Amplitude Errors in the Summed Response of Audio Crossover Filters

[JrmEng]

Hope you find this useful:

http://xenotron.home.comcast.net/Cascade.htm

JRM

[CharlieLaub]

Originally Posted by JrmEng

Hope you find this useful:

Amplitude Errors in the Summed Response of Audio Crossover

JRM

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

[JrmEng]

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

[Speedskater]

Siegfried Linkwitz just updated his page on a similar topic:

Woofer crossover & offset

[JrmEng]

Originally Posted by CharlieLaub

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

[CharlieLaub]

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

[JrmEng]

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

[CharlieLaub]

Originally Posted by JrmEng

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

[phase_accurate]

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

[JrmEng]

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"?