# Features

## Measuring Loudspeakers, Part Three Page 7

Polar Response/Dispersion
Looking at the anechoic response at one point in space can be instructional, but it must not be forgotten that loudspeakers emit sound in a full sphere [67]. I examine how a loudspeaker's amplitude response changes in two planes, vertical and horizontal, using the DRA Labs system's ability to plot an arbitrary number of FFT-derived response plots against a third, arbitrary variable [68]. The loudspeaker is rotated on a commercial stepper motor-driven turntable (made by the Italian company Outline and available from Old Colony Sound Lab) in 5 degree steps, an impulse response being captured/calculated at each position. There is a practical problem, which is that a loudspeaker's acoustic center almost never coincides with its center of mass. Performing polar response measurements in this manner therefore involves some complicated balancing acts: as a result, the more off-axis the measurement, the more error will be introduced.

Other than in the case of multi-directional designs, I limit the range covered from 90 degrees on either side of the reference axis and from 45 degrees below that axis to 45 degrees above. With conventional forward-firing designs, the response to the rear is predictable and correlated with the physical size of the loudspeaker. All such designs are omnidirectional at low frequencies.

Fig.32 shows the resultant forward dispersion in the horizontal plane for a typical two-way design—it uses a woofer/midrange unit with a 180mm or 200mm (8") chassis and a 1" (25mm) dome tweeter—centered on the tweeter axis. The microphone distance was 50" (of necessity a little farther away for the extreme off-axis angles). The on-axis response of the speaker has been subtracted from each of the curves to highlight the manner in which that response changes to the speaker's sides.

Fig.32 Horizontal dispersion of typical two-way loudspeaker (from 90 degrees on one side to 90 degrees on the other side), normalized to response on tweeter axis.

Below 300Hz the dispersion is approaching omnidirectional, the physical size of the speaker being significantly smaller than the sound's wavelength. However, the loudspeaker's output drops quite rapidly to its sides in the 2-3kHz region. This is because the 8" woofer is a little big to be crossed-over this high in frequency. It starts to beam when the radiating diaphragm starts to become of the same order as the wavelength. From 3kHz to 10kHz, the speaker system's dispersion becomes very wide, due to the tweeter being much smaller than the wavelength of the sound it is emitting. The tweeter's dispersion subsequently narrows above 10kHz when its size becomes significant compared to the wavelength.

It is hard to predict the effect of this discontinuity in the dispersion in the crossover region. If the speaker's on-axis response is flat, unless the listener's room is heavily damped with drapes and carpets, the speaker in fig.32 will probably sound bright. There will be too much energy in the room in the mid-treble region compared with the low treble. However, this particular loudspeaker has a slight peak at 3kHz in its on-axis response (fig.24). As a loudspeaker's perceived balance in a room will have contributions from both the on-axis and off-axis responses (see later), the on-axis peak will to some extent be compensated by the off-axis lack of energy in the same region. I believe that much of the fine-tuning performed by loudspeaker designers—commonly referred to as "voicing" a design—involves balancing the on-axis and off-axis responses to give an overall flat perceived in-room response.

Fig.33 shows a very different horizontal dispersion plot. This speaker uses a smaller woofer and therefore has wider dispersion in the crossover region. There is a little bit of excess energy off-axis at the base of the tweeter's passband, and there is a ridge of off-axis energy in the top audio-band octave because the tweeter has a plastic "phase-plate" over the diaphragm. Otherwise the overall dispersion is remarkably even, the design gradually and uniformly becoming slightly more directional with increasing frequency. If its on-axis frequency response was flat (and it doesn't suffer from audible colorations due to resonances), then this loudspeaker will tend to sound neutrally balanced in a typical listening room. I'd be surprised if it had an identifiable character. Reflections of its sound from room sidewalls will not vary significantly from its on-axis sound, other than a reduced high-treble content. All things being equal—pair-matching in particular—this well-controlled way in which a loudspeaker's off-axis sound changes is always associated with good, precisely defined stereo imaging. I haven't come across a speaker I've measured like this that didn't have good stereo imaging.

Fig.33 Horizontal dispersion of loudspeaker (from 90 degrees on one side to 90 degrees on the other side) recognized as having good stereo imaging, normalized to response on tweeter axis.

The fact that almost all designs use a vertical array of drive-units means that vertical dispersion is strongly affected by the crossover used. Fig.34 shows the vertical dispersion family for a small two-way design, again normalized to the tweeter-axis response. The crossover-induced lobing can be seen: there's a lack of energy in the crossover region between the woofer and tweeter above the reference axis. This design needs to be used with reasonably high stands if it is not going to sound hollow.

Fig.34 Vertical dispersion of loudspeaker (from 45 degrees below the HF axis, front, to 45 degrees above, back) recognized as having good stereo imaging, normalized to response on tweeter axis.

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