The Subwoofer DIY Page v1.1
4th Order Bandpass Systems: Frequency Response Calculations
last updated: 9th January 1997

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)
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