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Multi-Way Conventional loudspeakers with crossovers

Crossover and time delay/offset, for horns particularly.
Crossover and time delay/offset, for horns particularly.
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Old Today, 04:28 AM   #1
Dave Zan is online now Dave Zan  Australia
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Default Crossover and time delay/offset, for horns particularly.

Crossovers for cone/dome drivers on flat(ish) baffles are pretty well understood.
Typically the physical layout issue is that the tweeter is a little too far forward on a flat baffle.
The tweeter can be physically moved back or a little time delay added to it in the crossover, especially convenient with a DSP crossover.
All well documented.

But almost the opposite issue occurs when horn mid/tweeters (assumed 2 way for simplicity) are used with cone woofers - the depth of the horn means the mid is delayed.
It is possible to push the horn driver forward to the woofer plane but this can be problematic - physically awkward with a substantial horn and a potential source of diffraction problems for the woofer.
It is possible to delay the woofer but this seems to miss an opportunity.
The delay of the mid would seem to allow a closer approach to a linear phase crossover but without any DSP step.
I have seen little analysis of this, there was a thread a while back but the OP seems to have lost interest.
"Quasi-optimal" crossover for high-efficiency loudspeaker system.

I read the Vanderkooy & Lipshitz articles referenced in the 1st post that supposedly prove the idea is unworkable.
A closer study shows that certain assumptions in their analysis are too restrictive, a practical solution may be possible after all.
It will require asymmetric crossovers for the HP and LP, and probably non standard shapes.
I have found the maths a little difficult, presumably why V & L only looked at the simple symmetric case.
Anyone have any references or ideas on this?

I will start with an example.
Since we have a time delay an obvious candidate for the Low Pass would be a Bessel filter.
First is a Bessel LP, it has maximally flat Delay.
Second is a HP "Bessel" created by the usual method, the frequency response is mirrored.
But a Bessel is not about frequency response so this does not create a HP with maximally flat delay, as is obvious in the plot.
A closer match would be a HP filter with maximally flat delay.
Anyone know what this is called or have a reference so I don't have to create it from scratch?

David
Attached Images
File Type: png Bessel_HP.png (30.9 KB, 70 views)
File Type: png Bessel_LP.png (30.0 KB, 76 views)

Last edited by Dave Zan; Today at 04:39 AM. Reason: Tried to put thumbnails in line in the post?
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Old Today, 05:23 AM   #2
AllenB is offline AllenB  Australia
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Quote:
Originally Posted by Dave Zan View Post
It will require asymmetric crossovers
I've had no problem in the past hitting one side harder than the other, and getting phases and response just where I want them.
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Old Today, 06:48 AM   #3
Dave Zan is online now Dave Zan  Australia
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Quote:
Originally Posted by AllenB View Post
I've had no problem in the past...phases and response just where I want them.
Can you show examples, details please?

Best wishes
David
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Old Today, 12:23 PM   #4
AllenB is offline AllenB  Australia
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I went digging for plots, then I thought I'd just do something fresh. This is based on flat drivers, crossed at 1kHz. One has a second order filter.

The other is delayed by -250uS (I did this rather than the other at +250uS, so the plots would be easier to read). This delay amounts to 90 degrees, or two extra orders at 1kHz. It has a 4th order filter. It is also inverted as per usual.
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Old Today, 12:28 PM   #5
AllenB is offline AllenB  Australia
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Then I found some old work. I have a mess of these files so I just picked something. Here I have 1st and 3rd order coming together, phase agreeing through the cross, no particular response trend, IIRC I could usually find a way to get it flat. Picture of the design for distance (that's a 15" woofer). Delay appears fairly consistent.
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File Type: png Image52.png (16.4 KB, 55 views)

Last edited by AllenB; Today at 12:33 PM.
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Old Today, 07:57 PM   #6
marco_gea is offline marco_gea  Italy
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Quote:
Originally Posted by Dave Zan View Post
I have seen little analysis of this, there was a thread a while back but the OP seems to have lost interest.
"Quasi-optimal" crossover for high-efficiency loudspeaker system.
Hi!

I was the originator of that thread.

The reason I later "lost interest" was the realisation that none of those "quasi-optimal" crossovers had a chance of being correctly implementable in real life, when also duly taking into account the fact that all real exponential or hypex horns already exhibit a "natural" 4th-to-6th order high-pass behaviour at Fc. Therefore, all those nice asymmetrical crossovers that call for a 2nd order high-pass on the tweeter leg are a physical impossibility.

Additionally, what I have come to realise is that what really matters most of all is not minimizing phase rotation of the summed response per se, but rather achieving the best possible phase matching between the two filtered drivers, in a wide frequency range around the acoustical crossover frequency, and up/down to where each driver's response is -12dB.

All of this has led me to re-evaluate the goodness of Pioneer's original passive crossover designs for their Exclusive studio monitors of the '80s and '90s, namely:

- a 6th order electrical LP on the woofer (essentially Linkwitz-Riley)
- a 2nd order electrical HP on the tweeter/horn (quasi-Butterworth)

with BOTH branches wired with the same (+/+) polarity, and the front-to-back offset adjusted so as to achieve the desired optimal inter-driver phase tracking at and around the crossover freq.

This combination seems to work very well indeed for the typical: 15" woofer + ~300Fc Hypex horn, ~600-700Hz crossover, and ~20-25cm offset.

But, the final, real acoustic high-pass transfer function of the tweeter is a combination of the intrinsic acoustic high-pass of the unfiltered tweeter and 2nd order electrical high-pass, and it looks nothing like a textbook high-pass filter (and is certainly NOT 2nd order!).

Cheers,
Marco
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Old Today, 11:03 PM   #7
Dave Zan is online now Dave Zan  Australia
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Quote:
Originally Posted by marco_gea View Post
The reason I later "lost interest" was the realisation that none of those "quasi-optimal" crossovers [were] implementable in real life...
Hi Marco.
Yes I think this is a critical point and well observed.
But it didn't reduce my interest, just made me curious about what can be implemented in real life.

Quote:
...(and is certainly NOT 2nd order!).
Yes, the final product will have to factor in both the acoustic and electrical slopes.
If we solve the idealised case, we can consider it as a target and then adjust the electrical response to allow for the acoustic curve.
We don't have to consider the ideal case as some impossibility that needs "mass-less speakers of infinite bandwidth".

Best wishes
David
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Old Today, 11:27 PM   #8
Dave Zan is online now Dave Zan  Australia
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Quote:
Originally Posted by AllenB View Post
This is based on flat drivers
As explained in my response to Marco, I think this is the way to study the problem.
Once we understand the idealised case we can include real world effects.

Quote:
The other is delayed by -250uS...
I see no delay for physical offset in your post, have we failed to understand each other?
Here is an example, it is a Link/Riley with some delay on the tweeter that corresponds to a physical offset.

Best wishes
David
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File Type: png LR_with_delay.png (9.3 KB, 0 views)

Last edited by Dave Zan; Today at 11:29 PM.
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