The Subwoofer DIY Page
6th Order Bandpass Systems: Box Calculations
last updated: 15 April 2006

The Subwoofer DIY Page

Due to the considerable design flexibility of 6th order bandpass systems, a hand-calculator method does not exist for determining optimum box size and tuning. However, I've provided two tables below that will allow you to design two 6th order bandpass alignments for a particular driver. These systems will have flat (or very nearly flat) frequency responses within their passbands, and, in most instances, the front and rear volumes will be sufficiently large to prevent power compression from using excessively small port diameters to achieve the required tuning. However, if you do use these tables, please examine the predicted results CAREFULLY, to see if they match your requirements. You will likely have to measure the frequency response of the built system and adjust the port lengths accordingly, as the tables assume zero losses.

An alternative method for designing a 6th order bandpass system is to use the frequency response equations and some trial and error to find a 6th order BP alignment whose frequency response matches your needs.

To use the following calculations, you will need to know the following:

Vas = equiv. air compliance (litres)
Qts = driver Q at its resonance frequency
Fs = driver resonance frequency (Hz)

First of all, using the driver's Qts value, determine the values of Vf/Vas, Ff/Fs, Vr/Vas, Fr/Fs, F3h/Fs, F3l/Fs and Gain from one of the tables given below:

Table #1:

Qts Vf/Vas Ff/Fs Vr/Vas Fr/Fs Fh/Fs Fl/Fs Gain
0.18 0.190 1.950 0.440 1.000 2.370 1.052 -2.3
0.19 0.200 1.960 0.460 1.000 2.410 1.013 -1.9
0.20 0.212 1.960 0.465 1.000 2.410 1.070 -1.4
0.21 0.215 1.980 0.470 1.000 2.460 1.076 -1.1
0.22 0.217 2.020 0.510 1.000 2.590 1.060 -0.9
0.23 0.223 2.032 0.530 1.000 2.640 1.060 -0.6
0.24 0.230 2.040 0.550 1.000 2.680 1.060 -0.3
0.25 0.252 2.010 0.580 1.000 2.620 1.060 0.2
0.26 0.270 1.988 0.600 1.000 2.570 1.060 0.6
0.27 0.294 1.960 0.630 1.000 2.510 1.064 1.1
0.28 0.308 1.950 0.660 1.000 2.500 1.060 1.4

 

Table #2:

Qts Vf/Vas Ff/Fs Vr/Vas Fr/Fs Fh/Fs Fl/Fs Gain
0.25 0.142 2.608 0.270 1.000 3.952 1.398 -0.3
0.26 0.162 2.520 0.291 1.000 3.740 1.368 0.3
0.27 0.183 2.438 0.315 1.000 3.529 1.353 0.8
0.28 0.203 2.385 0.341 1.000 3.423 1.323 1.1
0.29 0.210 2.347 0.370 1.000 3.360 1.293 1.3
0.30 0.225 2.316 0.391 1.000 3.297 1.281 1.6
0.31 0.246 2.263 0.420 1.000 3.170 1.262 2.0


Then, use the steps below to calculate the front and rear enclosure sizes and tuning for the 6th order bandpass system.

1. Calculate the front volume parameters using the following equations:

Vf = (Vf/Vas)*Vas
Ff = (Ff/Fs)*Fs
Fh = (Fh/Fs)*Fs

where,

Vf = net front volume
Ff = front tuning frequency (Hz)
Fh = upper -3dB cutoff frequency (Hz)

2. Calculate the rear volume parameters using the following equations:

Vr = (Vr/Vas)*Vas
Fr = (Fr/Fs)*Fs
Fl = (Fl/Fs)*Fs

where,

Vr = net rear volume
Fr = rear tuning frequency (Hz)
Fl = lower -3dB cutoff frequency (Hz)