Mixed-slope crossovers

[Saurav]

I've seen many examples of elliptical-style crossovers where a notch filter is used to increase the crossover slope in the immediate stop-band, while relaxing it (sometimes with a bounce) as you get further into the stop-band. I'm assuming the primary reason to do that is the get the higher initial slope without increasing the component count. In other words, an LR4 with a notch that gives you initial LR8, can be built with fewer components than a regular LR8 crossover.

So, first question, is that reasoning correct for the reason why someone would try this? Meaning, is there any advantage to the fact that the transfer function bounces up, and settles down to LR4, or is that a side effect of getting LR8 in the initial octave?

And then, getting to what I was thinking about - as I understand it, one of the downsides of high order crossovers is a sharper notch in the power response at the crossover frequency. So I was wondering, how would it work to turn things around? I was considering a crossover that was B3 over the first octave, then transitioned to B5 for the rest of the stop-band. Or L2 / L4. If I'm thinking about this right, that should give me smoother power response through the crossover region, while still giving me better driver protection as I get further into the stop-band.

I'm sure there's stuff I'm missing, so I figured I'd ask first before I try building something. How would these crossovers sum? I have no idea, but I can probably sim something up in Speaker Workshop and/or LspCAD. With a digital crossover, the component count becomes mostly a non-issue. With the DCX I'd have to use the XO and notch filters to arrive at the target response, but if I had something like the miniDSP with the custom biquad plugins, I believe I can set up multiple HP and LP filters on the same channel, so I could implement something like this more directly.

I'm sure I'm not the first one who's thought of something like this, so any insight into this would be helpful. Is it a good idea? Reasons why it won't work? Worth giving it a shot? And so on.

Thanks.

[Saurav]

I threw an L2/L4 sum together in Speaker Workshop. I'm actually more interested in B3/B5, but SW can't do a B5 curve.

Anyway, the LP (LR2 @ 2kHz, LR4 @ 4kHz, then multiplied together):



Same for the HP - LR2 @ 2kHz, LR4 @ 1kHz:



And the sum:



Red is with one driver inverted. Hmm, now that I look at this, I'm not sure what this means, or if it's worth pursuing. The in-phase sum isn't too bad, the lowest point of the ripple is -1.2dB my driver response would be worse than that. The reversed response... I guess it looks like LR2 in the middle, with LR4 on the sides?

I also tried a .02ms delay in the LP response, and the overall response didn't change much, maybe by 0.2dB at the most. So this shouldn't be too sensitive to AC offset, if I'm reading this right?

This may just be a pointless academic exercise I'll see if I can get a B3/B5 sim with LspCAD. I could also try pushing the LR2 and LR4 corner frequencies further apart.

[BOBinGA]

This looks a lot like John K's transient perfect second order filter. He used to have a paper on it one his site, but I think he withdrew it. Curt also did a speaker (the Mavericks I think) with a transient perfect second order cross. But it does the same thing. It starts out first order and adds in a second order filter to arrive at something in between. He solved the problem of the ripple in the response by making the filters with a high Q which added a bump in each where there would be a null with the lower Q filters.

-Bob

[Saurav]

Thanks, that's great info. I'll go look for those references. Using a high-Q filter to fill in the dips sounds like a great idea, I wouldn't have thought of that. I was thinking in terms of the DCX, where I could add some 'global' (i.e. on the input) EQ around the XO frequency.

I don't know how to calculate the impulse or step response of these transfer functions. And honestly, I really wasn't thinking about that when I had this idea. I was mostly wondering about how I could get a B3 power response from my drivers, specifically, the Neo3, which won't really work with a straight B3 crossover at 1800Hz, which is what I'd like to do. So I thought about mixing B3 and B5 to get the protection the tweeter needs.

What would be interesting would be to find out a way to calculate the power response of these crossovers.

[Saurav]

Played around with LspCAD for a bit. Here's an attempt at making a B5 filter using an LR4 and some notch filters:



And here's how well that matches with a B5 target:



This is with 30 seconds in the optimizer, range set to 1 octave on either side.

Summed response:



Not sure if that's better than the L2/L4 case. With that, a shallow peak filter right at the crossover would raise everything nicely, but this swings around 0dB in both directions.

Of course, I can't build the crossover I've shown here, with 2 DCX blocks per channel. I'll have to use the combined output as a target, and optimize a single block to that. But first, I can try improving the targets to something that sums flatter by changing filter / notch Q, while still maintaining the overall B3-going-to-B5 (or L2->L4) transfer function.

But the real question is, what does this buy me over a straight LR4 crossover. I got here by thinking about B3 vs. LR4 power response. But I have no idea how to calculate the power response for this pair of transfer functions.