Phase-alignment based method of designing multi-way speakers

To be frank I can't imagine doing this without tools as the interactions are touchy and complex. To show this I've removed the LC before the woofer, which I only used because other methods were proving difficult in fixing both the acoustic response and phase at the same time.

The woofer doesn't suffer any issues that would really need a notch filter and the response is not very different to the first case, but look at the phase...
Quite honestly I'm not sure what I should be looking for. They look 'the same but different' to me. What 'tools' should be used?
 
Not familiar with that one, but i found this one which seems informative:
http://audio.claub.net/tutorials/Consideration of Phase in Loudspeaker Design.pdf


Eric, that is a well done paper, recommendable. There is a new insight in it, at least I hadn't thought about it before:

-quo-
If active electronics are used, there is an easy way to completely remove the problems resulting from the
tweeter’s phase response. The Linkwitz transform is a filter that implements a bi-quadratic transfer function
(BTF). In general, a BTF circuit can “transform” the response of a driver in a sealed box (in terms of its low
frequency response, characterized by the parameters F
b and Q) to any new set of Fb¢ and Q¢.
-unquo-

However, when I try to calculate it through a spreadsheet like can be found here http://www.trueaudio.com/downloads/linkxfrm.xls, for an actual tweeter situation, it comes to bizar results. Anyone any thoughts?

vac
 
when I try to calculate it through a spreadsheet like can be found here http://www.trueaudio.com/downloads/linkxfrm.xls, for an actual tweeter situation, it comes to bizar results. Anyone any thoughts?

vac[/FONT]

I think I can be of some help here...

What exactly are you trying to calculate with the LT spreadsheet?

Typically you specify the "physical" response, e.g. the actual Fo and Q of the tweeter, and the desired response (another pair of Fo, and Q) and then you calculate what biquadratic filter response is needed to convert one to the other.

Note that Sigfried Linkwitz's circuit does not work for some combinations of these parameters...

Let me know what you are after, and I will help you out.

-Charlie
 
Hi Charlie,

What I found interesting is the thought that in an active xover, you may use a biquadratic filter on the tweeter in stead of for example a 2nd order Sallen Key filter to get a 12 dB slope, but that while doing so you would at the same time compensate for mechanical phase shift caused by the tweeter roll off. Sallen Key doesn't do that.

Now, the thing is how to calculate, and I found out that the spreadsheet I linked to does not work for this particular use of the Linkwitz Transform. If you have a link to a site where it is explained how to do these calculations, that would be interesting.

Thanks,

Vac
 
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@ LafeEric, I'll put it another way.
I theorized that I could put the crossover point at the frequency whose period is 0.38 ms (2600 Hz) then at the crossover point it would be in phase, even though 360 degrees delayed,
Firstly, I have doubts about it being in phase even at that one frequency. The acoustic phase will have unique variations beyond the delay, even before you consider the effect of the impedance on a stock filter. Then...
If I use a 4th order XO it should keep the deviation interferences to a minimum.
Fourth order will be a good option for this reason and yes, you'll probably have deviations. The deviations will be due to the phase of one driver crossing the other as you said earlier. It guarantees you'll probably have some frequencies in phase and others not. If you can make the slopes parallel, you'll ensure that you'll either have it close to all right or close to all wrong (in which case you can swap the polarity).

The phase slope broadly speaking means delay, and delay can be countered by a higher order of filter on the woofer in this case.

This is what I believe KSTR suggested earlier.
 
If you have a link to a site where it is explained how to do these calculations, that would be interesting.

Here is Sigfried Linkwitz's web page, with a section on the LT (section #9):
Active Filters

The spreadsheet is one of the links at the end of the section. Look for "pz-eql.xls". Not a very user friendly spreadsheet, but you can use it to calculate the values you need for tweeter equalization.

There is other info on the LT on his site. Look at the other links in that section. He also has pages from the original paper in which he described the circuit posted elsewhere on his web site. There is lots of good stuff, but a lot of material, so just poke around.

-Charlie
 
Quite a bit of misinformation in this thread...
Just to cite a few random points:

- you seem to confuse electrical phase with acoustical phase (they are NOT the same)

PHASE COHERENCE: must be achieved at this point! Will be fine tuned at the end.
- acoustical "phase coherence" is certainly NOT achieved by your described procedure

CROSSOVERS: now that woofer and tweeter have flattened impedance and phase curves in crossover region it is easy to ruin it all by combining even and odd order filters for the drivers to match the different steepness of natural roll-off slopes of drivers. Don't. Orders must be the same type for both drivers as each order turns phase by 90 degrees. Doing the opposite would create obvious phase misalignment again.
- except that driver roll-on and roll-off also affect phase. Since most drivers are "minimum phase" devices, it does not really matter whether phase shift is induced by the driver's natural roll-off or by the electrical filter. It is the final TARGET function that matters.

Regarding tweeter polarity: in case of both being 1-st order we have to invert the tweeter polarity as we have summed relative phase shift of 180 degrees. With both being 2-nd order – don’t invert (180+180=360=0). With third – invert again (270+270=540=180). With fourth - don't (even hope to build one correctly passively).
- you got this backwards (assuming the drivers are on coincident planes and we are talking about true acoustical n-th order crossovers, which we should).

Generally all filter orders higher then the first are said to negatively impact driver's transient response. Never measured it by myself, still i find first order filter to be the most pleasant sounding. With sensitive drivers (>93dB/2.83V) you can achieve decent sound levels without getting too close to cone breakup.
Let me guess: by "first order" here you mean "electrical first order" right? i.e. one cap and one coil. Fact is, such filters almost NEVER end up being first order acoustically (and again, the acoustical slopes are the only ones that matter)...


- etc. etc. etc.

That's about it! Questions, corrections and additions are welcome.

I have just provided some of those. Hope you don't mind and don't take it as a personal attack, which it most definitely isn't.

Cheers,

Marco
 
also, flattening the impedance peak at resonance does not change the phase behavior of the driver output, so you will still have that to contend with... there are only difficult tradeoffs to choose from I am afraid.
-Charlie

Charlie,

This is where my opinion is different. It definitely changes (flattens) electrical phase response, so it must influence total phase behavior.. I guess.

I just read your research "A Consideration of Phase in Loudspeaker Design". It is very inspiring work you have done and reminds not to forget some obvious things like minimizing distance between drivers, and also that 4-th order isn't panacea if other factors are not kept in mind. Great work!

As quoted:

"In this case, the source
of the rotation is the slow fall of the tweeter’s phase to zero because the Q is low (~0.6). Increasing the Q of this
driver would decrease this effect, but only slightly."

I'm not sure about this. It would be interesting to see similar experiments done with HF driver with flattened resonance.
 
Quite a bit of misinformation in this thread...
Just to cite a few random points:

- you seem to confuse electrical phase with acoustical phase (they are NOT the same)

Marco,

well, a common error, still I believe I'm looking at them as different issues that sum at the end. Could you be more precise what makes you think so?

- acoustical "phase coherence" is certainly NOT achieved by your described procedure

By finally aligning drivers physically? There will be inter-sums and cancellations due to distance between acoustic centers at different frequencies, so summed electrical an acoustical phase will not be perfectly aligned vertically nor horizontally but finding "sweet spot" at least for crossover frequency along with first order cross-over should give reasonably good result (guess why the low filter order plays the nice guy here).

- except that driver roll-on and roll-off also affect phase. Since most drivers are "minimum phase" devices, it does not really matter whether phase shift is induced by the driver's natural roll-off or by the electrical filter. It is the final TARGET function that matters.

This somewhat lessens importance of your previous statement regarding acoustical "phase coherence", unless quotes mean that you're referring to something that doesn't exist.

Let me guess: by "first order" here you mean "electrical first order" right? i.e. one cap and one coil. Fact is, such filters almost NEVER end up being first order acoustically (and again, the acoustical slopes are the only ones that matter)...

That's right, combined response for each driver will be somewhat 12dB/oct by summing with the slope of the driver itself. That's why I'm going to try the method with "easy" or "matching" drivers first and then with "hard" drivers (as proposed later in thread) with not very big expectations for the latter, still to have it done for comparison's sake.

The point of the method is to minimize electrical phase shift, the acoustical phase shift and then to find the drivers that naturally match. And restart the whole thing if they doesn't. And to fine tune HF driver position by ear at the end.

As opposed to taking drivers that are good for themselves from specs, cross actively with high order, mount conveniently on baffle, model, analyze for irregularities and invent necessary additional DSP-based or analog filtering and time-delay corrections. Which is also hard and respectable way to achieve the same target.

I have just provided some of those. Hope you don't mind and don't take it as a personal attack, which it most definitely isn't.

Definitely not :) Thanks for joining in!
 
Charlie,

This is where my opinion is different. It definitely changes (flattens) electrical phase response, so it must influence total phase behavior.. I guess.

If the source is a voltage source, then the voltage across the driver terminal does not change because the RLC network is in parallel. The network does not change the input to the driver, only the impedance seen by the amplifier, so the driver output remains the same. Thus acoustic phase will not change.

I just read your research "A Consideration of Phase in Loudspeaker Design". It is very inspiring work you have done and reminds not to forget some obvious things like minimizing distance between drivers, and also that 4-th order isn't panacea if other factors are not kept in mind. Great work!

As quoted:

"In this case, the source of the rotation is the slow fall of the tweeter’s phase to zero because the Q is low (~0.6). Increasing the Q of this
driver would decrease this effect, but only slightly."

I'm not sure about this. It would be interesting to see similar experiments done with HF driver with flattened resonance.

The active case is different. The active network changes the output of the amplifier, both in amplitude and phase. This has the effect of changing the behavior of the driver's output just as if you had changed the mechanical properties of the driver.

Regarding the Q and phase, if you look at the first two plots of phase in my paper, for a variety of Q values, you will see that low Q responses undergo the phase rotation more slowly, and therefore over a larger range of frequencies, compared to higher Q responses. The point I was trying to make is that a low Q driver's resonance has (phase) effects even as much as 2-3 octaves away.

The phase response of the driver is important to consider if you want to cross over anywhere near resonance. Let's call this "phase change avoidance principle" - to try and operate the tweeter well away from resonance in order to minimize the effect of the phase change around resonance (there are lots of other good reasons to avoid the response near resonance, and some were stated earlier in this thread). But you can choose the opposite "embrace and work with the phase change" - this is the approach using the active biquadratic filter (e.g. LT) that I describe in the white paper. Using the LT you can change the response (amplitude and phase) into something that will be useful, rather than being stuck with what the manufacturer gives you. When designing certain crossovers, this can work to your advantage, and you can do some interesting thing with the LT that I didn't even go in to in the paper!

Don't forget: electrical phase and acoustic phase are NOT the same...

Have fun!

-Charlie
 
Hi,

That the problem. Its a sweeping generalisation. Your assuming zobelling
drivers and compensating tweeter impedance peaks gives you a better
starting point. They can do but a lot of the time they simply don't.

One problem with the simulating x/o sticky is flattening impedance is optional.

It all depends on the particular drivers used and the design of the speaker.

Blindly applying a "method" is not the same as working out what needs
doing and what doesn't. The method is called "phase aligned" but I
still can't work what the meaningful definition of the term is.

Take this two way design : Zaph|Audio

audio-speaker17-crossover.gif


As its 4th order L/R acoustic the drivers are wired in phase.
The phase is not minimal, it wraps through 360 degrees.
The phase wrap causes inevitable group delay.

How would you apply the "phase aligned method" to the above design
and what would it meaningfully change in the above design ? nothing AFAICT.

rgds, sreten.

Worth a look : Crossovers

Duelnd_3way_tg1.jpg


The delay is inevitable due to the phase wrap at each crossover point.

Fine design indeed with drivers probably unsuitable for using along with the method.

I studied paper of Duelund's 3-way - very clever indeed, still quite complex to build. Thanks for pointing to that one.
 
@ LafeEric, I'll put it another way.

Firstly, I have doubts about it being in phase even at that one frequency. The acoustic phase will have unique variations beyond the delay, even before you consider the effect of the impedance on a stock filter. Then...

Fourth order will be a good option for this reason and yes, you'll probably have deviations. The deviations will be due to the phase of one driver crossing the other as you said earlier. It guarantees you'll probably have some frequencies in phase and others not. If you can make the slopes parallel, you'll ensure that you'll either have it close to all right or close to all wrong (in which case you can swap the polarity).

The phase slope broadly speaking means delay, and delay can be countered by a higher order of filter on the woofer in this case.

This is what I believe KSTR suggested earlier.
Thanks Allen.

The way I was hoping to go about this was to actually measure the acoustic phase delay between the drivers. Though it is apparent the acoustic and electrical phase do not track consistently, at that one frequency electrically delaying the phase should correct any acoustical phase delay - I think yours and others suggestions that I correct it through this method supports this.

Phase difference causes cancellation, thus nulling. With a 360 degree phase shift I would expect to see no cancellation at the XO freq, but as the frequency rises and falls away from the XO I would expect to see variations on either side of the XO - which is what the graph in post #57 actually shows.

The vertical separation is another complication, but until I can take some measurements and see what I am going to have to deal with I haven't a clue what to think.
 
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Paid Member
The way I was hoping to go about this was to actually measure the acoustic phase delay between the drivers.
OK.
Though it is apparent the acoustic and electrical phase do not track consistently,
The impedance phase doesn't track at all, it doesn't even change. (On a side note there is a special relation between the impedance phase and the acoustic phase, but I don't believe there is a benefit to understanding it for these purposes here.)

The thing that will 'track' the acoustic phase (if we wanted to do things the hard way ;)), will be the voltage/phase at the driver terminals, ie. the drive to the voice coil. This does have a connection with the driver impedance (essentially an incidental connection though) as well as at least two other complex factors (complex meaning they have a magnitude and phase).

You can avoid some of the details by using a crossover simulator, or a measurement based trial and error approach.

I would expect to see variations on either side of the XO - which is what the graph in post #57 actually shows.
In post 57, the phase plots are dotted and the same colour as the response plots for the respective driver. The black and the yellow traces are the totals.

The phase plots are mostly parallel and lining up with each other. The point to the post was to show the extra componentry on the woofer to add rotation to the woofer phase, compensating for delay.

The vertical separation is another complication, but until I can take some measurements and see what I am going to have to deal with I haven't a clue what to think.
I would suggest that this could wait for a while. ;)
 
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Here is Sigfried Linkwitz's web page, with a section on the LT (section #9):
Active Filters

The spreadsheet is one of the links at the end of the section. Look for "pz-eql.xls". Not a very user friendly spreadsheet, but you can use it to calculate the values you need for tweeter equalization.

There is other info on the LT on his site. Look at the other links in that section. He also has pages from the original paper in which he described the circuit posted elsewhere on his web site. There is lots of good stuff, but a lot of material, so just poke around.

-Charlie

Hi Charlie,

thanks for the link; actually I had come to this page before at Sensei Linkwitz's site, but had sort of limited his transform to sealed subwoofers, the idea to use it higher up in the food chain was new to me, and it still is an interesting thought. So, I tried Linkwitz's spreadsheet, but it does not seem to work for tweeter use either, just like the other spreadsheet I had found.

So, before really diving into the math to figure this one out, I decided to have a quick look at the problem it intends to address first. So, here is a measurement I took on a middle of the road tweeter ( Fs=1100 Hz, Qts 1,56, no ferrofluid). tweeter.jpg

Left hand scale is phase, right hand SPL. At low filter orders crossing over relatively low, there might be some problem in the sense that the dominant lobe would shift in the vertical plane. I do 24dB octave usually, so there would be very little of that effect happening even crossing over @ 2Khz. So, it is good to have learned a potential source of problems, and once I encounter it, I'll try to sort out the math.

Actually, it is a good argument in and by itself to use steep filters (on top of the other reasons for doing so, given active xover).

vac
 
Hi Charlie,

thanks for the link; actually I had come to this page before at Sensei Linkwitz's site, but had sort of limited his transform to sealed subwoofers, the idea to use it higher up in the food chain was new to me, and it still is an interesting thought. So, I tried Linkwitz's spreadsheet, but it does not seem to work for tweeter use either, just like the other spreadsheet I had found.

So, before really diving into the math to figure this one out, I decided to have a quick look at the problem it intends to address first. So, here is a measurement I took on a middle of the road tweeter ( Fs=1100 Hz, Qts 1,56, no ferrofluid). View attachment 283860

Left hand scale is phase, right hand SPL. At low filter orders crossing over relatively low, there might be some problem in the sense that the dominant lobe would shift in the vertical plane. I do 24dB octave usually, so there would be very little of that effect happening even crossing over @ 2Khz. So, it is good to have learned a potential source of problems, and once I encounter it, I'll try to sort out the math.

Actually, it is a good argument in and by itself to use steep filters (on top of the other reasons for doing so, given active xover).

vac

Both of the spreadsheets that you are trying to use to calculate the LT values for the tweeter work just fine. Let me help you by explaining how to use SL's spreadsheet. Download it again if you don't have it handy:
http://www.linkwitzlab.com/pz-eql.xls

As before put in your 1100 for F0 and 1.56 for Q0 (make sure not to use a comma as the decimal separator!) in cells G7 and G8. Let's say you want this tweeter to do a 3k Hz LR4. You need two second order HP stages, each at 3kHz and with a Q=0.707. So enter 3000 for fp and 0.707 for Qp in cells G9 and G10. Using this LT, the tweeter would be one second order stage, and you would need another electronic stage, second order Q=0.707 at 3k Hz to pair it with to create the LR4 HP response.

THE NEXT STEP IS TO CHECK TO SEE IF SL's CIRCUIT CAN REALIZE THIS FILTER! The value for "k" in cell D18 must be greater than zero. If not, you can not use this circuit to create the biquad "transform" filter (it just doesn't work for some Q and f pairs). If it's greater than zero, all is OK and you may proceed...

At this point, you are probably wondering why you can't see the plot of the filter on the graph... well, it because the graph starts at a frequency of 10 Hz. You can change this by entering a new frequency start point in cell B37. Try 200Hz - now your graph appears.

So, let's assume you want to actually BUILD this circuit. Now what??? The next step is to calculate the component values (for the resistors and caps). It turns out, like most active circuits, that you can "scale" the values for R and C components using a "scaling factor" that will increase the R's while decreasing the C's or vice versa. This is provided as parameter "M" in cell G18. You also need to choose a capacitor "seed" value, and I recommend that you enter 100nF in cell G11. M can be any real number, and you want to try and find a value of M that gives you not only "easy" values for the components, but also values that are practical as far as the real circuit goes. For instance with 100nF in cell G11, if M=1, R1= 0.10, R2=0.73, R3=0.01, C1=21811.0, C3=162230.4, and C2=100.0 (values in kohms and nF). Not very useful values... Try M=100... see the changes? Keep trying new values for M until you find some more or less practical component values. Keep resistors below 1M and caps above 1nF.

Now the dirty details... the problem is that you typically can not purchase resistors and capacitors that are exactly the same as the values that are listed. Also, whatever components you do buy will have some tolerance, e.g. a resistor with 10k ohms and 1% tolerance. The tolerances have a real and significant effect on the accuracy of the final circuit's filter, especially the capcitors. SL tries to provide a couple of "test" entries (in the sections "3a" and "4a") where you can enter trial values for each component and see what filter shape comes of it. This not all that helpful IMHO, and still doesn't tell you anything about the effect of component tolerances.

Funny that this is all coming up just now. I have a few items that I am posting to my web site in the very near future, and one of these is a LT circuit designer that addresses these issues by helping you answer:
1. What value of the scaling factor "M" should I pick?
2. What is the effect of component tolerances?
3. Should I try to use multiple capacitors for better accuracy?
Basically, I do a bunch of random trials for the component values within the user-specified tolerance levels after identifying some "best options" for M. The results are plotted graphically and in a table. This is very helpful when you are planning what to buy and how to build the circuit.

Check my web site in a few days if you are interested:
Charlie's Audio Home Page

-Charlie
 
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Hi, i can't really see the point of the above, unless that is the point, rgds, sreten.

Hi Sreten,

The last month or so I have been fooling around with a new design I concocted for a power supply with very low noise and output impedance. I get about 0,25 uV noise (20-20K) on a 15 V DC output. That is more or less the same proportion as a 1 meter high mountain would have to the radius of the Earth.

Now, I seriously doubt the relevance of such low noise figures for audio, but it turned out into a competition against myself to see how low I could push the noise floor.

More relevant I think for a power supply is very low output impedance. When you look at the rails of a working piece of line level audio electronics, you may be surprised by the amount the signal modulates the power supply lines. Because of high PSRR's of good opamps, this may or may not be a problem, but in the spirit of making everything better as much as you can, it will do no harm either. Right now, my power supply has about the Johnson noise of a 33 Ohm resistor, and the output impedance below 2 Khz of a typical resistor lead.

It is most likely complete overkill for opamp use. However, for discrete designs there might be an advantage if you can work with rock solid supply lines coupled to a rock solid ground. Baxandal (see reprints by Jan Didden's LA) did a very interesting survey of sources of distortion, and supply line modulation was one of them.

After I sorted some things out, I may post the outline of this design on diyAudio,

vac