How to calculate a bass reflex enclosure

audio receipes




I have extract the following formulas from a software I wrote in basic for Atari. It is based on the Thiele and Small (TS) parameters of the driver. I used it for the 3 way column and 2 way column enclosures calculation.

Driver TS parameters

  • Vas in liter (l)
  • Qts
  • Fs in Hz
  • Vd in liter (l)
  • Becareful, use Qts'=1.1*Qts for taking into account the resistances of the circuit (amplifier, cables, low pass filter inductance)

Loudspeaker parameters

  • S=5.7
  • Ka=0.39
  • Qb=7
  • Those values give the flattest response.
  • You can change it, use mainly S and Ka.

Enclosure volume Vb

  • Resonance frequency, Fb(Hz)=Ka*Fs/Qts
  • Enclosure volume, Vb(l)=S*Qts^2*Vas

Port Calculation Sp, Lp

  • Minimum area, Spmin(cm2)=8*Fb*Vd
  • Maximum lenght, Lpmax(cm)=34000/12/Fb
  • Let's calculate Kp=1000*(170/PI/Fb)^2/Vb
  • If you know your port area Sp(cm2)
    • Ap=Sqr(Sp/PI/10000)
    • Lp(cm)=Sp*(Kp-0.465/Ap)/100
  • If you know your port lenght Lp(cm)
    • B=PI*0.465^2+2*Kp*Lp/100
    • Sp(cm2)=2*Lp^2/(B-Sqr(B^2-4*(Kp*Lp/100)^2))

Frequency response

  • A0=(Fb*Fs)^2/Fs^4
  • A1=(Fb*Fs^2/Qb+Fs^2*Fs/Qts)/Fs^3
  • A2=(VAS*Fs^2/Vb+Fs^2+Fb^2+Fb*Fs/Qb/Qts)/Fs^2
  • A3=(Fs/Qts+Fb/Qb)/Fs
  • Let's write Fr=F/Fs where F is the frequency of interrest
  • G(Fr)=20*log10(Fr^4/Sqr((Fr^4-Fr^2*A2+A0)^2+(Fr*A1-Fr^3*A3)^2))
  • G(Fr) in dB
  • You can extract the -3dB frenquency from G(Fr) table