Another Time and Phase thread

Hello guys I found this post on another site.Please explain as this stuff seems to get more and more confusing to me.Which is it time and phase or not.This was posted by an AA member.
Thanks in advance!

I see much stuff about phase and time with confusion. If there are two drivers mounted on a baffle, say a midrange and a tweeter, then it would be nice if the acoustic radiation from the two drivers were in phase. Linkwitz Reily 24dB/octave accomplish this when the two drivers are in the same acoustic plane (voice coil alignment is very close to this with an offset baffle) In this case, for one octave above and below the crossover, the electrical signal applied to the drivers are 360 degrees out of phase. For continuous signals applied to the two drivers through the crossover and at the crossover frequency the motion of the midrange is one cycle behind the motion of the tweeter. This allows the main acoustic radiation axis to stay on the same axis as the individual drivers. The problem with the LR crossover is that half the energy applied for those two octaves around the crossover is thrown away by the form of the crossover. The transfer function has 4 terms plus a constant. Only the first term and constant appear in the acoustic output.
As far as that minimum phase stuff. Everyone seems to forget that the drivers must acoustically sum (low and high add together) somewhere in front of the speakers in the acoustic environment. With out of phase drivers that summing point starts down (midrange below the tweeter with applied signal of midrange lagging tweeter signal) and then moves up relative to the axis of the speaker depending on frequency. If you do this in a circuit, the summing is literally a point and so no such physical axis even exist. Speakers are not points and are not circuits though. A 6dB/octave crossover has a phase of plus 45 degrees for the tweeter and minus 45 degrees for the midrange at the crossover point. This is why the crossover is -3dB. With the two drivers 90 degrees out of phase, cancellation must occur. In this case. Half the energy is canceled out by the destructive interference from the two drivers at the crossover frequency. Also, if the voice coils are aligned as before, at the crossover frequency the acoustic center of radiation for the tweeter has moved forward in phase (effectively may be thought about as moving forward in space for analysis purposes) and the acoustic center of the midrange has moved back. The axis of radiation where the two drives sum and are in phase has been tilted down. The angle of tilt is directly related to the distance between the two drivers and the crossover frequency. If the drivers are more than one wavelength apart at the crossover frequency, then the tilt is so much that a second radiation axis occurs. This axis point way up with a acoustic radiation null between these two axis. Wave length in inches is equal to 13500/frequency of interest. This part about radiation is all basic physics) physics 102 from radiation from multiple sources.

As far as driver frequency response is concerned. Let us take that midrange and start at 200Hz and go to 4000Hz. Also, let us say the mid has a cone plus half the surround diameter of 5 inches. So this may be a nominal 6.5 inch driver. As we increase frequency we observe that the response if pretty flat and as frequency is increase the angle of radiation decreases such that the response may be fairly flat until around 650Hz. At this point the radiation angle of the driver starts to look fairly constant. How can this be? The outer edge of the cone starts to act more like a surround with the center of the cone moving in and out. As all this works out in a real driver, the radiation angle slowly decreases as the effective radiating area decreases toward the center of the cone. Many aspects: effective moving mass; radiating area; angle of radiation; and other factors serve together to make the ON AXIS response flat. It is very important to under stand that acoustic radiation resistance increases as frequency increases. This is why a woofer is big and a tweeter is small. Radiation resistance has increased at the higher frequency. Basic physics tells us that when the driver diameter is equal to 1/4 wavelength that the angle of radiation will be reduced to 45 degrees from the original angle at 200Hz of 180 degrees. For our mythical driver this occurs at 1350Hz. As we increase frequency more, the angle of radiation must continue to shrink if on axis frequency response is to remain flat. At 2700Hz the angle of radiation would be much smaller if a real driver ever made it to that frequency without acting like a drumhead where the center moves forward and the outer parts move back. This is not cone breakup as it is a normal motion. Cone breakup refers to irregular patterns of motion. This is drum head motion. Above the frequency drum head mode sets in, the on axis radiation is out of phase (-180 degrees) with the drive signal. This is known as incoherent. The energy response may be perfectly flat but the time response causes the energy to be useless for listening or summing to the tweeter on our two speakers with a baffle.

As far as tweeters go, if you have a 1 inch dome radiating at 17,000Hz, if is pretty clear the source is much larger that the wavelength. If the tweeter is flat on axis at 17kHz, then the angle of radiation is less than 22 degrees and it is in drum head mode of motion causing all the radiated energy on axis to be out of phase. Only tweeters with horns attached, tweeters with some physical means to control radiation pattern, very small tweeters, (<1cm) or tweeters that become extremely directional have a chance of going high in frequency without getting out of phase. For our 1 inch dome to stay in phase at 20kHz the angle of radiation would be on the order of 10 degrees. This means that a reading of 30 degrees off axis of the output would be some 20dB down. A good rule of thumb is if a tweeter is flat above 12kHz then it is out of phase. Having tested about 700 manufactured tweeters from Scanspeak, Morel, Audax, Seas, Phillips, Accuton, Focal, Dynaudio, Vifa, Becker, and Heil, and others none of the domes stay in phase (go into drum head mode) above 8.5kHz. It is really easy to tell by looking at a frequency response graph because the tweeter will be flat. If the tweeter rolls off at -6dB per octave starting around 12kHz then it may stay in phase. There are a very few (I know of three direct radiating tweeters, not horns) that do stay in phase up to 20kHz but will not tell you other than the Isophon. PLEASE NOTE- the electrical phase graph published with so many loudspeakers in no way reflects the acoustic phase of the driver. Except near resonance frequency, these two different aspects may be and almost always are totally unrelated for all drivers!!! The electrical characteristics are useful for crossover design. The unpublished acoustic characteristics (time and phase) are required for the acoustic design. Lots of luck on that one.

So with these things in mind it is pretty clear that our two drivers need to be at most one wave length of physical separation at the crossover frequency with less separation being desirable, say at most one wave length at double the crossover frequency. It also appears that some method to keep the midrange and tweeter in phase through the crossover region is desired to allow proper acoustic summing and keep the main axis of radiation on the same axis as the tweeter and midrange are away from the crossover. This can possibly be accomplished by an all pass filter aligned to cause lag in the tweeter signal around the crossover to match the midrange. If acoustic summing is to be deemed "minimum phase" then the criteria of no axis of radiation tilting (and therefore no cancellation) must be followed. Any speaker with more than one wavelength of driver separation at crossover frequency or with drivers canceling by being out of phase cannot be a minimum phase system. Several of us take in phase to mean less than 22 degrees of error between drivers. This concept is thrown around a lot but never appears to apply. High order crossovers often fail also. One approach was built by Bang and Olsen (sp?) covered by the paper in AES about 1975 using a "filler" driver between the midrange and the tweeter which corrects the phase error and provides the necessary acoustic output to achieve minimum phase using three drivers in what was essentially a two way speaker. This is a novel a valid approach.

This is not to say some speaker may or may not sound pretty good but do not pretend that some absurd claim about minimum phase or flat response means very much. Absurd in this case can easily be identified by crossover frequency compared to driver separation. In general, all the small two ways I have tested from 100-10,000Hz (almost 7 octaves) have at least half the energy radiating on the axis as incoherent. At least the good ones did, the rest were far worse. One recently tested, popular, and very widely used loudspeaker was incoherent from 430-4,000 and 5,600-10,000 Hertz. This same speaker appears in many recording studios!!! Remember, this is the age of marketingism, advertise what you don't have as your prime feature. Find, create, or academically publish misinformation which supports your claims. And most of all, smile when you deceive.