What makes a High Efficiency Speaker

Warrenh - As Duke pointed out - the way the measurements are performed and the room environment can swing the results substantially. Not to slight the "Zu boys" who are apparently nice guys that really enjoy what they do, or the Zu speakers, which some people love - but nobody in history has designed a true 101db conventional cone-based speaker in a 2 cu. ft. cabinet and they never will. It's a marketing claim that undermines their credibility in my eyes.

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Here's why - and not to bash Zu (although that IS fun), but because it's an important issue about the original topic here, lets talk about "Hoffman's Iron Law". Here's a simple definition from hometheatermag.com:

"Hoffman's Iron Law, described by Henry Kloss in the mid-1950s and later turned into an exact mathematical formula by engineers Thiele and Small, governs the behavior of woofers. Essentially, it says that a woofer's efficiency is proportional to the volume of its cabinet and the cube of the lowest frequency it can produce before losing relative level (aka the cutoff frequency). Take, for example, a woofer whose response is flat down to 40 hertz in a 2-cubic-foot enclosure. To make its response flat down to 20 Hz, you must either increase the cabinet volume by eight times (to 16 cubic feet) or use eight times the amount of amplifier power to achieve the same listening volume. Given these requirements, you can see how difficult it can be to get respectable low-frequency response from small "full-range" speakers."

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To get more technical -

Hoffman's Law relates efficiency, the desired low-frequency -3dB point, and speaker box volume by way of a constant; for efficiency in percent and size in cubic feet the Law is stated as follows:
%eff = k * Vb * f3
where the efficiency constant k ~= 1.4x10^-4 for electrodynamic radiators in vented boxes.

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Now, from the Loudspeaker Designer's Selection Guide:

"Hoffman's Iron Law states that the efficiency of a woofer system is directly proportional to its cabinet volume and the cube of its cutoff frequency (the lowest frequency it can usefully reproduce). The obvious implication is that to reduce the cutoff frequency by a factor of two, e.g. from 40 Hz to 20 Hz, while still retaining the same system efficiency, you need to increase the enclosure volume by 23=8 times! In other words, to reproduce ever lower frequencies at the same output level you need an extremely large box!

However, box size isn't the only variable… You can continue to use a small box by accepting a much lower efficiency. In order to retain the same sound pressure level (SPL, meaured in dB's), though, this requires both a very large amplifier and a driver that can handle a lot of power and move a lot of air (requiring high excursions). Furthermore, it must be able to do so with minimal distortion. This is exacerbated by power compression, a phenomenon where the power heating of the driver's voice coil results in a non-linear relationship (read "distortion") between the electrical power in and the acoustical power out."

"Another variable not often mentioned is bandwidth. You can provide the perception of violating Hoffman's Iron Law by using a bandpass design, which can provide a lot of bass primarily across a very limited bandwidth. In all too many bandpass designs, the impressive bass is produced around a single frequency.

This is often referred to as "one-note bass". It can rattle the furniture and impress your friends, and may even be OK for sound effects in action movies, but don't expect too much accuracy when listening to music with a lot of low bass content."

(Back to the Zu's - Looking at the measurement chart link in my previous post, this EXACTLY what is going on - centered around 100hz. All other bass under about 180hz is extremely variable. A few Zu fans have tried to discredit these independent measurements, but I don't buy that for a second. They were performed at the National Research Council of Canada, a serious government lab, in a proper standardized anechoic chamber. And they actually show precisely what any designer would predict from a similar vented design.)

"Summarizing, Low-frequency capability, box size, and efficiency form the three key aspects of system design. To increase any of the three, you HAVE to give up something from the other two, with box size being the most sensitive."

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Here a quote from a similar discussion over at the High Efficiency Speaker Asylum website:

"I have heard (literally) tons of loudspeakers that will make lots of sound using test tones. You put the tone on, and read the dB meter, or your ears, and think, "my but that's loud and efficient". Then you check it out with a real time analyzer, and notice that the 40HZ tone is actually the same, or sometimes many dB down from the 80 and 160 HZ harmonic that the speaker is creating, rather than reproducing, making for the high spl level. If a speaker happens to produce even order harmonics (distortion) it will still tend to sound musical, even though it is grossly innacurate."

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Now for a quick industry bashing - By plugging the relevant variables into Hoffman's Iron Law, you'll find that true (reasonably flat) 100db music would be achievable with a vented enclosure about 20 times the volume of the Druid's. The Zu's may hit 101db at certain freq.'s, but a coil inside a magnet, connected to a cone of a certain mass and stuck into a box has predictable characteristics. There is nothing different enough about the rather conventional Zu mid/woofer to suggest they could have circumvented physics to such a large degree, especially when faced with objective measurements indicating no such effect.

The fact that various "glowing" reviewers don't trust basic design theory enough to at least intelligently question the claims - or are ready to believe it's all been changed by back venting through a motorcycle muffler because an enthusiastic 30 year old tells them so - is well, typical.

BTW - The only patent (issued or pending) attributable to an inventor named Griewe since 1976 in a search of the United States Patent and Trademark Office database is a pending "Corn Toss Game".

Clearly, it's been a slow day at work. Cheers!

An exception to this would be highly directional Low bandwidth horns...and I am thinking of a Bullhorn, such as used by police and fire departments for crowd control. These must be well over 100 dB.

Swampwalker - thanks for your kind words! Regarding line source loudspeakers, maybe I can offer a few thoughts.

From a point source, radiation intensity falls off at 6 dB for every doubling of distance, and from a line source radiation intensity falls off by 3 dB for every doubling of distance. With a point source the radiation is expanding in all three dimensions, but with a true line source (which would extend infinitely in one dimension) the radiation is only expanding in two dimensions - hence the more gradual falloff with distance.

In practice how well a speaker approximates a true line source depends on the height of the radiating line or line array, the height of the room, the wavelength being reproduced, and the distance from the line-source-approximating speaker to the listener. As a general rule of thumb, line source characteristics will hold up quite well out to about four times the height of the line-source-approximating radiating element(s), then begin transitioning to point-source characteristics.

There is yet another type of source - a planar source. With a true planar source (infinite extension in two dimensions), there is NO falloff in SPL with distance! Up close to a large elecctrostatic panel, planar source characteristics dominate - but we're talking distances of only a few feet at the most.

Getting back to line sources, I once measured a point source speaker and a line source speaker at 1 meter and again back at 8 meters (practical limit in my room). Anechoic theory predicts the point source speaker's radiation would fall off by 18 dB over that distance, and it fell off by 11 dB. That extra 7 dB came from the reverberant sound field. Anechoic theory predicts that the line source speaker's radiation would fall off by 9 dB over that distance, and it fell off by 4 dB, with the reverberant field contribution making up the difference. As you can see in a real-world room the line source speaker's radiation fell off by 7 dB less over that distance (1 meter to 8 meters) than the point source speaker's did. That's a significant difference. But in this case the point source speaker was still more efficient than the line source speaker even measured back at 8 meters.

Opalchip - very good explanation of Hoffman's Iron Law. Having scratched my head about the Druids quite a bit, I think that they are exploiting undamped pipe resonance to extend the bass deeper than it would normally go, but the tradeoff is the deep 150-hz notch revealed in the SoundStage measurements (indicative of a roughly 90 inch long pipe). Having built undamped pipe speakers myself I'll say that they measure worse than they sound - the ear is surprisingly forgiving of that deep notch.

Let's look a little bit more closely at the Zu specs though, and give 'em the benefit of the doubt just for kicks. The Druid is a 12 ohm speaker, so what if when they claimed 101 dB "sensitivity" (implying 2.83 volts input) they really meant "efficiency" (implying 1 watt input)? If so, then translating that to 2.83 volt sensitivity we'd come up with about 99 dB. SoundStage came up with 97 dB/2.83 volt sensitivity. That's pretty close, especially if we let Zu use an "in-room" rather than "anechoic" or "simulated anechoic" measurement.

Next let's look at the claimed bass extension. Zu claims a "bandwidth" of 38 Hz to 25 kHz. We're used to thinking of the bandwidth as the -3 dB points or maybe -6 dB points, but that might be a mistake on our part. In prosound use, the -10 dB point are often given as the limits of a speaker's bandwidth.

Now let's go back and look at the SoundStage measurements. See that little response bump at 38 Hz? I think that's the 1/4 wavelength pipe resonance (though can't correlate it with the impedance curve). Relative to the 97 dB sensitivity determined by SoundStage in a free-air measurement, that 38 Hz bump is 19 dB down. With the reinforcement of three room boundaries, we'd add 9 dB and then we'd be only 10 dB down. And -10 dB fits the prosound definition of bandwidth.

I don't know if this is how Zu arrived at their specifications, but it might be. I welcome correction from anyone who knows the real story.

One final comment on the perceived loudness of the Druid's bass. If indeed the Druid's enclosure is an undamped or minimally damped resonant pipe, then it will sound louder in the bass than it measures. This has to do with human hearing - if two fairly short-duration sounds are exactly the same frequency and sound pressure level, but one lasts longer than the other, the longer-lasting sound will be perceived as louder. So if we have relatively slowly-decaying bass resonances in the Druid's enclosure, the bass will sound louder than it measures. As to why the Druids don't sound resonant and boomy, I think it's because the shape of the frequency response curve keeps us from perceiving it that way. If so, then the Druid's bass loading system (based on a patented automotive muffler design) would not work well with a speaker that measures "flatter" in the bass region. The height-off-the-floor tuning, which apparently is critical to getting the bass to sound right, mght be adjusting the decay of the muffler-like pipe resonances. It may well be that Sean and Adam and the crew of Zu are really pretty darn advanced in their design work if they've taken advantage of psychoacoustics to this extent.

The above paragraph is purely speculation on my part, and once again correction is welcomed.

What Zu has done is build a speaker whose perceived bass extension is much better than I ever would have thought possible in that box size and efficiency combination. I don't think the Druid is without sonic issues, but it is at the very least an intriguing design.

Duke

Thanks Duke your was the easiest to unnderstand after that it became more like Quantum physics to me.

The reason I asked was I am getting a pair of sixpacs and my speaker is the Gallo Ref 3's, which as I understand now is far from a High Efficiency speaker at 88db at 1w
But if I am not mistaken its 34hz-50khz is prety good in the sensitivity area
The Gentlman I am getting them from said he ran a High Efficiency speaker (klipsh cornwalls) with horns my concern is am I getting the wrong Mono Blocks for my speaker.
The room is small 18X13 and with kids and the wife I dont get to "crank" them up.
But I would hate to contine to make expensive mistakes in my journey to find that sweet sound I have yet to discover.

Very interesting. Great thread, one and all. Thank you for taking the time to provide all of this info. To this I would only add that having never heard the Zu speakers, if they sound good, then they are good, regardless of how they measure or how much hype or creative "accounting" their marketing department uses. And if they are only 97 dB thats still a pretty darn efficient loudspeaker and should be capable of being driven by small SET amps. To quote Duke "What Zu has done is build a speaker whose perceived bass extension is much better than I ever would have thought possible in that box size and efficiency combination." And that is quite an accomplishment, in my (technically ignorant, but interested) opinion.