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Harnessing The Power Of Digital Signal Processing
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In the previous segment, we looked at the basic process of using a high-resolution FFT (Fast Fourier Transform) analyzer to view the frequency and phase response of a 12-inch cone driver in a typical 12-inch/2-way loudspeaker.

In that segment, we established that the 30-degree off-axis response of the cone driver is substantially lower in level (12 to 18 dB), as well as highly irregular in phase and frequency above approximately 2 kHz, when compared to the driver’s on-axis response (Figure 1).

This information allows us make an educated guess at the range where the cone driver should be crossed over.

In this particular case, the 30-degree off-axis response is linear up until about 1.28 kHz, after which the output until about 2 kHz. At 2.1 kHz, the output level begins to descend rapidly as the driver enters its breakup mode (see sidebar for discussion of “breakup mode”).

Therefore, the optimal crossover could be as low as 300 to 500 Hz (for loudspeakers that employ a mid-range driver) to as high as perhaps 1.3 kHz, while still maintaining a 60-degree angle of vertical dispersion.

However, if the 12-inch cone is to be mated with a 90-degree (or wider) HF horn and driver, approximately 1 kHz should be the upper limit, as the off-axis response at 45 degrees will be much worse than at 30 degrees. Further, if the cone driver were to be 15-inch in diameter rather than 12-inch, as is common in many 2-way loudspeakers, its off-axis response will become irregular at even lower frequencies than the 12-inch cone driver, due to the larger diameter of the cone. 

Figure 1: The 12-inch LF driver displays a rapid loss of output and irregular phase response above 1.3 kHz when measured 30 degrees off-axis.

As a general rule, 12-inch cone drivers exhibit approximately a 90-degree conical pattern at 1 kHz, while 15-inch cones exhibit approximately a 60-degree conical pattern at 1 kHz. This is only a general rule because the cone geometry specific to a given model of driver is the determining factor.

The primary point is that measuring the cone driver, both on-axis and off-axis to determine its dispersion versus frequency characteristics, is the first logical step in determining an optimal crossover point.

A Word About Measuring
If your measurement microphone is roughly 1 meter from the loudspeaker, and the loudspeaker is 3 meters (or further) from any barrier surface, the measured results will be reliable in the region of the crossover. Measuring outdoors at greater distances from barrier surfaces (ground, buildings, walls, etc) is ideal for obtaining an accurate response for spec sheets, though not necessary for merely aligning LF, MF and HF drivers that operate in the 500 Hz or higher range.

In this discussion, we’ll factor in the HF driver and HF horn. The HF driver and horn will always have a low-frequency cut-off point that must be respected to avoid rapid driver damage, as well as loss of directivity from the horn. While this frequency is often stated on manufacturer data sheets, it’s far more revealing to look at the response of the HF driver and horn combination on the analyzer.

What you’ll see is some form of response curve that – you hope – stays fairly flat for a reasonable segment of the spectrum, but will suddenly exhibit a rapid roll-off in the low frequencies that does not “come back up” as the spectrum lowers. This is the combined effect of the horn uncoupling, which means it’s no longer seen as a horn by the driver, and the driver being unable to efficiently reproduce frequencies below a certain frequency.

A horn (which is classically stated to be an acoustic transformer), only behaves as a horn within a frequency range that is a function of its dimensions. Make it too long and large – or with a sub-optimal flare rate – and upper HF energy can be cancelled within the throat so that it doesn’t appear at the mouth at all. Make it too short and small, and it will uncouple early, forcing the HF driver to “flap in the breeze” as the driver is no longer acoustically loaded by the impedance of the horn.

Neither condition is desirable, but the latter can lead to early driver damage unless the crossover point is set high enough to avoid damage – but possibly resulting in a gap in response between the LF and the HF. What exactly is the danger point that can cause early driver damage? That’s what we’ll determine by measurement.

Safe For The HF
In Figure 2, the trace shows that the horn rolls-off sharply below 800 Hz. Unless we’re actually designing the loudspeaker, we don’t really need to worry about whether the roll-off is due to the horn, the HF driver, or the sum of the acoustical output of the two, as this information is more academic than “must have.” 

Figure 2: The HF horn and diver display a fairly uniform frequency response (upper trace) and phase response (lower trace) until the horn uncouples at about 800 Hz (see trace marker). Immediately below 800 Hz, the phase response makes an abrupt shift and the frequency response crashes into the noise floor of the measuring equipment.

What we do need to know is the point it’s no longer safe to send energy to the HF driver to avoid damage. This is readily determined by viewing the trace; the crossover should be set so that it’s at least 12 dB down at the “corner” frequency where the HF trace begins its rapid descent.

We also want to look at the relationship of the LF driver’s high-frequency roll-off to that of the HF driver’s low frequency roll-off. In all normal cases, the LF cone driver will roll-off gradually as the frequency increases, while the HF driver/horn combination will roll-off very rapidly as the frequency decreases. If there is not sufficient overlap between the upper region of the LF response and the lower region of the HF response, a dip or gap in the overall system at crossover will result.

While this gap might mean that the system is begging to have a mid-range device added, it’s more likely than not that you’ll need to make do with what you’ve got. This is a legitimate reason to consider applying different crossover slopes to the LF and HF, and sometimes even different crossover rates such as Bessel on the LF and Linkwitz-Riley on the HF.

Source: Live Sound International

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