Amplitude Errors in the Summed Response of Audio Crossover Filters

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This is a nice first step. You might want to throw in the phase and amplitude response of the drivers in to the mix and then see just how much your results change. You might be surprised to see just how much the drivers' own phase response mucks up the results of "crossover only" modeling. It should be pretty easy to include a driver model in your SPICE simulations.

-Charlie
 
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We published these graphs by request of a former co-woker and loyal customer. Any further analysis options would require system design specifics and we do not offer that service.

A cursory web search revealed there is no other collection of crossover responses of this type all in one place, so we were happy to oblige.

Jerry Martin
JRM Engineering
 
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This is a nice first step. You might want to throw in the phase and amplitude response of the drivers in to the mix and then see just how much your results change. You might be surprised to see just how much the drivers' own phase response mucks up the results of "crossover only" modeling. It should be pretty easy to include a driver model in your SPICE simulations.

-Charlie

As you requested, the anlysis now includes driver models for mid-bass and mid-range sections.

JRM
 
Hmmm, OK now this is getting interesting. Your last figure caption:

Fig. 15 Spice simulation as in Fig. 14, optimized 3rd order Butterworth including drivers and LFEQ for Sec. B and C.

LFEQ implemented as inverse 2nd order high-pass filter with F and Q same as driver.

MLSSA analysis in a semi-anechoic environment has validated the efficacy of the LFEQ compensation.

Since you didn't provide details, I am assuming that you are essentially flattening the response of the driver to DC using equalization. This would push the phase response down to DC as well, essentially removing it. However, if that is the case, is the result not essentially a first order filter on the driver, for the low pass section?

Can you provide more details about this approach?

-Charlie
 
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Our LFEQ implementation of inverse 2nd order high pass filter is a proprietary design. However, it only provides enough boost to make the summed response reasonably flat in the crossover region, based on the requirements of specific drivers. With 3rd order filters, the boost need only extend down about 1 octave, typically.
Replacing the 3rd order high pass filter for the upper section with a first order high pass will not give the right answer because there would be no way to account for the Fc and Q of the upper section driver(+box). We experimented with that approach, but after mathmatical analysis, realized it was not a viable solution. Our approach provides exact compensation for any Fc, Q of the upper section at any crossover frequency, as verified mathmatically and by measurements. Actually, if the Q of the upper driver(+box) is 1, then with a first order high pass tuned to it's Fc, the approach will work, but the crossover would then have to be fixed at the Fc of the upper driver(+box).

JRM
 
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Our LFEQ implementation of inverse 2nd order high pass filter is a proprietary design. However, it only provides enough boost to make the summed response reasonably flat in the crossover region, based on the requirements of specific drivers. With 3rd order filters, the boost need only extend down about 1 octave, typically.

This is a DIY forum. People usually share design info to expand and share knowledge, but I understand if you must keep it "proprietary".

My concern is that your "inverse second order filter" is reducing the attenuation provided by the 3rd order Butterworth filter in that one octave where you are boosting. I can imagine how your proprietary circuit works, however since you don't give any details, I can't be sure. I assume that you only do this for the HP part of the filter, in order to change the phase characteristics of the driver+filter+inverse filter so that you get flatter frequency response and smoother overall phase response.

It seems to share some characteristics of subtractive type filters, e.g. HP = 1 - LP, including the reduction in overall attenuation to 6dB/octave.

Anyway, thanks for the info, even if it's somewhat limited in depth/scope. It's always interesting to see different approaches to crossover and loudspeaker design.

-Charlie
 
It seems to share some characteristics of subtractive type filters, e.g. HP = 1 - LP, including the reduction in overall attenuation to 6dB/octave.

Aside from the fact that not all subtractive crossovers have 6dB/Octave attenuation one has to pay attention on the crossover point. If your tweeter's original resonant frequency is 1 kHz and you EQ it flat to 500 Hz and at the same time you cross over at 2 kHz with 18 dB / Octave then you actually have 18 dB / Octave between 1 and 2 kHz and then it continues with 6 dB/Octave down to 500 Hz where it turns into 18 dB /Octave again. Which would be sufficient IMO.


Regards

Charles
 
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You can implement the inverse 2nd order high pass anyway you choose, you will get the same answer, as long as the transfer function is not corrupted. It is not a modification of the 3rd order crossover filters, it must be implemented with an additional gain stage. An inverse filter does not share any characteristics with subtractive filter topologies, which by the way, are inherently flawed. Also, it cannot be simulated with an equalizer type stage. It is the only way to accurately compensate the 2nd order high pass response of the driver(+box).

We are professional audio engineers and don't work for free. The purpose of this post was to clarify in a single document the analytical properties of various popular crossover topologies in 3-way and higher implementations. All of the information can be found scattered in various reference literature. The results should be considered a starting point for any subsequent design.

If we provide you with all the answers, what's the fun in "Do It Yourself"?
 
That's right, 3rd order is the practical limit for 3-way and higher. Non-inverting Sallen-Key will have unacceptable distortion.

What's the basis for that? Q too high? There are other topologies besides the SK... MFB for instance or leapfrog.

I really can't see any reason why 3rd order is any kind of limit. I'd like to see this explained in detail without a reference to your product page or proprietary technology. This is a DIY site...
 
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What's the basis for that? Q too high? There are other topologies besides the SK... MFB for instance or leapfrog.

I really can't see any reason why 3rd order is any kind of limit. I'd like to see this explained in detail without a reference to your product page or proprietary technology. This is a DIY site...
What web site? The analysis is too extensive to be contained within DIY, so an external link is provided. The answer to your question(s) are addressed there if you had bothered to look and read. All of the technical information used in the analysis is readily available in textbooks, technical journals, and on the internet for DIY'ers to find. The analysis is what it is, can't help if you don't like the results.
 
What web site? The analysis is too extensive to be contained within DIY, so an external link is provided. The answer to your question(s) are addressed there if you had bothered to look and read. All of the technical information used in the analysis is readily available in textbooks, technical journals, and on the internet for DIY'ers to find. The analysis is what it is, can't help if you don't like the results.

What web site you say??? It's the very one you linked to! Oh yes, I bothered to looked at your links before. One goes to a :no: product you are selling :no: and the other to a bunch of SPICE sims (your "Cascade" web page) that is such a random torrent of info that is is difficult to determine much of anything from it. And then you have the balls to say "its in the textbook"! This is a DIY web site where you are supposed to enter into discussions about these kind of things, not point to some unnamed textbook and say that the analysis is "too extensive"...

One thing I can say: It would be a bad idea to use crossovers with filters having 11th order. Have you heard of group delay? You should calculate that for your filters and system sum, and then compare that against the studies of GD audibility. There is a reason why the telephone company spent a lot of time investigating this phenomonon... 11th order will definitely be audible, so you are introducing a bad effect in your effort to reduce distortion. Why not just use a better suited driver in the first place? This is one of the main reasons why you don't see crossovers at orders higher than 5 or so (already 5th has pretty peaky GD).

It would be beneficial to all if you described the point of what you are simulating in your SPICE models instead of just posting "Oh hey everyone I just some more stuff, come take a look" which I can only assume is just another attempt to drive traffic to your crossover product page, which is one of the links you posted under the guise of "Additional info can be found here" although the only content on that page is for your $2,950.00 3PX8 crossover box. I find that pretty distasteful. :mad:
 
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There is no link to a commercial web site, or any external site, on the original analysis page. JRM Engineering does not have a web site.

I have noticed there are numerous threads which reference Linkwitz commercial web site, as well as other manufactirers, in order to clarify some technical point.

Spice simulation has no way to display group delay; group delay is calculated for 2nd and 3rd order topologies, Fig. 6,7,11,12,13. The term "excessive phase shift across the spectrum" implies group delay too high.

A local audiophile has built an 11th order 4-way system that has received some favorable observations, and that analysis was done to see if measured response agreed with theoretical. Another audiophile wanted to see results if implementing a 3-way version with 1st or 3rd order for the tweeter resulting in tweeter signal now only having 1 active gain stage = lower distortion in tweeter.

The purpose of the original post was to demonstrate the properties of various xover topologies which might be beyond the capabilities of average DIY'ers, to help them make a more informed decision about which design might yield acceptable results.

One cannot twist the math to justify one design over another. Given the facts, one has to decide which parameters one is willing to compromise.

An additional topic "Conclusions" has been added to the analysis. You may choose to agree or not.
 
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