Does the amplifier voltage swing limits headphone dynamics?

[solderdude]

I read a couple of times but don't understand your point here. Are you saying emf damping is valid or not?

For headphones the damping factor is nonsense. Voltage division is the culprit of the change in sound when the impedance varies.
You have seen the math and impedances involved.

Do you happen to have an stepper motor at hand? If yes, try to turn it with open wires and than with shorted wires. Its getting much more difficult to turn with shorted wires, cause the generated voltage is shorted and you get an current flow acting as brake.

Let me ask you to measure the DC resistance of the stepper motor windings... Then you'll understand why the stepper motor is damped so well. Also the way the coils are layed out in the motor have something to do with that behavior.

This is the same effekt you will have at your speaker. Shorting terminals will counteract / damping motion of the coil in the magnetic field. This effect is less effective if you not short the terminal but include an resistor. And this resistor is corresponds to the output resistor of the amplifier. The higher the resistor - the less the damping effect.

Read my post again.. this is not about speakers with heavy cones and low resistances. This is about headphones with light membranes that are damped acoustically and mechanically a lot better and do not rely on electrical damping.

And yes, increase of THD is actually increased distortion. Voltage division is linear and doesn't cause distortion. THD is caused by nonlinear transfer function.

How come that when I measure headphones with a microphone and compensated for frequency response and applied amplitude I don't see an increase in THD ?

Did you not understand the principle of THD measurements and the role a higher output resistance plays (voltage division) when measuring THD at the output of a black-box (amplifier + output resistance) ?

 

[lucian]

Since I don't like discussion out of subjective old grey matter I did dig a little deeper. You find quite some stuff, but its difficult to get the really interesting paper's for free. Here are also some nice info's on dyaudio.

So at the end, current driving has significant advantages - but also lot's of drawback. It's ofc more significant for speaker with heavy masses, especially for subs.

For reference here is a really nice paper comparing voltage/current for a microspeaker - which comes close to headphones and here is practically no difference. I guess for planar (impedance flatliners) here is the least influence.

https://hal.archives-ouvertes.fr/hal-01112181/document

So voltage driven is currently the best compromise to be able to use speaker with analog filters and to match any amp with any mechanical transformer.

Therefore speaker/headphones are optimized for voltage driven source. You could actually optimize them for current drive, which would bring the advantage that your are getting independent of amp's impedance - every amp would have the same sound. Actually this is the effect high impedance headphones (600Ohm) do.

 

[lucian]

I guess we have the same basic understanding just about different boundary conditions.

However:

How come that when I measure headphones with a microphone and compensated for frequency response and applied amplitude I don't see an increase in THD ?
Did you not understand the principle of THD measurements and the role a higher output resistance plays (voltage division) when measuring THD at the output of a black-box (amplifier + output resistance) ?

If you have a electrical signal with THD and you apply this to an resistive load, you get current which also has this THD. If this current is feed to a coil (and inductance neglected) you get mechanical forces which also have this THD. In this case it doesn't matter how big this resistor is. And if you have a resisitve devider it just change the amplitude - the % part of THD stays constant.

So what do you mean with voltage division? We clearly talk about different things.

 

[solderdude]

So what do you mean with voltage division? We clearly talk about different things.

I'll try to explain once more.

THD is the ratio between the original signal and unwanted signals.
It's a number or can be lots of numbers (in the form of a graph/plot)

Suppose we have an amplifier with 0.001% distortion at 1kHz. This means all the crap, at different frequencies summed over say 20kHz bandwidth that is not supposed to be there is 100dB below that of the 1kHz tone.

Let's assume the output resistance is 0.1 Ohm and is connected to a 30 Ohm resistor we will measure the 0.001% of course.
Let's assume the output resistance is 10 Ohm and is connected to a 30 Ohm resistor we will measure the 0.001% of course (or extremely close to it).

Now we are changing the odds and connect it to a resistive load that has a 150 Hz sinewave generator in it that has an amplitude of about half that of the applied 1kHz signal.

Let's assume the output resistance is 0.1 Ohm and is connected to a 30 Ohm resistor with a 20dB lower 150Hz signal in it.
We will measure the THD at the output of the amplifier box.
30 Ohm source feeds into a 0.1 Ohm (are in series, thus there is voltage division)
This means the -20dB 150Hz source voltage is attenuated at the output of blackbox by 50dB so a total of -70dB of 150Hz will be measured as wel as the 1kHz at 0dB. So the distortion number goes up to 0.03% when measured 1kHz and the 150Hz tone is present as well.

Let's assume the output resistance is 10 Ohm and is connected to a 30 Ohm resistor with a 20dB lower 150Hz signal in it.
We will measure the THD at the output of the amplifier box.
30 Ohm source feeds into a 10 Ohm (are in series, thus there is voltage division)
This means the -20dB 150Hz source voltage is attenuated at the output of blackbox by 12dB so a total of -32dB of 150Hz will be measured as wel as the 1kHz at 0dB. So the distortion number goes up to 2.5% when measured 1kHz and the 150Hz tone is present as well.

This is what is measured and the number that is generated is higher. Fact remains the 1kHz that is heard still has 0.001% distortion products and is just as good sounding yet the measured number will have gone down from 0.03% to 2.5% just because of voltage division and the measurement that has been taken somewhere in a series circuit.

Now imagine the dynamic driver has some resonances and when one applies a peak that is short it will also excite the resonances in the driver and after a pulse it vibrates on its own frequency. This is easily shown in many of my square-wave plots of headphones.

As I explained before in the damping factor bit changing from 0.1 Ohm to 10 Ohm will lower the damping current (which is what damps the motion) is only slightly lower as the resistances are in series. There is a factor 100 in output resistance and factor 1.3 in current.
There also is a factor 100 in measured voltage + a factor 1.3 due to lower current. so factor factor 1300 in voltage division between the output R's.

So while the measured (a voltage, not a current) THD number goes up the actual signal isn't as bad as the distortion doesn't actually go up.
Instead the actual signal + in a different factor attenuated (the voltage division part) signal that is measured gives 'false' readings.

The distortion doesn't go up in reality, just the measured number due to the method, and the damping current isn't lowered nearly as much as most folks have been told/believe it will.
For voltages (what we measure) the 30 Ohm driver is in parallel to the source + output resistance and it would appear that there is a huge difference in damping because we hardly measure any voltage.
That is because the current in the cricuit (which is series not parallel) is always determined by the source + load resistance and not source in parallel to load.

 

[lucian]

Thanks for taking the time to follow up, even though you made it quite complicate and difficult to read trough


So let's synchronize:

1) You don't deny electrical damping. Your point is, that especially for headphones, this effect is neglect-able or at least very small.

I completely agree. For typical headphones (especially planar magnetic) the mechanical damping factor is much higher than the electrical, due to low mass, higher resistance ... However, I don't know of any real measurement to be able to quantity that effect, except the paper I linked. And this shows that here is obviously no effective damping. (But for big woofer still is.)

2) You point is, that additional measured THD comes from voltage source of uncontrolled movement/deformation of the membrane (voice coil) of the speaker.

And this I don't understand. You said you don't measure any higher distortion at the speaker with a microphone. But in this example your internal source is caused by unwanted movement of the speaker. So you have higher distortion in the speaker!

Or did you mean the relative distortion between amp out 0.1Ohm vs. 10Ohm doesn't change, cause of ineffective damping?

Than I agree to. The effect is here - it is just neglect-able for headphones.

3) High THD is generated by the electrical/mechanical converter. And the feedback of this depends of course at the coupling between source (amp) and sink (phones). And this depends at the damping factor.

If you look at the paper I linked, you see at the step response (figure 16) clearly the effect of electrical damping - but also that for the microspeaker (table 3) doesn't change anything in terms of effective distortion at the speaker.

But this actually implies, that for headphones current drive actually had the advantage that you don't have a change in sound between different amps. ofc in this case the frequency response of the headphones would need to be adapted to current source. Which they are not.

So, at least for me, we were talking about the same, but from a different perspective.

 

[solderdude]

1: What I am saying is that for headphones there is virtually no difference in damping between say 0.1 Ohm and say 10 Ohm.
Damping is done by current. Current is determined by the voltage source and the resistance it meets.
The voltage source in the case of speakers/drivers is movement other than that dictated by the applied waveform.
This differs between music and a constant sine-wave.

The only way to measure the electrical damping is to measure the current.
The difference between 30 Ohm and 40 Ohm is just a factor 1:1.3 where the so called damping factor in the example 1:100

This is why I say it is nonsensical. That what is heard with some headphones is because of voltage division and when one measures distortion with a dynamic transducer isn't actual distortion of the amplifier but a misinterpreted/misunderstood voltage measurement.

In other words the actual damping effect isn't nearly as big as it is said/thought/reported/'measured' it is.

For this reason most of the headphone amplifiers I designed have selectable output resistance for a reason. For some headphones a higher R is beneficial and for others a lower one. Making it selectable creates an opportunity for owners.

And this I don't understand. You said you don't measure any higher distortion at the speaker with a microphone. But in this example your internal source is caused by unwanted movement of the speaker. So you have higher distortion in the speaker!

When I measure a planar from 0.1 Ohm or 120 Ohm and compensate the level so in both cases the driver puts out the same amplitude then I don't measure any different distortion levels. So one can conclude a higher output resistance does not mean distortion increases. One can also conclude (and this is true) that my electret measurement mic and amplification of that signal are higher in distortion than that of the used amplifier and are masking a possible increase in distortion.


The reason I more or less object to the word damping factor is that the ratio between the load and source resistance has almost zero relation to actual 'damping currents' in the driver.
OLRR would be a far better description than using the word damping. (Output Load Resistance Ratio).
The word 'damping factor' should be described by the formula (Zdriver+Zoutput)/Zdriver in which case one actually has a relation to the actual damping current.

But this actually implies, that for headphones current drive actually had the advantage that you don't have a change in sound between different amps. ofc in this case the frequency response of the headphones would need to be adapted to current source. Which they are not.

When using a current output amp using a planar there is no sonic difference with one using a voltage output amp.
In case an extra resistance is added in both situations and the voltage amp is corrected for the voltage drop due to voltage division the result will be the same. Both cases it will sound exactly the same.

Things differ when the impedance differs and the tonal balance changes depending on the different voltage division.
3 different current out amplifiers will sound the same
3 different voltage out amplifiers will sound the same and different from the current drive ones.

When one were to use a current out amplifier and corrects the FR according to the impedance swing it too would be indistinguishable from a voltage output amplifier and at the same SPL would measure the same in all aspects.

Besides the few current output amps aren't pure current outputs but rather a voltage limited and peak impedance limited amplifiers.
Without a minimum load such an amplifier would output a signal as if it were going through a comparator switchin between + and - max output voltage of the amp. So in practice these current output amplifiers are actually 'sort-off' and 'partial' current output amplifiers.