Crossover Experts! Hole in 12dB/octave, (both sides), response? Help!!

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diyAudio Moderator Emeritus
Joined 2001
Years ago., the loudspeaker books were telling us that if you have a 12 dB/octave slope on both sides, there will be a hole in the response right at the crossover frequency.

Therefore, they recommended that the higher frequency speaker-either the midrange or the tweeter-reverse it's polarity when hooked up to a 12 dB/octave crossover.

I am told that this solution is little used today.

Two questions, then.

A) Is there in fact a hole in the middle of the response at the crossover frequency in a 12 dB?octave, (both sides) crossover?

B) If so, and they don't reverse the polarity of one of the speakers, then what methods do they use to deal with it?
A) Yes.

B) I'm not a crossover expert, but I would imagine that the next best thing to reversing the tweeter's polarity is to introduce an approriate amount of delay to either driver. Delay network(s) or offsetting either driver can introduce the needed phase difference. I would imagine a delay somewhere around 180/(360*fc) is a good starting point. But this delay seems to introduce ripples around and above the crossover point, fc.

You could probably offset either driver. Personally, I'd rather reverse the tweeter's polarity :)

hth :)
diyAudio Moderator Emeritus
Joined 2001

Thanks for the response. I should have mentioned that I was talking about passive crossover networks. With all the emphasis on active crossover networks today, I should have made that clear.

A) Is what you are talking about-2 Linkwitz-Riley networks in series-attainable in a passive crossover?

B) If the two drivers together add 3 dB, should we then tailor our crossover so that the respnse of each driver is 3 dB down at the crossover point? I know that seems obvious, but I thought I would make sure.

Finally, I would like to invite you to add your thoughts to the related thread here:

PS: Am going to Linkwitz's website right now.
diyAudio Moderator Emeritus
Joined 2001

So there is a hole! Thought so.

Okay, suppose I wanted to dodge this by keeping the woofer a 12 dB/octave slope but making the tweeter:

A) A 6 dB/octave network. Does this eliminate the hole? If so, how many dB should the tweeter be at crossover?

B) An 18 dB/octave slope. Does this eliminate the hole? If so, how many dB should the tweeter be at crossover?

I have read some loudspeaker designers are less than enthusiastic about having one driver's slope even order and the other driver's slope odd order, but it seems to me a nice way to dodge a problem. Have you heard of any big problems with making one slope odd and the other even?

I fully realize that there is no such thing as a perfect passive crossover. If you want an advantage in one direction, you have to give up something else. Everything is an uneasy compromise.

I'm just looking for reasonably flat on-axis and off-axis response. I really don't care that much about a 1 dB ripple here or there. That is not really hearable to a normal person, and the drivers have ripples themselves.

Finally, I would appreciate any thoughts you might have on this related thread:
A, B) The null would be reduced. But you'd really have to experiment with actual measurements rather than theoretical data to know for sure.

I'm not sure why it would be bad to have unequal order filter slopes, but if it gets the job done, why not :) Experienced builders might have more to say on this :) The example filter I applied to the DIY2000 FRD files can be seen at Crossover Simulator's site. As you can see, a 2nd-order LP filter with a 3rd-order HP filter produces a reasonably flat system response (though I should mention the actual woofer delay of 70uS was not considered in the above example filter set).

As much as I'd like to recommend xoversim, it is not yet finished. Have you tried Speaker Workshop for your current 2-way project?
diyAudio Moderator Emeritus
Joined 2001

Thanks for the response. I eagerly await the release of Crossover Simulator.

I've tried to get Speaker Workshop going on my computer but it always seems to be more involved than I have time for. This might be a good time to give it another crack.

I have done some measurements that lead me to believe that there is positive reinforcement between woofer and tweeter when the centers of the drivers are one wavelength apart at the crossover frequency. The measurements did not outright prove it, but they did suggest it.

I have also read some mention of positive reinforcement at the wavelength and negative reinforcement at the half wavelength .

I did not see any mention in Crossover Simulator about the space between the centers of the drivers you are trying to cross over. Do you plan to take this phenomenon, (if it exists), into account?

I would think that might be important.
Joined 2002

One aspect of the complete system that your overlooking is that the woofer response is attenuating at about 6db/octave near your proposed crossover point. This will add a 1st order slope and phase shift to any xover you use. So if you use a 2nd order, 12db/oct xover the woofer response will have a 3rd order, 18db/oct lowpass cutoff slope.

I'm not sure what this will do to the total response, but it won't be the theoretical response of the symetrical 2nd order butterworth filter.

Rodd Yamashita
A) It is posible to obtain passive Riley-Linkwitz filters by adding two identical butterworth filters,the resulting filter is a 4th order high or low pass.
B) The high and the low pass is down -6db at crossover frequency(because the 2 butterworthfilters they consist of have -3db each),one branch has +180 degree phase,the other -180 degrees,so you don't have to invert your tweeter.
2 times -6db add up to -3db because they are in phase,the fact that both drivers work in phase add another +3db's ,it's the ideal crossover for D'appolito speakers.
You'll get a maximum flat response on axis.
If I may clarify, two drivers both at -6dB and in-phase when added sum to 0dB, remember that you're adding acoustic pressure or volume velocity values, which means you would use 20, not 10, in front of log10(). You would use 10*log10() if you were adding power levels.

2nd and 4th order Butterworth filters sum with a 3dB bump at the crossover frequency while LR filters sum flat. Linkwitz-Riley filters are all even-order filters for the reason presented by yeti :) You can also have 2nd-order LR filters -- cascade two 1st-order Butterworth filters.

diyAudio Moderator Emeritus
Joined 2001
Thank you all very much. Great answers here from everyone.

Roddy: You are right! The woofer does roll off at 6 dB/octave, how could I have missed that? I am going to have to think about using the woofer's natural rolloff alone or adding an inductor to make it 12 dB/octave.

Yeti, F4ier, Schizeckinosy: Than you for your time explaining 12 dB/octave crossovers to me. Frankly, up until know ai just kept subsituting values until I got a reasonably flat on-axis response. Now I can take a more informed approach.
diyAudio Moderator Emeritus
Joined 2001
Okay, that still leaves 2 questions:

1) The positive reinforcement if the centers are one wavelenth apart at crossover frequency. Does this happen and how do I compenste if it does? I am thinking of running some tests this weekend to finally settle this anyway. But I am always open to someone else's experience.

2) How about if I use a 6 dB/octave slope on the tweeter crossing over at 1800 Hz. Is that advisable? It is a Peerless 811815 tweeter. In the past, they usually said that a dome tweeter should have a 12 dB/octave or greater slope if it crosses over at 2,000. Is that still the rule today?

Again, thank everyone very much for the help you have already given.
Joined 2002
Hi Kelticwizard,

If you're in the experimentation mode, there might be a couple things you could try.

If the 12db/oct Butterworth (hi and lo) is suppose to give you a bump in the response at xover, reverse the polarity to give you an electrical null at xover (The lo-pass would be 6db/oct natural roll-off + 1st order filter). The driver spacing should than give you an acoustical boost at x-over and the total response will be flat. Mind you, this is strickly theoretical.

Another idea might be to stagger the hi-pass and lo-pass cut-off points. Using the natural roll-off of the woofer for the lo-pass + a 1st order filter, and moving the hi-pass cut-off to 2000Hz or 2200Hz or ????Hz. Do not use less then a 12db/oct slope on the tweeter because you're too close to it f3 as is. The idea is to spread the cut-offs far enough apart to create an electrical null between them and again use the acoustical boost of the driver spacing to fill the gap.

Just some thoughts; have fun.
Rodd Yamashita
I believe it's worth it to think about 1st order filters,because they have an excellent impulse response.
The problem is that you need bass-drivers that go at least one octave above the crossover point and a tweeter that is capable of handling the frequency one octave below the crossover point.
There were approaches that used two 6" drivers and a 1" tweeter inbetween at xover frequencies between 1800 and 2500 Hz.
You can match the response by shifting the xover frequencies for both branches of the filter.
I myself used a MP capacitor (the kind you find on motors) for the high pass.
Although they were reasonably priced, they delivered a stunning stereophonic panorama.


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