The Subwoofer DIY Page
6th Order Bandpass Systems: Frequency Response Calculations
last updated: 15 April 2006
The Subwoofer DIY Page

To calculate the frequency response of a 6th order bandpass system,you will need to know the following:
Vas = equivalent air compliance (litres)
Vf = net front volume (litres)
Ff = front volume tuning frequency (Hz)
Vr = net rear volume (litres)
Fr = rear volume tuning frequency (Hz)
Fs = driver resonance frequency (Hz)
Qts = driver Q at system resonance
Ql = box losses (Ql=infinite (10000) can
     be assumed for most cases)


Then at frequency F,

    a = abs(Ff^2-Fr^2)*F^4
    b = F^6
    c = (Fr^2/Ff/Ql+Fs/Qts+Ff/Ql)*F^5
    d = (Ff^2+Fr^2+Fs*(Fr^2/Ff/Qts/Ql+Ff/Qts/Ql)+
            Fs^2*(Vas/Vf+Vas/Vr+1))*F^4
    e = (Fs^2*(Ff/Ql*(Vas/Vr+1)+Fr^2/Ff/Ql*(Vas/Vf+1))+
           Fs/Qts*(Fr^2+Ff^2)+2*Fr^2*Ff/Ql)*F^3
    f = (Fs^2*(Fr^2*(Vas/Vf+1)+Ff^2*(Vas/Vr+1))+
           2*Fr^2*Ff*Fs/Qts/Ql+ Fr^2*Ff^2)*F^2
    g = (Fr^2*Ff*(Ff*Fs/Qts+2*Fs^2/Ql))*F
    h = Fs^2*Fr^2*Ff^2
    i = -b+d-f+h
    j = c-e+g
    dBmag = 20*log(a/(i^2+j^2)^.5)