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Multi-Way Conventional loudspeakers with crossovers

An exercise in converting a speaker to time-phase coherent
An exercise in converting a speaker to time-phase coherent
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Old 23rd November 2019, 01:11 AM   #1
andy2 is offline andy2  United States
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Default An exercise in converting a speaker to time-phase coherent

I've been doing some simulation on how to convert a regular speaker to time-phase coherent. The software is Xsim which has enough basic stuffs for basic simulation.

But first let's get some terminology out of the way. The definitions use freq. and phase response so there won't be any ambiguity. I am sure different people might have different terminologies but with respect to what I did, here are three types of first order speaker, from easiest to hardest.

Here are three:
1. First order/No Time-Phase coherence: this speaker will use first electrical order, but there is no time-phase coherence. It will not be able to produce a proper step response. It's more or less conventional with the exception that it uses first order filters.

2. First order/Time-Phase Coherence, BUT NO "Time coincidence"
(which will be explained in #3).
This speaker will be able to produce a proper step response, BUT and an important BUT. It may not be able to produce an excess phase of 0 degree from say 50Hz to 20KHz. This means that the speaker, for example, may have a phase shift of 50 degree or more or could be a full 360 degree at 15KHz, but only 5 deg at 500Hz. That is its excess phase will vary especially at higher frequencies as the tweeter approaching 20KHz. John Atkinson would agree this speaker meets his definition of "Time-Phase Coherence" since it could produce a proper step response. My guess is most speakers that were measured by John Atkinson would fall into this category. I've seen some measurements done on Vandersteens speakers and I was like ... hmmm... I am not quite sure. But the most stringent definition is reserved for #3.

3. First order/Time-Phase Coherence AND Time-coincident: this is the most difficult definition for any speaker to meet. That is it has to be able to produce a proper step response like in #2, BUT it also has to be able to have a 0 degree of excess phase from 1Hz - 20KHz. In reality, no speaker will have absolutely 0 degree, but the variations should be very small. I believe Thiel claims that their speakers excess phase shift is only a few degrees (less than ten). To be honest, I am not sure many speakers in the entire history can meet this definition.

So to summarize, you have three distinct possibilities from easiest to hardest:
1. First order/No Time-Phase coherence
2. First order/Time-Phase coherence BUT NO "Time coincident"
3. First order/Time-Phase coherence AND "Time coincident" (the most stringent)
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Old 23rd November 2019, 01:15 AM   #2
andy2 is offline andy2  United States
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This is #1 case: First order / no time-coherent.

This is also the starting point. This speaker will then be converted to time-phase coherent later on.

As you can see from the attached pic below, it is basic a first order, with tweeter inverted, so it's not that too different from any other speaker.
Attached Images
File Type: jpg IMG_0693.jpg (935.3 KB, 656 views)
File Type: png Inverted_overall.png (59.4 KB, 691 views)
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Old 23rd November 2019, 01:24 AM   #3
andy2 is offline andy2  United States
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Case #2: This is case #2. Time-Phase coherent BUT no Time-Coincidence because it has excess phase toward 20KHz. It will produce a proper step-response.

First let's make the tweeter polarity positive. But now we have a dip at the xover point because of the phase mismatch. See the first pic.

One way to fix that is introduce a fix time-delay on the tweeter. For example, if the xover point is at 3KHz, calculate the phase mismatch, then dial in a fix delay on the tweeter so that the phase of the mid and tweeter would match at 3KHz. See the second attached pic. This can be done with DSP for example. But the problem is you end up having an excess phase at high frequency as you can see on the second pic. The consequence of this is the initial spike on the step response.

I think you may be able to see this on Troels latest speaker design. He uses DSP to adjust the delay on the tweeter. But his step response show a rather big spike on the step response.
Ekta-2D

I suppose this is OK, but we need a speaker that can meet #3 criteria! No excess phase.
Attached Images
File Type: png Inverted_reverse_overall.png (58.0 KB, 669 views)
File Type: png FirstOrder_excessPhase_overall.png (57.4 KB, 659 views)
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Old 23rd November 2019, 01:27 AM   #4
andy2 is offline andy2  United States
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So let's see how we can convert the original xover to one that can meet the #3 criteria!

Let's look at an ideal first order time-phase coherent/time coincident - absolute zero phase from 1Hz to 20KHz.

The simulation attached shows an example. Notice 0 degree phase shift from 1Hz to 20KHz. Also notice how the tweeter phase and woofer phase track each other at 90 degree, but the overall phase of the system is 0 degree.
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File Type: png Coherent_ideal.png (55.4 KB, 660 views)
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Old 23rd November 2019, 01:28 AM   #5
andy2 is offline andy2  United States
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Case #3: Let's take a first shot at the original xover and convert it to time-phase coherent/time-coincident.

Notice the excess phase is very close to zero. Yes, ideally the excess phase should be zero, but in real world condition, it's very difficult. Maybe with modify baffle or some baffle tilting or tuning can help minimize the excess phase.

Compare to the non-coherent version #1, #1 has an excess phase of -180 degree.

But xover may be able to be fine-tuned to improve the phase matching at low frequency and high frequency.
Attached Images
File Type: png Coherent_firstshot_overall.png (72.3 KB, 235 views)

Last edited by andy2; 23rd November 2019 at 01:33 AM.
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Old 23rd November 2019, 01:35 AM   #6
andy2 is offline andy2  United States
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Case #3: Here's an improved version. The phase on the low frequency and high frequencies are slightly better matched.
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File Type: png Coherent_overall_improved.png (69.6 KB, 222 views)
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Old 23rd November 2019, 01:44 AM   #7
andy2 is offline andy2  United States
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Case #3: Here's another example using a three way speaker. This is an old speaker I made awhile ago. It's not an ideal candidate to make a time-phase coherent/time coincidence but it serves to for an illustration. The cabinet has some odd diffraction so there quite a bit of ripples on the freq. response.

Drivers are Seas tweeter, 5.5in mid, 8in woofer.
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File Type: jpg pms.jpg (864.4 KB, 281 views)
File Type: png PMS_timecoherent_overall.png (76.3 KB, 289 views)
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Old 23rd November 2019, 01:50 AM   #8
andy2 is offline andy2  United States
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A few words regarding the step response:

When it comes to first-order coherent and non-coherent, there has been some misundertanding with regard to the step response. For non coherent speakers, invariably, the polarity of the different drivers will be different, that is the tweeter may be inverted polarity and the woofer will be positive polarity. Therefore in the step response, the tweeter will "APPEAR" (notice capital letter for emphasis) to go negative with respect to the woofer. But that misses one subtle but very important point that will lead to a crucial insight to the phase of coherent vs. non coherent design.


Most people came familiar with step response measurements by way of Stereophile John Atkinson measurements, but his measurements only show the overall step response without the measurements of each single driver. Once each single response is shown, there is further truth to be gained.

I will use one of my project to illustrate the misunderstanding. See pic of speakers here:

IMG_0693 | Andy VJ | Flickr



Below is the xover design. Notice the tweeter is inverted polarity and the woofer is positive. Also notice the step response on the lower right corner. Also notice the phase of the speaker response on the upper right corner of the plot. That is the phase starts at about 0 degree, and gradually go to -180 degree. Also notice each individual component freq. response and the cross over point.

Inverted_overall | Andy VJ | Flickr


At first glance, the tweeter seems to go completely opposite of the woofer (the initial dip of the step response). The time-coherent proponent will say – wait a minute, that’s all wrong since how can the treble be completely opposite of the woofer? But that is not quite right. The tweeter ONLY opposite of the woofer at very high frequencies, but at low frequencies, below the xover point, the tweeter and the woofer actually go up together.


I here have a zoom in pic of the step response. You can see the tweeter and woofer go up together after the initial high frequencies. It’s subtle but it’s there and it’s very important.

Green – system

Red – tweeter

Yellow - woofer

inverted_stepResponse_zoom | Andy VJ | Flickr


What does this mean? If you look at the frequency response below, you see that the phase of the system is only at -180 at 20KHz, not the entire plot. But below the xover point, the tweeter and woofer are more or less “in-phase”. For example, at 2KHz the phase is only at -60 degree, at 3KHz the phase at -80 degree. As I said before, since our perception is not very sensitive at high frequencies, most of us may not “hear the difference”. Most of the musical contents occurr below the xover point which is about 3KHz in this case and that’s where most of the phase shift has not occurred.

Also the phase change is not at a constant -180 degree everywhere but only at exactly at 20KHz. For example, the phase change at 20KHz is only a few degree vs. 19KHz and likewise 19KHz is only a few degree vs. 18KHz … and so on. It’s a gradual shift in phase so our hearing may be able to adjust to it.

But on the other hand, if this -180 degree occurs at 500Hz, trust me, you will definitely HEAR it! I think high order can get away with it because the phase shift occurs at high freq. where our hearing may not be so sensitive.

Overall_inverted_freqResponse | Andy VJ | Flickr
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Old 23rd November 2019, 03:49 AM   #9
bwaslo is offline bwaslo  United States
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An exercise in converting a speaker to time-phase coherent
And there's also another approach: an FIR equalizer.
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Old 23rd November 2019, 04:50 AM   #10
ScottG is offline ScottG  United States
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Quote:
Originally Posted by andy2 View Post
..about 3KHz in this case and that’s where most of the phase shift has not occurred..
That's the important part, and really it's 1-1.5 kHz. (..where most ITD/interaural-time-delay is lost.) Considering variability in listeners, my guess is that 2.5 kHz "limit" is a safe bet for just about anyone.
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Last edited by ScottG; 23rd November 2019 at 04:53 AM.
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