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

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

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