First Order Crossovers: Pros and Cons

I hear what you are saying about xovers, Roy.
But the fact remains that in there own pass bands tweeter and woofer are
working 90deg apart. If I now want to replay say a large cymbal with a fundamental at 440Hz and strong harmonics all the way beyond our hearing range (in our case past the xover point) it still means the fundamental will be 90deg out of phase with (some of) its harmonics.
I don't really care what vectors do as I don't hear vectors but I hear phasing.
We all do since, with the exception stereo recordings, all our spatial information derives from phase differences. You can test that next time you have a bad headcold that cloggs up one ear: Listen to your stereo and its like mono, go outside and you can easily tell where a noise comes from. This also works with a small ball of cotton wool, if you haven't got a cold handy.
But anyway, what I understand as phase coherent means that the entire output is in phase ideally independent of listening position.
The only speakers capable of this are full-range, single driver designs.
But Tannoy makes an acceptable(to me) compromise. Seperate drivers on a vertical line are just one step too far for me.

Still can't accept your time/phase 'explanations' it goes against everything I have ever learned and would directly contradict my two relevant college lecturers, my Professor at the Technical University Berlin ,
Guy R. Fountain ( Founder Tannoy)
Peter Walker ( Founder, Quad)
Peter Voigt ( Lowther )
and pretty much everybody else I know who's worked with AC current and/or acoustics. I don't think your lone voice is enough for me to budge on that one.Again lets look at sinewaves and lets only regard 3 points (max., null point and minimum)of it curve for the moment: to be time coherent 2 sine waves need only to start at the same moment, they could start at any of our 3 points: max and falling; min and rising; nullpoint either rising or falling.
Thus we have 4 ways in which our two sine waves can be in time.
To be in phase our 2 waves have not only start at the same moment but also the same point. There are now 3 ways in which our 2 waves are in time but not in phase.

You mention some distortion regarding my Tannoys, fair enough they distort. So do all speakers, but of course total distortion is very easily measured and mine measure up thus: for 90dB SPL, 50Hz-20kHz less than 1%;for 110dB less than 3%. How do yours do?

The thing with your test tones is quite amusing since you should be using pink noise or white noise to measure for phase coherence. Its not difficult to find a driver thats in phase with itself and one single tone from another but that does not make it phase coherent.

I'm sure you could hear the comb-filtering going on if you'd honestly compare to speakers which do not exhibit this particular problem.
I can and, compared to some people, my hearing isn't that good.
Its the comb filter effect thats (partially) responsible for the sweet spot ie the sweet spot is the area where the comb filtering is at its minimum. With speakers that emulate the point-source ideal (planars,Tannoy DC's and full-range drivers) this is much less pronounced although fr-drivers teend to produce their own version of the sweet spot due to beaming.

Some great points from Golix and i agree with some of the points that he's making here too. This is the reason that i love my modified Ohm F's, warts and all, and why i've said what i have about them. You've got one driver that is both phase and time coherent, covering the entire audible range with great bass weight and a phenomenally spacious radiation pattern. Other than that, and as i've mentioned before, any other attempt at loudspeaker design becomes extremely complex with multitudes of trade-off's involved. Juggling the trade-off's boils down to the personal preferences of the design engineer and the individual buying / listening to the speakers. As such, it is a no-win argument, just a discussion of various beliefs and preferences. There is only one way to achieve specific levels of performance, and at this time, even that approach has limitations. Sean
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Golix: I have to back up Roy on this. In a first-order, both drivers are at zero phase in their PASSbands, and at 90 degrees in their STOPbands. (Close, anyway. The only places either of them truly reach 0 or 90 is at DC and at infinity, both of which are well outside the audioband.)

However, when either driver is at 90, the output amplitude is ZERO, by definition, so it contributes nothing to the sound. Its major contribution comes within its PASSband, where its phase is close to zero.

Now, in beween DC and infinity, both drivers make a contribution depending on the frequency relative to the crossover frequency. In a first-order, they are ALWAYS 90 degrees out of phase, regardless of the frequency, and they ALWAYS sum to unity and zero phase. If this isn't clear, you need to look into the math (including complex variables and vector addition).

At the crossover point, for example, one driver is at .707, +45, and the other is at .707, -45, as I stated previously. Due to the fact that this is vector addition, they sum to unity at zero phase. And they do this not only at the crossover frequency, but at every single point from DC to infinity. The first-order is the only crossover that does this.

If you wish to prove this to yourself, it is easily proved by doing some math. If you want to avoid the math, it can still be proved by simply drawing sine waves. First, draw a single sine wave with amplitude of 1.0 and any phase you choose. Next, draw two identical sine waves, each of amplitude .707, one shifted 1/8 wavelength to the left of the original one, and one shifted 1/8 wavelength to the right. Now simply sum their values. What you will find in that the summation is an EXACT replica of the original sine wave, in both phase and amplitude.

This principle works the same way with speakers. As long as your ear is equidistant from the two drivers, you will be utterly unable to distinguish the crossover. This is because the output summation IN THE AIR is identical to the original signal (in both time and amplitude), no matter what the frequency. (Again, this is true of the first-order only!)

Now, it must be said that the real world is not so perfect, and most drivers have rolloff-related and impedance-related phase shifts that add into the equation, giving a less-than-perfect end result. For this reason, designing a good first-order crossover is harder than it sounds.

>But anyway, what I understand as phase coherent means that the entire output is in phase ideally independent of listening position. The only speakers capable of this are full-range, single driver designs.

Since that last sentence is not true in all cases, nor in the majority of cases if we want to talk about phase and time alignment, which we do want to in this thread, primarily. There are other threads to talk just about phase coherent speakers which are not time coherent.

Note that I am agnostic on whether first order crossovers and stepped baffles are always the best selection of tradeoffs or not. I've mentioned near field listening situations as one situation to consider.

"At the crossover point, for example, one driver is at .707, +45, and the other is at .707, -45, as I stated previously. Due to the fact that this is vector addition, they sum to unity at zero phase. And they do this not only at the crossover frequency, but at every single point from DC to infinity. The first-order is the only crossover that does this."

Karls, thanks for that explanation ... now I completely understand why the first order crossover can work in amplitude and phase terms through the region where both drivers are contributing to the sound. The power output of both driver is 3dB down at this point (amplitude is reduced by 1/(square root of 2), and they are 90 degrees out of phase, but the vector addition of these two waves results in a sine wave that is in phase and 0dB down in amplitude.