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Steve F

Bass alignment methods and group delay

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The matter of which bass alignment method (sealed, bass reflex, bandpass, transmission line, etc.) provides the “best” bass has always been a point of contention among audiophiles and professional designers alike. Many of us here on the CSP site are partial to the classic acoustic suspension designs of the ‘50’s-‘70’s. We apply amusing, colloquial terms like “tight,” “musical,” “fast,”, and “detailed” to describe their sound, and we opine how bass reflex speakers sounded “tubby,” or “bloated,” or “slow” by comparison.

We never had an actual statistical/measurement basis for these opinions, of course. Frequency response and THD didn’t explain the “athletic” or “sluggish” character of the different sounds.

But I remember an article by Peter Mitchell many years ago in Stereo Review where he addressed these very issues and did, in fact, quantify them. I went back into the archives yesterday and found the article.

December 1995 Stereo Review, p. 144, in his column “The High End,” entitled ‘A Measure of Bass Quality.’ In this article he states that the subjective quality of bass reproduction (its ‘quickness’ and ‘detailed texture’) is very closely associated with group delay. Systems that exhibit lower group delay have a subjectively higher quality level of bass reproduction.

In the article, he states that sealed systems have consistently lower group delay (around 10 milliseconds or less in the low bass range), compared to vented or bandpass systems, which can exceed 40 or 50 milliseconds of group delay in the audibly-critical bass range (around 50 Hz). Mitchell further states that, “Psychoacoustic studies have shown that 20 milliseconds is the critical threshold at low frequencies.”

He goes on to say that although this argument seems to conclude that sealed enclosures would provide the “best” bass, that was not necessarily true. Two excellent systems that he’d just recently reviewed were bass reflex systems, but “they had been designed for unusually low group delay.”

So, two questions (mostly directed to Ken and Speaker Dave, the real pros on this site, although everyone is certainly free to add their comments):

1. What is your opinion/reaction to Mitchell’s findings? Do you agree that sealed systems have lower GD than vented/bandpass? Is group delay a predictor of bass quality? Does it ever figure into your design thinking?

2. How do you design for “unusually low group delay”? What are the actual trade-offs/considerations that must be taken into account in your overall system design in order to achieve low group delay? What else has to “give,” in other words?

Steve F.

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The matter of which bass alignment method (sealed, bass reflex, bandpass, transmission line, etc.) provides the “best” bass has always been a point of contention among audiophiles and professional designers alike. Many of us here on the CSP site are partial to the classic acoustic suspension designs of the ‘50’s-‘70’s. We apply amusing, colloquial terms like “tight,” “musical,” “fast,”, and “detailed” to describe their sound, and we opine how bass reflex speakers sounded “tubby,” or “bloated,” or “slow” by comparison.

We never had an actual statistical/measurement basis for these opinions, of course. Frequency response and THD didn’t explain the “athletic” or “sluggish” character of the different sounds.

But I remember an article by Peter Mitchell many years ago in Stereo Review where he addressed these very issues and did, in fact, quantify them. I went back into the archives yesterday and found the article.

December 1995 Stereo Review, p. 144, in his column “The High End,” entitled ‘A Measure of Bass Quality.’ In this article he states that the subjective quality of bass reproduction (its ‘quickness’ and ‘detailed texture’) is very closely associated with group delay. Systems that exhibit lower group delay have a subjectively higher quality level of bass reproduction.

In the article, he states that sealed systems have consistently lower group delay (around 10 milliseconds or less in the low bass range), compared to vented or bandpass systems, which can exceed 40 or 50 milliseconds of group delay in the audibly-critical bass range (around 50 Hz). Mitchell further states that, “Psychoacoustic studies have shown that 20 milliseconds is the critical threshold at low frequencies.”

He goes on to say that although this argument seems to conclude that sealed enclosures would provide the “best” bass, that was not necessarily true. Two excellent systems that he’d just recently reviewed were bass reflex systems, but “they had been designed for unusually low group delay.”

So, two questions (mostly directed to Ken and Speaker Dave, the real pros on this site, although everyone is certainly free to add their comments):

1. What is your opinion/reaction to Mitchell’s findings? Do you agree that sealed systems have lower GD than vented/bandpass? Is group delay a predictor of bass quality? Does it ever figure into your design thinking?

2. How do you design for “unusually low group delay”? What are the actual trade-offs/considerations that must be taken into account in your overall system design in order to achieve low group delay? What else has to “give,” in other words?

Steve F.

Steve, before this discussion proceeds, I think we should agree on exactly what is meant by group delay. I take it to mean the time difference between the point in time when an electrical signal is applied to the voice coil and the point in time when there is a corresponding mechanical motion of the coil/cone assembly. This measurement would be made right on the cone itself so that the delay due to propagation through air would not add to the delay if say a microphone were to be placed in front of the speaker at some distance of even a few inches or if it were, that time would be calculated and deducted. Also the delay in the response of the microphone in converting from mechanical motion to electrical output would have to be taken into account unless it is negligable. Is that what it means?

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Group delay is the phase lag expressed in milliseconds. It is derived from the slope of the phase response....

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Group delay is the phase lag expressed in milliseconds. It is derived from the slope of the phase response....

Phase is measured in degrees, time is measured in milliseconds. Can you be more specific?

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For any phase offset at a particular frequency, there is an equivalent time delay.

A wavelength at 10 Hz is longer than one at 20 Hz, whereas the velocity of propagation is constant. Thus a 36° (1/10 cycle and 1/10 wavelength) phase lag, for example, comprises twice the delay in time at 10 Hz relative to that same lag at 20 Hz.

A different way of expressing and interpreting the same parameter, is all.

Pop quiz: Compute the time delay equivalent of a 36° phase lag at 10 Hz.

Extra credit: How "far" off is it at that frequency...?

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For any phase offset at a particular frequency, there is an equivalent time delay.

A wavelength at 10 Hz is longer than one at 20 Hz, whereas the velocity of propagation is constant. Thus a 36° (1/10 cycle and 1/10 wavelength) phase lag, for example, comprises twice the delay in time at 10 Hz relative to that same lag at 20 Hz.

A different way of expressing and interpreting the same parameter, is all.

Pop quiz: Compute the time delay equivalent of a 36° phase lag at 10 Hz.

Extra credit: How "far" off is it at that frequency...?

Zilch;

period of 10 hz = 1 second/10 - 100 ms

36 degrees/360 degrees = 0.1

36 degrees & 10 hz = 0.1*100 ms = 10 ms.

Just testing to see if we are on the same page as they say.

Now here's a quiz for you.

A complete Bodie plot consists of a plot of both amplitude as a function of frequency and phase as a function of frequency. When is there a direct correlation between them and when isn't there a direct correlation?

Extra credit;

What is the difference between a Nyquist diagram and a pole zero diagram?

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We are on the same page.

Phase is the first derivative of frequency.

When the FR amplitude is flat, phase is zero degrees, and flat also....

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We are on the same page.

Phase is the first derivative of frequency.

When the FR amplitude is flat, phase is zero degrees, and flat also....

I confess it has been so long, longer than I'd like to think about, I've forgotten a few things. As I recall, there are some types of systems where phase and amplitude response can be made independent of each other and the relationship breaks down. These systems involve parallel paths. In a negative feedback system, the phase shift associated with amplitude falloff has to be such that the amplitude gain is less than one when the phase shift reaches 180 degrees or the system isn't stable and you have an oscillator. As the systems become more complex, multiple parallel paths may affect the relationship that exists for a single forward gain path. I'd have to go back and crack open my books...if I can find them :P

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I believe the subject is acoustic phase of loudspeakers here.

[if I am wrong, there is no shame in having tried.... :P ]

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I believe the subject is acoustic phase of loudspeakers here.

[if I am wrong, there is no shame in having tried.... :P ]

Is group delay the same as propagation delay? What does that have to do with acoustic phase except where two drivers operating at the same frequency have different delays?

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Is group delay the same as propagation delay? What does that have to do with acoustic phase except where two drivers operating at the same frequency have different delays?
For any given driver in a particular alignment, the amplitude, phase, and group delay all vary with frequency. Here are the plots for a driver I'm currently working with, in the same box, closed (Blk), vented (Vio), and assisted vented (Grn), the latter two with 30 Hz tuning:

post-102716-1269586038.jpg

post-102716-1269586078.jpg

post-102716-1269586432.jpg

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For any given driver in a particular alignment, the amplitude, phase, and group delay all vary with frequency. Here are the plots for a driver I'm currently working with, in the same box, closed (Blk), vented (Vio), and assisted vented (Grn), the latter two with 30 Hz tuning:

Zilch

Based on your previous statements, there seems to be a problem. You said that the phase response was the time derivative of the amplitude frequency response. Yet the black and violet curve for amplitude response seem very close while there is a strong anomoly in phase response starting at 30hz and going downward for the violet phase response which the black curve doesn't exhibit. How do you explain the discrepency? BTW, this is exactly what I'd expect for a vented system. Producing flat frequency response for a tuned vented system should be very difficult to impossible. The tuning of the vent must be exactly complimentary to the falloff of the driver in the enclosure. Any mismatch would result in a severe FR peak or dip.

In Newton's second law of motion, f(t) = md2x/dt2 + bdx/dt + kx, the problem for a vented system is that k is strongly a function of frequency. At the tuned frequency k in the vent will be very low and also low for integer multiples of that frequency, rising to a peak at a point halfway between the tuned frequeny and its first harmonic and integer multiples of that frequency. Did you add the amplitude response of the output of the port to the driver output? Combined they should show a peak which would be more in line with your statement about the relationship between phase and amplitude response which IMO is correct BTW.

In a purely AS system, k is not a function of frequency, it obeys the ideal gas law PV=nRT and P1*V1=P=2*V2. Tuning is by means of adjusting the trapped air volume, mass and damping factor which control k, m, and b. The stuffing amount, density, and arrangement controls b. This is the aerodynamic frictional drag the driver works against. It should be kept in mind that the stuffing displaces the amount of remaining air and so increases k for a given volume. The AS driver also has lower internal k and b making it much less frequency dependent. I have not studdied Theil Small to see how they reconcile the problem of overcoming the driver characteristics in a vented system with the resonance tuning of the vent. It doesn't interest me. AS systems have another advantage. Since the restoring force is due mostly to internal air pressure, it is applied uniformly over the surface of the cone. In a vented system where mechanical restoring force is applied mostly at the perimeter, the variation of force around the perimeter and between the perimeter and the spider if it applies any restoring force will create a shearing force across the thickness of the cone tending to flex it into harmonic breakup modes. This is one reason why AS systems have inherently lower harmonic distortion than vented systems.

In theory either design could be made to respond down to any arbitrary frequency if cost and size are no object. A monster sized vented speaker could respond to very low frequencies but it would not be practical for use in a home and its cost would be very high. Its advantage of course is efficiency which means little in an era when a 300 wpc amplifier costs less than $500.

The Empire 9000 speaker was interesting. I wondered how a vertically mounted 15" driver would not sag after decades. The answer is that it has a stiff accordian pleated suspension. The back of the speaker is an infinite baffle while the front is slot loaded. By restricting the air volume of the slot to a 1" high 45-50" circumference, the front of the speaker is forced to squeeze air through the slot. The effective slot area is actually much lower than that due to a metal grating which obstructs probably at least 50% and possibly more of the slot. This increase in air pressure effectively loads the front of the speaker in a way making the size of the infinite baffle, approximately 2 cubic feet) effectively the equivalent of one much larger that is not slot loaded. Rooms don't load speakers as some audiophile believe. A load is the force the machine works against. Working into a space that offers no air resistance means that drivers that are not slot loaded don't compress the air in front of them to any degree that would result in a force pushing back against them. Even though the Empire driver has a magnet with a total flux of over 1 milllion lines according to the ads, bass response for 3 of them is no match for a pair of AR9s with 4 12" AS woofers.

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1. What is your opinion/reaction to Mitchell’s findings? Do you agree that sealed systems have lower GD than vented/bandpass? Is group delay a predictor of bass quality? Does it ever figure into your design thinking?

2. How do you design for “unusually low group delay”? What are the actual trade-offs/considerations that must be taken into account in your overall system design in order to achieve low group delay? What else has to “give,” in other words?

Steve F.

You may remember that KEF had a box they used to sell called the KUBE. It was a bass equalizer that was intended for a particular product and extended its bass response, much like the Allison Electronic Subwoofer.

This was actually a byproduct of their impulse measuring system. They had a large transient test room that in spite of its size wasn't big enough to get a complete "anechoic" measurement before the reflections started. It was found though, that if a system had a high enough cuttoff, that its impulse response could be "complete" before the first reflection. Measurements would be perfect with no LF "funnies" going on due to truncating an unfinished tail as a result of the LF cuttoff. The solution was to electronically force a high cuttoff for any system and then correct the response, in software, after the measurement. A BDC (bass diminishing circuit) would have the f and Q of the system under test dialed in. That f and Q would be precisely undone and replaced by a 200Hz Q of .5 corner, a rolloff with low group delay or fast ringing, always done before the room reflections come. (Hang in here, this is going somewhere).

So, yes, the transient response hangs on for frequencies near the band edge. Raise the Q, raise the order (vented over sealed) or lower the frequency and the transient response will last longer. Dick Small, in his orriginal series of sealed box/vented box papers goes into this and has some useful graphs. Raise the cuttoff to 200 Hz and get a quicker impulse response for measurement purposes.

So once this KEF technology was working they realized that they could extend response as well as diminish it. An experimental box was made with 4 knobs; f and Q of your current (second order) system, and f and Q that you would like to replace it with. You could very precisely equalize out your system's current LF corner and "dial in" any corner you want. Small speakers could be extended to 20 Hz, or lower, if you dare. Bigger systems could be tried with any Q you wanted.

With this device, I specifically remember trying some tests with it, along the lines of your question. "When I increase the Q of a system, will I detect ringing and a change of character of the bass?" "Does higher Q equal sluggish bass?" Of course higher Q means more bass around the corner. If you double Q you get 6dB more at resonance. In the end, that difference in bass amount is what I heard. For the most part, changing Q or f and Q just seemed to give more level to instruments in the vicinity of the corner. Rather than a special character, it was perceived more like a frequency related volume control: the low parts of string bass got "weightier" when Q increased. But I didn't note a particular quality difference, i.e. "slugishness".

This is not to say that "quick" and "slow" aren't valid subjective impressions. It just didn't seem that reasonable Q changes led to big bass character changes.

Some things to ponder: If you extend the response lower, you always lengthen the transient response. Extend to 5 Hz and transient response rings on 10 times as long as 50Hz. But your music may contain nothing to excercise that 5Hz ringing and the net effect is "faster" bass. Finally, we found that power handling generally went through a danger zone when extending small speakers. Program material might get you into trouble when extended flat to 40 Hz, but if you were okay to there, you could probably extend down to 5Hz with no problem (real program material was falling off fast enough). A number of people commented on better perception of acoustic spaces when really extended LF response was tried.

David

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BTW, this is exactly what I'd expect for a vented system. Producing flat frequency response for a tuned vented system should be very difficult to impossible. The tuning of the vent must be exactly complimentary to the falloff of the driver in the enclosure. Any mismatch would result in a severe FR peak or dip.

Flat response from a vented system isn't difficult. It is a 4th order system rather than second order so there are 2 more variables to play with, but plenty of solutions for flat response.

I have not studdied Theil Small to see how they reconcile the problem of overcoming the driver characteristics in a vented system with the resonance tuning of the vent. It doesn't interest me. AS systems have another advantage. Since the restoring force is due mostly to internal air pressure, it is applied uniformly over the surface of the cone. In a vented system where mechanical restoring force is applied mostly at the perimeter, the variation of force around the perimeter and between the perimeter and the spider if it applies any restoring force will create a shearing force across the thickness of the cone tending to flex it into harmonic breakup modes. This is one reason why AS systems have inherently lower harmonic distortion than vented systems.

You are assuming that vented box woofers must be mechanically stiffer or that air pressure isn't providing the restoring force of a vented woofer. I don't believe this is the case. Vented systems can be designed with any suspension stiffness and system response is surprisingly imune to compliance changes. So air pressure as a restoring force can easily be greater than suspension stiffness if desired. As to distortion comparisons, vented boxes generally do well in comparison to AS systems due to the large null in excursion that the vent tuning gives.

In theory either design could be made to respond down to any arbitrary frequency if cost and size are no object. A monster sized vented speaker could respond to very low frequencies but it would not be practical for use in a home and its cost would be very high. Its advantage of course is efficiency which means little in an era when a 300 wpc amplifier costs less than $500.

Vented systems can extend as low as sealed systems. In fact, since they have a higher efficiency constant (the combinational figure of merit combining box size, efficiency and response extension) they can be designed to go lower than AS systems for the same sensitivity and size.

David

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A complete Bodie plot consists of a plot of both amplitude as a function of frequency and phase as a function of frequency. When is there a direct correlation between them and when isn't there a direct correlation?

A minimum phase system is one that has no excess phase, it has the

minimum phase shift possible for a given frequency response. An all-pass

or phase compensation filter is not minimum phase. Sections of a

speaker are usually minimum phase the summed response is most

often not:

http://en.wikipedia.org/wiki/Minimum_phase

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You may remember that KEF had a box they used to sell called the KUBE. It was a bass equalizer that was intended for a particular product and extended its bass response, much like the Allison Electronic Subwoofer.

This was actually a byproduct of their impulse measuring system. They had a large transient test room that in spite of its size wasn't big enough to get a complete "anechoic" measurement before the reflections started. It was found though, that if a system had a high enough cuttoff, that its impulse response could be "complete" before the first reflection. Measurements would be perfect with no LF "funnies" going on due to truncating an unfinished tail as a result of the LF cuttoff. The solution was to electronically force a high cuttoff for any system and then correct the response, in software, after the measurement. A BDC (bass diminishing circuit) would have the f and Q of the system under test dialed in. That f and Q would be precisely undone and replaced by a 200Hz Q of .5 corner, a rolloff with low group delay or fast ringing, always done before the room reflections come. (Hang in here, this is going somewhere).

So, yes, the transient response hangs on for frequencies near the band edge. Raise the Q, raise the order (vented over sealed) or lower the frequency and the transient response will last longer. Dick Small, in his orriginal series of sealed box/vented box papers goes into this and has some useful graphs. Raise the cuttoff to 200 Hz and get a quicker impulse response for measurement purposes.

So once this KEF technology was working they realized that they could extend response as well as diminish it. An experimental box was made with 4 knobs; f and Q of your current (second order) system, and f and Q that you would like to replace it with. You could very precisely equalize out your system's current LF corner and "dial in" any corner you want. Small speakers could be extended to 20 Hz, or lower, if you dare. Bigger systems could be tried with any Q you wanted.

With this device, I specifically remember trying some tests with it, along the lines of your question. "When I increase the Q of a system, will I detect ringing and a change of character of the bass?" "Does higher Q equal sluggish bass?" Of course higher Q means more bass around the corner. If you double Q you get 6dB more at resonance. In the end, that difference in bass amount is what I heard. For the most part, changing Q or f and Q just seemed to give more level to instruments in the vicinity of the corner. Rather than a special character, it was perceived more like a frequency related volume control: the low parts of string bass got "weightier" when Q increased. But I didn't note a particular quality difference, i.e. "slugishness".

This is not to say that "quick" and "slow" aren't valid subjective impressions. It just didn't seem that reasonable Q changes led to big bass character changes.

Some things to ponder: If you extend the response lower, you always lengthen the transient response. Extend to 5 Hz and transient response rings on 10 times as long as 50Hz. But your music may contain nothing to excercise that 5Hz ringing and the net effect is "faster" bass. Finally, we found that power handling generally went through a danger zone when extending small speakers. Program material might get you into trouble when extended flat to 40 Hz, but if you were okay to there, you could probably extend down to 5Hz with no problem (real program material was falling off fast enough). A number of people commented on better perception of acoustic spaces when really extended LF response was tried.

David

Interesting background David.

I just thought I'd add that many refer to this circuit as a

Linkwitz Transform (LT). He used it in his very old article

in Speaker Builder (on the tweeter actually); I'm not certain

who did it first:

http://www.linkwitzlab.com/filters.htm#9

It is easy to build with OP amps.

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A minimum phase system is one that has no excess phase, it has the

minimum phase shift possible for a given frequency response. An all-pass

or phase compensation filter is not minimum phase. Sections of a

speaker are usually minimum phase the summed response is most

often not:

http://en.wikipedia.org/wiki/Minimum_phase

I think that's what I said. I'd only seen it briefly over forty years ago and I don't remember the terminology minimum phase however it boils down to the same thing.

From the link;

"A system is invertible if we can uniquely determine its input from its output. I.e., we can find a system such that if we apply followed by , we obtain the identity system . "

"When we impose the constraints of causality and stability, the inverse system is unique; and the system and its inverse are called minimum-phase."

Therefore there is a uniqe and determinable relationship between amplitude or what the link calls magnitude (author must be british) response and phase response.

As a note, the criteria for stability of a negative feedback system is that for Gain= G/(1+GH) where G is the forward gain as a function of frequency and phase and H the reverse gain, GH being the loop gain, the overall gain being less than unity when the phase is -180 degrees.

And here it is;

"A minimum-phase system, whether discrete-time or continuous-time, has an additional useful property that the natural logarithm of the magnitude of the frequency response (the "gain" measured in nepers which is proportional to dB) is related to the phase angle of the frequency response (measured in radians) by the Hilbert transform."

Conversely, where a system is not inverse, it is not what is termed minimum phase and there is no determinable correlation between the input amplitude and phase response and the output amplitude and phase response. As I recall, these were forward gain elements in parallel whose amplitudes and phases added at the output.

As a side note in a link in the referenced Wikipedia article for group delay;

"Group delay is a measure of the transit time of a signal through a device under test (DUT), versus frequency. All signals are delayed when transiting through a "device" such as air, an amplifier or a loudspeaker. This small delay is usually not a problem, but if the delay is different for different frequencies and the signal is built up by more than one frequency, then the shape of the signal is distorted. This difference in delay for different frequencies is what group delay is all about."

Threrefore the phase response or group delay can be considered to be equl to a constant component which is not frequency dependent and a component whose function is. This frequency dependent component is the relatative phase response which I think is the point of interest for a single system such as an amplifier outside its useable passband or a loudspeaker driver. As loudspeakers are inherently resonant devices, that is their amplitude response is highly irregular and extend over a limited range, phase response even within its passband is of interest. It is only when you get two operating simultaneously at the same frequency such as a woofer tweeter combination where the constant parameter is different for the two that time generated phase interference becomes a serious issue. The flaw in the argument for so called time aligned speaker systms is that there are phase response interferences that are geometrically related as well. Therefore two drivers operating a the same frequency with the same constant component group time delay response will still generate interference patterns with phase additions and cancellations due to path length differences between the two sources and the listener. The only way to correct this is to make them coincident in space, hence the coaxial or triaxial design. These were popular in the 1950s before time base correction circuits were thought about so those had crossover FR anomolies as well. The greater the distance between drivers compared to the wavelength both are operating at simultaneously, the more complex and intense the number of points in space where phase interference will be experienced. This however assumes a steady state input signal such as a sine wave test tone. When the signal is of a non periodic nature, that adds orders of magnitude of complexity to the problem because when the signal from one driver arrives at a given point in space, the corresponding signal from another driver will not have arrived yet or may arleady be gone.

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Flat response from a vented system isn't difficult. It is a 4th order system rather than second order so there are 2 more variables to play with, but plenty of solutions for flat response.

You are assuming that vented box woofers must be mechanically stiffer or that air pressure isn't providing the restoring force of a vented woofer. I don't believe this is the case. Vented systems can be designed with any suspension stiffness and system response is surprisingly imune to compliance changes. So air pressure as a restoring force can easily be greater than suspension stiffness if desired. As to distortion comparisons, vented boxes generally do well in comparison to AS systems due to the large null in excursion that the vent tuning gives.

Vented systems can extend as low as sealed systems. In fact, since they have a higher efficiency constant (the combinational figure of merit combining box size, efficiency and response extension) they can be designed to go lower than AS systems for the same sensitivity and size.

David

"Flat response from a vented system isn't difficult. It is a 4th order system rather than second order so there are 2 more variables to play with, but plenty of solutions for flat response."

Designing an additional electrical filter that is the compliment of amplitude and Q of the resonant peak at the center frequency of the vent seems to me to be a tough chore. Below the resonance frequency, the system falls off at 24 db per octave which is too steep to extend bass with equalization of the input signal. An AS design can be extended at least half an octave, sometimes more if the drivers are small and efficient or have enormous power handling capabilities. Getting AR9 whose system resonance is at 28 hz with critical damping down to 20 hz flat can be done. Surprisingly, getting Bose 901 series 1 and 2 (AS design) whose resonance frequency is over 180 hz (mine I think are around 250) with about a 7 db peak and crosses the 0 db mark referenced to 1 khz at around 90 hz to respond down to 30 hz is doable but with enormous power requirements. At least two such system pairs with over 500 wpc available would be necessary to produce loud tones at those lowest frequencies in the 2000 cubic foot room it's installed in.. At least 3 and possibly more pairs with 1000 wpc would required to equal AR9. In my installation, 138 wpc with a single pair is easly swallowed up and sends my Marantz receiver into hard clipping if driven at all hard at low frequencies. Within its rating though it is obvious that 901 series 1 can produce extremly low frequency undistorted tones. Low enough to cause acoustic feedback in my well suspended Empire 698 turntable.

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Interesting background David.

I just thought I'd add that many refer to this circuit as a

Linkwitz Transform (LT). He used it in his very old article

in Speaker Builder (on the tweeter actually); I'm not certain

who did it first:

http://www.linkwitzlab.com/filters.htm#9

It is easy to build with OP amps.

Nice reference and very germain to the discussion. He shows that an electrically extended response has better mid-bass group delay, albeit with more ultimate LF delay. Certainly better overall step response with less ringing.

This illustrates the best answer to Steve's question: lower Q gives better step response. More bass extension may give less group delay at mid bass frequencies but, ultimately, more at the extremes.

I'm not sure who did it first either. It is more of an application than an "invention". By the way, the KEF Kube was sold for the 103/2, the 104/2 and the 107. We always wondered how many dealers (and customers) ended up connecting them.

David

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A minimum phase system is one that has no excess phase, it has the

minimum phase shift possible for a given frequency response. An all-pass

or phase compensation filter is not minimum phase.

I like the definition that an all-pass comes from having mirror located poles and zeros on the S-plane. Similarly, minimum phase comes from creating the transfer function with the minimum number of poles and zeros. Since poles and zeros come from the transfer function and the tranfer function can be broken down into op amp filter sections, then the minimum phase version is the simplest one that can hit a given filter shape.

Getting at least an intuitive understanding of complex plane (S plane) concepts helps understand of a lot of these filter issues.

David

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Nice reference and very germain to the discussion. He shows that an electrically extended response has better mid-bass group delay, albeit with more ultimate LF delay. Certainly better overall step response with less ringing.

This illustrates the best answer to Steve's question: lower Q gives better step response. More bass extension may give less group delay at mid bass frequencies but, ultimately, more at the extremes.

I'm not sure who did it first either. It is more of an application than an "invention". By the way, the KEF Kube was sold for the 103/2, the 104/2 and the 107. We always wondered how many dealers (and customers) ended up connecting them.

David

David, I should probably add that your observations with the Kube are right in

line with what I would expect, however I've not used an LT to do controlled experiments

so it was interesting to read yours. Thanks for your insights.

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Most full-range systems do not reproduce really low bass all that well (at least if we are talking about serious extension down really low), but the ones with sealed enclosures have seemed to work better when I checked out the things for product reviews than bass-reflex types. The sealed-enclosure Dunlavy and Allison models I reviewed all had better bass than most of the reflex models I also auditioned for reviews.

Subwoofers are a different matter, however, and they will be better indicators of deficiencies in low-bass performance than typical full-range models, simply by virtue of their ability to go really low, either cleanly or with distortion. I have reviewed a number of them and have found that the better bass-reflex models (Hsu and SVS, for sure) work just as well in subjective terms (extension, distortion, quickness, etc.) as the good sealed-box systems. Indeed, unless we are talking about servo types (Velodyne, and some Paradigm models), most of the ported subs worked better in terms of extension. Room acoustics and system positioning have more to do with low-bass performance than things like group delay from the sub itself, and probably from full-range system woofer sections, too.

Low-bass speed is generally a non issue with good subs (reflex and sealed), with the midrange and treble drivers determining the attack speed in transients and most source materials tapering off fast enough for the tail end of a sub's handling of bass signals to be more than "fast" enough. A bass driver that sounds "sluggish" probably has a design flaw that is unrelated to group delay. It probably just has a bad response curve.

Howard Ferstler

Flat FR to a very low frequency at reasonably high volume with low harmonic distortion in an anechoic chamber is just the beginning of accurate bass. Like other portions of the frequency spectrum, variables of room acoustics and source material is also critical. One valuable piece of information Floyd Toole gave us is that four subwoofers are sufficient to provide reasonably uniform bass response in most areas of most rooms. These can be in the four corners or at the middle of each of four walls. The extra subwoofers fill in areas where cancellations would occur with fewer subwoofers.

Precise balancing of FR to match each recording is also very important. Variations from recording to recording are enormous. Sound systems having too much bass response with a particular recording can be even more annoying than systems with little or none at all as overpowering bass will dominate everything. Adequate system bass response brings with it other problems such as acoustic feedback especially with turntables and low frequency disturbances that are present on a surprising number of recordings that are not heard with lesser systems. Sometimes filtering these disturbances out is preferable to flatter more extended response leaving them in.

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Great discussion, all.

But I'd like opinions as to Mitchell's very specific contention that low group delay has a direct correlation to perceived bass quality.

Howard has opined that he doesn't think so, per se, especially since "full-range" bookshelf and floor speakers do not extend down into the truly low bass range the way that the best powered subs do.

But, again, I'd like Speaker Dave's and k's direct opinion on this one very narrow question:

Do you feel--as Mitchell does--that there is a correlation between low group delay and the perceived quality of bass reproduction from a loudspeaker? Yes or no?

That's the question I want your opinion on: Any correlation, y/n?

If yes, do you design for it, or does it just 'come along for the ride' as part of a well-balanced, correctly-executed design?

Steve F.

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Great discussion, all.

But, again, I'd like Speaker Dave's and k's direct opinion on this one very narrow question:

Do you feel--as Mitchell does--that there is a correlation between low group delay and the perceived quality of bass reproduction from a loudspeaker? Yes or no?

That's the question I want your opinion on: Any correlation, y/n?

If yes, do you design for it, or does it just 'come along for the ride' as part of a well-balanced, correctly-executed design?

Steve F.

I thought my rambling response gave my feelings but I'll try again.

I can't directly answer whether Peter was correct or not regarding 10ms being acceptable and 50ms being unacceptable. I haven't done that specific test. Forced to choose, I would say "no". Certainly, I do not believe that Acoustic Suspension systems are "good" and vented systems are "bad". That is much too simplistic. Given the same cuttoff and same corner shape, then AS systems will have lower group delay but I'd have to do a number of simulations to see where various allignments fall on the 10 to 50 ms continuum. It would be easy to design an AS system with high Q and a vented system with a soft corner and the vented system, in that case, would have better group delay. Also, as I said, you can put a system's corner much lower than 50 Hz, have huge group delay because of it, and still be able to pass a music waveform with no distortion.

I just don't believe that the typical variation of group delay is a real world factor in speaker preferences. The KEF Kube experiment I tried probably ran the gamut from a Q of .5 to a Q of 1.5. Bass level varied considerably but it was never a clear quality factor as in "tight' vs. "slugish".

There are a lot of practical issues when you are choosing between AS and vented. Starting with the same woofer an optimum vented box needs to be larger, typically twice as large as the ideal acoustic suspension design. That costs money. If you redesign the woofer to best suit the same box size, then the woofer will need more magnet and that costs money. The upshot is that a lot of vented systems have too little magnet and/or too little box volume. Corner Q is therefore higher than it should be. I believe these practical factors are where some of the stereotypes of woofer character come from.

As others have pointed out, the room effects are likely to overshadow the relatively minor differences between system types and cuttoffs.

David

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