Crossover and time delay/offset, for horns particularly.

...The point is that it has half the excess phase of a similar filter without offset...

It occurs to me that this depends on what it means to say "similar" filter.
The excess phase is low for a similar 8th order lo-pass.
But more or less identical excess phase to the not-very-steep hi-pass.
So no real improvement if the constraint is the hi-pass, and it usually is.
Simpler to just put in an all pass delay in the woofer and be done with it.
Have to think if the idea can be saved.
Otherwise, phase linearization could be done with rePhase as an option, to learn if it makes any difference.

David
 
Its group delay is approximately 70% less than that of an LR 4 @ 1 khz. If a high order on the lowpass plus lower group delay is your concern then go for it.
I use some topology myself that would have about 50% more group delay than yours but which is 3rd order on the highpass and whose group delay is slowly dropping (like two cascaded 2nd Order Filters with a Q of 0.4). But it is only 2nd Order LP doesn't compensate for the delay of the horn offset. That one I do with an additional Bessel LP on the woofer path.

Regards

Charles
 
...

4. The hi pass is 3rd order, probably the practical minimum when both acoustic and electrical roll-off combine.

...

With a typical real-world horn, you'll find that even a 3rd order high-pass is not achievable in practice. What you'll end up getting, invariably, is a non-standard acoustic slope, with two separate "knees", one at Fx (crossover freq.) and one at Fc (horn cutoff). The result is a higher slope below Fc, AND more phase shift at and below Fx than predicted by a "simple" ideal high-pass.

The best way to approach this kind of simulation is not to try and simulate any combination of textbook HP & LP filters (even if asymmetrical) applied to ideal infinite-bandwith drivers.
Rather, it is to start with a simulated horn driver (with a 4th order or often even 6th order "natural" high-pass at Fc), and then superimpose the electrical HP on that.

Marco
 
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Yes, a horn can cut off sharply with a lot of phase changing. A waveguide has much less group delay and can more easily be manipulated through this region.

I feel that it might be better once delay goes up as frequency drops, that it should stay on this new level. Feel free to set me straight if that's not true.
 

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I did show a real world example in post #5

You are right, but I don't think it matters. The first point of this exercise was to show that you can use electrical manipulation to take a delayed driver and sufficiently bring both phase and response into line at the same time.
 
Hi,

I'm exploring how to reduce group delay in a system (3-way prototype) and tried fiddle with horn / mid xo. The xo posted by AllenB seems to work except the horn high pass ended up being very roughly 4th order with weird knee shape and mid low pass is 8th order Bessel. I'm able to get rid of ~0.5ms delay on the mid that was required with more closely approximated LR4 filters. So, compensating for the physical offset of the devices with asymmetric slopes seem to work somewhat fine and got reduced group delay although I'm not sure if it is was audible at all to start with. Anyway, a quick experiment. I haven't compared if there is difference.

Interest in this was due to discussion of group delay in the Camplo 2-way mega thread and found this thread by searching. The deeper horns (exponential) have group delay in the design (cutoff) and from my own prototype projects I've found out that to get a crossover to work it seems the deeper the horn/waveguide is the more delay required on the mid for smooth response at the xo. I have observed the added delay on the mid woofer appears in the system group delay as well and reasoned that a shallower waveguide means less group delay for the system. Does this seem reasonable? In which case one should not use so deep a horn that generates system group delay close to audibility threshold. The xo slopes affect as well and the proto got a lot less group delay (at lows) with the W-M crossover with bessel filters as well, in comparison to LR4 for example.

I didn't optimize the slopes or did other changes on the attached xo sim. Need to checkout if the predicted in-room response can be closely matched to compare if either sounds somehow better in the prototype.

Still many questions for me to figure out. For example how a FIR filter that would linearize the phase and group delay would get rid of the physical misalignment? The concept is hard for my brain :D Thought to post here so that I remember to investigate this aspect further some day.

Attached GIF shows the effect of different M-T crossover slopes. The one with 0.5ms delay is roughly symmetric LR4 and the other is slap on 8th bessel low pass and a bit modified LR4 high pass. While the in-room response estimate stays almost the same group delay is reduced by the 0.5ms on the mid woofer bandwidth. Group delay is the dark gray trace on the top right graph.
 

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Interest in this was due to discussion of group delay in the Camplo 2-way mega thread and found this thread by searching. The deeper horns (exponential) have group delay in the design (cutoff) and from my own prototype projects I've found out that to get a crossover to work it seems the deeper the horn/waveguide is the more delay required on the mid for smooth response at the xo. I have observed the added delay on the mid woofer appears in the system group delay as well and reasoned that a shallower waveguide means less group delay for the system. Does this seem reasonable?

Still many questions for me to figure out. For example how a FIR filter that would linearize the phase and group delay would get rid of the physical misalignment?
Tmuikku,

As David McBean pointed out in that thread, group delay (GD) is the negative derivative in milliseconds of the phase response. It is a measure of the rate of change of phase with respect to frequency, and is positive when the phase slope is negative.

The depth of a horn does not determine it’s phase response, it’s frequency response does.

The steeper a driver, or horn/driver, or crossover filter’s roll off, the more phase change per frequency, hence more GD.

Time alignment delay of different acoustic origin points is not GD.

FIR filters are capable of flat phase response, though still require delay for time alignment of drivers with different acoustical points of origin.

Art
 

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Thanks for precise answer Art!

I think there is few things that threw me off. First is the fact that the simulator shows system Group Delay which is of course derived from the system minimum phase and not what some individual transducer does alone. For some reason this was hard to my brain to draw relations :D

Another thing that threw me off is the fact that phase is measured in degrees but group delay in (milli)seconds which has inverse relation to frequency. Thus, when testing a filter on 500Hz or 5000kHz there seems to be equal change in the system phase graph but to see the change in group delay plot on high frequencies one would need zoom in to see it.

Delay on individual parts (ways) of the system could affect the system phase which shows in the group delay. Attached is GIF animation where all else stays the same but mid woofer has 0.5ms delay block on/off which smoothens the response by compensating the depth of the horn above. This affects the system phase and shows in group delay as well. If system response and phase was flattened with (FIR) filter the GD would become flat again, alright.

The takeaway in my example and experience is that it is not the delay block as such that causes more group delay but it is the resulting system phase gradually changing which gives rise on the group delay. See from the GIF, when there is no delay block the system phase (light green line, top left) change is more constant on the mid pass band, and the group delay is less.

I need to study more closely what is the concept of excess group delay.

Then I need to find out what it takes to make constant change in system phase :D Asymmetric filters seem to result less group delay, but investigating in the opposite perspective should be much more effective learning process I think. Starting from the basics, what makes flat derivative, where is my old math book?

ps. tried the yesterdays example in the DSP and the sound was weird, kind of out of phase sound no matter how I flipped the mid driver phase. Maybe the relation between tweeter and woofer on the mid passband was hearing through and made the system sound off. Perhaps this kind of xo works in a three way system if the mid band is wider? Not sure if I got it right in the DSP so might investigate some day.
 

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From math book, flat line would yield flat derivative. Straight line phase, with an angle, would yield straight derivative as well. But since the GD plotted in ms the line would look curving up even though the derivative of phase was straight. Alright, maybe not concentrate what the GD plot looks like, only care about what the scientific studies have found to be audible and be happy with it :)

Derivative Rules
"
There are rules we can follow to find many derivatives.

For example:

The slope of a constant value (like 3) is always 0
The slope of a line like 2x is 2, or 3x is 3 etc
...
"
 
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Hi,

group delay has been subject of discussion in the member Camplo 2-way thread recently and I noticed I haven't paid too much attention to group delay before since it has been a bit hard thing to grasp. I thought it was finally time to try and understand what group delay is and means in a system. Tried to get the handle with my current prototype project and noticed there was difference with different xo slopes for example.

My conclusion currently is that as long as group delay is below audibility threshold there shouldn't be any worry about it. Tried to lower the GD with the prototype project but I'm not sure if it has anything to do with sound quality. Quite contrary I think better sound was with response that looks better on other metrics in the simulator but has bit more group delay.

Anyway, it was necessary to try hands on how to affect it to get better understanding what it might be.

See this PDF I found Googling that kind of has similar conclusion. https://www.audiosciencereview.com/forum/index.php?attachments/group-delay-pdf.31763/
 
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Yes, I noticed Campio hotly debated GD. Elsewhere GD has never been part of design and optimization parameters or procedures, hence my asking.

Not a single manual of the various filter sim packages (e.g. Calsod/Leap/LspCAD/XSim/VCad) I am aware of ever mentions GD as a design parameter to my best of knowledge.
 
I am reviving this old thread after carefully studying also the thread about quasi-optimal crossovers linked in the opening post.
I am a total newb on the subject and came across these threads as I was looking for info on specific crossovers for horn loudspeakers, since I am in the process of designing a passive crossover for a three way speaker system with a direct radiation woofer, exponential mid horn and biradial horn tweeter.
The loudspeakers offset is a total mess as the exp horn is about 34cm back from the woofer and the tweeter is about 20cm ahead (considering placement on the same baffle).
X-over frequencies would be roughly 900 and 5k.
From what I understand none of the proposed crossovers (neither in this nor in the other thread) is capable of even nearly compensating such offsets, but it may well be that my assumption is wrong as I may have totally misunderstood the matter because a newb.
I am trying to understand if, in the described scenario, it is worth pursuing the design of a crossover aimed at improving phase and offset issues, or if the result would not be worth the extra effort vs. a simple Linkwitz-Riley second order which I have been considering this far.