The Subwoofer DIY Page v1.1
Sealed Systems: Power Response Calculations
last updated: 13 April 2011
To calculate the power response of a sealed enclosure system, you will need to know the following:

    Vas = equivalent air compliance (litres)
    Qes = electrical Q of driver at resonance
    Fs = resonance frequency of driver (Hz)
    PEmax = maximum input power for driver (W)
    Fb = resonance frequency of the system (Hz)
    Qtc = final Q of the system at resonance
    Dia = effective diameter (cone + 1/3 surround) (cm)
    Xmax = peak linear displacement of cone (mm)

then,

    Sd = pi*(Dia/100)^2/4
    Vd = Sd*Xmax/1000
    n0 = 9.64*10^(-10)*Fs^3*Vas/Qes
    SPL = 112 + 10*LOG(n0)
    K1 = (4*pi^3*Ro/c)*Fb^4*Vd^2
    K2 = 112+10*LOG(K1)
    Amax = Qtc^2/(Qtc^2-0.25)^0.5 for Qtc >(1/2)^0.5,
           1 otherwise
    Par = K1/Amax^2
    Per = Par/n0
    PeakSPL = SPL+10*LOG(PEmax)

where,

     pi = 3.14159265359
    c = speed of sound in air (345 m/s)
    Ro = density of air (1.18 kg/m^3)
    n0 = free-air efficiency
    SPL = driver output @1W/1M
    Par = maximum linear power output
    Per = electrical input required to produce Par
    PeakSPL =  Thermally-limited SPL in passband

At frequency F,

    Fr = (F/Fb)^2
    dBmag = 10*LOG(Fr^2/((Fr-1)^2+Fr/Qtc^2))
    SPLd = K2+40*log(F/Fb)
    Pmax = K1*((Fr-1)^2+Fr/Qtc^2)/n0
    SPLt = dBmag+peakSPL

where

    SPLd = displacement-limited SPL at F (dB)
    Pmax = power required to produce SPLd at F (W)
    SPLt = thermally-limited SPL at F (dB)