Request: Study of Damping Factor and Planar Magnetic Headphones

Looks like they were just measuring the back EMF at the amplifier and not acoustic output.

U = R*i + Le (di/dt) + BL (dx/dt)
F = BL*i = Mms(d²x/dt) + Rms(dx/dt) + Kms(x)

BL is force factor, U is voltage, i is current, x is displacement and associated time derivatives.
You can get that system of equations from the T/S parameters and arranging it to fit the form of a series circuit and damped resonator.

BL (dx/dt) represents the voltage of the back EMF from moving a perpendicular arranged wire in a magnetic field. The coil arrangement gives rise to Le, driver inductance. If the wiring were flattened out, Le voltage would drop out but it is still a wire in a magnetic field.
Voltage generation is the dual of magnetic damping, the force lost from the driver motion is converted into electrical potential. The back EMF drives up the impedance at the velocity maximum of the driver, near resonance(s),
The lack of impedance rise, or even a tiny blip, would point to the magnetic damping component being negligible in most planar dynamics.

 

It's just a linear model, and it neglects much acoustics. If we're focusing on the impedance, BL is non-linear, inductance is not so constant itself and generates its own magnetic flux.
There's more to actual mechanical motion, viscoelastic damping, and I'm sure I forgotten something else as well.
Model assumes zero ohm source impedance. R is the driver real resistance, and back EMF drop would be entirely across the driver itself,

AFAIK they usually are modeled with limited order for general cabinet design, lumped parameter box solvers and the like.

On a related note, a non-linear modeling tutorial for your pleasure.

 

I put together a measurement rig (link describing that coming soon) and compared three headphones: my stock Sony MDR-MA900, my modded HD-650, and my stock Mr. Speakers Alpha Dog. I wanted to see whether moving from the 0.47ohm to the 47ohm output of my Geek Out 1000 would make a measurable difference. Check out the attached plots to see what I found.

Caveat: I'm a complete measurement n00b and have tried to do a good job w/these measurements, but who knows if I screwed something up along the way. If it looks like from my plots that I did screw something up, please skool me.

My takeaways:

* The Alpha Dogs (a T50RP planar mod) show the least changes in frequency response when changing amp output impedance
* The Sony MA900s show the most, which is predictably seen as an increase in bass & midbass volume
* The HD650's show a very subtle change.

Sorry I didn't have time for subjective listening tests.

Interesting side-note: my first round of tests was at a higher volume, like ~110dB. After looking around at others' plots I see that measuring at around 90dB is more common, so I did a second round of tests (the plots shown here are from that second test). The differences in bass and midbass FR were more pronounced at the higher volumes, FWIW.

PS - Imgur album of plots if that's easier to check out: http://imgur.com/a/i1bRn

 

Nice!

I think your FR measurments looks fine and comparable with other measurements.
If you've measured (FR) the Alpha Dogs a few times with 0.47 Ohm and 47 Ohm and you always get very similar results, I guess we can asure that FR is not altered by the Low Damping Factor in this case (Flat Impedance). Exactly as the (voltage divider) model suggests.

On the other hand, your Harmonic Distortion measurements intrigue me quite a bit.
If we compare your graphs we might end up thinking there are no apparent/noticeable changes in harmonic distortion, but I'm still not sure if we can rely on your harmonic distortion measurements because they don't look very 'normal' to me.

Here we have HD650's plot by Marv

Second order distortion is not as spiky, then 3rd and 4th order distortions are much lower in level.

Same for MA-900 (Hands)
www.superbestaudiofriends.org/index.php?threads/sony-mdr-ma900-impressions-and-measurements.1302/

I think your harmonic distortion measurements should be consistent with those of other people before we can start concluding things based on your harmonic distortion measurements.

Then:

What's up with those Harmonic Distortion measurements?
Why they don't seem to match Marv's or Hand's measurements?

I guess, someone more knowledgeable about measurement rigs might be able to help us here in order to make your rig consistent with other rigs.

Thanks for your positive attitude!

 

Hey, news here!

The main topic of this thread is the measurability of the effects of Low Damping factor, beyond the equalization in the shape of the impedance (vs frequency) plot that can be explained using the voltage divider model.

For most practical applications, how does a planar magnetic headphone (flat impedance) measures when driven with an amplifier with relatively high output impedance (ie. Low Damping Factor)

So, here we go.

Equipment Used (@philipmorgan 's)

Measurement System: #106

Headphone A:
Mr. Speakers Alpha Dog
Type: Planar Magnetic
Impedance: Flat (47 Ohm) pink trace here

Headphone B:
Oppo PM-3
Type: Planar Magnetic
Impedance: Flat (28 Ohm) pink trace here

DAC/Amp
LH GeekOut 1000 (two audio outputs with different output impedance)
Output 1: 0.47 Ohm
Output 2: 47 Ohm

Measurements ( courtesy of @philipmorgan )

Alpha Dog – 0.47 Ohm – FR and Harmonic Distortion (High Damping Factor)


Alpha Dog – 47 Ohm – FR and Harmonic Distortion (Low Damping Factor)


PM-3 – 0.47 Ohm – FR and Harmonic Distortion (High Damping Factor)


PM-3 – 47 Ohm – FR and Harmonic Distortion (Low Damping Factor)

Slight variance in Harmonic Distortion 50dB below is acceptable and can be attributed to natural limitations of the measurement system (mainly external noise)

Conclusions:

I think we have solid data to support a few key points here.
Considering DampingFactor = 1 for the AlphaDog and DampingFactor = 0.6 for the PM-3

1- Low Damping factor didn't affect the Frequency Response (significantly)

2- Low Damping factor didn't affect Harmonic Distortion (significantly)

Frequency Response and Harmonic Distortion are probably the most important characteristics when it comes to perceived sound quality. As this study suggest, low damping factor won't affect these when it comes to planar magnetic headphones with flat impedance and thus sound quality differences between high and low damping factor should be very subtle or even negligible in these particular cases.

It’s important to keep in mind that the total voltage that an amplifier can provide to a headphone depends on the Damping Factor and thus the conclusions (1 and 2) of this study are meaningful as long as the amplifier has enough voltage to drive the headphone at the desired levels despite the voltage drop caused by the low damping factor.

Further analysis would include CSD plots and extreme cases such as using a receiver with 500 Ohm output impedance to drive the headphones.

Big Thanks to @philipmorgan for the time and effort put into making all these measurements.

 

No inductance = no dependency of damping factor on freq. response chart. Nothing to argue about.