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Tuesday, June 19, 2012

Woofer Distortion 101

Recently there was a discussion in regard to speaker distortion.  It was about what happens when you have two woofers in one box, but have them crossed-over at different points.

A poster wasn't able to articulate his point, and as a result of some confusing expressions, left people thinking he was 'trolling'.

In fact, he was right on the essential point, which I'm going to illustrate with some diagrams here:

Diagram 1:  Two Separate Cabinets vs. One Cabinet

What actually happens when two woofers share the same cabinet?
Well, in the above diagram, there isn't much difference between the two situations.   If this isn't clear, the following diagram should help out:

Diagram 2:  Front and Back Radiation

Above we assume that both speakers are wired "in phase", which means that regardless of whether they are in series or in parallel, the coils are set so that a positive voltage across the marked terminals makes both speakers move outward, while a negative voltage makes the speakers move in.  You can test this with a small battery.

The sound waves are pushed simultaneously in the same direction out the front, and they make a large parallel wavefront, twice as powerful as either speaker alone.   In the back, a sound wave of opposite phase is pressed against every wall of the inside of the cabinet, with only a short delay from the speaker to the cabinet-wall.

By inspection, we may note that the sound pressure is applied equally to both sides of the separating wall in the first cabinet.  When the speakers are moving out, they create suction inside, and when the speakers are sucking inward, they increase pressure in the cabinet.   That is, while the action inside the cabinet is the opposite of that outside,  the same thing happens in both compartments at the same time, either high pressure in both, or low pressure.

 This means that the pressure is equal on both sides of the separating wall at all times, and according to classical mechanics, there is then no net-force on the separating panel, and no energy will be exchanged between the two partitions.   From this it should make no difference if the wall is removed, as in the speaker cabinet on the right.  The forces (both pressure and vacuum) are equal and opposite, and cancel inside the box.

 Distortion from Excursion

Another thing to observe, is that the loudness of a sound of a given frequency will be based on how much air is pushed, or the area of the woofer surface.  It follows that doubling the number of speakers will give us one of two options.

(1)  If the two speakers are in parallel, and are presented with the same voltage (speakers are voltage-operated devices), we will have twice the air and twice the power used, which means a lot more loudness.

(2)  Alternately, and this is much more interesting, we can instead put half the power into each speaker, and get the same volume, with each speaker doing half the work.  So what?  Well, it means that each speaker only needs to physically move half as much, for the pair to move the same amount of air.

Why is (2) significant?  If speakers move too much, the result is distortion.   Speakers have a limited excursion, that is, they can only move so much before they put up too much resistance, and start either clipping the signal, or they might get out of control.    The excursion is a measure of headroom, or freedom to respond to signals.  If the speaker is already playing a loud bass-note for instance, and is moving at its maximum swing, it can't respond when another musical note is added on top.  There is no more headroom, and the new signal is either attenuated, or otherwise distorted.  This can be referred to as Intermodulation (or I.M.) distortion, and happens at higher volumes as the speaker puts up more resistance and changes the wave-shape, which automatically adds harmonics or sidebands, and attenuates other frequencies.

Splitting the bass-load between two speakers will then cut back a large amount of distortion, and leave headroom for more  musical input, with much less I.M. distortion.   Of course this is very similar to simply using a larger speaker, which can then output more bass with less motion, and less distortion.

Thus many people might presume that this can only be a good thing, and that there is no trade-off in musical quality by doubling the speakers (other than cost!).  We will see if that is always the case, below.

All this is just the necessary background to the discussion at hand, which originally took place on the DIYaudio forum. 

Here is the link, although some of the discussion may have been subsequently deleted.

3.5 way speaker design, should I put the woofers together?

In the original discussion, the speaker builder wanted to have two speakers, but with only one speaker  carrying some midrange also.  This is done simply by having a different crossover-point for each woofer.  One speaker would just carry the bass, while the other would carry both bass and lower mids.

The argument was as to whether or not there was a musical drawback to the method of doubling the woofer, operating the two woofers across different bandwidths, while having them share the same box.

The poster felt that there would be distortion because of this, and he was essentially right. 

Diagram 3:  Midrange Bleed-Through
Lets assume the top speaker is the one that will carry the extra midrange musical content.  In the separate compartments, the out-of-phase back-wave from the speaker would mostly be absorbed by the box, and only a small amount would feedback to the originating speaker, resisting and affecting the signal radiating out the front.

Now look at the diagram on the right:

Without the barrier, the back-wave from the top speaker will also reach the bottom speaker, and radiate out through the cone.  From the point of view of the cone, it matters not whether the signal is imposed upon it from an electrical signal via the coil, or mechanically from the back via the air.  The cone will move (vibrate), and the sound will radiate out.  The cone is a relatively thin and pervious veil over the lower hole, and permits sound to escape the box.

The Flange-Effect

However, this new copy of the midrange signal is not identical to the original.  It has now been time-delayed, much as the sound from a port is.  Here however, the midrange sounds are very short wavelengths, and will alternately cancel and reinforce the original signal, depending upon wavelength.  This acts as a fixed-frequency comb-filter, as well as a phase-shifting filter.

Compounding this comb-filter/delay flanging effect will be the secondary I.M. distortion added by the moving lower speaker, pumping bass.  Almost the same amount of I.M. distortion being added to the midrange already via the top speaker will also be added to the inverted signal radiating out the bottom.

Diagram 4: Intermodulation Distortion

This does not negate the gains achieved by doubling the bass-woofer.  But now the midrange being reproduced by the system is accumulating distortion of an entirely different kind than would have originally been the case for a single driver with no radiator or port.  And it should be remembered that the same gains in lowering I.M. distortion could have been achieved with a single larger woofer.

Thus two questions need to be asked: 

(1)  Why would you choose to have two smaller woofers rather than one larger one?   The answer ought to be, that some other benefit is achieved, namely a different frequency response, or cabinet resonance, or speaker specs, which would move the builder to take on the extra work of designing for two speakers.

(2)  Secondly, can anything be done to minimize the drawbacks introduced by two speakers in one cabinet?   Well, the answer is a definite yes!  The simple act of dividing the cabinet into two compartments, and stuffing the top with absorbent materials, should eliminate the undesirable 'flanging effect' we can expect from single compartment.

Thus, that poster was right when he insisted that the design could be significantly improved by partitioning the cabinet.

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