 Home Products Shop Support Forum News About us Contact us    Introduction  The VAS test normally follows the Q and Fs test and generally involves some kind of driver modification. The two most commonly  known tests are the delta mass and delta compliance methods that seek to measure the driver's moving mass and suspension by  modifying the opposite parameter. That is, if a mass is added to the already existing moving mass, it stands to reason that the  resonant frequency will decrease. If the before and after resonances are properly measured, a bit of math will then reveal  the opposing parameter that determines mechanical resonance, which is the spring stiffness.  Spring and Mass Resonances  To begin, it helps to understand the equation for spring and mass resonance. Many people with a technical background may  remember the equations for the resonant frequency of a mass and spring. In this equation, spring stiffness,'K', is  given in Newtons per meter of displacement units and mass, 'M', is in kilograms. The important part is to notice that 'K'  is in the numerator and 'M' is in the denominator. Therefore, if the spring becomes stiffer, so will the resonant frequency.  Similarly, if mass, 'M', becomes heavier, the frequency decreases.  In Thiele-Small modeling, the terminology 'Kms' and 'Cms' are related as the inverse of each other; or Kms = 1/Cms. Cms, or  suspension compliance, is one of the capacitive elements of the equivalent speaker electrical model. It is the inverse of the  mechanical spring stiffness of the system, Kms. ``` F = sqrt(K/M)/2*PI Frequency in Hz; K=spring stiffness in Newtons/meter M=moving mass in kilograms W = sqrt(K/M) Frequency in Radians/second where W=F*2*PI Fms = sqrt(Kms/Mms) Free air resonance freqeuncy of moving Mass Mms and suspension stiffness Kms ```  Spring and Mass Resonances  The delta mass test works on the principle that the resonant frequency of a mass and spring will change if the moving mass is  changed. This is accomplished by adding a known mass to the cone. If we know the drivers free air resonance from the  Q and Fs Test, a solution for Mms and Kms can be found from the new modified mass resonance. ``` Fms = sqrt(Kms/Mms) Equation for free air resonance Fmass = sqrt(Kms/(Mms+Madd) Equation for delta mass 'Madd' modified frequency Mms = Madd * Fmass^2/(Fms^2 - Fmass^2) Kms = Madd * (Fms^2 * Fmass^2)/(Fms^2 - Fmass^2) ```  Delta Compliance Test  Math behind the delta compliance test is similar to the delta mass test except that the suspension stiffness is modified and  not mass. This is easily accomplished by mounting the driver into a sealed box with a known volume. The air inside the box then  acts like an air spring, 'Kbox', adding to the suspension spring Kms. If you don't have a test box available, start with the  delta mass test, design and build a box (slightly larger than planned) and then retest the driver with your new box and the  delta compliance test.  Efficiency and Cone Area Test  This test is not intended as a primary method for calculating the remaining Vas parameters. The math is based on reversing the  equation for efficiency by knowing cone area, free air resonance (Fms) and Qes. This in turn can be used to reverse Vas and  BL. Normally, this test is not used to calculated a TS parameter list. Rather, this test is used to create electrically  accurate models that can be used with crossover design packages.  Calculation of Sd, Vas, BL, Rms and Efficiency  Between the Q and Fs and Vas tests, Mms, Kms, Fms, Revc, Qes, and Qms are now known. The remaining TS parameters are then  calculated using the following equations: ``` Sd = PI*Diam^2/4.0 Cone area in m^2; Diameter measured with a ruler Vas = C^2*DensityOfAir*Sd^2/Kms; Vas in m^3 BL = sqrt(Revc*Kms/(Qes*Fms*2.0*PI)) Motor force in Newtons/Ampere Rms = 2.0*PI*Fms*Mms/Qms Mechanical resistance Eff = 9.64E-10*Fms^3*VasL/Qes Wattage conversion efficiency ```