First-Order Fourth-Order filters: Please explain

Posted by Howard Ferstle [IP: 128.186.164.59] on August 25, 1999 at 12:12:22
Using Mozilla/4.61 [en] (Win95; I):

In Reply to: First-Order Fourth-Order filters: Please explain posted by Don Coleman on August 24, 1999 at 20:43:07:

Hi, Don,

Filter types will mainly determine the high-pass (HP) and low-pass (LP) roll-off slopes of the subwoofer and satellite systems involved.

A first-order slope will allow a signal roll off of 6 dB per octave. That is, if the output is flat at, say, 80 Hz and a first-order LP slope is applied, the response will be attenuated 6 dB at 40 Hz (one octave down) and 12 dB at 20 Hz (another octave down). A second-order slope will be 12 dB per octave. A fourth-order slope will be 24 dB per octave. Some designs will be third order, which will give 18 dB per octave, but the only crossover I know of that has this is the X-30 that is used with the big Paradigm Servo 15 sub.

Now, what does this mean? OK with the satellites, you would want a fairly steep HP slope (second, third, or fourth order) if they are small and the crossover point is fairly low. If this is not done, the gradual rolloff (what you would get with a first-order slope) might allow excessive bass to leak to the small satellite "woofers." If your satelites are reasonably large and robust, you would probably have no problem with a first-order crossover, however.

With the sub, you would want a fairly steep LP slope, particularly if the crossover point was in the 80-100 Hz range. (I do not advise a crossover point higher than 100 Hz, unless you are prepaired to locate the sub somewhere between the satellites, up front.) You want the slope to be steep (and the crossover point to at least be fairly low) in order to keep middle bass, and even midrange, artifacts from being reproduced by the sub.

In most cases, a first-order filter will be passive, meaning that it works without outboard power. This keeps the design simple, and minimizes phase artifacts that upset some people. Higher-order filters, at least when subs are involved, are usually active. That means that a true, powered circuit is employed to give the necessary transitions. (Most full-range speaker systems employ higher-order filers that are passive, simply because the demands at higher crossover frequencies allow this to be the case; it is difficult to pull off in the low-bass range, however.)

OK, with most systems, the logical thing to have would be to have both the LP to the sub and the HP to the satellites be identical in terms of their respective slopes. You would then get symmetrical transitions. Hence, since a first-order slope is potentially a problem (at least if the satellites are small), you would want them to be second, third, or fourth order. However, not all of audio is logical, and while this will often work quite well, it may not be exactly what you want.

For example, if you have small satellites that already are rolling off the bass down at the bottom of their ranges, using a crossover with identical HP and LP slopes will possibly result in the actual electro-acoustical HP slope being too steep. This might result in a dip just above the crossover range. With identical LP and HP slopes, you probably want satellites that are flat to at least one octave below the crossover point, unless maybe a 24 dB HP/LP crossover is used. That would roll off the output so rapidly from the satellites that it probably would not matter all that much.

So, this is why some companies have different slopes. For example, THX-certified satellite speakers have a natural roll off of 12 dB per octave beginning at about 80 Hz. THX processors have a fourth-order, 24 dB LP slope but only a second-order, 12 dB HP slope. However, when the latter is combined with the natural rolloff of the satellite "woofers," net result is a 24 db rolloff. Quite neat.

Another example is Velodyne, who uses a 12-dB LP slope that is adjustable over a wide range, combined with a 6 dB HP slope that is switchable to either 80 or 100 Hz. With bigger satellites, you would use the 80-Hz setting, and with really small ones, you might use the 100-Hz setting. (I have yet to see a decent small satellite that is troubled by the 80-Hz setting, however.) Then, you would adjust the subwoofer level and the variable LP controls to dovetail properly with the HP slope that resulted from the shallow one applied by the crossover and the one that was added to it with the satellite itself. The result would not be perfect, but it should be quite good, when one takes into consideration other low-bass anomalies (boundary interactions with the woofers, standing waves) that impact bass smoothness.

So, there is really no inherent advantage of one design over another. What matters are room acoustics, the size of the satellites, speaker placement, and the way you adjust levels and crossover points. All can work fine.

Howard Ferstler
Author of The Home Theater Companion

Follow Ups:

• First-Order Fourth-Order filters: Please explain - Don Coleman 13:59:24 08/25/99 (0)

Return to the new SMR Forums Menu

Design & HTML © SMR Home Theatre, Images © SMR Home Theatre cannot be reproduced without permission.  The images on this page are digitally watermarked.  New forum messages should be posted into SMR Forums v2 - http://www.smr-forums.com/

	The Web   SMR Archive