Measuring driver acoustic offset using excess group delay ?

[keyser]

If I'm reading Simon's post correctly, he isn't really concerned with finding out if the crossover works properly, rather he wants to find the relative delay between drivers. Maybe not relevant in many practical cases, nevertheless an interesting exercise.

Some time ago I helped a friend design an electo-dynamic dipole speaker that was supposed to radiate completely symmetrical front and back. In order to do this, aligning the acoustic centers was elemental. Probably not very important for the sound, but it was a good engineering challenge.

I tried many different ways to accurately find the acoustic centers, but most failed. I used the 2-channel mode in ARTA, to make sure the time-delay of the measurement system was constant. A friend told me to look at the starting time of the impulses of both the mid and the tweeter and then subtract to get the delay difference, but because the tweeters' bandwidth extended much higher than that of the mid the advice was useless. One trick that got me close was a brute-force approach with a lot of DSP: I'd EQ the responses of both the tweeter and the mid flat and use the same DSP to do a textbook crossover with one driver out of phase. Subsequently I tried to get the null straight on-axis.

The aggravating thing about it was that once I got it to work reasonably well on one side, the other side may still look pretty bad. Apparently I had to EQ the drivers over quite a large bandwidth to get meaningful results.

Ultimately I went a similar route as Simon suggests. It dawned on me that you had to get rid of the effect the frequency response of the drivers has on their phase response, because you wanted to look at only the phase rotations caused by the air-path delay.

What I ultimately did and how I'd do it now is use the highest possible sampling rate and put the marker well before the impulse of the earlier arriving driver. Then I use ARTA to get the minimum-phase - which I save as an overlay - and I look at the measured phase, which will contain a lot of excess phase rotations because the marker is placed well before the impulse. Consequently I estimate the time difference between the marker location and the start of the impulse and I enter the estimated value in the "delay for phase estimation (ms)"-window. Then I just keep fiddling with the delay to get the overlay of the minimum phase and the measured phase to be as close as possible.

Then I look at the second driver and I keep the same time-window. Again I'd save the minimum phase response as an overlay and experiment with the value in the "delay for phase estimation (ms)"-window to get the measured phase and the minimum phase to track as best as possible.

The final step is to subtract the values I had to enter in the "delay for phase estimation (ms)"-window and I have the difference in air-path delay.

It is not always possible to get the measured phase and the minimum phase to track each other perfectly over the entire bandwidth. Maybe that's because the sampling rate (192khz) is too limited or maybe the drivers aren't 100% minimum-phase over their entire bandwidths. I can usually get them pretty close though. With the dipole it moreover was only important close to the crossover-point, so I made sure the curves tracked well in that frequency region.

Of course this whole procedure is a lot more cumbersome than Simon's method. I think the idea makes sense. However, I tried his method and I don't get consistent results. The exact placement of the marker has a very significant effect on the measurement results. I don't understand why this happens.

[keyser]

Hi David,

Our posts crossed. You submitted your post while I was busy typing my mine. I'll have a look at your article!

[Pano]

Here's another way of looking at it via impulse and pretty much what I do.
Below you will see the High and Low pass impulses of ideal Linkwitz-Riley 4th order filters @ 1KHz. With no delay or shift the peak of the low pass is 15.8 cm behind the high pass impulse peak. That's an ideal filter, computer generated.

If your acoustic slopes where both 1Khz, L-R 4th, then ideally your impulses would look like this. By moving one driver until the low pass peak is 15.8 cm (0.4 ms) behind the high pass peak, or as near as you can get them, then you've got the alignment right for that slope.

Of course you have to know the acoustic slopes of your driver sections, but that's another matter.

[Tom Danley]

Hi
Conceptually getting rid of the phase shift through crossover is desirable, it makes the time position fixed instead of moving around (as first discussed by Richard Heyser). The idea of making an upper and lower driver knit into one acoustic source is also appealing from a dispersion point of view.

About 12 years ago the company I worked for began selling a horn in commercial sound called a Unity horn that I had designed.
This was an attempt to sum several frequency ranges within a single horn body. These had good pattern control and less phase shift in the sum than the slopes would suggest but It wasn’t until about 7 years ago that I was able to make a 3 way passive speaker that appears to be one horn driver. This improved version is called a Synergy horn.

As suggested here, if that can be accomplished, reproducing a square wave is possible, if the drivers add coherently too, that is possible at any location in front of the cabinet and not just one location or one frequency.
Fooling around with square waves “back then”, a post here with some pictures.

Making Square Waves?

Personally, I think Dave’s advice is sound (haha), it is the phase response that is the most useful indicator of where one is.
Normal crossovers look like an all pass filter (flat response with phase shift, upper range ahead of lower), when these Synergy style crossovers work, there is no phase shift.
Also, keep in mind that if one sums a normal crossover to make it nice and flat, then you offset the time and polarity to fix the step in GD, what you get now is not nice and flat. If you assign the upper and lower ranges to the same time and also try to get no phase shift, you don’t get any combination that works using normal named filters.

Also, while much of the world is in love with the idea of an impulse response, it is harder to read in many ways that a real magnitude and phase plot, it is a different view of that same information after all.
I have ARTA and like it but I have not used it for taking the crossover data yet.

For that data, I use a TEF machine. What I do is measure the hf driver’s ETC (energy vs time) and use it’s location at 20KHz to locate the “zero time” for the next step.
I take a TDS measurement which provides the hf drivers magnitude and acoustic phase, then, the mid and low sections but without re-setting the time reference. The TEF has a real phase detector and so preserves the phase relationships between the drivers and reflects the different locations they are in. These are used in the computer model.

I would guess that ARTA can do this but I have not used it for that.
Anyway, if you’re trying to make a phase shift free crossover, start in the computer.
Make two band pass filters, an upper and a lower.
Ponder the phase responses of each and think, how close do these phase curves have to be before the upper and lower band pass phases are say about 90 degrees apart (meaning they will sum with only a little gain hint hint).
When in doubt start with a higher order Bessel high pass and a shallower low pass.

Then, remember you are really going to be adding the filters responses to a set of driver’s magnitude and phase responses.
Lastly, in the computer, filters add like signals and resistors, the result is unilateral, coherent addition.

If you invert one of two equal signals, they cancel out. Drivers can do that too BUT that only takes place when the drivers are less than about 1 / 4 wavelength apart, they add coherently and feel each other’s radiation resistance.
Once the spacing is about 1 / 2 wavelength or more, the two sources radiate as individual sources and produce an interference pattern recognizable as a pattern of lobes and nulls. At 1 / 2 wl spacing one has a figure 8 pattern, the larger the spacing the greater the number of lobes and nulls. When radiating independently, if you reverse one of the two sources, the sound isn’t canceled out but the pattern of lobes and nulls is re-arranged.

For my work, this part was very important as in commercial sound one wants as much of the energy as possible to be in the front radiation and as little as possible outside. By getting all the drivers to add coherently in each range within the horn, a dusty old prototype 50 by 50 degree speaker like the one shown in the link above is still -20dB at 90 degrees off axis at 500Hz, about -10dB at 300Hz at 90 off.

Having all the drivers coherently sum puts the horn in charge of controlling the pattern over the entire band, no lobes (other than the one front lobe) and nulls, a much lower SPL to the sides and behind = a good thing in commercial sound, no phase shift through crossovers and close to a single point in time radiation = good for the ears.
Best,
Tom Danley
Danley Sound Labs

[gornir]

Originally Posted by dlr

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.

Yes, this is my favorite method. It works perfectly and it's very accurate, fast and easy to use.

I usually measure like this without moving the microphone or loudspeaker between measurements:

1. Measure the tweeter at 1 or 2m distance at tweeter axis.
2. Measure the woofer at 1 or 2m distance at tweeter axis.
3. Measure the tweeter and woofer (reference measurement) simultaneous at 1 or 2m distance at tweeter axis.
4. Import the “reference” measurement (tweeter+woofer), the individual tweeter and woofer measurement in a cross-over simulation software like e.g. LspCAD 6 Pro.
5. Adjust the z-axis distance for the woofer until the total output (tweeter+woofer) frequency response matches the “reference” measurement. Then you have the relative acoustic offset between the drivers.
6. If the measurement was performed at 1m and you want to simulate the drivers response at e.g. 2.5m, use trigonometry to calculate the distance difference.

It’s very simple give it a try.

Regards

/Göran

[Elias]

It is not possible to measure the acoustic offset between two drivers unless a specific frequency is given where the measurement should be fullfilled, because both drivers are having nonlinear group delay since they are fundamentally causal.


- Elias

[David_Web]

REW (Room EQ Wizard) can calculate both mini and excess GD.
So I have been planning to use that to get somewhat good tracking.

[dlr]

Originally Posted by Elias

It is not possible to measure the acoustic offset between two drivers unless a specific frequency is given where the measurement should be fullfilled, because both drivers are having nonlinear group delay since they are fundamentally causal.


- Elias

I beg to differ, empirical results dispute that. I've used this method since 1996 and never once had it fail to yield very accurate results no matter the crossover point. The crossover Fc has at times gone from 1500Hz to as high as 3500Hz. The relative acoustic offset remained unchanged and the measured result always closely matched the model summed response. If the measurements and models from them are made properly, it works.

Dave

[DBMandrake]

Originally Posted by keyser

If I'm reading Simon's post correctly, he isn't really concerned with finding out if the crossover works properly, rather he wants to find the relative delay between drivers. Maybe not relevant in many practical cases, nevertheless an interesting exercise.

Thanks keyser, for being one of the few who replied to get the point of my post.

I think many others misread the purpose of my original post. I specifically said I was presenting (and looking for feedback on) a potential way of easily and accurately measuring acoustic centre offset of two drivers, besides the usual impulse method which isn't too reliable or accurate in practice.

I wasn't really looking for a debate on whether acoustic centre alignment actually matters or not, nor was I looking for a way to measure or design the phase tracking of a crossover.

Acoustic centre alignment and phase tracking are related but orthogonal problems. You can have acoustic centre alignment without phase tracking, you can have phase tracking (through the overlap region at least) without acoustic centre alignment, and you can have both (or neither!) at once.

Some people think acoustic centre misalignment doesn't matter, that's fine, however I'm still interested in ways of measuring it.

I'll reply to a few specific points in following replies. (I go away for one day and a whole raft of replies come though )

What I ultimately did and how I'd do it now is use the highest possible sampling rate and put the marker well before the impulse of the earlier arriving driver. Then I use ARTA to get the minimum-phase - which I save as an overlay - and I look at the measured phase, which will contain a lot of excess phase rotations because the marker is placed well before the impulse. Consequently I estimate the time difference between the marker location and the start of the impulse and I enter the estimated value in the "delay for phase estimation (ms)"-window. Then I just keep fiddling with the delay to get the overlay of the minimum phase and the measured phase to be as close as possible.

Then I look at the second driver and I keep the same time-window. Again I'd save the minimum phase response as an overlay and experiment with the value in the "delay for phase estimation (ms)"-window to get the measured phase and the minimum phase to track as best as possible.

The final step is to subtract the values I had to enter in the "delay for phase estimation (ms)"-window and I have the difference in air-path delay.

That's similar to one approach I tried, however I found it difficult to determine the tracking of phase and minimum phase accurately enough.

It is not always possible to get the measured phase and the minimum phase to track each other perfectly over the entire bandwidth. Maybe that's because the sampling rate (192khz) is too limited or maybe the drivers aren't 100% minimum-phase over their entire bandwidths. I can usually get them pretty close though. With the dipole it moreover was only important close to the crossover-point, so I made sure the curves tracked well in that frequency region.

If you're only checking the phase tracks through the crossover region, you're only checking phase tracking, not acoustic centre alignment. To compare the acoustic centres you need to look at the excess phase and see if the excess phase near the middle of each drivers passband has the same slope.

Near the crossover frequency the all-pass action of the summed filters will add its own excess phase, however far enough away from the crossover frequency in the middle of the driver passbands the only significant excess phase should be the linear phase introduced by the distance from driver to mic.

Excess group delay is excess phase differentiated, so an equal group delay at two different frequencies means the excess phase slope at both frequencies is the same. Thus excess group delay is visually much easier to compare on a graph than trying see if the excess phase has the same slope. Instead of looking for the same slope you're only looking for the same height on the graph. Same information, different visual presentation.

Of course this whole procedure is a lot more cumbersome than Simon's method. I think the idea makes sense. However, I tried his method and I don't get consistent results. The exact placement of the marker has a very significant effect on the measurement results. I don't understand why this happens.

Interesting. Which marker are you referring to ? Start marker or end marker ?

Are you saying the results are not consistent from one measurement to another ? Or do you mean with different driver/crossover combinations ?

Do you have ARTA set to keep the same start and end markers between measurements ? I find that very helpful when repeating measurements, to ensure I don't put the markers in slightly different places. (File->Options->Retain cursor and marker position)

If you move the start marker between measurements, the "Delay for phase estimation" setting will become invalid.

I found very consistent results when I tested, even when reversing the phase of a 3rd order crossover when the drivers were aligned - the group delay peak is vastly different but the "saddle" on either side near the middle of the drivers bandwidths are almost identical, with an error amounting to less than 4mm difference in the calculated position.

[dlr]

Originally Posted by DBMandrake

Thanks keyser, for being one of the few who replied to get the point of my post.

I think many others misread the purpose of my original post. I specifically said I was presenting (and looking for feedback on) a potential way of easily and accurately measuring acoustic centre offset of two drivers, besides the usual impulse method which isn't too reliable or accurate in practice.

Which brings me back to my first comment. To repeat, I'm a bit puzzled by attempts to measure acoustic offset in various ways when there is a simple, straightforward way to do it that can be very precise.

I'll add that this is for the specific driver FR models created, the models should not be altered later. A fixed model set is what one generally uses in the design phase anyway.

Dave