squarewave and impulse

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Square-wave response

I think it is important to REALIZE that squarewaves are not present in any music signals NOR can they be recorded and reproduced ‘faithfully’. Square-waves are used by technicians to more easily show the ‘boundaries’ of the product and to quickly spot overshoot, slew-rate and other bandwidth problems.
They say NOTHING about the ‘attack’ of musical instruments as the ‘flanks’ of those signals doesn’t come anywhere NEAR the flanks of this artificially generated signal.

A square-wave and pulse signal (almost) instantly changes the DC levels of the applied electrical signal.
In essence (and in practice for audio frequencies) a square-wave (and needle pulse) is an instant voltage change.
When such a signal is applied to a headphone the membrane should also move instantaneous, which of course it can not.
It takes time for the membrane to reach the correct position as dictated by the DC signal.
This rise-time is visible in the angle of the vertical transitions.

A driver is limited in speed by physical properties. It has a mass and is not rigid.  It will thus overshoot and vibrate in frequencies, and amplitudes, determined by the mass and compliance (rigidity) of the membrane + voice-coil + its suspension.
These (unwanted) vibrations are easy to spot in the square-wave/needle impulse signals.

The vertical scale of these oscilloscope plots is NOT in dB but in a linear scale (Volts). This makes the plot look ‘worse’ than when the vertical scale were to be displayed in dB. A dB-scale is ‘closer’ to how we actually hear (logarithmic) and thus more representative.
The vertical scale is thus ‘stretched’ compared to dB-scales which can show the amplitude response of larger signals in greater detail.

Another interesting thing about square-wave response plots is the horizontal ‘part’ of the measured signal as this also, kind-of, shows the frequency response but in a miniature and ‘reversed’ linear scale.
Of course this ONLY applies when the frequency range of the measurement chain is actually ‘flat’ over the entire frequency range. In this case it most likely is not due to the used microphone and possibly not entirely correct frequency compensation.

Stock HD650 old pads 440Above the square-wave response of the HD650 fitted with old pads on a 440Hz signal.

On the left side of the horizontal part of the trace we see the highest part of the frequency range.
On the right side of that horizontal part of the trace we see the lower side of the frequency response (right before the polarity of the square-wave changes).

A horizontal red line thus indicates an even (flat) frequency response. An upwards ‘sloping’ line shows a ‘darker’ signature. Overshoot above the green trace (on the left side, i.e. rising edge/flank) shows ‘peaky’ frequency behavior. A bit of overshoot/ringing (when very short in time and a high frequency) is not a problem.
A level below the green trace near the left rising edge shows the treble is relatively rolled off. A level above the green line shows the treble is too emphasized/hot.

The squarewave plot above shows a frequency response that is tilted to the ‘warmer’ side of sound as the left side of the red trace, where the higher frequencies are, is not reaching the ‘target’ level.

When the squarewave is closer to the original signal then the frequency response is closer to ‘flat’.
As an example below the squarewave response of the exact same headphone (HD650) but now fitted with new pads.

Senn foam 440This is already a lot closer to the original square-wave and indicates a more linear response.

When the left part of the horizontal line overshoots the headphone is ‘brighter’ than flat.
Depending on how much overshoot there is and how much it ‘vibrates’ after the rising- and falling-edge this could sound edgy or bright to shrill in more severe quantities.

Below the same HD650 driver but using other foam in front of the driver.

white foam 440HzThis resulted in a slight overshoot but far from levels where it becomes very audible or disturbing. The HD650 is actually quite exemplary in this aspect.
More detailed measurements and info on HD650 measurements can be found HERE.

The lower frequencies (the right side of the horizontal trace) do reach the desired target level.
Notice the
time delay between the stimulus and the measured response.
This time delay is actually the time it takes for the sound waves to travel the small distance between the driver and the microphone measurement plane. The speed of sound is thus the cause of this small delay.

The reason why squarewave responses of websites like Innerfidelity show considerable different looking 300Hz plots with a seemingly much higher amount of ringing is because I suspect the raw (uncompensated) signals coming from the HATS are shown. These include the ringing added by the artificial ear canal inside the HATS.

HD650 IF 300HzAbove the 300Hz plot taken from one of Innerfidelity’s excellent database sheets. The plot above is also from the HD650.
It would appear as that there is a LOT of ringing in the 3kHz area BUT I suspect that what is really shown is the ringing of the artificial ear canal. No compensation for this seems to be applied.

Because a 440Hz (or other frequency in that range) only says something about the lower mids to lower treble part of the frequency range sometimes lower frequencies are also measured but at a much lower frequency.
Frequencies between 20Hz and 50Hz can tell more about the linearity of the lowest part of the frequency response.

Below the Low Frequency response of the stock HD650 (fitted with new pads) when a 40Hz signal is used.

new pads 40HzThe steeper the horizontal lines drop the less low frequency extension there is.
The more horizontal the lines ‘run’ more horizontal the lower frequency response is better.
Below the same headphone but with EQ that raises the bottom part of the frequency response (kameleon amplifier)

Kam 2 40Hz SQRThe more linear response of the horizontal part of the lines shows improved LF response.
It is impossible to have the horizontal lines to run really horizontal because the whole measurement chain is NOT DC coupled.

Needle pulse response

A needle response can say something about how fast a membrane can rise and the behavior of the membrane when it returns to the same ‘neutral’ position as where it originally came from.
This differs from a square-wave because in a square-wave the applied signal switches between a positive and negative voltage continuously.
The time period of the pulse (why its called a needle pulse) is much shorter.
For the measurements used on this site the time period is 100
ms = 0.0001 sec which is the same pulse width as a 5kHz square-wave has. When a square-wave would be used you cannot see what happens to the membrane after 200ms when it would be moved again. For this reason the needle pulse is only repeated in a 24ms rate (50Hz) so high frequency resonances that continue beyond 200ms can easily be spotted (Low Frequency resonances can not be seen as they take up too much time.
The time scale in the needle plots is limited to 2ms. A 500Hz square-wave would fit in one screen.
Lower frequency resonances can thus not be seen BUT higher frequencies a lot better. It’s these frequencies that are of interest.

Most people that measure impulse responses of speakers use 50ms pulse widths. Because I want to make sure the membrane reached its final level I made the pulse 2x longer. The rising edge is clearly visible this way and not running the risk of not reaching its final value before the stimulus is removed again.

For the trailing part (after the falling edge) it really doesn’t matter (that much) how long the pulse was held high. This can be seen on the square-wave response plots.

The 440Hz square-wave is used to set the amplifier level. The needle pulse test is done after that under unchanged conditions.

Below the reproduction of a 100ms duration pulse of a stock HD650 fitted with old pads. (scale 50ms/div)

stock old HD650 100usThe stimulus and measured signal

Below the same headphone but fitted with new pads:

Senn foam 100usWhat these needle plots show is how fast the membrane can move and if it reaches the desired level.
Severe overshoot (when visible) can say something about the upper part of the frequency range and how well the membrane is damped.

Below a more ‘stretched’ needle response plot.

risetime HD650 old padsThere are a few points of interest to such a pulse signal.
The first one is leading (rising) edge/flank of the square-wave. The stimulus practically rises instantly to the desired level. The measured signal can NOT follow this for several reasons.

1: It has a mass which takes energy to move. In order to move it ‘instantly’ the amount of power needed would also be almost unlimited and a ‘counter energy’ would need to follow directly behind it in order for it to make a ‘dead’ stop. The applied VOLTAGE of the stimulus is NOT such a pulse.
The slower movement in the first 10
ms in the graph is (probably) caused by the mass that needs to be moved.

2: The microphone which has an upper FR limit of 27kHz in this case.
The spectrum of the needle pulse runs all the way up to 1MHz (and even beyond). 1MHz = 1000kHz.

3: The biggest reason the rising edge is limited in speed, however, does come from the fact that the HD650 has a voice-COIL.

Another thing that may need some explaining is why the stimulus and measured signal in the square-wave and needle pulse do not ‘overlay’ in time but are shifted is actually caused by the limited speed of sound (approx 330m/s) and the driver to microphone distance.
As the driver is approximately 33mm away from the ear and sound waves travel 330m/sec the measured signal simply arrives about 100
ms after the driver has reacted to the signal.In the square-wave plots the delay seems smaller but this is only because of the horizontal time scale being different.

Another, and more interesting, part of the plot is the horizontal part of the trace directly after the falling edge.
In an ideal world the membrane would come to a direct stop and show no ‘signal’ as in the stimulus.
Of course the reality is quite different and (parts of) the membrane will still want to carry on moving.
That moving slowly will grind to a stop over time.
The higher the amplitude the less ‘controlled’ the membrane still vibrates.
The closer the ‘wiggles’ are in time the higher the ‘ringing’ frequency is.

The same ‘comments’ for Innerfidelity’s needle plots apply, no compensation seems used and (parts) of the visible ringing is not there in reality. Also it is not known how high the peak should have reached nor how wide the stimulus was.

A needle response plot can thus say something about how fast a membrane can move and how much time it takes for it to stop moving again. Also it shows how much ‘ringing’ is present after the membrane was supposed to stop moving and at which frequencies.
A caveat here is that the plots are linear scale and signals -30dB below the stimulus can not be ‘seen’ any more but are still audible.
The CSD (a.k.a. waterfall) plot can show these smaller signals and show them in their specific frequencies.

impulse step response

Step response is another way of judging impulse behavior.
ideal
Above a plot of an ‘ideal’ impulse response. This plot shows an extremely flat and very wide bandwidth (flat even below 20Hz) without any resonances (wiggles after the initial rise).
It is not a plot of a real headphone. Such a headphone simply does not exist. It is merely to show what an ideal response would look like.

The vertical scale is 5dB/division the horizontal scale is 1ms/division.

It is a bit akin an oscilloscope shot of a step response. The ‘target’ is the top line after the initial rise the line should run in a straight horizontal line from there. The rising edge should reach the top line in a short as possible time. The wiggles after the rising edge should be as small as possible in amplitude. The time it takes for the wiggles to ‘die out’ should be as short as possible.

Below the step response plot of the HD800 as an example. It shows a fast rising signal but also considerable ringing and downwards sloping horizontal line indicating a good bass extension (as it is almost a straight line) but not on a desired level (downwards sloping instead of horizontal.

Step HD800 R

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