Optimum crossover frequency?

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A lot of the time I find myself taking a step backwards and looking into the supposedly trivial to find a solution for the complex.

Often it is much more difficult to something simple than something difficult however strange this may sound.
Albert Einstein said "Everything should be made as simple as possible, but not simpler".
And I believe he was right. In simplicity lies the genius.

So onwards to the question at hand.

What are the optimum crossover frequencies one should aim fore and why?
Let's make life difficult and start with a 2-way speaker.

Even though I have read a bit in the past it would be great if you consider me a n0ob for the discussion's sake.

Obviously the drivers will post limits but lets assume we start with the crossover points and choose drivers to match.

Fletcher-Munson curves and the theory behind it talk about hearing sensitivity dependant on frequency. Where will the crossover be most detectable to the human hearing and where is it easier to get away with?

Most of us I believe like to have bass packing a good punch but we dont want to have a bad midrange.

Talking about bass we probably want to go low as well and that will have a serious impact on the choice of driver.

Then we have the matching of phase, impulse response and directivity.
Everything is supposed to blend nicely togeather.

And last but not least we have sonic signature and type of enclosure. Not everything will blend well.

How do you do it?
Where do you actually start?
What is the best target frequency for the crossover?
Is there a way to have it all?
What are the compromises?

In this particular thread I would like to focus on finding the optimum crossover frequency taking into account human hearing and perception.
 
If you consider directivity down to the hundred hertz and up to the Khz area to be important, a two way becomes very difficult. If you go really low, and loud, you get doppler distorsion too. Depending on your room, you may also not want the lows to be placed at the same physical point of the midrange.
What amazes me is that you still read in French Hifi magazines about these two ways that cross the tweeter around 3k that they avoid the most sensitive zone, which is pure BS, it's a lie, that's exactly the MOST sensitive zone and you know why they do it, because a tweeter that crosses lower is expensive. And people don't check, whilst they woofer is beaming like hell.
I actually read Greisinger's last paper again yesterday, if you want to have a look..the one about Pitch. Really interesting.

http://www.davidgriesinger.com/
 
I start with a driver that tickles me, see where it needs to be crossed with regards to dispersion, FR and, if known, distortion and then find another that is suitable.

But may be I'm doing it wrong.

Other than that I generally agree with lolo. 3k is usually way to high for 2way unless you use the tiniest of midwoofers and the 2.8-3.5k region is where the ear is the most sensitive.
I also like to cross drivers steeply (and actively) within their linear response region so I don't have to bother too much about electrical and acoustical slopes.
 
There is one, and only one, correct answer to your question: "It depends"

Some simple questions just plain have no simple answers. Even two designers building a speaker in the same box will have very different ideas. Go look at the ZAPH design competition. Same two drivers, same box, many different "optimal" choices.
 
Ah, the engineer answer... ;)
I'm not so much looking for a single answer as much as a discussion where one can make up his/her own mind based on your own preferences.

3k sounds awfully high and smack in the middle of the sensitive area.
I was tinking maybe 1.5kHz +/- 0.5kHz?
I don't have an answer myself so I'm curious to hear what you people thinka about the subject.
 
If you want some opinion backed up by expertise, experiment read Dr Geddes justification for directivity control with CD waveguides for small room acoustics - resulting phsyics constraints leading to his 2-way speaker designs
http://www.gedlee.com/ and here at diyAudio

very aproximately - need tweeter waveguide and mid/woofer dia to ~match for smooth directivity over XO frequency range

lowest possible XO frequency is enabled by compression driver with large dia waveguide's efficiency - below 1 kHz with Suma 15" waveguide and 15" LF driver
 
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Do read the above discussion by the good Dr. Earl.

If you insist on some elaboration,
In practice.... I find very few conventional one inch tweeters that behave in acceptable distortion or energy decay below 2K or so. SB29, lower, XT25, higher. It depends. I find precious few mid-bass that can get much higher than 2.6K without impinging on breakup problems. Metal being more difficult than coated paper. It depends. Slope matters, to keep away from resonance peaks and breakup modes, a steeper crossover may allow a different crossover than a shallow crossover. It depends. Does it give that much advantage in more uniform off-axis response, or is the complexity of the crossover going to overshadow the gains? It depends. Does you environment depend more or less on diffuse or primary reflections? It depends. How loud? In my office, I may get away with a lessor slope, or lower crossover because the levels are not what I use in my living room. It depends.
 
For reference, my most successful to date are LR4 acoustic at 2.6K. Seas drivers. My next most acceptable pair are Daytons with Seas tweeters at 2.4K, asymmetrical 3rd/4th acoustic crossover. These were finalized by the physics of the drivers, my bank account, and when I just plain reached as far as I wanted to go on a given project. The pair I am working on right now is first order at 4.5K. How did I go so high? Fountek FE85 which is a 2 1/2 inch full range, A.K.A. a midrange. Computer desktops so 125 F3 is just fine. It depends.
 
agreed. My mains are xo at 3.5k 2nd order, actual slope nearer to 3rd or higher. No issue with my mids. Trying to push higher and use ribbons instead i mod xo to 4k. Not bad but the change in polars was discernable. Im currently playing with an Alpair 5 playing to 6k and the ribbon from 6k. Both 2nd order. The polars seem to match very well. Next i aim to try the 1st order LP for the woofer that will underpin the whole design. In short a 3" mid is the easiest match, for me, to keep polar pattern behaved thru the range 500-5khz, and match my ribbons. Surprisingly they dont complain at the 2nd order @ 6k. THAT made my day.
 
Where do you actually start?
What is the best target frequency for the crossover?
Is there a way to have it all?
What are the compromises?

In this particular thread I would like to focus on finding the optimum crossover frequency taking into account human hearing and perception.


Start with a design goal, knowing trade-offs involved in that design.


The best target freq. for a crossover is relational to the driver's performance on a real baffle (..assuming a baffle is used).



I'll take a brief look into one aspect of a loudspeaker's design:

The low-pass filter freq. "limit".


In a traditional multi-way design (particularly with "cone" drivers), a good place to start with regard to a low-pass filter is simply looking at the driver's diaphragm diameter in relation to wavelengths. For a shot at maximum performance at higher freq.s, crossover an octave (or more) lower than the driver-diameter's wavelength.

Ex. 6.5" driver typically has a **cone/diaphragm** diameter (not surround) around 5". Start plugging in freq.s to a wavelength calculator until you come up with that distance: Wavelength

2.7 kHz in this case. Then divide that number by 2 = 1.35 kHz for the max low-pass filter upper freq. limit.

Again though, that's for a shot at getting *maximum* performance from the speaker at it's upper freq..

It's a generic starting-point where you start to make compromises. Often a bit higher in freq. for a higher order filter, lower for a very low order filter. (..an "average" filter would likely be a LR 2nd order.)


This design constraint imposes several favorable qualities:

1. typically similar dispersion matching between drivers at crossover on a standard baffle,

2.* usually (or primarily) within piston operation (..as opposed to bending-wave operation),

3. wavelength vs. acoustic center for the two drivers being crossed over have a better chance of producing fewer combing artifacts, and

4. moving mass of the driver tends to be better at the top of its pass-band. (i.e. the higher the freq. the lower the mass - produces better results both objectively and subjectively.)

*piston operation is a more linear mode of operation (..and is how the driver is designed to operate), however even at this relatively low low-pass freq. you still need to be concerned with un-damped modes in the cone "bouncing" off of the surround and interacting with each other - which tends to produce a dip in response with a resulting linear resonant mode (..which can easily be seen in a CSD plot).

Ex. Tangband W4-1757S at 2.1 kHz
http://www.zaphaudio.com/temp/Tangband-W4-1757S-CSD.gif

(..a resonant build-up in the cone profile insufficiently damped by the surround. Note: this is a flat-profile diaphragm that exacerbates this condition).

Note that this is different than the break-up mode(s) of the particular driver. Break-up mode(s) occur at a point where the driver is no longer operating as a piston (..which tends to be slightly higher in freq. than the wavelength of the diaphragm's diameter). Of course moving an octave lower for the low-pass than the break-up modes of the driver is one of the major benefits under #2 above.
 
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My (activley biamped) 2-way speakers are crossed at 450 Hz LR/24 to the bass bin and 380 Hz LR/24 to the tweeter (a 2" driver). I always thought the crossover would be at the same Hz or the tweeter might cross higher. I never expected a tweeter driver, even a 2" might be crossed lower than the bass bin.
 
I built a pair of 3-way speakers

Used 375Hz for the woofer to mids and 6KHz for the 3" mid to tweeter crossover points. Found that I prefer the crossover points to be well out of the traditional female vocal range and let one driver take care of that.

In a way, it reminds me of the "helper woofer" and "helper tweeter" the full range speaker crew advocates but not the 150Hz and 10KHz cross points.

Since I "steal" information from the full range forum, the multi-way forum and the subwoofer forum... I don't follow any specific acoustic religion.

Thankfully, the concept of taking a full range, adding a tweeter and running an active woofer at 200Hz and down is much easier now. With the price of inductors going through the roof, adding a 100 watt amplifier with 200Hz active filtering is getting close to price parity with passive.

My next project will be just that, Mark Audio 5" full range, small tweeter crossing at around 8K or so with just a cap and a 100 watt active amp with electronic filter. A simple T amp to drive the wide band mid/tweeter at 10 watts or so and the 100 watt amp to drive the inefficient 6.25" subwoofer. My theory is to crossover way out of the vocal/guitar/piano bands and adjust the bass actively with plenty of power to spare for computer based EQ. The desktop speakers will then be complete.
 
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Like tvrgeek said, it depends! what does it depend on? Well I would say a lot of things but most importantly it depends on what compromises you are willing to make, and on how the chosen drivers actually perform.

I would suggest that unless you have very well matched and behaved drivers that the "best" crossover point is going to be more dependent on the drivers and baffle setup than it is on any theoretical best point :)

for my MTM's I ended up going with 2.8Khz 4th order acoustic Bessel because that was what worked best for me.

Attached are off axis measurements mids are 5" units. I think that the result is quite acceptable personally :) I will eventually be adding in my 10" stereo subs somewhere between 200 and 300Hz but they play very nicely as is right now.

Tony.
 

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Narrow directivity isn't thought to be as important at 500Hz as we aren't as sensitive down here. An omni pattern (as most speakers will either have or be moving towards) will still support reflections that cause colourations, but we all deal with those.
 
It's been a busy weekend on my part and I feel like I'm close to flatlining my eeg at the moment but I'll post a thought anyway.

Looking at equal loudness-contour plots hearing looks to shouw roughly the same sensitivity between 500Hz and 4kHz at 80Phon which would indicate a reasonable listening level (80dB). (2-4kHz extra sensitive)

Human voice fundamentals are often referred to as 80-1100Hz.
I've seen claims that advocate frequencies above the previously mentioned 1100Hz as very important to details and nuances in voices and music.
Frequencies above 5kHz doesn't look to important for voices. Some added details but nothing critical.

Combining the equal-loudness plots/hearing sensitivity with human vocal range, keeping the crossover as low as possible looks sensible.
A wideband/fullrange speaker crossed to a woofer looks like an interesting alternative.

Geddes designs with waveguides put the x-over in the 1-1.5kHz area somewhere I think?
This would be well withing the sensitive (but not super sensitive) area of hearing perception but still allowing the tweeter to handle most of the important nuances.

Linkwitz also seem to favour a crossover in the 1-1.5kHz area when you look at both the Pluto and the Orion.

Geddes looks to be relying much on directivity control and phase coherence?
From what I've read phase coherence is importat at the crossover +/- 1 octave depending on the order of the filter.

I haven't really been able to grasp the directivity bit fully so far.

It's much like laying a puzzle with an image of half ocean and half sky. Definately a challenge.
These are just a few thoughts of mine, I'm very much learning from you guys.

The rule of thumb mentioned above using a crossover at least one octave below the matching wavelength for the driver diameter seems to fall within sound design thinking. :)

I'll stop my rambling now.

P.S. Reasonably sized horns and waveguides seem to have a hard times handeling frequencies below 1kHz or am I imagining things? (Just looking at the high frequency spectrum at this point, not counting mid or bass horns.)

Let's hope I haven't confused everything. Lol
 
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