Electrostatic Headphone Measurements

[Robbo1802]

Hi arnaud,

A quick note. The main reference "Loudspeaker and Headphone Design" 3rd ed by John Borwick is currently in an active torrent and is also up on usenet in alt.binaries.e-book.technical

Regards,

Bob

[Tyll Hertsens]

Yeah, doesn't sound like a SR-007 to me. Same is true about statements that the SR-007 is less smooth than the SR-009, not true to these ears unless you are listening at whisper quiet levels. The SR-007's crowning achievement is to remain smooth even at silly levels. Push the SR-009 just a little bit and they bite, hard.

Thanks Birger, I'll listen more.

[arnaud]

Edit: 9/24, different mic positions and cleaner pics / animations

Here is an initial attempt at understanding what makes the SR-009 measure how it does. It's all very very fresh and largely guessed properties so I could be totally off the map with these predictions, but at least I have some pretty pictures and animations to share .

Here's the simplified geometry of the model (note that the earpads are currently modeled as rigid surfaces. Since there's a thick leather cover, it shouldn't that far off (little absorption):

Here is the resulting SPL at some locations ~1cm above the "ear surface" (currently assumed to be a rigid surface, I may be able to add actual dummy head geometry later on). The microphones at above 1cm apart so you can see typical variations as the headphone is moved around:

Then, some illustration of the pressure response around the headphone at the 3.6kHz resonance as well as 6.6kHz where you see lobes in some of the microphones response:

Finally, an animation of coupled structural/acoustic dynamics at the the same frequencies. Note that the diaphragm material is bogus as I have absolutely no idea of the tensioning and resulting natural frequencies. I just used a 1.5 micro meter nylon with increased stiffness to simulate the tension and adjusted that to get the first diaphragm "piston" mode at about 50Hz. This turns into over a thousand wiggling modes in the diaphragm by 10kHz...:

http://www.youtube.com/watch?v=_cV_0vsZX38

http://www.youtube.com/watch?v=HrcnUQ-DXmQ

Edited September 24, 2011 by arnaud

[arnaud]

Arnaud how did you generate those comparison plots for frequency response? I am using Tyll's data and getting something that looks different. I checked it 3 times.

Using the 'Headphone Data' sheet, column AH for the time vector, columns AK and AL for the impulse responses of Left/Right ears respectively. Let me know, I could certainly have goofed of somewhere.

[Dreadhead]

Ah. I used the frequency response channels.

[Tyll Hertsens]

You, sir, are insane .... insanely cool! Great stuff!

[purrin]

^^It is interesting, eh?

Maybe the math geeks and engineers can chime in on this one, but if you look at the impulse response of the 009, just prior to the impulse there's some pre-ring. I'm wondering if there is something going on that, with very fast headphones, causes artiacts that aren't exactly representative of what's actually going on. The first spike on the HD 800 also is very fast and has significant spike and undershoot. Also, we have to remember that while the FR plots are compensated, the square waves are not, so what appears to be an error (big initial spike) may actually be desirable. Dunno. Love to hear some thoughts.

Tyll, looking through your data download sheets, I can't seem to find any correlation between headphone characteristics and pre-ringing. For example, the HE6 ,T50RP, and LCD2 look clean, the HE5 exhibits obvious pre-ringing, the HD800, T1, and RS1 exhibit very minor pre-ringing. I haven't thoroughly checked through my own data, but I think everything I've got has some pre-ringing, which could be an effect of the reactive components (caps) in the amp that I'm using.

As far as the square wave initial overshoot and following undershoot, it's hard to say what's supposed to be ideal. I like to think of this similar in a way to how a car suspension (shocks) works. My personal view is that some overshoot is good. To me the HD800 and SR007 are just right. The Grados and HE6 are a bit way too much (they sound etched), and the LCD2 is a bit over-damped. And this correlates very well with your data.

In the end, it's what you said - trust our ears.

Edited September 22, 2011 by purrin

[Robbo1802]

Hi Tyll,

^^It is interesting, eh?

Maybe the math geeks and engineers can chime in on this one, but if you look at the impulse response of the 009, just prior to the impulse there's some pre-ring. I'm wondering if there is something going on that, with very fast headphones, causes artiacts that aren't exactly representative of what's actually going on.

Yes I note the pre-ring is also in the 007 tests but none of the others I downloaded from your site seemed to have it (that I can see in the smaller plots). Pre-ring implies a time machine or prescient headphones. I'll stick with the time machine (digital delay lines) so it is most likely an artifact of your measurement rig, It looks suspiciously like the pre-ring of a high order, low pass, Finite_Impulse_Response Filter. Have you changed anything lately? Perhaps a filter setting or windowing function??

The first spike on the HD 800 also is very fast and has significant spike and undershoot. Also, we have to remember that while the FR plots are compensated, the square waves are not, so what appears to be an error (big initial spike) may actually be desirable. Dunno. Love to hear some thoughts.

One thing to note on the 007 vs 009 is that there's a significant rise in the treble at 10kHz on the 007 that's not there on the 009. Also there's more noise in the long tail of the 007 impulse response.

Another thought that's come to mind is that when we're talking about splitting hairs with great cans, hte ear may be better at identifying the character of the headphone than the measurement system. Measurements slice the apple in numerous ways for a good looksee, but it's nothing like biting into it for a taste.

I will have to think about some of this. My initial thoughts:

The square wave and impulse responses are really testing the same thing when it comes to the early part of the waveform. The speed of attack, ringing etc is always a balancing act where damping sometimes has all the subtlety of a lump-hammer. The quest for lower and lower moving masses is all about reducing the stored energy and making it easier to damp out ringing without loss of attack. The compensation ( I assume you mean the free field etc) probably will not greatly affect what you see in the square waves. I am surprised by how different the impulse responses are between the two Staxs without huge differences in CSDs.

The ears are surprising good at detecting some things,but it is a learned skill and it needs a reference point - what do these instruments really sound like? My own testing way back with the pianos and speakers involved listening to the piano for at least half an hour before auditioning the speakers - there were no recorders involved,the guy was a pianist and had a sound insulated studio complete with concert grand and another sound insulated room that was his music room (where the speakers were auditioned). When auditioning the speakers, the sound path was piano>mic>preamp>lineamp>power amp>speaker.

Regards,

Bob

A rough estimate of the ring places the transition frequency of the filter at about 32Khz, have you done an electrical loopback test of the impulse test?. A second look at the CSDs for the Staxs does correlate with the impulse response, the problem with the CSDs is the linear frequency scale, so much of the important information is compressed on the left side that it always skews my perceptions.

Edited September 23, 2011 by Robbo1802

[Robbo1802]

Hi Arnaud,

I don't really know what to say. The power of modern software - astonishing!

This is an edge clamped uniformly tensioned membrane,isn't it? In the last animation what are we looking at,displacement/velocity?

I am rather confused by the large modal variation (what are we going to call the peaks and hollows?) at the edge of the diaphragm, intuitively the least likely spot for such variations. Quite frankly, at 3.7khz I would have expected a much lower mode (annular too),much more heavily damped - there goes my insight, fluttering away like that diaphragm.

Still in all, very impressive,

Bob

BTW

If you find some data on the compliance of real Mylar, remember that the bias voltage creates a negative compliance thus reducing the net compliance of the membrane.

Edited September 22, 2011 by Robbo1802

[Dreadhead]

Using the 'Headphone Data' sheet, column AH for the time vector, columns AK and AL for the impulse responses of Left/Right ears respectively. Let me know, I could certainly have goofed of somewhere.

I think that using the straight up sweep based frequency response curves for comparison between the HD800 and 009 is probably a lot more accurate considering the delta omega problems that such a short time history give you as far as accuracy goes.

Also the numerical solution you put up was very very cool but I wonder what boundary conditions were used to prevent acoustic reflection on such a small computational domain. Again though it's very cool you have access to that kind of software to waste time on this stuff

[arnaud]

You, sir, are insane .... insanely cool! Great stuff!

Thank you, insanely tired too, those 4 hour nights are starting to be felt .

Hi Arnaud,

I don't really know what to say. The power of modern software - astonishing!

This is an edge clamped uniformly tensioned membrane,isn't it? In the last animation what are we looking at,displacement/velocity?

I am rather confused by the large modal variation (what are we going to call the peaks and hollows?) at the edge of the diaphragm, intuitively the least likely spot for such variations. Quite frankly, at 3.7khz I would have expected a much lower mode (annular too),much more heavily damped - there goes my insight, fluttering away like that diaphragm.

Still in all, very impressive,

Bob

BTW

If you find some data on the compliance of real Mylar, remember that the bias voltage creates a negative compliance thus reducing the net compliance of the membrane.

Hi Bob, the diaphragm is modeled as a circular membrane and edges are assumed pinned. In regards to the animation, actually I should have mentionned: it is NOT to scale! It is just an animation of one of the "coupled" modes around 3.7kHz. Velocity range is actually visible for the 2 peaks where I show the contour plot. But again, properties I used for the membrane are bogus so really the diaphragm velocity isn't too trustable... BTW, I assumed 10% damping for the diaphragm and not actually modeling the perforated stators.

I think that using the straight up sweep based frequency response curves for comparison between the HD800 and 009 is probably a lot more accurate considering the delta omega problems that such a short time history give you as far as accuracy goes.

Also the numerical solution you put up was very very cool but I wonder what boundary conditions were used to prevent acoustic reflection on such a small computational domain. Again though it's very cool you have access to that kind of software to waste time on this stuff

Also the numerical solution you put up was very very cool but I wonder what boundary conditions were used to prevent acoustic reflection on such a small computational domain. Again though it's very cool you have access to that kind of software to waste time on this stuff

Good question dreadhead... The acoustic boundary condition is simply rho *c (acoustic impedance in free field). But I was indeed concerned about how large the box should be around the headphone to get reasonable results when I did the same kind of simulation for the HD800. I have been looking at another type of simulation (using boundary element method referred above) where the headphone would actually be modeled along with the whole radiation space but not quite satisfied yet with the HD800 results. I may try it with the SR009 geometry...

[Tyll Hertsens]

Is it bad that I have a chubby?

[morphsci]

My problems with the 007 is mainly in comparison to the Omega and has to do with a more compressed soundstage and a tad bit of slowness that mushes up the clarity when the music gets complex. I do not listen at Ray Smuel levels either.

[Tyll Hertsens]

I do not listen at Ray Smuel levels either.

Good choice. Thanks.

[Robbo1802]

Hi Nevod,

I initially missed your post

I believe (as in, I don't have anything to back up) that this could also be due to damping. To cancel even harmonics, you need symmetry, and usually, there is no symmetry in headphones - outer side radiates freely into air, inner is loaded by a sealed cavity. Granted, backside is usually damped, but it is still nowhere near symmetric. To obtain symmetry, one would need ports on the inside, and the ports should provide resistance equal to backside resistance. To make this controlled you'd also need well sealing earcups..

Different side to side diaphragm loading (or damping) should not create asymmetrical diaphragm movement and thus 2nd order harmonic distortion. The diaphragm 'sees' the load on both sides as the total load, and will respond to the total load ( again from both sides) independent of the direction of travel. Now if the behaviour of the damping material was asymmetrical, that is, there was more resistance to the air moving in one direction than the other, then it would produce asymmetrical movement of the diaphragm and thus even order harmonic distortion.

And, I don't want to steal any discussion, but..What really bugs me is LCD-2s square wave and impulse responses - they look near perfect. Minimum overshoot and flat zones are really flat on square wave (though I guess that en even more mighty amplifier for Staxes would correct that). But impulse responce seems to be much better than any other headphone, regardless of technology - most of them dip instead of peaking on the impulse, while LCD-2s plot looks like "it's just as it should be". Makes wonder about the construction of the driver and damping.. Or, reciprocally, why all other phones, Stax included, dip on the impulse.

Yes the LCD-2s do seem to show the best measured performance, certainly the distortion plots are very good with an outstanding CSD. Indeed the CSD shows far less stored energy in the midrange than any others I have seen shown here, the bass is astonishing, okay there are a few small ridges but....

The slope on the square waves is mostly a function of the now airtight the ear cup is, the flat part of a square wave is after all DC - consider a square wave of 1hz, the air will leak out.

When you say dip are you referring to the absolute 'phase' of the headphones, that is, a positive voltage spike creates a positive pressure spike? I will not get into the debate over absolute 'phase' except to ask: are you sure that Tyll's test rig has correct absolute 'phase' and doesn't invert the signal, perhaps it is LCD-2s that are inverted?

Regards,

Bob

Hmmm, The ESP-950s do seem to have ports in the stators rather than the usual holes, they appear to be asymmetrical with one end curved and one straight end, possibly..... nah, I just don't believe it, the fluid velocity could not be high enough for asymmetrical turbulence.

Edited September 23, 2011 by Robbo1802

[Dreadhead]

I have a hard time thinking that the impulse response of anything ever looks perfect.

The question is really perfect for what? If you have no overshoot then you have either incredible high frequnency response (unlikely) or too much damping to respond quickly (much more likely). A transducer with a lot of damping will look awesome on a CSD plot but that does not necessarily mean that it sounds good or even correct. To be honest at least to my looking at things your phone should reproduce the overshoot pattern of 22.05 kHz band passed data or some such with post-ring and all.

[Tyll Hertsens]

except to ask: are you sure that Tyll's test rig has correct absolute 'phase' and doesn't invert the signal, perhaps it is LCD-2s that are inverted?

At one point I was curious myself. So I found a pair of headphones in which I could see the driver, hooked it up to a battery in proper polarity and could see the driver moving in the right direction, and then tested it. So I have manually checked the polarity and it looked proper.

[spritzer]

My problems with the 007 is mainly in comparison to the Omega and has to do with a more compressed soundstage and a tad bit of slowness that mushes up the clarity when the music gets complex. I do not listen at Ray Smuel levels either.

I don't listen at insane levels either but I do think the SR-007 needs to be pushed a bit to truly excel. Not to insane levels mind you but this "MOAR POWAH!!!" crap has some truth to it. When the SR-Omega (and to a lesser degree the SR-009) start to misbehave the SR-007 still just takes it all and asks for more. If any of you are brave enough, listen to the intro of Megadeth - Trust at silly levels and report back. The SR-009 doesn't like it one bit but the SR-007 is just fine with the BHSE maxed out... Still, I only try this for academic reasons.

[edstrelow]

.I am enjoying this thread a great deal. It is nice to see some real data on these phones as opposed to the normal, purely subjective assessment.

Of course the interpretation of data then leads to debate as to how accurate the data collection is, how it was collected and what the data then mean to the listener which the ultimately gets you back to the subjective..

Hi Tyll,

Yes I note the pre-ring is also in the 007 tests but none of the others I downloaded from your site seemed to have it (that I can see in the smaller plots). Pre-ring implies a time machine or prescient headphones. I'll stick with the time machine (digital delay lines) so it is most likely an artifact of your measurement rig, It looks suspiciously like the pre-ring of a high order, low pass, Finite_Impulse_Response Filter. Have you changed anything lately? Perhaps a filter setting or windowing function??

Good point. The discussion of square wave response may be premature if there are artifacts in the measurement system.

I am not sure about the various waterfall graphs which have been posted here either, in part since I assume they must also be based on some sort of impulse signal which would presumably be subject to the same artifact noted above. I am have having some problem following some of this discussion as to what is an actual measured response, what is derived from existing data and what is some kind of hypthetical simulation.

The Frequency response data seems interesting and uncontroversial. But I would mention some additional points of testing or discussion which it would be nice to see clarified..

First whether the measuring set-up is properly compensating for pinna and ear canal effects so as to measure "flatness." comparable to measurements of speakers. It is my understanding that the system does ini fact attempt to do this but exactly how I am not sure.

Secondly there is the issue of repeatability. To what extent you are getting positioning effects such that the measured response could change with a slight tweaking of position of the phones i.e. if the same phone is measured at different times is the response going to look the same.

There is the question of how repeatable the measurements are across other examples of the same model or whether there may not be individual differences between examples of the same model. One simple example could be that changes in stiffness and compression of ear pads could give different results. Then there is the possibility that the manufacturing process for phones does not give exactly the same result every time.

Finally, could some-one give an explanation as to why the high frequency responses of many phones is so much less smooth than the lower and mid frequencies. Are the transducers this erratic or is this the result someting like cancellations from reflections within the ear cups?

Of course these are issues that measurement can clarify and I hope that will happen here.

On the subjective side, there is little doubt that a reasonably flat frequency response is desireable in a headphone simply because this indicates that the phone is neutral. However when you get up to the high frequency range you probably want some roll-off in part because there is a natural high frequency roll-off with distance from a sound source and most recordings are made with microphones closer to the source than one would normally hear. Plus there seems to be an awful lot of high-frequency equalizing boosting in recordings, especially rock-pop. It looks like most of the phones are in fact giving some high frequency roll-off.

But this is a great thread and Tyll has provided some important new information to anyone with a serious interest in headphones.

[purrin]

My CSD plots are on HF for the SR009.

[catscratch]

My problem with the 007, if there even is one, is that it's too laid-back. With sources that are too polite it's easy to make a rig that sounds distant and dull. But with bolder, ballsier sources it's more engaging, though I would still prefer a more forward sound. On the other hand I find the tonal balance near perfect and anything substantially brighter would be an issue. All joking aside I listen fairly loudly but nowhere near rock concert levels; those I can't ever go to without earplugs. A headphone without treble/bass emphasis does sound more linear the louder you push it, and the 007 does open up more and more as you crank it up.

[arnaud]

@Marv: I wouldn't mind using your raw data for my model... It's with anechoic plate, isn't it?

@Ed: Here's a reason why I shouldn't have posted my simulation result in this thread. I will create a new thread and post there (did the same on HF http://www.head-fi.org/t/572968/modeling-headphone-s-acoustic-performance#post_7774290 , it'd be better to have it all in 1 place though).

There are no assumptions in the processing of test data. Only thing is that my CSDs and FRF comparisons are for a single position and not equalized (yet... Expect some update today on this). For the data acquisition, there is maybe something going on with artificial smoothing to get the signal to die within 3ms but this still needs to be investigated (difficult to compare directly the results with those of Marv due to entirely different recording process).

[Clarkmc2]

I don't listen at insane levels either but I do think the SR-007 needs to be pushed a bit to truly excel. Not to insane levels mind you but this "MOAR POWAH!!!" crap has some truth to it. When the SR-Omega (and to a lesser degree the SR-009) start to misbehave the SR-007 still just takes it all and asks for more. If any of you are brave enough, listen to the intro of Megadeth - Trust at silly levels and report back. The SR-009 doesn't like it one bit but the SR-007 is just fine with the BHSE maxed out... Still, I only try this for academic reasons.

I think the SZ3 likes the dBs too. Any progress, oh busy one, on trying to modify SZ2s and SZ3s towards the 007? Might a thread be created once the quest is done? My 3s are still dead stock.

[arnaud]

I have a hard time thinking that the impulse response of anything ever looks perfect.

The question is really perfect for what? If you have no overshoot then you have either incredible high frequnency response (unlikely) or too much damping to respond quickly (much more likely). A transducer with a lot of damping will look awesome on a CSD plot but that does not necessarily mean that it sounds good or even correct. To be honest at least to my looking at things your phone should reproduce the overshoot pattern of 22.05 kHz band passed data or some such with post-ring and all.

I agree that there is no such thing as a perfect impulse response as it equals a headphone with unlimited bandwith. In the present case, the microphones may be rolling-off before the headphone and remember that all the measurement chain is lumped on the result...

As for using too much damping, it's probably a bit difficult to answer when it is or not appropriate. I guess we all agree that sharp peaks in the magnitude response (and subsequent long ridges in the CSD plot) are not too desirable. On the other hand, maybe extreme damping on the surfaces of the earcup might actually sound unnatural, like giving too much of a feeling of a direct sound coming from the transducer (I hate to have the sensation that the driver is very near my ears, which does occur with some headphones). Another typical trick is actually using the resonances to enhances the tone (e.g. John Grado's headphones which certainly have a fanbase).

First whether the measuring set-up is properly compensating for pinna and ear canal effects so as to measure "flatness." comparable to measurements of speakers. It is my understanding that the system does ini fact attempt to do this but exactly how I am not sure.

Finally, could some-one give an explanation as to why the high frequency responses of many phones is so much less smooth than the lower and mid frequencies. Are the transducers this erratic or is this the result someting like cancellations from reflections within the ear cups?

The graphs Tyll shows - at least the FRFs - include results that are both averaged (across 5 or so headphone positions, averaging is done in dB directly so it smooths things out heavily) as well as compensated for the dummy head response. I am not clear yet at what angle of incidence (it's not diffuse field and referred as "Independent of Direction Equilization Parameters", maybe Tyll can clarify).

As for the erratic behavior at high frequency, this is inherent to the physics in place. In particular, imagine that the acoustic wavelength (=340 / frequency) is ~1.5cm at 20kHz... That means that the sound pressure inside the earcup - if it was undamped - would have 40dB swings when you move the microphone of barely 8mm (half a wavelength at 20kHz). Similarly, just pushing the earpads by say 3mm would have also a huge effect on the results.

To illustrate the point, I have updated the simulation results (I said I would not talk about this in this thread anymore but you're asking for explanation and there's nothing better than an image here with SPL from microphones placed ~1cm apart. In the animation plots, you can see it's fairly homgoneous SPL in the base of the earcup (mics location) at 3.5kHz but starts to go a little more wild in the 6kHz one. I can't do these simulations easily up to 20kHz but you'd essentially get even more complex pressure field.

Original post:

FRF:

Animation 3.5kHz: http://www.youtube.com/watch?v=_cV_0vsZX38

Animation 6kHz: http://www.youtube.com/watch?v=HrcnUQ-DXmQ

Edited September 24, 2011 by arnaud

[purrin]

@Marv: I wouldn't mind using your raw data for my model... It's with anechoic plate, isn't it?

Yup. I'll do another measurement with the solid plate too. I figure the more data, the better for your models. I would send you LCD2 data too, but the driver production variances are too extreme, even among those on the same headphone.

Edited September 24, 2011 by purrin