Concise, but not quite correct.

Posted by RoyJ (M) on August 7, 2003 at 04:19:02

In Reply to: Time and Phase of multiple driver loudspeakers posted by audiographic on August 5, 2003 at 10:36:55:

Audiographic's (Russ's) assertions about what constitutes a time-coherent design are concise, but some are too general, or he is a bit wrong in his interpretation of the math.

Although my time is limited, here are some discrepencies I see, with as brief of a response to each as can be made, point by point (I hope you see I am not attacking, nor being a smart-ass, and that I actually support my claims here with the math and give references, and also in my replies seen in the "Time Coherence" speaker thread at Audiogon):

Russ says in his opening post that "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."
Yes. And that total 90 degree phase-difference remains constant at all the frequencies above and below the crossover point, as far as the circuit's electrical outputs. Which means there is no relative phase shift in the signals to the two drivers. Of course, the drivers have their own mechanical phase shifts, and electrical ones. It is up to the designer to find drivers with the least mechanical phase shift, to engineer a rear-of-the-cone loading that minimizes acoustic reactances, and to then design Zobel circuits that actually reduce the electrical phase shift caused by the voice-coil inductances.

Fyi, most Zobel circuits do not do a good job of reducing the electrical phase shift- the "perfectly flat HF electrical-impedance curve" that we want the driver/Zobel combo to exhibit without the crossover circuit. The results the designer wants are hidden by the driver's mechanical impedances from the cone's mass, any lack of rigidity, its suspension's compliance, and its reactance with the enclosure volume and damping behind it. This imperfect Zobel construction is one reason designers often speak of needing to "voice" their speakers, necessary as they do not know how to "measure thru" those added mechanical and acoustic impedances to get that Zobel circuit right from the beginning.

Russ continues: "...plus 45 degrees for the tweeter and minus 45 degrees for the midrange at the crossover point. This is why the crossover is -3dB."
No, sorry. The response for the mid driver is 3dB down whether or not the tweeter crossover even is hooked up, or with the tweeter replaced with a resistor so we don't have to listen to it. The same is true for the tweeter vs. the mid. Why? The response rolloff of the mid alone (or the tweeter alone) is there because for an 8 Ohm driver, the crossover's series impedance is also 8 Ohms at that crossover point (it continues to double every octave higher you go for a 1st-order low-pass filter). Thus, this -3dB attentuation is just from that series impedance creating a voltage drop on the way to the mid or tweeter. The -3dB down has nothing to do with phase, and there is no math which will support that claim.

Russ continues: "With the two drivers 90 degrees out of phase, cancellation must occur."
No cancellation occurs.
90 degrees is 1/4 wave- one driver is always an eighth-wave ahead, one an eighth-wave behind. That is called "operating in quadrature".

An example of "quadrature" is pushing a child on a swing at the top of her arc, not at the bottom. You are applying force just as she is changing direction, for the most efficient transfer- you are applying your input at a moment 90 degrees out of phase with her velocity- she stops while you start- and you continue to push till she gets away from you (which is the fundamental principle behind radiation resistance, too). This is merely a good example of what quadrature means, and only related in a really roundabout way to the discussion at hand. But it is, by the way, exactly why a woofer has a 90 degree lag at its resonant frequency, which CAN affect the phase at the crossover point, if the crossover point is too close to that frequency.

N*180 degrees is cancellation (= N/2 wavelength path-length difference or N/2 wave-period time delay).
Cancellation with a first-order crossover signal supplied to both drivers comes when the drivers are not mechanically in phase (including the actual path-length distance to the listener), from the drivers drifting out of phase from non-linearities and their bandwidth limits, and from using a "poor" Zobel on a driver- one that yields a non-uniform electrical impedance for the driver's load on the crossover (it changes the phase of the crossover away from that +/-45 degree ideal).

Russ: "[thus] Half the energy is canceled out by the destructive interference from the two drivers at the crossover frequency."
No, sorry. See above, and note that all measurements show this is not true. Look at the AES papers, including the B&O papers among many others. Look at the accepted Voltage transfer function of the electrical output from first-order filters, high and low pass- printed in the B&O papers, and in any filter-theory book intended for EE's. You will see that the sum of V(low) and V(high) is 1. Which means no cancellation. At any frequency.

Russ: "Also, if the voice coils are aligned as before [acoustic centers = same distance from listener, right?], 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."
I assume Russ is referring to the +/- 45degree lead/lag he mentioned above. It is NOT true that the acoustic centers move. The CONSTANT phase difference of this crossover means the tweeter is always ahead of the mid, by the same total of a 1/4 of the wave's period, no matter what that frequency is. The tweeter and mid are not "moving". So if one driver's acoustic center is ahead while the other stays behind at all frequencies, then as one goes up the scale, the result is NO net change in the mutual, actual acoustic center. So the measured (and heard) point of sound-origination remains fixed. And this agrees with all the math, including the principle of the superposition of two waves having the same wavelength.

Russ: "[thus] The axis of radiation where the two drivers sum and are in phase has been tilted down."
No- see above. The "tilt" can certainly come from the tweeter being physically mounted ahead of the mid's acoustic center- such as on a flat, non-tilted-back baffle, with the tweeter placed at ear level. Thus, for that cabinet, "down" indeed is where the distance to the tweeter's acoustic center equals the distance to the mid's acoustic center.

Russ: "The angle of tilt is directly related to the distance between the two drivers and the crossover frequency."
Sure. For the flat-baffle design, for any design.
"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."
To support that statement, one must know how far the listener is away from the speaker.
Regardless, in which direction is that second axis? To know that, one calculates just the path-length from the ear to the mid, and from the ear to the tweeter- sides of triangles.
Where the path-length DIFFERENCE equals one FULL wavelength at the crossover point is where the drivers will come back "in phase" (although 360 degrees out), at that one frequency. You can see how the distance to the listener is fundamental to this calculation... For the "typical" first-order design with its offset drivers (tilted-back baffle), that second axis happens to be ~straight up in the air, which hardly amounts to any output in that direction, as the mid-driver's dispersion at that 75 degrees off-axis `taint very much at the commonly used ~3kHz crossover frequency.

In Russ' third paragraph: "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 [6.5"] driver this occurs at 1350Hz."
What occurs at 1350Hz is that this driver is -3dB down (approx) at 45 degrees off axis, assuming no cabinet-reflection interferences (this is usually not the case, and those reflections muddy the dispersion pattern from being a smooth fall-off to the sides. See any of the Stereophile speaker tests and look at the off-axis curves). And with a first-order crossover, the tweeter's output down there at 1350Hz still counts for something, which widens that dispersion back out.

For the math on this, see the ~1976 Acoustic Research papers in the AES Journal- which is NOT basic physics. Without cabinet reflections, Mr. Kates shows there, how the equation for "directivity" is a complicated integral taken over each point of the radiating diaphragm. He is not the one who created this integral- it's widely accepted as the only way to calculate the directivity of a diaphragm without cabinet reflections.

Inside that integral lies a Bessel function. Which is not something one can integrate. However, if you throw out the higher terms of the Bessel function (because they are considered "small" numbers, not necessary for a ballpark approximation), then you can have a simpler function, which can then be expanded into a power-series. Then you can finally have a computer numerically integrate that expression. Why bother? Well, from it you get strong indications that the original integral was indeed right (which was set up via std. path-length geometry from the ear/mic to the all points on the dome/cone, and took into account the wavelength/frequency as a variable). So one can compare the resulting predicted directivity, frequency-by-frequency, to one's measurements/observations. So you don't have to measure as much when figuring out a new design, because you can predict the general nature of the dispersion pattern. Which does not match the numbers Russ supplies.

Russ: "As we increase frequency more, the angle of radiation must continue to shrink if on-axis frequency response is to remain flat."
Off the top of my head, I do not know of the math or physics supporting this position. Perhaps he forgets that radiation resistance levels off, and does not "continue to increase with frequency".
I would like to see how he comes to this conclusion. The notion of "power response" also comes to mind, but here that would be about integrating that single driver's output over all angles, not just paying attention to the on-axis sound only...

Russ: "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."
No, it is not normal motion. It is indeed cone breakup- the first mode of break up.
In the first breakup mode, the tendency with most moving systems, including a cone, is for the outer portion to come to nearly a standstill, while the inner, driven portion continues to move. And there are some mid and mid/woofer drivers by the way which do make it to much higher frequencies than Russ states, nearly an octave higher, before entering their first break-up mode. Some drivers- not many.

Russ: "Cone breakup refers to irregular patterns of motion."
It can, but I think Russ is speaking of the higher-order breakup modes. Of course, all the breakup modes are audible, including the lowest-order one. Lord Rayleigh's math from his "The Theory of Sound" in 1877, and his experiments show nicely what these the various modes look like- portions of the diaphragm moving in, others moving out, at the same time. Celestion and KEF both published laser-interferometry results 25+ years ago which validated his math and experiments.
Most high-order breakup modes are generally not "irregular", except via substantial imperfections in the cone, like a randomly-placed thicker/thinner x-section. With modern cones/domes, these inconsistencies in density/rigidtiy are small, and thus affect usually very short wavelengths, such as 10kHz, in a 6.5" woofer/mid. There are other causes for "irregularity", like eddy currents in and around an aluminum VC former, making it ring/rock.

Russ: "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."
Russ is including the 1st-order cone-breakup in this analysis, so the correct statement is actually the opposite: the radiation angle INCREASES as the effective radiating area decreases. This has been known for a very long time, and is the reason you see the rings pressed into the paper cone for a 15" PA speaker woofer/mid. Those rings are not for cone stiffness- those are hinge points of induced weakness, so that the effective radiating diameter becomes smaller with increasing frequency, so that the dispersion remains ~90 degrees wide to match the HF horn. But it also means that voice coil sees less and less moving mass at higher frequencies, as less and less of the outer portion of the cone moves. So the speaker exhibits a rising response, with a "dirty" modulation signature from those "noisy" hinges. But the less moving mass and the rising response does mean 100dB sensitivity in the midrange. Down at 100Hz, where that entire cone moves as a piston, the sensitivity is ~94dB. Look at the irregularities in a driver's impedance curve to see some of the breakup frequencies. They correspond to the ringing frequencies seen on waterfall plots.

Russ: "If the tweeter rolls off at -6dB per octave starting around 12kHz then it may stay in phase."
Much of what he says in this paragraph is true, but "-6dB"? Relative to what kind of low-frequency reference for that tweeter? Usually it means mounted flush in a wall (not my idea of a hi-fi cabinet-face free of reflections). If he means with reference to that tweeter's low-end output when it's mounted totally freefield out of a cabinet, then he is not allowing for the low-end boost of the reflections from the tweeter's own mounting plate. Those "push-up" the bottom end of a tweeter, like putting a subwoofer in a corner. The tweeter manufacturers know this, so they flatten the measured response by putting on really large magnets, which over-damps the tweeter's low end. But that measured response still includes those reflections. Which are audible. The direct arrival from that tweeter, with a rigid dome, would be tilted up on the way to 20kHz. Which does not agree with his assertation that the response should fall.

Russ: "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."
This is actually used as an indicator of how wide will be the listener's vertical sweet spot. What is missing from this statement is the listener's distance away. The "less than one wavelength" is certainly important when measuring at one meter distant. Our little Europa speaker has a 6" woofer, and the center-to-center distance from it to the Morel dome tweeter is 5.5 inches. They are mounted only about a 1/2" apart. The crossover point is 2850Hz = 4.75" wavelength, so we are "close" to Russ' spec, for what that's worth. We know the Europa's drivers sum, in phase, for listeners from 5' to 25'. To keep the path-length to each driver the same, then the closer you get, the higher this speaker has to be, such as using a 24" stand, then a 28" stand, for sitting 15' away vs 8' away, respectively, on a comfy sofa. We also hear and measure no "second axis" standing up anywhere, even near the speaker. Nor has this been reported in any test on the other time-coherent designs from Thiel, Vandersteen, Dunlavy, Duntech, and Meadowlark.

Russ makes some really good points here, and my purpose here was to correct some mis-interpretations of the math. Those interested, have a look at my postings at the Time Coherence thread on Audiogon, wherein any claim I make there I also try to clearly substantiate (it is easy to make technical statements which sound factual). If you are skeptical, that's cool, but go and listen. Do play any music you can, from bluegrass to Bach, to reveal if we have done things correctly. And do include the many not-even-close-to-good recordings, especially those with energy straddling the crossover point(s), to hear if these recordings are more clear, less fatiguing, and more enjoyable than on speakers which lack time-coherence. It is why we are still in business after 12 years.

Some here ask for measurements- we don't make those available. But do look at our original Diamante speaker test by JA in Stereophile, 4/94 where he validates our time-coherency. In the same issue is the B&W Silver Signature's time-domain results, and the one from Velodyne (a great deal wrong there). The 3-way Diamante's impulse response looks like that of an original Quad's (the new Quad is not time coherent). In the Diamante, the mid-tweeter spacing was about 5" center-to-center, with a crossover at 3kHz. The woofer-mid spacing was ~8.75", with a crossover point of 350Hz. You will also see how it has a remarkably smooth off-axis dispersion, because of the validity of the math I stated above- it is not magic.

Our current speakers are `way more time coherent than the original Diamante.

Hope this helps clarify a few mis-conceptions. By the way, it is important to remember that papers in the AES Journal are peer-reviewed for accuracy in their physics-setup of a problem, and for how the math is applied, then solved, and perhaps interpreted, before the papers are ever published. So the results are truly useful to other engineers, and not just puffery.

Best regards,
Roy Johnson
Green Mountain Audio

This post is made possible by the generous support of people like you and our sponsors:

Follow Ups Full Thread

Topic - Time and Phase of multiple driver loudspeakers - audiographic 10:36:55 08/5/03 (48)

Concise, but not quite correct. - RoyJ 08/7/0304:19:02 08/7/03 (6)

Re: Concise, but not quite correct. response - audiographic 15:23:33 08/9/03 (3)

Correction? - RoyJ 19:24:12 08/9/03 (2)

Re: Correction? Corrected - audiographic 22:56:22 08/11/03 (0)

Some Other History... Not about Green M - audiographic 21:06:09 08/11/03 (0)

Small correction--Diamante review - randallt 06:32:31 08/8/03 (0)

Re: Concise, but not quite correct. - MJ 07:15:38 08/7/03 (0)

Even more important though.... - chris.redmond2@bushinternet.com 14:24:48 08/6/03 (1)

For a suitable fee, I can design 'face fairings' and smooth ear covers with choiceo of flare - Tom Dawson 14:49:24 08/6/03 (0)

Why does this matter? - hifi heretic 13:58:34 08/6/03 (1)

Re: Why does this matter? - MaxxC 14:51:14 08/7/03 (0)

Thanks for your very well written post! - Jeff Joseph 11:58:13 08/6/03 (0)

Re: Time and Phase of multiple driver loudspeakers - 7V 06:50:32 08/6/03 (0)

Re: Time and Phase of multiple driver loudspeakers - Tom Dawson 23:40:22 08/5/03 (2)

Re: Time and Phase of multiple driver loudspeakers - audiographic 07:43:43 08/6/03 (1)

Re: Time and Phase of multiple driver loudspeakers - Tom Dawson 14:31:26 08/6/03 (0)

Re: Time and Phase of multiple driver loudspeakers - mauimusicman 19:54:43 08/5/03 (0)

What [if anything] would this infer about: A. single-driver systems or B. Electrostats? - High-end Dreamer 18:52:49 08/5/03 (4)

Re: What [if anything] would this infer about: A. single-driver systems or B. Electrostats? - audiographic 07:19:24 08/6/03 (0)

My speakers (Quad 63 USA Monitors) can replicate a squarewave perfectly. - mark maloof 22:07:21 08/5/03 (1)

Re: My speakers (Quad 63 USA Monitors) can replicate a squarewave perfectly. - mac 22:49:44 08/5/03 (0)

Re: What [if anything] would this infer about: A. single-driver systems or B. Electrostats? - mauimusicman 21:17:32 08/5/03 (0)

Interesting reading! - Chris D 18:41:11 08/5/03 (0)

is there an audible time delay? - Magpie 17:21:20 08/5/03 (7)

Re: is there an audible time delay? - audiographic 07:33:29 08/6/03 (0)

How much delay is audible down low?? Whats the magic numbers?? - Robert Hamel 20:48:09 08/5/03 (3)

Re: How much delay is audible down low?? Whats the magic numbers?? - Jon Risch 21:22:03 08/6/03 (0)

Re: How much delay is audible down low?? Whats the magic numbers?? - audiographic 08:03:38 08/6/03 (0)

Re: How much delay is audible down low?? Whats the magic numbers?? - Tom Dawson 22:30:27 08/5/03 (0)

Re: is there an audible time delay? - mauimusicman 19:56:35 08/5/03 (0)

Re: is there an audible time delay? - tomservo 18:39:54 08/5/03 (0)

The above is "the answer" to GM Europa and mauimans bogus claims of time and phase coherency - campy 14:39:25 08/5/03 (2)

Re: The above is "the answer" to GM Europa and mauimans bogus claims of time and phase coherency - mauimusicman 20:06:57 08/5/03 (1)

Re: The above is "the answer" to GM Europa and mauimans bogus claims of time and phase coherency - Newk 05:30:21 08/6/03 (0)

Re: Time and Phase of multiple driver loudspeakers - MJ 14:00:52 08/5/03 (0)

Interesting post, thanks for the work...-t - rp1@surfnetusa.com 13:26:11 08/5/03 (0)

Burn in Hell - Larry I 11:44:25 08/5/03 (11)

Re: Burn in Hell - audiographic 14:19:17 08/5/03 (10)

Couldn't resist, Audiographic - mauimusicman 21:37:36 08/9/03 (0)

Re: Too Hot - tomservo 16:47:50 08/5/03 (8)

Re: Too Hot + Hilbert Transform - audiographic 18:52:43 08/5/03 (4)

Re: Hilbert Transform - tomservo 07:54:36 08/6/03 (3)

Re: Hilbert Transform - Rich Brkich 17:04:12 08/6/03 (2)

Re: Hilbert Transform - tomservo 05:33:27 08/7/03 (1)

Intersonics Sub - Rich Brkich 06:36:12 08/7/03 (0)

Re: Too Hot - audiographic 17:11:30 08/5/03 (2)

RE TEF and Hilbert - Jon Risch 20:51:35 08/5/03 (1)

Subs - audiographic 08:14:04 08/6/03 (0)

Follow Ups

Concise, but not quite correct. - RoyJ 08/7/0304:19:02 08/7/03 (6)

Re: Concise, but not quite correct. response - audiographic 15:23:33 08/9/03 (3)

Correction? - RoyJ 19:24:12 08/9/03 (2)

Re: Correction? Corrected - audiographic 22:56:22 08/11/03 (0)

Some Other History... Not about Green M - audiographic 21:06:09 08/11/03 (0)

Small correction--Diamante review - randallt 06:32:31 08/8/03 (0)

Re: Concise, but not quite correct. - MJ 07:15:38 08/7/03 (0)

You can not post to an archived thread.