First Order Crossovers: Pros and Cons

So by "phase coherent" you really mean that a first order filter remains entirely true to its 90deg phase separeation between tweeter and woofer?
Thats a new definition to me, maybe we have to start with defining every term properly first.
Also a speaker which has the drivers on a vertical axis can only be phase coherent at one point in space. This of course is a purely geometrical problem independent of any electrical feature.

Last but not least a time coherent speaker can easily be not phase coherent if the crossover separates the phase between drivers (as they all do). On the other hand a phase coherent speaker has got to be time coherent as well as a slight time mis alignment MUST result in a phase shift. Indeed a phaser works by splitting the signal in two and then time delays one with respect to the other before merging the signal again. If you modulate the delay you get a phaser/flanger sound , if you don't its a chorus. I hope you get the idea: all phasing is done by playing in the time domain.
Basically a phase coherent speaker is one that is not only in time but also in phase; a time coherent speaker is one thats in time but not in phase.
And most speakers are neither.

Tannoy manages to get theirs phase coherent by fitting the treble coil exactly half a wavelenght (at crossover) behind the bass coil and then using crossover characteristics and a very simple delay circuit. Thus there is no phase separation between tweeter and woofer at all (except some small aberration at crossover). They are thus in phase acoustically and electrically AND independent from the listening position.
And no I am not trying to sell Tannoy, I don't actually like the new ones with their plastic cones.
Personally, I think the aforementioned geometrical phase problem is the reason that conventional speakers have a sweet spot where everything sounds better and the stereo image snaps into place. Tannoy don't really have that: they sound the same where ever you are although the imaging shifts if you stand to the side, like looking through a window at an angle.

Having had a look at your website I see you claim a phase error of 2deg!
A bold statement, care to back that up with some measurments?
I am sure you've got access to an anechoic chamber and the necessary equipment.

Cheers Golix

Step function tests seem to show all of this very well. Stereophile performs these tests on speakers, but they fall down in not drawing any conclusions from the results.

"This speaker simply can't pass a transient correctly, therefore it's crap, no matter how much a listener may like it." :-)

I will chime in here; Roy is correct as usual. It is not possible to fix the inherent phase problems in a second-order crossover, because they are frequency-dependent. This is simply a mathematical absolute, at least in the analog domain. And phase inversion of one driver is a Really Bad Thing, no matter what the reason for it, because it completely screws up the original signal. Now it may be that the Tannoys are good-sounding speakers for many reasons (not having heard them myself, I can't comment), but true time-and-phase coherence is certainly not among them.

Skrivis's comment about the Stereophile step response measurements is right-on and needed to be said. I still remember several years ago when they reviewed the Quad 988 or 989. JA published all the measurements, and then scratched his head in a rhetorical sense, saying something like the measurements were "enigmatic" because most of them looked horrible in comparison to average loudspeakers (as did the ESL-63 when Stereophile reviewed it decades ago.)

After all those years, he still literally couldn't comprehend how a speaker that measured so poorly in the "traditional" ways (i.e., in the frequency domain) could possibly sound as good and as "right" as the Quad does. And all the while the step response, that beautiful, glorious, near-perfect step response, was staring him right in the face.

Of course, this isn't to say that full-range electrostats are perfect; far from it, especially when they have to be put in a listening room. But it can't be argued that what they do well, they do spectacularly. That is, they reproduce the signal in the time domain more correctly than just about anything else ever made. And in so doing, they set a shining example for us all.

Best,
Karl
AudioMachina

A previous poster has made the statement that using a 1st order crossover causes the LF and HF drivers to be 90degrees out of phase and this confuses me. At what frequency ?

If the LF driver uses a 1st order butterworth type low pass filter, and the HF driver uses a 1st order butterworth type high pass filter, with the -3dB frequencies at the same point (to give a flat amplitude response) doesn't this automatically put the two drivers in phase at the crossover frequency ? I must admit it's a long time since I studied filter design (since I went over to the dark side of software).

That would be a phase-coherent time for me ... the two drivers in phase at the crossover frequency, with linear phase response in the low pass and high pass filters as you move away from the crossover point ensuring phase response continuity elsewhere in the frequency response.

Such a speaker should have a good step response, because linear phase filters offer the least distortion of the original waveform.

I am assuming that this is what the Green Mountain Audio designs attempt to approximate (given that everything in real life is an approximation).

The output of a crossover network is a vector sum with real and imaginary components in polar coordinates. What you have in a 1st order at the crossover freq is one vector at .707, +45, and the other at .707, -45, which adds to unity in vector space with a combined phase shift of zero. But because the vectors rotate together with frequency, they are always 90 degrees apart, and they always add to unity voltage and zero phase in vector space, no matter what the frequency.

To say it differently, the combined output of the two drivers is always unity at zero phase, even though the two vectors are always 90 degrees apart. This is difficult to conceptualize, but the math behind it is relatively simple.

For obvious reasons, this is called a constant-voltage minimum-phase transfer function, and the first-order is the only crossover type that has this characteristic. I should note that this presumes identical drivers mounted very closely together and resistive loading, which is hard to achieve in the real world. But with some effort, one can come close, and the effort is well rewarded in the listening.