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[Mark Wilkinson]

I tend to think of group delay as simply phase deviation from zero, converted into time, at a given frequency.
I don't think of  physical distances between drivers, or constant processing latency, as contributing to group delay. 
Those are simply time delays, with a linear phase slope vs freq, when freq is on linear scale.
To me group delay means some kind of non-linear phase vs freq, again when freq is on linear scale.
IOW, if group delay is a constant, it means it ain't group delay, it's time delay.
Which means to me, Yes, group delay has to vary by freq, by definition.

I also see group delay as an instantaneous value only, like any derivative, with no meaning over any larger interval.

I've played with making each pass-band in multi-way systems exhibit flat zero degree phase behavior using FIR, with a corresponding 0 sec group delay.
 
When 0 deg phase is achieved for each pass-band, time alignment is simply a function of the physical distance between the acoustic centers of the pass-bands' drivers, and the time value doesn't change as x-over freq is moved up or down within the range of each drivers ability to hold flat phase at zero.

If I go back and change FIR to traditional IIR, the group delay at x-over freq does explain most of the differences in delay finder readings in adjacent pass-bands. But that's about as much value as I can find in paying attention to group delay.

Comments or corrections to my understandings very welcome..

[Merlijn van Veen]

Maybe this thread will shed some more light on the conundrum.

[Peter Morris]

I can tell you with great certainty that beginning measurement students absolutely do not understand that different frequencies are arriving at different times.  But you already knew that.... :-)

Are we talking science or simple field alignments?  For the overwhelming majority of FFT software users, "frequency dependent delay" gets the point across.  This is where the group delay view becomes so useful. Rather than "looking down the phase tube" just display group delay to make the point.

Now, it's quite obvious to novices that the subwoofer is 20-30ish msec behind the rest.  If you zoom in sufficiently one can see more delay present as we go lower in frequency, at least in a typical LF section of (for example) a 3 way loudspeaker.

P.S.   Merlijn ... love your Cello picture :-)


So for this majority of users, the biggest hurdle is the legendary sub alignment problem. I posted elsewhere in the forum about a method for using group delay to quickly get "in the neighborhood" re: delay value at crossover at the chosen alignment place.   Yes it's group delay, s/n issues can cause it to display negative time in some places, but it's a fast path to a proposed delay value which can be fine tuned with the phase display.

The user can then decide if this delay value is reasonable (no 88 msec is not reasonable:-), inspect phase which should be close at this point, and determine if it sums.  I'll leave the "how do I choose my alignment spot" to Merlijn and his excellent recent piece on this. 

This leaves (at least in my old roadie mind) the next logical step, unrelated to the alignment task but still something most want to know:

What mechanical/physical/electrical circumstances cause every loudspeaker ever constructed (thanks 6o6) to display this behavior?

If we can explain this in a way that makes sense without overloading beginners' already roasted brains, the logical conclusion is the demonstration, and in my experience group delay view is very helpful.

I’m a bit late to the party … I don’t know if this is useful but if you consider a speaker to a mechanical device that has:

-   Mass (cone and voice coil)
-   Spring constant (air in the box)
-   Dampening (from the suspension)
-   driving force (voice coil in the magnetic gap)

(This is a little simplistic)

Now if you watch this video https://www.youtube.com/watch?v=aZNnwQ8HJHU
and think in terms of:

-   Ball on the end of the spring = mass
-   Spring = spring constant
-   Motor / stick = driving force
-   Disk moving in the air as providing some dampening

Then you can see how phase changes with frequency and what happens at resonance with these type of systems ... you can do the same with a mass and rubber band.

@ Merlijn ... love your Cello picture

[Barry Singleton]

Peter that analog doesn't hold for a loudspeaker in a couple of ways.

First this would assume that you are driving the cone with the suspension as in shaking the motor basket assembly to move the cone.

It also ignores the coil as another force, a strong force when driven by a low impedance voltage source.

The example shows uncontrolled ocillation at resonance which does not happpen when a mass is driven by a stiff force ie a strong motor being voltage driven.

It is observed by me with a positioning laser with accuracy of 0.003" at up to 100kHz with less than 10 degrees phase drift from DC to 100k that the coil-former and dust cap follow the voltage signal nearly dead on until you reach a frequency where the inductance of the voice coil gets in the way where it begins to drift in phase as any single pole low pass filter does.

Since we are discussing subs, cone breakup need not enter this discussion.

Barry.
 

[Peter Morris]

Peter that analog doesn't hold for a loudspeaker in a couple of ways.

First this would assume that you are driving the cone with the suspension as in shaking the motor basket assembly to move the cone.

It also ignores the coil as another force, a strong force when driven by a low impedance voltage source.

The example shows uncontrolled ocillation at resonance which does not happpen when a mass is driven by a stiff force ie a strong motor being voltage driven.

It is observed by me with a positioning laser with accuracy of 0.003" at up to 100kHz with less than 10 degrees phase drift from DC to 100k that the coil-former and dust cap follow the voltage signal nearly dead on until you reach a frequency where the inductance of the voice coil gets in the way where it begins to drift in phase as any single pole low pass filter does.

Since we are discussing subs, cone breakup need not enter this discussion.

Barry.
 

Hi Barry,

As I said, this is simplistic ... perhaps too simplistic, but fundamentally this is what is happening. This is how all mechanical systems like this behave.
.
Yes I realize that the VC is connected directly to the cone, and this is where my analogy is a bit lose so I used the wording “think in terms of” … anyway if you write an equation that models the VC and its connection to the amplifier it starts to get complicated and the students will get completely lost.

As you know, the driving force actually comes from the BL product (the strength of the magnetic field in the gap multiplied the length of wire in this field) - this multiplied by the current in the VC gives you the driving force.
 
The problem is we are comparing the driving amplifiers’ voltage with cone movement, and driving voltage does not have to be “in phase” with the current that causes the force on the cone.

The electrical voltage / current phase relationship is in part a reflection of the systems mechanical behaviour … this is where it gets ugly and the student will get lost.

With respect to resonance here is a quote from Wikipedia … (save me typing)

https://en.wikipedia.org/wiki/Electrical_characteristics_of_dynamic_loudspeakers

“The moving system of the loudspeaker (including the cone, cone suspension, spider and the voice coil) has a certain mass and compliance. This is most commonly likened to a simple mass suspended by a spring that has a certain resonant frequency at which the system will vibrate most freely.

This frequency is known as the "free-space resonance" of the speaker and is designated by Fs. At this frequency, since the voice coil is vibrating with the maximum peak-to-peak amplitude and velocity, the back-emf generated by coil motion in a magnetic field is also at its maximum. This causes the effective electrical impedance of the speaker to be at its maximum at Fs, shown as Zmax in the graph. For frequencies just below resonance, the impedance rises rapidly as the frequency approaches Fs and is inductive in nature.”

… and it gets even more complicated when you put the speaker in a box/ horn and look at the phase of the driving voltage and compare it to the cone moment, not to mention resonate issues associated with the enclosure