Vas = equivalent air compliance for the driver
(litres)
Fs = driver resonance frequency
Qts = driver Q at Fs
The following equations will allow you to design a 4th order bandpass system
with a desired low frequency limit or a desired gain. You will need to choose a value for
"S" that suits your requirements. 4th order bandpass systems where S is less
than 0.7 will have a degraded transient response, but wider bandwidth and smaller box
requirements.
if S = 0.7, then b = 0.7206, passband ripple = 0.00
dB
if S = 0.6, then b = 0.9560, passband ripple = 0.35 dB
if S = 0.5, then b = 1.2712, passband ripple = 1.25 dB
4th order bandpass system with desired low frequency limit
Choose a value for Fl, the lower 3dB cutoff frequency,
then,
Fl' = (Fl*Qts)/Fs
Fh = (Fl'+b)*Fs/Qts
Qbp = (Fl'*(Fl'+b))^0.5
Fb = Qbp*Fs/Qts
Vf = (2*S*Qts)^2*Vas
Vr = Vas/((Qbp/Qts)^2-1)
Pa = -40*LOG(1/(Qbp*2*S))
where,
Fh = upper -3dB cutoff frequency (Hz)
Qbp = Qtc of sealed chamber
Fb = resonance frequency of vented chamber(Hz)
Vf = net volume of vented chamber (litres)
Vr = net volume of sealed chamber (litres)
Pa = gain (dB)
4th order bandpass system with desired gain
Choose a value for Pa, the gain in efficiency,
then,
Qbp = ((10^(-Pa/40))*2*S)^-1
Fl = ((-b+(b^2+4*Qbp^2)^0.5)/2)*(Fs/Qts)
Fh = Fl+(b*Fs/Qts)
Fb = Qbp*Fs/Qts
Vf = (2*S*Qts)^2*Vas
Vr = Vas/((Qbp/Qts)^2-1)
where,
Fl = lower -3dB cutoff frequency (Hz)
Fh = upper -3dB cutoff frequency (Hz)
Qbp = Qtc of sealed chamber
Fb = tuning frequency of vented chamber (Hz)
Vf = net volume of vented chamber (litres)
Vr = net volume of sealed chamber (litres)
Pa = gain (dB) |