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In Reply to: The most important question may be... posted by Jim Austin on February 23, 2007 at 04:44:02:
You certainly make some good points Jim, thank you.
Regarding Toole's opinion: For example, his papers about integrating subs with the main speakers tell us to place several of them in various locations and distances from you around the home-theater/family room. This shows he cares more for obtaining a smooth amplitude response (which is better than an irregular response of course), than he does transient response, which is one thing that time coherence always improves, by definition.
I have to say that in your #2 above, your second sentence is a common viewpoint that is simply wrong. What you wrote is actually true of high-order crossovers, not of first-order crossovers. Because of the way first-order crossovers change the phase (the time delay) as they crossover, the result is a CONSTANT time delay at ALL frequencies between the two drivers. This means then that there is no RELATIVE time delay occurring between those two drivers. Higher-order crossovers produce time delays between the two drivers that is always changing at every frequency, and thus can be 'right' at only one frequency. This is shown in the math of crossover filters. I can point to the 'filter transfer function' equations in an electrical engineering book, but can't do the derivative (calculus) that shows the time-delay changing with frequency!! But this is called a 'non-constant group delay.'
Can you clarify what you mean by your #3?
Follow Ups:
> > Because of the way first-order crossovers change the phase (the time delay) as they crossover, the result is a CONSTANT time delay at ALL frequencies between the two drivers. < <I'll answer this, but I'm going to be very measured because--though what I said makes sense to me, others who are clearly knowledgeable have disagreed with me in this thread. I am not a speaker builder or an engineer. I'm trained as a physicist and I think in terms of first principles--which when naively applied sometimes are too simple to apply to real-world problems. Furthermore, I've been out of research for more than a decade and earned my PhD more nearly 15 years ago--so I'm rusty. So until I can get to the point where I understand--and either agree with or can refute--their points of view I'm not going to write much more on this subject.
My understanding--which might be wrong--is that there is a constant, 90 degree PHASE DIFFERENCE between the drivers in a first-order crossover configuration. But 90 degrees of phase is equal to 1/4 of a wavelength--NOT a fixed time difference (because the speed of sound is frequency/wavelength independent the time it takes for sound to travel a quarter of a wavelength depends on HOW LONG that wavelength is). So, for example, 1/4 or a wavelength at 1 kHz is not the same distance as 1/4 wavelength at 1.1 kHz. If you offset the drivers so that they they emit a 1kHz signal so that it reaches the ear at precisely the same time, then, it seems to me, a 1.1 khz signal will have a small time offset relative to perfect time alignment.
As for my ponit #3, it's so obvious to me that if you don't understand I must have it wrong, and I'm not being facetious. I simply mean that if (say) a 100Hz signal reaches the loudspeaker from the amplifier intact, 1/4 wavelength--90 degrees of phase--is, what, two and a half feet, roughly?
So there you go. Hopefully I haven't humiliated myself too much.
"Thanks Jim. I should started by saying "there is a constant phase difference between the two drivers, which means there is no relative phase shift between the two drivers at all frequencies. Thus, the first-order circuit does not disturb the original phase differences of the fundamental and harmonics".
To think of this as time differences: For any given frequency, the complete first-order circuit injects a constant 1/4-wave-period of time difference BETWEEN the two drivers. More on this below... Thus, with that relative time difference between mid and tweeter remaining constant, a simple first-order circuit does not disturb the original time relationships of the fundamentals and harmonics.
What keeps a simple simple first-order crossover from working as it should?
Non-linear drivers (those with distortion and resonances)
Drivers with limited bandwidths
Drivers with tilted responses
Drivers with varying impedance curves (varying at each frequency, and with stroke)
Cabinet resonances, reflections and diffractions
Imperfect inductors and capacitors in the crossover circuit.
As with any man-made device, there is no perfect driver or cabinet or crossover part, only 'better'.
What should be made clear about a simple first-order crossover circuit used on a perfect mid and perfect tweeter is:
The upper range of the mid driver gets a varying offset (away from you = delay) as we go up the scale.
This changing amount of delay begins at zero down in the bass, and reaches +45 degrees at the crossover point, for a single inductor in series with the mid. We can also represent that 45 degrees as 1/8th of that wave's period, if we want to calculate the actual 'time delay' at that crossover frequency.
The bottom end of the tweeter gets a varying offset (towards you = advance) as we go down the scale.
This changing amount of advance begins at zero in the ultra-high frequencies, and reaches -45 degrees (or 1/8th of the wave's period) at the crossover point, for a single capacitor in series with the tweeter.
But how can we 'advance' time? We can't, so for this analysis, we are simply setting t=0 at say, 50kHz, and not worrying about anything else except what the plus and minus signs tell us relative to that arbitrary zero point up at 50kHz. What is really happening is that as we go down the scale from 50kHz, that tweeter's capacitor is injecting less and less delay, which can then be thought of as more and more of an 'advance'... I hope that's clear!
At the actual crossover point, the mid is delayed by 1/8-period of that crossover frequency, and the tweeter is advanced by that same 1/8-period amount, for a difference of 1/4 period.
As we go down the scale, the mid's delay goes back to zero, while the tweeter's advance levels off at 1/4-wave period advance, for a difference of 1/4 period.
As we go up the scale, the tweeter's advance goes to zero, while the mid's delay levels off at 1/4-wave-period delay, for a difference of 1/4 period.
At all other frequencies, the total difference between the two is always a constant 1/4-wave period.
Thus no RELATIVE timing change occurs between the two.
What then happens is that the outputs from this mid and tweeter sum together at your ear as if they could be replaced by ONE single driver that you and the measurement mic would believe was doing all the work at all the frequencies, with no time delays at any frequency.
In contrast, high-order crossovers inject advance/delay differences (varying phase differences) between these same two drivers, which means that there are 'frequency-dependant phase shifts' between the two drivers. Your imaginary 'one-driver source' is moving farther away or closer to you, depending on the frequency.
Any sine-wave's period is 1/(its frequency) = time
Example for a 40Hz sine wave: period = 1/40Hz = 1/40th of a second. 1/4 period of 40hz = 1/160th second or '90 degrees'.
Thanks again.
Nice job. Phase is not easy to describe in plain English, much less phase between two drivers.I would simply add that the points you made about non-perfect devices applies to all systems, not just first order. First order is just more difficult WRT taking the compromises into account.
For those who might like to see a graph, I've linked to a first order Butterworth response of theoretically ideal drivers, 90db each. Red is lowpass, green is highpass and blue is summed response.
This is the minimum-phase response, no excess-phase.
..the world would be an even better place.
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