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In Reply to: Re: Example please? posted by dlr on February 24, 2007 at 07:33:56:
Okay, by resonance I mean breakup. Wouldn't you say phase coherence require some kind of assumption of the drivers being minimum phase? By my reckoning it does. The nature of the breakup of an aluminum cone driver keeps it from being minimum phase.Aluminum cone breakup is caused by two things. One is too much energy reaching the affected frequencies. The other is excursion, which I believe is the increasing distortion with increasing excursion. Excursion based breakup for metal cones can happen within the limits of Xmax for certain drivers. Neither of these things is well controlled in a 1st order crossover.
Follow Ups:
Breakup IS minimum-phase. It's a common misconception. It's possible to model the breakup down to the smallest detail and get accurate FR/phase response. I've done that with a 10" drivers modeled to every detail of breakup to 20K. Were the breakup not minimum-phase, the model would fail.There were a number of detailed threads at the Mad board some time back. One of the posters showed the math derivation that was supporting confirmation of the empirical models.
There is nothing in breakup that prevents a driver from being minimum-phase. It is by nature minimum-phase. More evidence of this is in the Hilbert-Bode transform. A signal has to be minimum-phase to satisfy the requirements for the H-B transform. This is used by CAD software to generate the phase if measured phase is not available or not used. The H-B transform generated phase from the measured FR of all raw drivers, including the breakup area, shows a minimum-phase response.
There used to be a lot of questions about breakup and whether or not it was minimum-phase, but I've used CALSOD for many years and have always been able to model any driver's response and get perfect agreement between measured phase and the H-B generated minimum-phase after accounting for the excess-phase always present in measured phase.
There is an argument that can be made that the breakup and stop-band area prevent a number of true designs from being fully achieved for another reason. The is most true of anything that requires a first order driver response. No driver can ever produce a first order response deep into the stop-band. Drivers are second order passband by nature. This means that at some point, no matter how detailed the crossover, the driver will ultimately revert to 2nd or even higher if a crossover is included. However, this can easily be put into the noise floor making it inconsequential.
That's what one does with breakup. All drivers breakup, not just hard diaphragms. This is WRT to the FR.
WRT to driver excursion, distortion and breakup, all drivers exhibit this. By that definition, no driver could be considered minimum-phase, but that point is moot as the breakup is itself a minimum-phase phenomenon within a driver. The
Now motor distortion is another issue. All drivers also exhibit this and it is non-linear. It doesn't matter what the diaphragm material is made of, although it can exacerbate the issue. Hard coned drivers with their exaggerated breakup certain make its control more problematic.
What is important in this case is to cross the driver at a point, even first order, such that the breakup is well down into the stop-band. I think that Linkwitz discusses this at his site, though his designs are definitely not first order. It's an issue for any design. It certainly limits the usage of hard cones (I'm not a fan of them myself, I like doped paper mostly), but it does not preclude them.
So in the end it comes down to what compromises do you want to accept? All systems are simply different compromises in design. When a driver's Xmax is reached, distortion is going to increase. But this is true of every design.
A first order system has the most compromises, except that there is one that few other systems compromise more. That's the ability to closely reproduce a square wave, the most difficult signal to reproduce (other than a true infinite impulse). With all of its compromises, a first order system will still, even with the breakup, generally reproduce a square wave more faithfully than other designs, the exception being the few higher order crossovers that are also transient-perfect.
Of course, this opens up the whole other discussion as to the audible benefits of any transient-perfect design vs. non-TP designs.
So are you saying that an aluminum cone's resonance (often referred to as resonating like a bell) at breakup, clearly seen in any metal diaphragm driver's waterfall plot, is minimum phase? So then this cone resonance can be controlled by a basic notch filter? I have never seen anyone claim that before. I'm happy to accept that breakup is minimum phase. It's the cone resonance caused by breakup that I dispute is minimum phase. It's my understanding that once a metal cone is ringing it can't be corrected with filters, which would fit the definition of non-minimum phase. Does this make sense?
No, it doesn't make sense because it's not true. Whether or not the driver can be "corrected" has nothing to do with whether or not it's minimum-phase. Actually, being minimum-phase is precisely why it _could_ be corrected.The only reason a hard coned driver "can't" be corrected with filters is because the breakup peaks/dips are of very high Q and flattening the FR passively or even actively non-DSP can't be done easily due to the magnitude of the values needed and the number. High Q's may not be fully correctable due to insertion losses (coil resistances primarily), but that's a limitation of the real components, not a limitation induced to the physics. That is the one and only limitation to smoothing the response completely in the non-DSP world.
Think about it. Any and ALL areas in any and ALL raw driver responses are due to some form of resonance, or energy storage. Even the most gradual, minimal peak/dip of very low Q and low magnitude is a resonance. It's absolute no different than the high Q peaks at breakup. The only difference is that low Q resonances allow for components of reasonable magnitude to correct them.
It's also possible now to use DSP to completely linearize every last peak/dip of any Q/magnitude. It's a simple matter with the right software, I do it in SoundEasy. The only thing that is occurring in this instance is that there is essentially an unlimited amount of DSP-generated "filtering" going on that is limited in the analog domain whereas there is essential no limitation in DSP. I can take the worst hard-coned driver and make the breakup linear.
This works only on-axis, of course, since off-axis all drivers differ from their on-axis response. That part is no different than a driver that has decreasing dispersion at higher frequencies. You just have to take it all into account.
And again, as an example, I have many times used CALSOD (a DOS tool from the 80's into 90's no less) to create a driver model that perfectly matched the resonances in FR, as I said. The phase is then generated from this FR model. This generated phase perfectly matched the measured phase.
How does the software create the model you might ask? You start with an ideal, perfect 2nd order bandpass. Then you iteratively add minimum-phase elements (MPE) to the model. These are nothing more than a Q and magnitude at a selected Fc. This simply adds a resonance. I've gone up to as many as about 40, maybe more, to detail minutely up to the limits of the measurement, 22K. The generated phase matched the measured phase perfectly. Were either the measured breakup or the modeled breakup not minimum-phase, then the model would break down, the FR would not match and the phase would not match. It all does match, perfectly.
The most common method for using hard-coned drivers is simply to cross them lower. There is one aspect to breakup that can't be controlled through the crossover and that's harmonic distortion. High Q resonances will magnify any distortion components whose harmonics coincide. The best way to prevent this is to cross low enough to keep the fundamental down so that only higher harmonics may coincide, since in general as the harmonic increases, the magnitude decreases. This is true of all drivers, though, it's just that hard-coned drivers have breakup with higher magnitude, thus they "amplify" the distortion harmonics more. But all of that has nothing to do with whether or not the breakup is minimum-phase.
Ahhh, alright. I was under the impression that a resonating metal cone would ring long enough to become a time domain problem, which would preclude it from being minimum phase. I guess I'm wrong.Thanks for the info.
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