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RE: Clarifications on Time Coherence

Posted by villastrangiato on March 12, 2012 at 21:48:25

In Reply to: RE: Clarifications on Time Coherence posted by RoyJ on March 12, 2012 at 20:00:04:

Oh boy...where to begin....

Firstly, with respect to "reverse nulls", Mr. Johnson said -

"First, please note that no such cancellation occurs on a first-order type of speaker. "

Not sure what kind of first order speakers you've built but reverse null in speaker designing parlance means reversing the leads of one of the driver pairs and examining the drop off in amplitude across the entire crossover region. And believe it or not Roy, it happens with 1st order designs too. And if you just stop and think for a moment, your taking one vector out of top two quadrants and placing it in the bottom. Each leg is no longer operating in quadrature. Yes, the null isn't as severe as with an even ordered network but the null DOES EXIST. If you still doubt this, look at one of the most popular DIY speaker project documentations on the net here:

http://www.zaphaudio.com/WaveguideTMM-minimalist-FR-reversenull.gif

http://www.zaphaudio.com/WaveguideTMM-perfection-FR-reversenull.gif

Roy also said -
"Please know that this is a common mistake made in every electrical-engineering textbook I've seen, because the mathematics behind it was not presented from scratch using Time as the variable, not Frequency. What you'd find is that what appear to be damping issues are actually artifacts created by time delays that vary with frequency. There is an excellent AES paper on exactly this subject at"

Apparently you did not notice that I used the term "acoustic phase". Do you understand what acoustic phase implies?

Roy also asserts:

"The nice aspect about using a first-order crossover circuit is that the phase-shift DIFFERENCE between the low-pass and the high-pass filters is a CONSTANT 90 degrees at ALL frequencies, not varying with frequency as in higher-order circuits, and not just "about a particular crossover point" as you wrote above.

That word "Constant" is the clue behind the benefits of using first-order networks."

Every capacitive or inductive influence whether associated with the transducer's moving mass or a component in the crossover produces a change in ACOUSTIC PHASE. Acoustic phase shift by implication means an apparent time shift since the sinusoidal is represented by amplitude variations over time and the spatial phase shift is inextricably related to time shift. This is electrical engineering 101. I don't think anyone needs a lecture on the distinctions between time and frequency. The AES paper you cited is ancient history and does not disagree with anything I've stated. On the contrary, you don't seem to understand what group delay in the context of a crossover truly represents. For a simple illustration, I'd direct your attention here:

http://www.rane.com/pdf/ranenotes/Linkwitz_Riley_Crossovers_Primer.pdf

Group delay, as noted in the link above is the rate of phase change per incremental change in frequency and is represented in units of time. However this is not a measure of time or phase separation between the two driver outputs but rather a total time/phase shift of their sum from one frequency to the next since both outputs experience phase shift that is equal to one another at each frequency.

The focus in a crossover as far as "time coherence" is concerned is the melding together of wavefronts from the disparate sources so that they appear to hit the target AT THE ESSENTIALLY THE SAME TIME with a constant phase between them. You are asserting that group delay somehow creates PERCEPTIBLE TIME DELAYS between the driver's wavefronts and IT DOES NOT. In a crossover that takes into account each driver's minimum phase behavior, the rate of phase rotation between the two wavefronts IS HELD CONSTANT. IT DOESN'T MATTER IF IT'S 1ST ORDER (90 DEGREES) OR 8TH ORDER. Each driver experiences the same phase shift which may not be constant with frequency but they both maintain a constant phase between them from one end of the spectrum to the other. The phase plots shown in the link bear that out and the text also states on page 11:

"The resultant vector
is back in phase with the original input signal. So, not
only are the outputs in phase with each other (for all
frequencies), they are also in phase with the input (at
the crossover frequency)."

to describe a textbook LR crossover - one of the most popular crossover types in existence. And if you've built/modeled a typical L-R crossover - your own phase plots would bear that out.

What is not constant with the higher order networks is group delay. That's linear with the first order network but not linear with the others. This apparently is where you are getting confused. If you want further clarification, please read the RANE link above. And again, more modern studies (within the last 10-15 years) have found that humans can reliably detect group delay on the order of a few milliseconds at around 1khz. Fourth order Linkwitz Riley crossovers exhibit phase shift per unit frequency below that threshold. Your concerns for "time delays" in higher order crossovers is indeed a STRAWMAN argument.

As to the issue of transient response, again - that's electrical engineering 101. As you increase the number of poles and zeros in a circuit, the number of energy storage points is increased and instability (harmonics) is introduced. You can call them "artifacts" but Linear Control theory very explicitly defines the transfer functions and the various levels of Q associated with the resulting resonances.

This is old hat to me - something I learned about 25 years ago. You might be correct and both I and Rane Corporation among many others might be wrong but I highly doubt it.

Edits: 03/12/12 03/12/12 03/13/12

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