with higher resonance points do, however, present a challenge
as it is often difficult or impossible to add a suitable test mass. Quite often, the test mass buzzes or interacts with the cone to
create a secondary resonance. In these cases, the delta compliance test box method is more practical. Luckily, the ideal test box is
often readily available in the form of a large kitchen glass of coffee mug. Though a lab-grade, graduated cylinder would be ideal,
the volume can also be measured with reasonable accuracy using a measuring cup.
After completing the Vas test, the Woofer Tester simulator can be used to verify the results. The first step is to
Thiele-Small parameters, followed by an examination of the free air Q/Fs test sweep against the
simulated impedance and phase.
This is done by adjusting the simulator's test box to a large 'open air' like volume and setting the box vent frequency to something
very low (like 0.1Hz). If these curves closely match, the next step is to adjust the simulator to match the Vas test conditions. For
the delta compliance test, this simply involves adjusting the simulator's box volume to that of the test box. Again, the curves should
closely match. For the delta mass test you will need to manually adjust the Mms value, but again, the curves should match.
The final test comes when the sealed or vented speaker is complete. For the sealed box, you will want to perform an arbitrary
impedance and phase test and then compare the results to the simulator. If the curves are off, this is probably due to box loss or
overstuffing the box with damping material. In either case, adjust the simulator's box volume to get a close match, and then
examine the response. This should be reasonably close to the actual response. Performing and then comparing the vented box test
data to the simulator is slightly more complex, but again, when the curves match, the actual and simulated response should be