The Subwoofer DIY Page
4th Order Bandpass Systems: Frequency Response Calculations
last updated: 06 Jun 2018
The Subwoofer DIY Page

To calculate the frequency response of a 4th order bandpass system, you will need to know the following:
Vf = net front volume (litres)
Ff = front volume tuning frequency
Vr = net rear volume (litres)
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 = (1/Ff)^2*F^4
B = ((1/Ql+(Fs/Ff)/Qts)/Ff)*F^3
C = (((1+Vas/Vr+Vas/Vf)*Fs/Ff+(1/Qts)/Ql)*Fs/Ff+1)*F^2
D = ((1/Qts+(Fs/Ff)/Ql*(Vas/Vr+1))*Fs)*F
E = (Vas/Vr+1)*Fs^2
G = A-C+E
H = -B+D
dBmag = 20*log(F^2/(G^2+H^2)^.5)