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October 14, 2017 / consort3

Good bass from a low Xmax woofer

In celebration of 50000 hits, a lot of reads but not much comment, what it is to have the gift of exposition!  Anyway in honouring the occasion, I offer the following.

You cannot get good deep bass from a Woofer with low Xmax, right. Wrong, it can be done and here is a way to do it.  Thiele in 1961 realised that the equivalent circuit of a bass reflex speaker was a fiIter. Filter development is a method of selecting the poles (and possibly zeros) of a transfer function to meet a particular design criterion. Thus was born the scientific way of doing speaker design, Thiele-Small parameters and the concept of alignments, as in aligning filters.

In the old days you looked up alignments in tables . A bass reflex is a forth order filter. I was fascinated by the sixth order alignments which offered bass extension and control of the excursion by adding an external high pass filter. An underdamped second order filter has boost and can compensate for the drop off in frequency response at low frequencies. Because the speaker has to be active, the design has not been popular until recently for sub-woofer use.

The cone excursion on a bass reflex is at a minimum at the box tuning frequency determined by the port.  I realised that if you made the external boost filter peak at the port box tuning frequency , it would minimise the excursion. I did a design which worked well, then I discovered Don Keele’s paper describing the idea scientifically.

The two equations (possibly the 2 simplest equations in the whole of speakerdom!) describing the Keele alignment are these:

Vb=4.1 X Qts2 X Vas


Keele applies  a filter with 6db boost at the port frequency and this is also the -3dB response limit. These are good starting point for a design. The equations are approximations so it is worth checking using a modern computer program. Winisd is an excellent program for this type of design as you can call on a peaking filter and observe the cone excursion. In my case to keep the twin peaks of cone excursion level and below the Xmax limit I had to offset the external filter upwards from 44Hz to 50Hz resulting in a slight drop of response which I corrected by making the boost 8db.

System response showing 44Hz 6dB peak filter and 50Hz 8dB filter:


Cone excursion with the 2 filters


Filter response of the 2 filters


I looked up the damping factor needed for 8db boost in Don Lancasters Active filter cookbook. Fig.3.25 gave me a figure of 0.4. I used the Japanese filter website to come up with a circuit.

However  when I simulated the design I got 4dB boost. So I used a figure of 0.2 as damping factor and got the 8 dB boost and this circuit:


Such a simple circuit to solve all those problems! You do need to drive the speaker with a good power amplifier capable of supplying current at the peak frequency. The low frequencies and small boxes allowed by the technique give a port problem. The long port typically required  is difficult to realise. I am going to use the speaker stand as a port tube.

More detail on the technique:


I noticed enviously that the Dynavox  drivers  and the BR-1CAB enclosures at Parts express were available at a reasonable price. I wondered if the Keele alignment would work for this combination. I plugged the numbers into Winisd, but alas the system would only work up to 5 watts input before Xmax was exceeded. Ye cannae change the laws of physics Cap’n.


So I tried finding a filter that would work up to 50 watts input and came up with a 3rd order Bessel filter with 70Hz cutoff which gives this response similar to the famed LS3/5a but louder.


The cone excursion


I used Uwe Beis filter design page here to come up with an actual filter which nearly matched the graph in Winisd. The cutoff frequency in Winisd is at -6dB whereas the cutoff on Uwe’s site is at -3dB so you have to find -3dB on the Winisd graph and enter that value on Uwe’s site. A better match is obtained if R1 is 22k and R3 is 18k

A single section Bessel filter is possible i.e one op-amp the caps are 100nF and the resistors are 16k, 11k and 62k.

Note that the port would need changing, to a a larger diameter shorter port tuned to 70Hz.  It would be best to use the round rather than the truncated driver and easier to surface mount it. Also according to the Baronettes project  the actual Qts is higher at 0.7, in which case the bass goes up 1dB. By the way the driver is the LW6004.

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