Crossovers, frequencies and rolloff slopes (1 Viewer)

[Saurav]

Hi,
I posted this over on a different board, but got no responses. I decided to try the DIY board on HTF, since the more technically inclined people seem to hang out here. I hope this post qualifies for this board, because I'm asking for information on building a line level crossover, so technically this is related to DIY
Here's my original post. I don't expect anyone on this board has built the GR Research Paradox 1 kit, so please ignore the question(s) specific to that speaker.
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Could someone help me with some theory please? I'm trying to understand the issues involved in adding a subwoofer (probably an Adire Rava) to small monitor speakers (in this case, GR Research Paradox 1) using a line level crossover (because my 8W tube amps would be happier without the bass). This isn't a question about line level vs. speaker level - I've found enough on that in the archives, and I think I have some idea of the pros and cons involved. Anyway, here are some of the "rules of thumb" that I've come across:
* Bass above about 80 Hz is "directional", so it should typically not be going to a mono (summed bass) subwoofer.
* The XO point should be chosen so that the sub can play "flat" for an octave above it, and the mains can play "flat" for an octave below it. "Flat" here is defined as the -3dB point, as I understand it.
* 2-way 4th order Linkwitz-Riley crossovers are supposedly a good thing, for phase and amplitude considerations.
The Paradoxes are "fairly flat till 50 Hz, after which they fall off pretty steeply". I'm not sure what that translates to exactly in terms of crossover order.
Questions:
* What is the reason for the "flat to an octave below" dictum? Is this based on an assumption of speaker rolloffs usually being of X order and subwoofer rolloffs usually being of Y order?
* Specific question for the Paradox 1's internal crossover, if anyone can answer this - is that 50Hz a property of the mid/bass driver, or is it in the electronics? Is there any way to change that crossover so that the "handoff" between the drivers stays the same, but the behavior around the 50Hz cutoff point is made flatter?
* Let's assume the above is possible, and also assume that I can disable the XO on the sub (turning it up all the way is the only solution I can see, and I don't know what this does to the phase). Now, if I have an active line-level 2-way XO feeding both the sub and the main amps - does the "flat to an octave below" rule still apply?
Basically, the vague idea I have right now is that I would probably be better off if I had full control (or, as much control as possible) on the high-pass and low-pass filter slopes, instead of trying to match the filter designs in the speaker and subwoofer. With my limited understanding, the 4th order L-R seems like a good choice for such an application. It also looks like I should try to 'disable' the inherent slopes of the speaker and subwoofer so that they don't interact with the XO's roloff.
Those are my thoughts so far. I would really appreciate it if someone more knowledgable in these matters could shed some light on this.
Thanks in advance,
Saurav

 

[Patrick Sun]

For your reasoning edification:

Theoretically the order of a filter yields multiples of -6dB/octave to the slope at the corner frequency where the filter "kicks" in.

L-R filters are supposed to be -6dB at their corner frequency, and when low pass and high pass filter responses are summed, you should get a flat response at the crossover frequency region.

Butterworth filters are supposed to be -3dB at their corner frequency, and when you sum the filter responses together, you'll get a 3dB bump at the crossover frequency.

So if you have a 4th order L-R high pass filter at 80Hz, then, at 80Hz, the response should be -6dB down (from its nominal response an octave above 80Hz, around 160Hz), and the slope of of the adjacent octave (down to 40Hz) should provide -24dB of attenuation around 40Hz (from its nominal value of 160Hz). That's very strong roll-off in that region.

The lesser the order of the filter, the less the filter will roll off the response.

Bear in mind, this is just talking about theoretical filters. Each reactive component (inductor/capacitor) adds an order to the circuit when used in the conventional series/parallel connection.

The main objective is to produce the acoustical order filter response you desire by using the electrical filters (so you can take advantage of driver roll-off and incorporate the natural roll-off without have to add more components in the filters).

For some woofer drivers, to achieve a L-R 4th order roll-off around 2KHz, it may take just 2 components (an inductor with a capacitor in parallel) to produce the acoustical L-R 4th order roll-off when you take the driver's natural tendencies in that upper frequency range. Other times, it may take 3 or 4 components to get the job done. But in the final analysis, it's the acoustical response you are after, not just the number of electrical components to get there.

 

[Saurav]

Thanks for the response, that clarifies some things. Of course, it also creates more questions. For starters, I'll be building a 2-way line level crossover, to go between my monitors (and the amps driving them) and a powered subwoofer. The crossover inside the speaker is, I believe, a series crossover, I'm not sure what the order is. Anyway, I'm trying to figure out what I need to do with the line level XO to get smooth integration of the sub with the monitors.

The main objective is to produce the acoustical order filter response you desire by using the electrical filters (so you can take advantage of driver roll-off and incorporate the natural roll-off without have to add more components in the filters).

OK, I understand that. So, if the final acoustic rolloff is 4th order L-R on both the high-pass and low-pass sections, that will give me what I want. Which means, I should try and design the XO to try and get close to an effective 4th order L-R when combined with the acoustic/electronic rolloff of the speaker.

Is that more-or-less correct?

 

[Patrick Sun]

Yah.

 

[Saurav]

Thanks