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Old 28th November 2011, 03:41 PM   #1
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Default Measuring driver acoustic offset using excess group delay ?

Something that is sometimes desirable is a method for determining the relative acoustic offset of two drivers in a multi-way system, and most of the methods I've seen that are open to a DIY'er aren't that accurate or easy to do.

One approach that is sometimes suggested for even order crossovers is to simply reverse the phase of one driver (from its normal phase) and look for a notch in the response - as the tweeter is moved forward or back a deep notch will be found at the correct point.

The problem with this is that you are not really determining the time alignment of the drivers but rather phase tracking through the overlap region, which is not the same thing.

If the acoustic low pass and high pass transfer functions (filter+driver response) are perfectly aligned to their theoretical ideal (for example L/R 2nd or 4th order) then the notch will occur when the drivers are time aligned, but for any other situation it will not.

Many (most?) designs deliberately choose not to time align the drivers for practical reasons and simply bend the filter response(s) to ensure close phase tracking, in this case you have phase tracking but not time alignment, and no easy way to determine what driver offset would have given time alignment if you had so desired it.

A better approach is to measure the impulse response of each driver independently and compare the arrival time differences at a microphone whose height is equidistant between the centre of each driver. By comparing arrival times in fractions of a millisecond a distance offset can be calculated.

Many software measurement systems such as ARTA can do this, however there are some significant practical challenges to accurately measuring this way:

1) It requires a way to measure each driver independently. If its your own design this isn't a big deal - disconnect one driver and substitute a load resistor and vica-versa. If you want to measure a fully assembled speaker without dismantling it, you're out of luck however.

2) It's the beginning of the impulse rise of each driver that must be determined, not the peak. This is not too difficult for a tweeter with its sharp impulse rise, but a low pass filtered woofer will have a very slow impulse rise, making determining exactly where it begins to rise very inaccurate. You could easily be out by several samples.

Disconnecting the low pass filter and running the woofer direct is one option, but depending on the woofer the rise time may still be quite slow, and again it involves messing with the crossover.

3) Significant error due to the sample step size - even if you were somehow able to accurately judge where the woofers impulse begins to rise, you still have to select a discrete sample. At 48Khz 1 sample is ~21usec, which corresponds to an acoustic propagation distance of ~7mm.

This means that the +/- 1 sample uncertainty introduces a minimum error of +/- 7mm per driver, if the error for each driver stacks there is potentially an error of up to 14mm simply due to the sample time period and the inherent +/- 1 uncertainty. This compounds on top of the difficulty of establishing where the woofers impulse begins to rise. 96Khz sampling rate will halve the potential error, but it's still an issue.

4) Accurate time comparisons of two separately taken measurements on a PC is very difficult. To be really certain that both separate measurements are accurate to the same sample requires a dual channel measurement technique, which some software (Holm Impulse) doesn't support. Even for software like ARTA which supports dual channel, there are significant hassles and limitations involved with using dual channel mode that make its use less than ideal.

While pondering better ways to measure relative acoustic offset and looking through some of my measurements it suddenly dawned on me that maybe excess group delay could be use as a simple and fairly accurate way to measure the acoustic centre offset of two drivers, with one single channel measurement, and without touching the crossover in any way.

Group delay is a representation of the relative propagation delay of different frequencies through a system, so if you have two drivers whose acoustic centres are physically displaced, one providing low frequencies and one high frequencies there should be some net group delay difference between high and low frequencies.

Because group delay is derived from phase, and phase changes with amplitude response, so too does group delay. This means any irregularities in the drivers frequency response (and therefore phase response) such as peaks and dips will also generate group delay - in fact typically more than the group delay caused by the physical misalignment, making it unsuitable for our purpose.

However we can also find excess group delay, which is measured group delay minus the group delay calculated from the amplitude response, by doing this we factor out all the group delay caused by changes in the amplitude response.

What's left is group delay caused by the crossover function itself (which will cause a peak near the crossover frequency) and group delay caused by the driver offsets. (Which will cause a shelf in group delay straddling either side of the peak)

Provided we have sufficient measurement bandwidth on either side of the crossover frequency, the "saddle" on either side should be a good relative indication of the relative group delay of the two drivers, thus their acoustic offset, largely independent of the type of crossover that may be employed.

A practical measurement taken in ARTA would go something like this:

1) The microphone is set to a height exactly half way between the centres of the two drivers, and at sufficient distance so that the angle to each driver is minimal. (More on this later) Lets say 1 metre.

2) A normal impulse measurement is taken and the longest reflection free period possible is windowed on the impulse with the start marker just before the impulse.

3) Enter smoothed FR view and verify that the frequency response looks good and is free of obvious ripples due to reflections. In the view menu switch to group delay and also tick Excess group delay. It's probably a good idea to tick Time-bandwidth requirement in the view menu to remind us to ignore anything below the time-bandwidth requirement of the selected window size.

You will see what looks like a nearly flat line because we need to zoom in a lot from the defaults. This is a little bit clumsy but you basically need to keep clicking on the down arrow for Range to expand the range and also the up arrow for top, to keep the line on the screen. You want a range where the entire vertical axis represents about 0.5ms.

You will now see something perhaps similar to the attached screen shot. In this example there is a 3rd order crossover at 4Khz, drivers in phase, with a tweeter that is approximately (measured by other means) 30mm too far ahead of the woofer to be time aligned. Due to the filter orders and the offset the two drivers are fairly closely phase tracking.

4) Decide where you want your time zero reference to be - if the tweeter is further forward you probably want this to be time zero, so click and drag near the right hand side until you find the "saddle" where the time value is lowest, in my example at 20Khz. (For this to be accurate 96Khz sample rate may be required)

5) With the cursor still on this point go to Edit->Delay for Phase estimation, and adjust this value until the delay reported for the cursor at the bottom left of the screen is zero - you may have to manually enter a value if the arrow increments are too large.

6) Now you have your time reference set, click and drag the cursor to the saddle in the woofers frequency range (in my example around 700Hz) and you can directly read off the time delay - in my example 0.096ms. If you multiply this by 344m/s you will get a distance, eg 0.096x10^-3 * 344 = 33.024x10^-3 = ~33mm.

This suggests that the acoustic centre of the woofer is about 33mm further back from the microphone than the tweeter. Because the line from the microphone to each driver is at a small angle, it won't be exactly the offset between the two drivers, although you could easily calculate it with a bit of trigonometry, however it will be fairly close if the measurement distance is large compared to the driver separation.

The way I see it, there are many advantages of this technique compared to trying to measure time offset to impulse start:

1) No need to open up a speaker or tamper with its crossover, just perform a single on-axis impulse based measurement with the only proviso that the necessary microphone height is accurately calculated and measured.

2) No need for dual channel measurement mode.

3) No ambiguity of trying to visually judge where a slowly rising impulse starts on a woofer, and no 20us rounding errors due to having to select a specific sample. Due to the way the excess group delay is calculated, ARTA (at least) can interpolate it to sub-sample time periods, probably down to 1us.

What I'm interested to find out, from those who have more theoretical understanding of group delay than me, is have I got this right, and what are the sources of potential error ?

I've tried a couple of different speaker and crossover combinations, and it seems to be relatively free of error due to differences in the crossover provided that there is sufficient measurement bandwidth both below and above the crossover point so that we are able to see the group delay of each driver level out.

I'm only suggesting it as a possible method for midrange to tweeter crossovers as getting a long enough window time to measure a woofer to midrange crossover seems unlikely, however accurate measurement of small acoustic offsets at low frequencies isn't really necessary.

I'm also not wanting to start a debate (in this thread at least) on whether acoustic centre alignment of drivers is important or not, (over and above phase tracking) I'm simply presenting what seems to be a very convenient and hopefully accurate way of measuring it.

Thoughts ?
Attached Images
File Type: jpg Group Delay 1.jpg (183.4 KB, 674 views)
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Last edited by DBMandrake; 28th November 2011 at 03:52 PM.
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Old 28th November 2011, 04:11 PM   #2
Pano is offline Pano  United States
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Very nice, thanks for the ideas.
When developing my past few crossovers this is similar to, tho more sophisticated than, the approach I took. I used the "causal impulse" alignment in HOLMImpluse and then discovered the excess Group Delay on ARTA. They seem to agree with each other.

However, because of the size of my speakers (large) I put the mic about 5 feet away and on a line that went to the listening position. I used a string to find the line.

I've had a hard time getting the super tweeters aligned (if it matters) so will try your method and report back.
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Old 28th November 2011, 04:36 PM   #3
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I can't respond to every detail of your very long letter but want to make one point.

As you know group delay and phase response are related, but if we are talking about system construction from multiple parts then the phase allignment through the crossover region is the primary concern. Group delay considerations won't guarantee this.

Two units will have the same group delay if they have the same slope of phase curve. This really needs to be viewed in a linear frequency scale rather than the usual log scale. Also, a phase curve only implies a particular delay if it is linear and tracks back to 0 degrees at 0 Hertz.

Even then two curves can have a constant phase span between them (one won't track back to 0 at 0) and they will not add in phase. for this reason I would always rely on phase curves rather than group delay curves. It shows you what you really need to know.

I have played with time allignment via impulse response and also find it unreliable. For the most part it tells you about mid band time delay for each unit, when you again only care about phase through the regions of overlap. You can time allign two units (in the middle of their bands) and still have poor phase overlap in the crossover region, leading to poor combined frequency response.

Whats wrong with just measuring phase?

David
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Old 29th November 2011, 12:02 AM   #4
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HOLMImpulse suggests using its high and low pass filters to look at the impulse only thru the crossover region. I did this with 1 octave on either side and it seemed to work well.
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Old 29th November 2011, 12:15 AM   #5
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Presuming that they could be generated and recorded properly, are the restitution of square waves a good witness for this ?
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Old 29th November 2011, 12:29 AM   #6
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Quote:
Originally Posted by Pano View Post
HOLMImpulse suggests using its high and low pass filters to look at the impulse only thru the crossover region. I did this with 1 octave on either side and it seemed to work well.
I can see this working. Active subs with auto allignment (room correction systems) have the same issue and I believe some have used this approach.

Still, if you have the ability to measure phase you will directly see what matters most.

David S.
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Old 29th November 2011, 02:11 AM   #7
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Quote:
Originally Posted by Radugazon View Post
....are the restitution of square waves a good witness for this ?
Jean-Michel seems to think so. His tweaked 3rd order filter is supposed to do better square waves. (It does, I've tested it).

Quote:
Originally Posted by speaker dave View Post
Still, if you have the ability to measure phase you will directly see what matters most.
Most test suites do. We need to ask Simon again "what wrong with phase?" Tho I've often found it confusing, wrapped or unwrapped.
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Old 29th November 2011, 02:42 AM   #8
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Everyone should own a copy of D'Appolito's Testing Loudspeakers.

In the book, he suggests a simple technique for measuring driver offset. The microphone is setup on the axis of one driver (usually the tweeter) and that becomes the reference driver. The we measure the impulse response and calculate the unwrapped phase response. Then calculate the minimum phase response (amplitude variation) and subtract the minimum phase response from the total to get the excess phase. This excess phase comes from the "time delay between the application of the impulse to the DUT and its arrival at the microphone." The excess phase viewed on a linear scale is a straight line, meaning it is a pure time delay. Multiply by 344 m/s and you get the distance of the driver from the microphone. Do the same for other drivers in the system and use a bit of trignometry to calculate the driver offset.
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Old 29th November 2011, 10:58 AM   #9
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I've thought about this a little more and I'm not sure that pursuing equalized group delay will ever get you to the goal of well merged sections.

If we divorce this from speakers we can think in terms of summing electrical (or transfer function) bandpasses. I assume an in-phase LR approach is desired, although quadrature approaches can also be used.

Each driver section can be thought of as a bandpass of some high and low rolloff order. A 2-way may be a 50 to 3000Hz bandpass and the tweeter may be a 3000 to 25,000 Hz bandpass. We can work with any rolloff orders and they can be unequal. The phase curve that goes along with a given bandpass will have 0 phase shift in the center and then phase shifts at the end proportional to rolloff slope (1/2 the ultimate phase shift at the corner frequency). If we start with units with no delay then there will be 0 degrees phase shift in the center of the bandpass. Low frequencies will allways phase advance and high frequencies will always phase retard. If the band pass is sufficiently wide then there will be a region of approximately flat phase in the center which represents 0 group delay, otherwise the section will have some delay throughout its range.

If either unit has inherent delay (is recessed relative to the other) then it will have additional phase rotation (down at HF) and, yes, there will probably be lots of phase rotations to make the picture confusing.

Now the act of constructing a crossover is to get the down rolling phase of the lower section and the up rolling phase of the upper section to match sufficiently well over a sufficiently broad region of overlap (say until one unit or the other is 15 to 20dB down). On the other hand, time allignment means getting the group delays (phase slope) of the middle of the bandpasses to hang at zero. This has nothing to do with getting the crossover regions to merge.

Generally for the zero delay case the phases of the sections are bending away from each other. The woofer section bends down while the tweeter section bends up. The game is to get the down bend and up bend to the point where they add up to a 360 degree total divergence, i.e. come back into phase. Alternatively we may get them to just 180 degrees apart and flip the polarity of one unit.

Our two variables here are to modify rolloff slopes, or, if we can, adjust driver depth offset (plus the phase flip wild card).

The point of all this is that equalizing group delay between sections, i.e. setting their midband phases to the same, has very little to do with getting their crossover regions to overlap. In my experience, for typical driver offsets, I can always get sections to add in phase using the variables of polarity and various crossover slope. I think that if the sections were in time allignment that I could still get good phase blending but most likely there would still be phase rotation and a nonlinear total phase.

Hope that all makes sense.

David
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Old 29th November 2011, 01:15 PM   #10
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Default It's not a difficult task

I'm a bit puzzled by attempts to measure acoustic offset (the OP) in various ways when there is a simple, straightforward way to do it that can be very precise. It does require taking the measurements and creating a reasonably accurate model of drivers and system (3-d space location of drivers and mic) in design software, but if one can measure, any of the design packages, purchased or free (Jeff Bagby's PCD being a prime example of the latter) will do it exceedingly well. From that point forward, it's a matter of designing the crossover in classic methods.

All one need do is make three measurements. I always have done it with raw drivers, even the tweeter, because it does not require high power at this point as it provides better S/N in the tweeter highpass area allowing lower power, although some prefer to use a cap on the tweeter. With a system that has a feedback probe, you place it at the tweeter terminals to eliminate upstream components, cap and anything else. There's an article at my site originally published in SpeakerBuilder ONE:2000 that describes this approach. It works every time. I've gone to the point of making adjustments of 0.1mm for the best fit.

Finding Relative Acoustic Offsets Empirically

Trying to use excess group delay has several issues that make it less than an accurate method. The method described above will work no matter the crossover, whether all-pass or constant power. There is no need to create a crossover first.

Dave

Edit: I'm sure that others had been doing similarly or maybe the same before I worked this out for myself. I had no internet access back then and access to publications that may have described it were not readily available to amateurs.

Last edited by dlr; 29th November 2011 at 01:28 PM.
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