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Author Topic: Subs and minimal Group Delay, Decay time  (Read 15454 times)

Antone Atmarama Bajor

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Subs and minimal Group Delay, Decay time
« on: November 08, 2006, 07:09:56 pm »

     I've been thinking about Sub Group delay a lot, and was wondering if there are any aproaches and techniques to lower it that I am not aware of.

    As far as I understand it,

    Vented boxes, including Bandpass, exhibit spikes in group delay, as tuning is approached.

    Sealed Boxes significantly less group delay, but If you use a Parametric eq, some sort of Linkwitz Transform, or Dual integrator EQ you add more group delay which can be the same or worse than a vented box.

    Passive Radiators have fairly wild Groupdelay around resonance.

    Horns Exhibit relatively Tame Group Delay until you aproach cutoff (however path delay is an issue).

    From what I've read in Toms White papers Tapped Horns exhibit the least group delay down to cutoff as anything I have ever heard of (I am not aware of how path delay or decay behaves due to 2 effective horn paths rejoining).

     The only technique that I am aware of to correct for Sub Group delays is to Delay the entire singal to the maximum group delay of the sub, using things like Allpass filters.  In the case of my BS-212 that would be a minmum total delay of 24ms.  Which should be fine for a reproduction system but problematic for live use.

    I am very interested on what others experiences, and feelings on the subject are.

    I am speculating that High group delay is the reason why my BS subs lowest fundamental reprodution seem nebulous and slightly detatched from what I am playing on bass through them.  I've never played through anything else that has such authority down to and bellow 27.5Hz (my low A)  but it seems like there has to be some way of making it feel a little more attached and still have the SPL capability.  They certainly add an extra special something to a lot of modern recorded music.



Ales Dravinec 'Alex'

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Re: Subs and minimal Group Delay, Decay time
« Reply #1 on: November 11, 2006, 07:33:34 pm »

It is hard to believe, there is no replies to this post after THREE days...

Antone...maybe you just wait for few more days and eventually somebody will feel courageous enough to add up to your thoughts...I hope you (and others) are aware of  what you've started here....

Alex Cool
Ales Dravinec
R&D manager, owner

'There's no replacement for displacement' Carroll Shelby (Jim Bowersox, Tim McCulloch)
'Put speakers up in the air, where they belong' Bill Hanley

Antone Atmarama Bajor

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Re: Subs and minimal Group Delay, Decay time
« Reply #2 on: November 11, 2006, 07:54:33 pm »

It certainly seems like something that isn't easy to accomplish.

    People have spent a great deal of time attempting to achieve higher SPL sub bass reproduction.  Which in itself isn't that easy.

    I suspect certain rules of physics make low group delay/phase shift sub woofers unachievable (passively?).

    Ideally there would be none but even with DSP processing it is not easy I haven't even tried yet.  Maybe I should try with the sound web that is sitting around the shop.  I guess for post processing and reproduction the huge amount of Delay wont be an issue.


Ivan Beaver

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Re: Subs and minimal Group Delay, Decay time
« Reply #3 on: November 12, 2006, 09:16:44 am »

Here is the group delay for 1,2 and 4 Danley TH115's. measured outside @10M.  Essentially a flat group delay results in a very punchy. percussive cabinet.  Ie one that is able to reproduce transients well, wuch as kick drum.

Don't ask me how he does it, that is Tom's thing.

For every complicated question-there is a simple- easy to understand WRONG answer.

Can I have some more talent in the monitors--PLEASE?

Ivan Beaver
dB Audio & Video Inc.
Danley Sound Labs

Tom Danley

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Re: Group Delay, Decay time in reply
« Reply #4 on: November 12, 2006, 05:07:30 pm »

Hi All

Well, keep in mind this is not that easy of a subject to get ones head around, at least it wasn’t /isn’t for me.
Not being instinctively mathematical and understanding by visualizing things, I will try an explanation of how things are in my mind as of 11-12-06, with little math.

First, it is helpful (for this) to think of Delay in a second way, “phase delay”.
Normally, one thinks in seconds or milliseconds, rather, think of phase delay here as some fraction of the wave period.  
In other words, a 90 degree lagging phase shift  is the same amount of phase delay at 1KHz as it is at 100Hz while the Time delay (because the wave period at 100Hz is ten times longer) each represents is 10X different.
Also,  If one wanted to preserve the shape of the input wave, then one must have flat amplitude and  phase at Zero degrees or at –180 in an inverting system.
Flat amplitude but other than above, rearranges the harmonic structure of a complex signal in time because each frequency is then produced at a slightly different time than in the drive signal..

In the case of a speaker, one has “latency”, a time delay between when the signal arrives at the speaker and then when it reaches the microphone. If one looks closely enough, one finds a driver has a delay even after the acoustic path has been accounted for.
To see the systems phase, one has to remove all of the fixed delay from the phase, leaving the acoustic phase of the system under test.  
It is this acoustic phase which has is ideally zero degrees or –180 in an inverting system.

In the world of reactive filters (such as passive crossovers or a bass driver in a box) the response in magnitude and phase, is the result of the reactive and resistive elements in their equivalent or actual circuit.
When one is dealing with normal R / L / C filters, then, one can model exactly what any given filter arrangement will produce.  Any change in amplitude , (being minimum phase related) is mirrored in a change in phase.  Should one use EQ to fix a peak or dip cause by this interaction, it fixes BOTH magnitude and phase of the problem “perfect”.

When you have a high pass or low pass filter, one sees a change in phase associated with that change in amplitude.
One sees that the slope of the reactive filter governs how much total phase shift there is when you go from way below to way above the filter corner. There is 90 degrees of phase per order involved here.
So, up to now we have  closed passive filters, who’s magnitude response defines the phase response.

Group delay has two meanings, in communications it can mean the way different groups of frequencies are delayed with respect to each other AND it can define the rate of change of a systems delay, the latter view being used in audio.
Group Delay is not the same as Time Delay, Group Delay  is the derivative of phase thus shows the rate of  change in phase, that is it shows the rate the Time Delay is changing.  Keep in mind that Time Delay for a given frequency is found by the Phase Delay and wave period.
This is why two speakers with the same low corner slope but one an octave lower, the lower  MUST have two times more GD associated with that slope, the wave period is twice as long while the phase delays are identical.

So, what about speakers?

In acoustics, there is “Something completely different”.
If one finds a plot of radiation resistance VS a radiator’s size (in wavelength), one sees that if one has a small radiator, that as the size of the radiator increases, so does its radiation efficiency.
This is why two close coupled woofers have a sensitivity +3 dB greater than one alone, the effective radiation area has doubled and so the efficiency.
Now, unlike a reactive filter, this slope DOES NOT have the same change in reactance’s as one is used to with reactance governed filters..
Here, this is more like a frequency dependant resistor.
From this one might guess a speaker would have a rising response until it reaches the “flat part” of the radiation resistance curve, but why doesn’t it?
When one is on that slope part of the curve, it is the “Volume velocity” which is proportional to radiated pressure. As a result of that radiation resistance slope, one must reduce the Volume velocity as the frequency increases, to get “Flat response”.
That radiator Velocity, is rolled off to exactly “EQ” the changing radiation resistance by an electromechanical “R/C filter” which is within the driver.  It is comprised of the drivers Rdc which is the series R and the drivers moving mass as reflected back through the Voice coils BL factor, which forms a parallel C.

Now, with this R / C internal filter, in the middle where the response is “flat”, this filter also produces about a –90 degree phase lag in the acoustic output (radiator volume velocity).
This phase lag is present because the radiation resistance slope is more like a variable resistance and so remains while the amplitude is compensated.

In a real sealed box speaker, one has “more stuff” too.  The shape of the corner frequency for the R/C filer is partly set by a “Spring” or Inductor in parallel with the C which is the Sum of the driver suspension and air box spring constants.
Now, at the “resonant frequency” the C and L are equal but opposite and cancel out, leaving a high impedance set by the Radiation resistance (very little load) and mechanical and box losses (the higher the Qmb, the smaller the load this presents).

Below resonance, the spring or inductor causes a first order roll off of velocity (and the appropriate phase shift) which when combined with the first order slope on the radiation resistance curve, makes the sealed box roll off at a second order (-12 dB /oct) roll off.
Going from well below to well above the low cutoff, one finds 180 degrees of phase change.
At the high frequency end, there is another element in the circuit, a series L.
At the point in the impedance called Rmin, one finds the reactance of the series L and parallel C are conjugate and here, the acoustic phase like at Fb is also at Zero degrees but at an impedance minimum.
Above here, it goes inductive, below it is capacitive until you approach Fb, below which it is inductive again

In a vented box, an extra “low pass filter” is used in the form of a Helmholtx resonator.
At resonance this is a phase inverter (180 degrees) with a “Q” or ability to alter/ translate impedance.
Below resonance, the port  passes the signal, above it closes off.  This is a two pole filter comprised of the spring force in the box and mass reactance of the port / passive radiator for the reactive parts..
At the low cutoff, most of the output comes from the port, placing a large load on the drivers backside.
AS one would expect, the extra two orders of roll off also produces the corresponding extra 180 degrees of phase change.  Going from well below to well above the low cutoff on a vented box, produces 360 degrees of phase change.

So, getting back to radiation resistance there are horns to consider.
A horn (we will assume here  it is “full size” and at least 1 /2 wl long)  presents a constant acoustic load to the driver at the throat and so where the driver has a constant velocity, the pressure is constant.
A horn driver operation can be imagined by thinking about the driver at Fb in a sealed box.
Its impedance curve reflects the drivers freedom to produce Velocity because back EMF is Voltage.
Below Fb, one has the increasing effect of the compliance spring and above one has the increasing effect of the moving mass.
If one increases the motor strength, one finds the size of the impedance peak has increased, both in height and width.
If one then imagines the points on the impedance curve where the value is 2 times the Rdc and then one loaded the cone with radiation resistance of a perfect horn until you reached 2XRdc, one then has the efficiency bandwidth points and a 50% efficient horn.   Half the electrical power is in I ^2 * Rdc loss (heat) and half into the radiation resistance, hence 50% efficiency.

At the low cutoff, one has the radiation resistance of the “big end” coupled to the driver at “small end”.
Above the low cutoff, the active (impedance transforming) part of the horn retreats within the horn.
Mid band, this system has zero degree acoustic phase because the load is not relative, it is acoustic resistance, Voltage in see’s a resistance load.
This theoretically zero degree (in a perfect horn) phase is why they can preserve the input wave shape, not rearranging the signals harmonic distribution in time.
You probably guessed by now that this is a concern of mine.

A Horn is an inverting device, its efficient length is 1 / 2 wl because to be efficient, the driver and mouth both have to be at a Velocity maximum.
Most horns (all the bass horns I ever built) were only ¼ wl long and the mouths were much smaller than ideal and people still said “Hey Tom that thing is big.  
A horn that is ¼ wl long still produces sound but at the low cutoff, it places the driver at the Velocity minimum and the ouput is delayed 90 degrees. A 1 /4 wl  horn reaches its efficient range about an octave above the low cutoff when it is at least ½ wl long. When the horn is ½ wl long or more, it is an inverter and retains its –180 phase above, preserving waveshape (until the upper bandwidth limit is approached).

The Tapped horn case.
A write up is on the web site which probably covers stuff I missed here.

A horn that has a much smaller than ideal mouth can’t damp out the length wise resonant modes.
If one looks at the response curve, one see’s a series of peaks and dips.
The lowest frequency  peak is the quarter wave resonance, it is a peak because at resonance, it is strongly able to load the cone, which puts a dip in the impedance curve, which draws more current, delivering more power.
The problem is the lack of loading which results in the dips in between the peaks.
The acoustic load near the low cutoff isn’t purely resistive even on a large horn, on a  smaller than ideal the horn is, the more reactance there is associated with the peaks and dips.
The horns resonant modes are actually damped at BOTH ends of the horn, normally the driver end is “fixed” which the radiation end effectively changes.
In the Unity and Synergy horns, I found that Tapping into a horn forward of the throat, one “taps” into that acoustic system with some additional conditions.
The upper limit of operation of a driver set anywhere along the horn is set by the 1 /4 wl frequency to the throat where the signal is reflected and returns at –180 degrees (causing a deep cancellation notch).
It struck me that if I substituted another source for the end of the horn that was already –180 degrees, that they would add, not cancel.
In this way, one could have both faces of the radiator “feeling” the radiation load and more importantly, that the amount of “load” they could feel would change with frequency.

At the low corner, only the rear side of the driver “feels” the resonator, the other side is effectively canceled via reflection, being ¼ wl from the throat.
Also, as the horn has reactance which appears as increasing mass with decreasing F, the driver compliance is adjusted so that these cancel out to a lower frequency, which often puts an impedance peak at the low cutoff.  Depending on how much the mass can be pitted against spring, one is also effectively making the horn longer as the drivers radiator is in effect moving forward from the point of minimum velocity.

As the frequency is raised to where the valley in the response would normally be, here both sides of the radiator are fully additive within the horn so in effect the Sd has doubled.
Now, one has a driver who’s source impedance changes along with the changing radiation resistance of a “small” horn and the response is “Flat” or flatter than if driven normally.

So, to the extent that reactance’s produce a change in amplitude (such as the low corner in a direct radiator or vented box), one can expect the normal corresponding change in phase to accompany them.
On the other hand,  to what ever extent a change in response at the low corner of a horn are governed by changing resistance, then that phase relation is not preserved, with horns having less change in phase than the roll off slope at low cutoff might suggest.
Less change in phase is less Group Delay, less re-arranging of  the phases of the harmonics of a complex signal.

For those who haven’t fallen asleep so far, please read the work of Richard Heyser, inventor of the TEF machine.  If anyone can be said to be the “pioneer” to investigate what real speakers did in terms of time /phase / energy and such, it would have to be him.
His process is (Time Delay Spectrometry) is now often scoffed in audio circles (and often for imaginary reasons), yet, it is one of the few popular approaches that genuinely measures acoustic phase.
While that may be of little value setting up a sound system, it is critical thing if your making a crossover with real speakers.
A long time ago Intersonics bought one of the early “portable” TEF-10 machines and in the process I got to know Don Davis (an early Champion of the TDS system) through Synaudcon.  
At an AES show, Don and Carolyn came by the booth and invited me to walk the show floor with them.
That walk turned into dinner later on, one I’ll never forget.
Don, Mr. Heyser , Doctor Patronis and a number of other acoustic wizards were there “letting loose” and alternately talking sound like astrophysics it seemed like to me.
Anyway, I would like to think I understood some of it at least as it went by, but my reaction was to say nothing, I could think of nothing relevant at all unless Don Pitched me a slow one about my speakers.
Anyway, the man was brilliant and had a calculator in his head and had such a clear understanding of time.
I am not sure I would ever have been able to make the Unity and Synergy Horns without his invention.

Well this is too long already, so I’ll stop typing.
Best Regards,

Tom Danley


Thomas Harkin

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Re: Group Delay, Decay time in reply
« Reply #5 on: November 12, 2006, 09:13:35 pm »

Thank you.

I can now see the tiniest bit of light under the door that leads to my understanding of this subject.

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Antone Atmarama Bajor

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Re: Group Delay, Decay time in reply
« Reply #6 on: November 13, 2006, 01:17:47 am »

     Wow, thanks for those thoughts Tom.  I know it isn't an easy subject.    

    I started wondering about preserving the phase integrity of complex wave forms in my RF Technician class.

    We where discussing the degradation of phase relationships when one puts square pulses through rectangular wave guide.  I started trying to figure out what it would take to preserve or radiate a broadband RF Signal.

    The answer appears to be some type of horn or parabolic reflector as far as I can tell.  But It doesn't seem to be to commonly applied in RF.  Except some of the old Western Electric Parabolic horns.

Thanks again Tom,  I'm still a little unclear on what happens with how having two horn paths effect acoustic path delay?  Greater or less than the longest horn path??


Langston Holland

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Re: Group Delay, Decay time in reply
« Reply #7 on: November 13, 2006, 10:13:04 am »

Tom wrote on Sun, 12 November 2006:

It struck me that if I...

Your post is a gift - to me if feels as if I was given an inheritance that would take years to figure out how to spend. It will take years, very possibly more than I have, to figure out much of your post, yet the joy of the endeavor makes the hair stand up on my arms. Thank you Tom.
God bless you and your precious family - Langston

Soundscapes <><

Jens Droessler

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Re: Subs and minimal Group Delay, Decay time
« Reply #8 on: November 14, 2006, 06:13:14 pm »

Hi there!

In my opinion group delay is not a problem unless it starts to leap around, like when coming in range of a resonator. If it continously increases to low frequencies, it's not a problem  unless it gets very very high there.

Of course NO group delay would be very fine, but it is simply not realistic.

So my post won't help on understanding group delay, but maybe help some people see that it's not that important to know the cause, but more important to know the consequences.
"The man who trades freedom for security does not deserve nor will he ever receive either."
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