The resolution of Lorentz transducer (loudspeaker)

[Jazigo]

Hi everyone!

Sorry if this have been asked before or comes across as a silly question, but during a discussion about voice coils and precision in analog devices; the question about the resolution of a voice coil came about.

Gemini, the AI, told me that voice coils can reach closed-loop resolutions down to 10 nm. Super impressive per se, but a 6" loudspeaker excursions range is about 10mm (5mm each way).
If I divide the excursion range over the resolution, (10mm/0.00001mm), then we are left with 1 000 000 steps over that range, that is about 20 bit of steps.

So, can one say that loudspeakers voice coil can resolve about 20 bit of data or am I completely off with my thinking here?

 

[Cbdb2]

AI was talking about these "Zaber offers a wide variety of voice coil and other direct drive linear stages with optional built-in controllers. These stages are ideal for high speed and high precision positioning applications." I think that the 10 nm resolution means it can move in 10 nm steps. Not speaker voice coils which dont have steps or a "resolution".

 

[Jazigo]

I realize that a voice coils don't have steps per se, but if I ask it go to a certain position over the excursions range, then it can do about 1 000 000 unique steps with precision(?).

 

[bmc0]

Gemini, the AI, told me that voice coils can reach closed-loop resolutions down to 10 nm.

Different kind of voice coil. It's talking about a closed-loop linear actuator like what's used to control the position of the read/write heads in a mechanical hard drive.
The motor in a loudspeaker driver is (usually) open loop and does not have discrete steps. Additionally, the physical quantity that directly translates to sound pressure is acceleration, not position. Effective positional accuracy could be quantified, but it would be strongly dependent on frequency and level. I don't think it's very useful to think of it this way.

 

[NTK]

Here are the various nonlinearities in a loudspeaker driver by Klippel. Each driver, even from the same model, will be different. I'll let you figure out if the 10nm "resolution" is the ultimate bottleneck.
https://www.klippel.de/fileadmin/kl...rature/Papers/Klippel_Nonlinearity_Poster.pdf

 

[SHB]

Again, a voice coil doesn’t propel the loudspeaker driver in finite steps.

The driver starts at rest and its suspension wants to return it to that position. The electrical signal running through the voice coil pushes it in one direction or the other.

The signal sent to the voice coil is an alternating current.

You seem to want to know about a DC current. Yes, you can displace the speaker diaphragm by discrete distances from its resting position with a direct current.

That has no bearing upon the sound of the speaker driver because it’s drastically outside of the design of what a speaker is meant to do.

You can use a scalpel to chop an onion…

 

[Jazigo]

Here are the various nonlinearities in a loudspeaker driver by Klippel. Each driver, even from the same model, will be different. I'll let you figure out if the 10nm "resolution" is the ultimate bottleneck.
https://www.klippel.de/fileadmin/kl...rature/Papers/Klippel_Nonlinearity_Poster.pdf

Oh, that is cool! I shall study it.

Effective positional accuracy could be quantified, but it would be strongly dependent on frequency and level. I don't think it's very useful to think of it this way.

I am thinking like this: say I send a sine wave where I go between 500 000 and -500 000. And I then send a sine wave that goes between 499 999 and - 499 999. Will the voice coil actually be able to produce the difference accurately (given all other components in the chain are super perfect in every possible way)?

 

[SHB]

Simple answer: yes.

You’re quoting numbers that have no meaning so can’t comment on that more.

You don’t seem to understand that a voice coil is immersed in a magnetic field and that the polarity of the field and the direction of the electric current are responsible for the movement of the speaker diaphragm.

Dude, hit up Loudspeaker Physics 101.

 

[Jazigo]

Simple answer: yes.

You’re quoting numbers that have no meaning so can’t comment on that more.

You don’t seem to understand that a voice coil is immersed in a magnetic field and that the polarity of the field and the direction of the electric current are responsible for the movement of the speaker diaphragm.

Dude, hit up Loudspeaker Physics 101.

So, does this mean that they are infinitely accurate?

 

[SHB]

Nothing is infinitely accurate.

There will be a point where the suspension of the speaker will not allow the diaphragm to move because the force created by the electromagnetic circuit is too small.

You really need read up on this because you seem to have very little understanding about how a loudspeaker works.

 

[Jazigo]

Nothing is infinitely accurate.

Can we put a number on this then?

 

[bmc0]

I am thinking like this:

I understand what you're asking (more-or-less). I'm telling you that thinking about resolution in this way does not make sense for a loudspeaker driver. There is no practical limit[1] to the ability to reproduce arbitrarily small differences, but the limits of absolute accuracy are easily measurable. In other words, it can reproduce a million discrete steps just fine, but the steps won't be the same size.

[1]: For simplicity, I'm ignoring magnetic and mechanical hysteresis.

 

[SHB]

Can we put a number on this then?

Sorry, not being a guy who does the engineering on loudspeaker suspensions, I can’t do that.

Lars Risbo of Purifi would be the man to ask.

At this point, it’s obviously a wind up if it hasn’t always been one.

Here’s a thought: get a free, online subscriptions to VoiceCoil magazine. It’s fantastic, been reading it for years.

Please avail yourself of a universe of information you don’t know.

 

[Jazigo]

In other words, it can reproduce a million discrete steps just fine, but the steps won't be exactly the same size.

So it will have an error range (∓) for each step then, I presume. Is there any way to put some numbers to such an error range for a voice coil? Like mention before in this thread, it is probably very frequency dependent, but interesting none the less for a single frequency.

Edit: Gemini, says that accuracy and repeatability are often in the ±1 µm to ±2.5 µm range for standard high-dynamics stages in voice coil actuators (VCAs) utilizing Lorentz force principles. Maybe not the correct voice coil (this is for closed loop), so maybe not that indicative.

 

[NTK]

So it will have an error range (∓) for each step then, I presume. Is there any way to put some numbers to such an error range for a voice coil? Like mention before in this thread, it is probably very frequency dependent, but interesting none the less for a single frequency.

Edit: Gemini, says that accuracy and repeatability are often in the ±1 µm to ±2.5 µm range for standard high-dynamics stages in voice coil actuators (VCAs) utilizing Lorentz force principles. Maybe not the correct voice coil (this is for closed loop), so maybe not that indicative.

If you run some calculations (you may also ask your favorite AI chatbot to do it for you), you will find out that the diaphragm displacement of a 1 in tweeter producing 90 dB SPL at 5 kHz is in the order of several μm. Therefore, a tweeter motor must be able to do a lot better than 1 μm repeatibility (repeatibility as a small DC offset doesn't matter).

 

[bmc0]

Is there any way to put some numbers to such an error range for a voice coil?

Given a particular frequency and drive level, an approximation of the positional error could be calculated from estimated excursion along with the total harmonic distortion, assuming the driver nonlinearity dominates[1]. For a subwoofer at high excursion, the error may be on the order of a millimeter. For a tweeter at moderate SPL and high frequency, the error may be on the order of a nanometer. If one also considers the level dependency and the fact that the error expressed as a ratio decreases with decreasing level[2], it should be clear why any single number one may calculate would be essentially meaningless as some kind of general estimate.

[1]: Not necessarily the case for a tweeters or other drivers with very high local SPL, especially at high frequencies. Air nonlinearities may be dominant in those cases.
[2]: I've never seen an acoustic measurement of a properly functioning loudspeaker driver showing an increase in relative error as level falls that is not attributable to noise or low-level nonlinearities in the electronics (e.g. zero-crossing distortion in the amplifier). Presumably, there's some lower limit where diaphragm motion would become "steppy", but it seems to be well below what is practically measurable acoustically.

 

[Jazigo]

I am currently dissecting this paper: Why and How to Test Voice Coil Position in Production Line

It seems to mainly focus on offset from 0 (resting position), but it also touches on the envelope of movement to detect if the coil moves too far in one direction.

 

[kemmler3D]

As others have mentioned, the question is tricky and underspecified. You're trying to find the minimum amplitude error of a voice coil based driver, but what kind of driver, under what usage conditions, etc?

Once you determine all of that you can find the dominant source of noise or distortion and come up with a number.

I might also not rely on Gemini for this, it doesn't even seem to realize you're talking about audio.

 

[Jazigo]

As others have mentioned, the question is tricky and underspecified.

I realize I came into this from a strange position, but my view was that of an operator of a coil. In other words, how many effective number of bits to I need before it doesn't matter because of errors.

As you said, it is probably not one number for all frequencies or types of drivers. But maybe one could say that the only limit is in the accuracy of the voltage feed to the coil? Or the uniform magnet quality set the terms for the amplitude error.

Gemini

I am a horrible AI operator.

 

[kemmler3D]

But maybe one could say that the only limit is in the accuracy of the voltage feed to the coil? Or the uniform magnet quality set the terms for the amplitude error.

I think some math is involved before one could say this. And it probably varies by driver. Maybe a low quality magnet can be the limiting factor, but a high quality one won't be. I really don't know.

What @NTK posted is actually your best starting point in the thread. One of those graphs should point the way to the limiting factor on amplitude error. But I do think you have to know more than a tiny bit about voice coil drivers to say which one. That's not me.

how many effective number of bits to I need before it doesn't matter because of errors.

Number of bits in the input signal determines noise level. Generally even 16 bit noise is inaudible in use. So an easier way to approach this question is whether there is any distortion component in typical drivers that doesn't mask a -96dB noise signal. Driver distortion is correctly considered to be a much bigger problem than anything coming from DACs or amps.