Acceleration Factor

ist this arcticle describing in detail what you ment ? : The broken transients
I haven't had time to do more than skim it, but on a very quick once-over, sort of -it largely seems to be pointing out that a low tabulated Le value is not a guarantee of low levels of non-linear distortion, since overall motor design is critical to this and while Faraday shielding / shorting rings can drop the nominal figure, poor application of those can either mask issues elsewhere or in some cases make matters worse (all perfectly true). Although the phrase 'broken transients' appears a couple of times, it doesn't look like the author says exactly what he means by that, so YMMV -the issues he raises though restrict the upper limit of the mass-controlled (flat) BW, so by definition, the narrower the operating region of the raw driver, the more restricted the raw transient response will be. As has been mentioned above though, this is partly a moot point though since ultimately it's also a function of overall system response, LF alignment, what other drivers are being used and how you're handling the transitions (which is another way of saying 'use what drivers you have over their optimum operating ranges & preferably keep GD as low as practical for the intended use'). Raw response tends only to be relevant in practical use for unfiltered units / those with no electrical low-pass added, be they woofers in situations like the old Dynaco & current equivalent Seas A25 kit, or fullrange / wideband units, where TL modes in the cone & any sub-cones / domes etc. are used to extend the BW, in which case the basic electrical considerations have limited applicability, since as frequency rises you're moving into vibrational / bending mode operations of the substrates and the mechanical damping applied to them.
 
so what happened if a impedance correction (flattening the impedance line- not the peak) is established ?
how does this circuit (RC) impact le over frequency and transient response ?
I suggest you open Xsim or any crossover simulator and try it for yourself (DIY audio). The answer is, it depends. If the driver is directly connected to a low output impedance (voltage source) amplifier it does absolutely nothing to the response. Why, because the voltage source is driving almost the exact same voltage on the terminals of the driver. It will be sending some current through that RC network, but that won't matter. The reason for those networks is that a passive crossover filter has a relatively high output impedance and the filters only produce the desired frequency response when they have a uniform load impedance to drive. For instance if you use a simple capacitor for a tweeter crossover. The capacitor has falling impedance with frequency. If you have a uniform resistive load (not changing impedance with frequency) you get a variable divider ratio that raises the current to the load with increasing frequency. Now a voice coil has rising impedance with frequency that divider ratio will not change in the same way with rising frequency and the inductor defeats the crossover. So the RC network across the driver produces a fixed impedance with changing frequency to make the driver look like a uniform impedance load for the passive crossover. Again, try it in a crossover simulator and see what happens.
 
Your confidence in stating this falsehood is disappointing. The transient response is fundamentally linked to the frequency response and bandwidth. The two are absolutely inseparable and one can be precisely derived from the other using the Fourier Transform. Not everyone took the math class that explained that. Fourier Transform is a mathematical model which helps to transform the signals between two different domains, such as transforming signal from frequency domain to time domain or vice versa. It would seem you are just trolling us at this point. If you read the book on current drive of loudspeakers I referenced it explains in detail the relevant physics and electromagnetics. Using a simulator as mentioned before like Xsim or Boxsim will show you all you need to know. The manual for the measurement software Arta is a textbook on audio. Of course Arta uses the Fourier Transform to go back and forth between the transient response and the frequency response with the click of the mouse. It is past time for you to go and do your own homework.
 
Last edited:
Transient response is the ability how good a driver can play/follow a squarewave.
it has nothing to do with frequency response, neither with sensitivity or at least bandwith.

Simulate it ? With waterfall ?
I think it’s obvious. The simple truth isn’t satisfying. Albeit Fourier math isn’t that simple. But the physical phenomenon that the linearity of a system determines its ability to reproduce transients or square waves or whatever (think of wave trains) clearly doesn’t impress quite a few audio enthusiasts. I usually let them be in their belief (religious aspects there, mind you). But it’s no more than a belief. Point.
 
Yeah it's easy to imagine a waveform like square wave maps to driver motion so that the woofer would jerk out fast, then stay there, and jump back in fast and failing to do so fast enough would show in waterfall plot as overshoot or something. But this is not how it works, square wave is about all frequencies at once (odd harmonics of fundamental), so basically bandwidth and group delay issue.

Perhaps some distortion could affect square wave output, perhaps some stuff could be seen on waterfall plot as well. From waterfall, perhaps just look there is no serious issues so that it's smooth overall for best system performance. Then look at frequency response of the whole system, also group delay / step response to evaluate how well a square wave would come through on an oscilloscope. For ear it comes through quite nicely, even though oscilloscope would show the waveform distorted (due to bandwidth limit and some group delay).
https://en.wikipedia.org/wiki/Square_wave
 
Last edited:
Yeah 😀 Participating on such thread is good exercise in information search, and writing a post reveals that I don't actually know much of it. Publishing a post and getting commented is good opportunity to learn something and not something to be afraid of 🙂
 
  • Like
Reactions: NeonDriver
Beware of the crocodiles though... 😉
 

Attachments

  • Crocodiles.jpg
    Crocodiles.jpg
    118.4 KB · Views: 50
Yeah it's easy to imagine a waveform like square wave maps to driver motion so that the woofer would jerk out fast, then stay there, and jump back in fast and failing to do so fast enough would show in waterfall plot as overshoot or something. But this is not how it works, square wave is about all frequencies at once (odd harmonics of fundamental), so basically bandwidth and group delay issue.

Perhaps some distortion could affect square wave output, perhaps some stuff could be seen on waterfall plot as well. From waterfall, perhaps just look there is no serious issues so that it's smooth overall for best system performance. Then look at frequency response of the whole system, also group delay / step response to evaluate how well a square wave would come through on an oscilloscope. For ear it comes through quite nicely, even though oscilloscope would show the waveform distorted (due to bandwidth limit and some group delay).
https://en.wikipedia.org/wiki/Square_wave
If you look at the physics involved, a speaker driver follows the second derivative of the voltage waveform that is applied to it over the majority of its operating range where it is "mass controlled". Below the mass controlled range is it just distorting the signal. That is to say the voltage develops a roughly linearly proportional current in the voice coil. The current creates a proportional force F = BLi, Magnet flux * wire length * current. The force then produces a constant acceleration F = m * A solved for Acceleration = Force / mass, during that constant voltage across the top of that square wave. So the cone motion is accelerating faster and faster during the flat voltage & current waveform making a rising or falling exponential motion. Now because pressure produced by a moving cone is linearly proportional to acceleration, the pressure wave produce by the exponential motion of the cone will produce a square wave with flat tops in the pressure waveform, faithfully reproducing the recorded sound. I can't recommend this book enough. Magazines have spread disinformation about speakers for the last 30 years so successfully it is just sad. https://www.amazon.com/Current-Driv...inating-Distortion-Interference/dp/1450544002
 
  • Like
Reactions: stv
Hi,
not sure if I understand what you mean by distorted signal below mass control? otherwise seems legit for what I understand.

I haven't read the book, since I think this article of his contains enough information to understand how a transducer roughly works and how it all plays out and hints how to utilize the information in practice with any loudspeaker systems:
https://www.edn.com/loudspeaker-operation-the-superiority-of-current-drive-over-voltage-drive/

It explains the "mass-control" as well 🙂

It is fun to try imagine how a driver would actually move with input signal, and I've recently tried to get some handle on it imagining with sinusoidals. But this is really beyond what one needs to design and make loudspeakers with off the shelf parts so haven't got too far with it.
 
Last edited:
Addressing the behaviour as a 'mass controlled' range is too simple. It neglects the radiation impedance: a dynamic transducer isn't solely a mass-spring-system. Also, as I understand it, current drive is harder to implement in the range where the mass-compliance relation controls the movement. Over here we have a lot of folks that still are on the track of motional feedback: that I regard a valid solution for current steering systems.