Dispersion: A Show and Tell

How dispersion affects speaker design

The desire for broad dispersion is the main reason most home speakers are two-way designs (with separate woofer and tweeter) or three-way designs (with separate woofer, midrange, and tweeter). By switching to a smaller driver above a certain frequency, a speaker can maintain broader dispersion at high frequencies and more consistent dispersion from the midrange through the treble.

To demonstrate what a two-way design does for dispersion, I measured the frequency response of two speakers at horizontal positions from -90° to +90° in 15° increments. The first speaker is the Wharfedale DX-1 Satellite, a compact model with a 3-inch woofer and a 0.75-inch tweeter. The second speaker is an experimental model I made using a 4-inch, more-or-less full-range Dayton Audio driver. (You can see both speakers pictured in Figure 1.)

Figure 2 is a polar plot that shows the dispersion of the DX-1 satellite at five frequencies, from 1 to 8 kHz. The dispersion is broad — in fact, almost the same — at all frequencies.

Figure 3 shows the dispersion of the 4-inch full-range speaker at the same five frequencies. Even at 2 kHz, it starts to narrow a little. By 6 kHz, it’s quite narrow, and at 8 kHz it’s like a sonic flashlight, sending out a focused beam of sound.

Crossovers and dispersion

A speaker’s crossover can have a huge effect on dispersion. Consider a two-way speaker with a 6-inch woofer and a 1-inch tweeter. Using the formula from above, we can calculate that the woofer will get beamy above about 2.3 kHz. If the crossover is at 3 kHz, the dispersion will narrow between 2.3 and 3 kHz. Above 3 kHz, the tweeter takes over and the dispersion broadens again.

The solution here might seem simple: Move the crossover point down to about 2 kHz. Yet by moving the crossover point down, the engineer puts more low-frequency energy into the tweeter and runs the risk of higher distortion at best and blowing out the tweeter at worst. The problem is even more acute in speakers that use first-order (6 dB/octave) crossovers, because those crossovers allow more high-frequency energy to pass to the woofer (thus reducing dispersion) and more low-frequency energy to pass to the tweeter (thus increasing distortion). The late Jim Thiel proved it’s possible to design a speaker with a first-order crossover that has broad dispersion and low distortion, but it took him years of hard work and some pretty radical driver designs to achieve it.

The greater the disparity in size between the woofer and tweeter, the more the speaker engineer is forced to sacrifice dispersion or power handling. A speaker that has an 8-inch woofer and a 1-inch tweeter has to have a crossover point around 1.7 kHz or lower in order not to have a dispersion problem, and few tweeters can handle a crossover point that low without distorting. This is why many speakers with 8-inch woofers (and almost all speakers with 10-inch or larger woofers) add a midrange driver.

The interference issue

Dispersion problems aren’t caused only by putting too high a frequency into too large a driver. They can also be caused by interference between two drivers. If your ear is closer to one driver than to the other, the two drivers’ waves will be at least somewhat out of phase. As a result, they’ll reinforce each other at some frequencies and cancel each other at some frequencies. The further apart the drivers are, the more extreme the interference effects will be.

If the drivers are positioned one above the other, the effects aren’t so bad because your ears will probably be roughly at the level of the tweeter and about the same distance from each woofer. But if the drivers are positioned side-to-side, as in a typical center speaker, the effects can be troublesome for the same reason presented a few paragraphs back: The listener could be sitting at various places in the horizontal plane relative to the speaker, and could thus experience different frequency response depending on where she’s sitting.

To demonstrate this effect, I measured the Klipsch Gallery G-28 LCR (left/center/right) speaker on-axis, then at 45° off-axis with the speaker positioned horizontally and vertically. You can see the results in Figure 4. With the speaker standing vertically (green trace), the response at 45° off-axis is pretty smooth up to about 13 kHz. But with the speaker placed horizontally (red trace), a deep dip appears between 1 and 2 kHz at 45° off-axis. Careful crossover design and close positioning of the woofers helps minimize this effect. But the best solution, if space and cost allow, is to use a midrange and tweeter positioned vertically between two horizontally placed woofers, as in the Paradigm Signature C1 and many other high-end center speakers.

The same interference problem can occur between a woofer and a tweeter, because frequencies in the crossover range are reproduced by both drivers. In this case, the interference effects can be minimized by placing the drivers closer together and/or by using steeper crossover slopes such as 3^rd-order (18 dB/octave) or 4^th-order (24 dB/octave).

The problem persists

All speaker designers are aware of the phenomena I’ve described above, but surprisingly, some don’t make broad dispersion a priority. I still occasionally encounter a speaker with, say, a 7-inch woofer crossed over to a 1-inch tweeter at 3.5 kHz. Not long ago, I heard a prototype soundbar with 3.5-inch woofers crossed over to the tweeter at 6.5 kHz. When I played James Taylor’s Live at the Beacon Theatre DVD through it, it sounded like James was singing through a cardboard toilet-paper tube! But there’s a happy ending: The engineers later moved the crossover point down to 3.5 kHz and now it’s one of the best-sounding ’bars I’ve ever heard.