Uni-Q Background

Conventional electrical filter theory has been used for some time now to predict the response of loudspeaker systems [1]. Although it is well known that to predict system response it is necessary to use complex addition (either real and imaginary or amplitude and phase), the difficulty of measuring relative acoustic phase meant that for a long time designers struggled to produce systems by measuring the amplitude response only.

It was the arrival of computer-based test methods [2] in the early '70s that made routine measurements of phase possible and facilitated the calculation of the Hilbert Transform [3]. (It proved to be that in many cases, loudspeaker drive units are minimum phase devices and as such the phase response could be calculated from the amplitude response via the Hilbert Transform.)

There are many examples in the literature of loudspeaker response synthesis, on and off axis, based on the addition of various types and orders of filters [4,5,6]. These, coupled with the filter models supplied by the earlier work of Thiele [7] and Small [8], give engineers a complete design method, whereby the summation of target responses can be investigated and if suitable for the particular application, can then be reliably synthesised. Loudspeakers may be treated as filters, cascaded with other filters, electrical or acoustical, then summed vectorialy to predict their response at any chosen angle in any given acoustical environment.

However, the important difference between the manipulation of electrical filters and loudspeaker drive units is the additional phase shift/time delay due to the physical separation of the units.

The phase shift due to inter-unit time delays, drive unit bandwidth and drive unit roll-off rates must be taken into account as well as that due to the crossover filters. A great deal of unpublished work has been done by L.R.Fincham and M.E.Gough on developing filter manipulation techniques to incorporate these additional phase shifts into the design methodology. Latterly A.Jones [9] has taken these techniques further by developing a method which first manipulates filter parameters to achieve phase overlap in the crossover regions of the different sections. Then overall equalisation is applied to all sections to achieve the required response.

This latter operation does not affect the relative phase shift between individual sections and so does not perturb the summations. Multiple spaced driver loudspeaker design has been covered in great detail elsewhere [10], so, just one example will be cited to illustrate a typical problem. The summation of 3rd order Butterworth high pass and low pass filters, with time delay between sections (even assuming omni-directional sources), produces a lobe at crossover, as can be seen in Figs.1 and 2. A common method of dealing with this, particularly for floor mounting types, is to put the tweeter below the woofer [11], so that the flat summation axis, as in Fig.3, points upwards towards the listener's ear.

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