This could get a bit long, I apologize in advance. I'm working toward a crossover circuit for audio. My plan is for a 4-way crossover, but to begin with I was experimenting with just a 2-way.

I should mention that my understanding of filter design is a shabby hodgpodge of (mostly useless) info from low-level EET textbooks, various internet findings I never bother to bookmark, The Art of Electronics and an older version of The Electronic Filter Design Handbook, which pretty much goes over my head. I see transfer functions and my eyes glaze over; I have no idea how to relate them to anything practical.

So in various readings I got the impression that Butterworth filters are the general type used for audio, but I wanted to give Bessel a shot as well. Linear phase sounds like a good idea in audio; I know there are commercially made "linear phase equalizers", so at least someone else must have thought it was a good idea too.

I started with the Bessel, making and testing a simple 4-pole low pass filter. Works as expected. Then I made a simple 4-pole high pass. Works as expected, including this note's mention of Bessel high pass filters not exhibiting phase linearity. Also notice about halfway down that note, there's a graph showing a combined low- and high-pass output, in which there's a slight bump around the design frequency.

When I summed my otherwise normal Bessel high- and low-pass filters, I end up with a drop of about 12dB around the design frequency. This makes no sense to me since taken individually, the low- and high-pass sections are (of course) 3dB down at the design frequency. This is where I need help. What could be causing this? Is it a phase issue?

One difference in the filters I designed from the Bessel designs most references give is that I followed The Art of Electronic's method of equal component design. Equal capacitors and equal resistors in each section, with gain greater than unity. The math behind this escapes me (those transfer functions again) but I followed the tables given and got the expected results when testing the filters individually. Is there something about this method that could be causing the dip where I should see a rise according to the Rane note?

Also let me preempt a couple of responses I expect:

Why not do this digitally? - Because I don't want to, and because that would be even more beyond me. The ultimate goal is an analog processor.
Anything about SPICE/simulation - I don't have any simulation software. I don't know of any for Mac OS.

 

It is normal to alter one of the filters to reduce the dip.

I don't know if you have a phase problem (probably not), or a loading problem, because I can't see the rest of the circuitry, but bumping (pun intended) the frequency of one of the filters is the normal cure.

I didn't go look this up, buy my memory is pretty good.

 

It is normal to alter one of the filters to reduce the dip.

I don't know if you have a phase problem (probably not), or a loading problem, because I can't see the rest of the circuitry, but bumping (pun intended) the frequency of one of the filters is the normal cure.

I didn't go look this up, buy my memory is pretty good.

But do you have any idea why I would get exactly the opposite result from the Rane note I linked? And why the combined dip is so pronounced when the individual response of each filter is not?

 

Adding an even-order lowpass filter and an even-order highpass filter produces a notch (cancellation) at their crossover frequency because their phase difference is exactly 180 degrees.

Even-order crossovers networks are supposed to have one driver (usually the tweeter) connected in opposite phase to the woofer so their filtered phases are the same at the crossover frequency.

 

Thank you guru. I didn't pay any attention to phases when I was reading the filter book a few decades ago. I guess I was going to leave that part for after I had anything at all working. Then, when it worked, I never thought I should go back and read some more.

Eh, kids...what can you do?

 

Many commercial speakers have a crossover network that creates a notch at the crossover frequency because their designers don't know nuttin.

Many 2-way car speakers use only one capacitor (in series with the tweeter) as a crossover network.

Many 3-way car speakers have a woofer, a mid-range and a photo of a tweeter.

 

Adding an even-order lowpass filter and an even-order highpass filter produces a notch (cancellation) at their crossover frequency because their phase difference is exactly 180 degrees.

Even-order crossovers networks are supposed to have one driver (usually the tweeter) connected in opposite phase to the woofer so their filtered phases are the same at the crossover frequency.

This isn't actually a crossover for speakers, it's intended for multiband signal processing. But a phase issue is one of the things I suspected. So if I flip the polarity of one of the filter outputs before adding together I should expect to see the notch disappear?

Still I don't understand why the Rane note on Bessel crossovers I linked shows a bump instead of a notch for the combined output.

Thanks for the help.

 

This isn't actually a crossover for speakers, it's intended for multiband signal processing. But a phase issue is one of the things I suspected. So if I flip the polarity of one of the filter outputs before adding together I should expect to see the notch disappear?

Still I don't understand why the Rane note on Bessel crossovers I linked shows a bump instead of a notch for the combined output.

A Linkwitz-Riley even-order crossover circuit eliminates the bump when one driver has its wires reversed.