⚙️ ENGINEER LEVEL: Fourth-Order Bandpass and Extended Alignments
Transfer Function — Ported System
The ported system is a fourth-order bandpass filter at low frequencies:
H(s) = s² / (s⁴ + as³ + bs² + cs + d)
Where a, b, c, d are functions of Fb, Fc, Qtc, and the coupling between box volume and port resonance.
The vented box equations (small signal):
Defining:
h = Fb/Fs (tuning ratio)
α = Vas/Vb (compliance ratio)
The four poles of the system form two complex pairs. Their positions in the s-plane determine the response shape.
Popular alignments for vented systems:
Butterworth B4 (4th order):
h = 1/(√2 × Qts)
α = 1/(2Qts²) − 1
Vb = Vas / α
Produces maximally flat 4th-order response. F3 below Fs.
Quasi-Butterworth QB3:
h ≈ Qts^0.44 × (Vas/Vb)^0.18
More practical approximation. Less computation, similar results.
Alignment selection software:
Manual calculation for ported alignments is tedious and error-prone. WinISD, BassBox Pro, and the free UniBox handle this correctly. Enter T/S parameters, select alignment, and software calculates all box parameters. Trust the software over hand calculations for ported work.