Low freq. from small drivers? Is it possible

Hi Eldartford,

Basically, it is possible to describe the low-frequency acoustical rolloff (transfer function) of a sealed-box speaker as a second-order high-pass electrical filter. This is an "equivalence" in the mathematical sense. Because of this, it is also possible to create the inverse (transfer function) of the speaker's rolloff, in the form of an electrical filter, and apply it anywhere in the reproduction chain.

Now, this is very hard to "get your mind around" on first glance, but the result of appyling this inverse filter ANYWHERE in the chain (in our case, typically it is prior to the power amp), is identical. In other words, you have to consider the mathematical product of the transfer functions of the BOMB, amplifier, and UM all at once.

What this achieves is not only to totally flatten the rolloff out, but to exactly cancel its associated phase shifts as well. This is simply the mathematical result of multiplying a transfer function by its inverse: unity. In other words, it is a virtually perfect solution in both frequency and time domains, within the limits of tolerances on the speaker drivers and electrical components.

Now, if that is all you did, you would end up with perfectly flat response to DC and infinite driver excursion. So one must also insert a new rolloff (at a lower frequency) into the transfer function as well. The Linkwitz Transform accomplishes these two tasks in a single step, by what is known as a pole/zero transformation, using a single op-amp section. The new rolloff can be chosen for any frequency and system Q, but in this case was optimized for the best compromise between driver excursion, music SPL's, transient performance, and frequency extension. It has a -3dB point (anechoic) of 32Hz and a system Q of 0.7. This is about all that can be done with drivers of this size if one wishes to retain reasonable output capability. Fortunately, it gives a very satisfying overall result for typical listeners in typical rooms.

Best Regards,
Karl Schuemann
AudioMachina

Eldartford,

One more comment, about your statement that "it costs too much". While it is undoubtedly a very expensive system, that is not the whole story. In my opinion, and that of many others who have heard it, it significantly outperforms any of the well-known floorstanders in the range of $20-30K, when it comes to actually recreating the full and complete illusion of "live music" in a typical listening room at typical listening levels. Viewed in this light, and if one is able to close one's eyes and simply listen, it is actually quite a bargain. Not inexpensive by any means, but still a bargain compared to other choices which cost much more but don't deliver as much musical satisfaction.

It is only the obsession with size so prevalent in the USA that keeps many people from being able to take it seriously. Somehow, they feel that their dollars should be spent buying units of mass or volume, not units of quality. I don't share that view. In fact, many of the best qualities of this system are attributable precisely to the fact that it was made as small and simple as possible. The fact that it is expensive on a $/lb or $/cuft basis is merely a byproduct of the necessities of its design philosophy. It says nothing about its $/performance ratio.

While many will question the sanity of anyone who would spend $10K+ on a speaker system (see Sean's post above), there are nonetheless many people who are willing to spend that kind of money, simply for the joy it gives them in return. We all share the same obsession; it only varies by degree. Any outsider would still shake his/her head in wonder that we aren't perfectly happy with a Bose(R) system like everyone else has.

Best Regards,
Karl Schuemann
AudioMachina

Karls...Thanks for the info. For your sake I hope there are enough people willing to spend $20K on speakers to make your effort worthwhile. If they go for multichannel you have it made.

You cite 10 dB as the boost. When Bose did it I seem to remember that the "inverse transfer function" (to use your technical jargon) was about 40 dB. Bose operated the drivers BELOW resonance because of the smoothness of the response in that range. I think he had driver resonance at about 200 Hz. Do you operate (mostly) below resonance?

Michael: I simply posted comments in agreement with others that had taken the time to share both their personal points of view and / or scientific data pertaining to the situation at hand. Sorry if that offends you.

Karl: Thanks for taking the time to post a response. As i mentioned, it is quite obvious to me that a lot of love and thought went into this product. I hope that this was abundantly clear in my original post.

1) I am aware that they've made great advances in terms of reducing distortion byproducts as excursion increases, but as a general rule, longer excursion still equals more distortion. Some designs are obviously better at this than others. The laws of physics still apply and we can't yet get something for nothing. As you mentioned, there are trade-offs involved in every aspect of speaker design. The end product becomes a balancing act based on what the engineer was willing to sacrifice in order to achieve their desired goals.

2) "I pointed out that while there is a 10dB boost at the amplifier, there is also nearly a 10dB loss in maximum output at the speaker".

What do the losses at the speaker involve? From what i know about such designs, the losses are incurred due to inefficiencies in power transfer below the point of resonance. The end result is a high percentage of power being dissipated as heat. As you stated, the end result might sum to a neutral response, but at the expense of much higher thermal stress.

3) According to your post here, anybody that listens above 90 dB's is "insane". Call me and dozens of other audiophiles that i know "crazy" then. Especially if you are talking about 90 dB's at 1 meter. As far as i'm concerned, spl levels should be taken and compared at the listening position, not at 1 meter. Readings taken at 1 meter are only handy for sake of sensitivity or efficiency ratings, and even then, they don't tell the whole story due to differences in dispersion patterns.

El: The original and second series 901's were a sealed design. The curve for those EQ's is different than that for the series III and all those after that.

Bose obviously had to run the drivers below resonance as the drivers were run full range. Karl is doing the same thing in principle but limiting the top end of the drivers being EQ'd and using a fancier circuit. Due to the fact that the 901 drivers resonated higher in frequency, and they were applying X amount of db's to compensate for the roll-off per octave, the total boost figure for the 901's would be much higher than Karl's design. In the long run, the use of equalization below the point of resonance is nothing new. The end result is that one can increase bass extension by appr half an octave at the expense of increased power requirements, increased power dissipation in the drivers and a lower maximum spl for the same percentage of distortion. It is really a tough balancing act to do correctly and requires very close production tolerances, both in the speaker itself and the correction circuitry being used.

As a side note, Bag End makes use of bass extension technology via a calibrated EQ curve in their subs. They chose drivers that resonated above the intended band of use and then EQ it for flat response below that point. This is a very lossy method and quite out of the ordinary, but has many advantages. Woofers and sub-woofers especially are the only drivers in most speakers were "resonance" or "break up" are considered normal and acceptable, yet most engineers / designers try to avoid that circumstance like the plague with mids and tweeters. Bag End took the high road, but in this case, the efficiency and power requirements of the system was what they were willing to sacrifice to achieve their desired goals. Sean
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Sean...The original (sealed) Bose speakers are the only ones that I ever thought sounded good. All speakers generate output below the driver resonance, and many use equalization, but designers usually try to get resonance down as much as possible so as to minimize operation below resonance. The Bose idea was to deliberately push the resonance up, and equalize the hell out of the signal. I think that the speakers we are talking about here take somewhat the same approach, but not in such an extreme way as Bose.

Again I note that Bose's objective was not bass extension, but rather smoothness of the response curve because of the inherent smoothness of the drivers response when operating below resonance. LF roll off was taken care of by the drastic LF boost.