FAQ
 
 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

                


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