What is/are output impedance for? - Page 2

Quote:

Originally Posted by stv014 

 

It is not true that high impedance headphones inherently have greater impedance variations relative to the nominal impedance (as a ratio, not as an Ω difference). 

Maybe you should look at a few headphone impedance plots.  You'll quickly see that, on average (always some exception) the higher impedance models have more impedance variance with frequency than lower impedance models.  

Quote:

Originally Posted by jaddie 

Maybe you should look at a few headphone impedance plots.  You'll quickly see that, on average (always some exception) the higher impedance models have more impedance variance with frequency than lower impedance models.  

I think you are confused by the graphs having a linear scale, and the larger absolute Ω differences, which psychologically exaggerate the impedance variations of high impedance headphones. It is the ratio of the highest and lowest impedance on the graph that matters, and that is not significantly different for example between the 32 Ω and 600 Ω version of the DT880.

Quote:

Originally Posted by stv014 

 

I think you are confused by the graphs having a linear scale, and the larger absolute Ω differences, which psychologically exaggerate the impedance variations of high impedance headphones. It is the ratio of the highest and lowest impedance on the graph that matters, and that is not significantly different for example between the 32 Ω and 600 Ω version of the DT880.

No, I'm not confused.  I agree that in that specific case the plots are not significantly different.  However, if you look at a random sampling of higher Z phones vs lower Z phones, you'll see that on average there is somewhat more variance in the impedance of the high z phones.  It doesn't matter anyway, though.  In either case a low Z amp will take care if the issue. 

If you want to prove me wrong by citing a specific exception, that's fine.  I have no problem with exceptions, and I won't even disagree. 

Quote:

Originally Posted by stv014 

The damping and impedance interaction are actually related issues, in other words, damping the bass response of a dynamic transducer occurs through the impedance peak at its primary resonance frequency. From a voltage source with near zero output impedance, the current drawn at the resonant frequency will be lower because of the increased impedance, and that dampens the resonance compared to a current source ("infinite" output impedance) which would have no electrical damping at all. However, impedance variations with frequency can also be the result of other things than back EMF, like the inductance of the voice coil (which causes rising impedance at the highest audio frequencies), or the passive crossover network used in a multi-driver headphone or loudspeaker.

No issue with any of that either.  It's just that the magnitude of the damping issue in headphones is tiny compared to speakers.  You just can't focus only on damping, or set it apart as some sort of key issue when it's inseparable from impedance interaction.  If you solve one, you solve the other.  I was merely reacting to your earlier statements that implied damping and impedance interaction are mutually exclusive.  They aren't.

Quote:

Originally Posted by jaddie 

No, I'm not confused.  I agree that in that specific case the plots are not significantly different.  However, if you look at a random sampling of higher Z phones vs lower Z phones, you'll see that on average there is somewhat more variance in the impedance of the high z phones.  It doesn't matter anyway, though.  In either case a low Z amp will take care if the issue.

Only a comparison between headphones of similar design and drivers but different impedance is fair (e.g. HD700 vs. HD600/650/800), otherwise the differences in the amount of impedance variation could very well be the result of different factors. There are also very few high impedance headphones still in production, so whatever conclusion you try to draw from the data will be based on a small sample size. What you need to find is a plausible theory to explain why a higher impedance voice coil will inherently have significantly greater impedance variations (on a logarithmic scale) than a low impedance one under otherwise identical conditions.

Edit: by significantly greater impedance variations I mean large enough to cause more actual frequency response variations than the low impedance headphone with a realistic output impedance. For example, the T70 has somewhat more impedance variation than the lower impedance but otherwise similar T70p, however, even from a 330 Ω source, the bass response of the T70p will still be affected more, and only a ~700 Ω output impedance will make it about equal.

Just divide min/max impedance of headphones like the DT250/770/880/990 comparing 32, 80, 250, 600 ohm versions. There's no clear trend.

Generally speaking, you send an impulse through a device and record the output. This output is called impulse response. If the device has a crazy frequency/phase response, the impulse response will look nothing like the original impulse. There will be lots of ringing and the energy will not be concentrated near the start of the impulse.

Step response just uses a step function instead of an impulse. Since most headphones cannot contain the pressure you will see a roll-off of the step response at some point.

An impulse basically means that the signal is non-zero for a very short period of time (specifically one sample in a discrete time system, i.e. sampled digital audio), and zero at all other times. The important thing about an "ideal" impulse is that it contains all frequencies at the same amplitude and phase delay, therefore, the impulse response of a system with perfectly flat frequency and phase response is also an impulse. A linear time invariant system (one that does not have any non-linear distortion or time varying characteristics, that is, if you input the same signal to it multiplied by a and delayed by t seconds, its output will be exactly the same, just also multiplied by a and delayed by t) can be characterized by its impulse response alone. High quality audio reproduction devices are close enough to being linear time invariant to make the impulse response a very important parameter of the device. The output of a linear time invariant system can be predicted as the input convolved by the impulse response. It is also possible to calculate the frequency response from the impulse response using the Fourier transform. The image below shows an impulse before (left channel) and after (right channel) applying a 10 kHz lowpass filter, both in the frequency and time domain:

A step function is a signal that is zero for an indefinitely long time before a certain point in time, and then a constant non-zero level for an indefinitely long time. It is basically an integrated impulse. Since integration has a magnitude response increasing by 6 dB per octave towards 0 Hz, the step function has much more low frequency content than an impulse, so a step response is more useful to visualize the low frequency characteristics:

An interesting thing to know about impulse responses is that in practice they are often not measured by using a simple impulse as the input, but rather a maximum length sequence, which is a pseudo-random pattern that contains all frequencies at the same level, but different phase, such that the same amount of energy is distributed over a much longer time, allowing for greater signal energy at the same peak level, and thus attenuating the noise in the system. By convolving the maximum length sequence with its reverse, the impulse response can be extracted.

To show this in practice, here is a maximum length sequence (polynomial = x^20 + x^3 + 1, so it repeats after 1048575 samples) played at 96 kHz, and recorded from a headphone:

Of course, that does not look like an impulse response at all, but convolving it with the reverse sequence (polynomial = x^20 + x^17 + 1) does extract the actual impulse response, and that can be seen below with the frequency response:

The reason why maximum length sequences are useful for impulse response measurements is that they allow for reducing the noise floor. Compare the noise floor of the audio recorded from the microphone (on the left) to that of the extracted impulse response (on the right). Since the signal was amplified as well during the convolution, the difference is in fact even greater than it is visually apparent from the pictures.

From the impulse response, it is possible to derive the step response (top), 30 Hz square wave response (bottom left), and 300 Hz square wave response (bottom right) with convolution. Note that I did not actually record any of these signals, only the MLS shown on the first picture, everything else is calculated from that.

Of course, to get reasonably accurate results, the system (the entire chain of the DAC, headphone amplifier, headphones, microphone, microphone amplifier, and ADC) has to be close enough to linear time invariant. To verify that, I also show the frequency response and distortion vs. frequency calculated from a sine sweep played at a roughly similar RMS level. Fortunately, these are not Apple ear buds, so the distortion (much of which on the graph is actually microphone noise) is low enough, and the frequency response does not notably differ from that recorded with a completely different test signal and at a different time either.

Quote:

Originally Posted by stv014 

 

Only a comparison between headphones of similar design and drivers but different impedance is fair (e.g. HD700 vs. HD600/650/800), otherwise the differences in the amount of impedance variation could very well be the result of different factors. There are also very few high impedance headphones still in production, so whatever conclusion you try to draw from the data will be based on a small sample size. What you need to find is a plausible theory to explain why a higher impedance voice coil will inherently have significantly greater impedance variations (on a logarithmic scale) than a low impedance one under otherwise identical conditions.

Edit: by significantly greater impedance variations I mean large enough to cause more actual frequency response variations than the low impedance headphone with a realistic output impedance. For example, the T70 has somewhat more impedance variation than the lower impedance but otherwise similar T70p, however, even from a 330 Ω source, the bass response of the T70p will still be affected more, and only a ~700 Ω output impedance will make it about equal.

You are missing the point here.  Comparing different impedance version of the same model only proves that the mechanism isn't present in that model.  The impedance variation that can be seen in impedance plots of a sampling of higher impedance models is not, in and of itself, because they are high impedance, that's clear.  There is obviously something else going on.  I'm not offering any theories, and I'm not trying to explain why, that's WAY off topic here, and may even be impossible.  It's just that there seems to be a trend, though the specific variations are hardly similar.  

But, it doesn't matter!  This is all a moot point.  What difference does it make if a model that averages around 50 ohms peaks at 225?  Significant, if your amp has an output Z of 100 ohms.  Insignificant if your amp output Z is extremely low.  Another set within the same manufacturer has a ruler-flat impedance curve at 10 ohms.  What difference does that make? You have an issue with a 100 ohm output Z, non-issue if your output Z is very low.  

That's my point. 

Quote:

Originally Posted by jaddie 

You are missing the point here.  Comparing different impedance version of the same model only proves that the mechanism isn't present in that model.  The impedance variation that can be seen in impedance plots of a sampling of higher impedance models is not, in and of itself, because they are high impedance, that's clear.  There is obviously something else going on.  I'm not offering any theories, and I'm not trying to explain why, that's WAY off topic here, and may even be impossible.  It's just that there seems to be a trend, though the specific variations are hardly similar.  

Well, then high impedance is worse than low impedance in the same way CD is worse than vinyl (and sometimes even good cassette tape), because it tends to have very limited dynamic range, emphasized treble, and heavy distortion. Correlation is not causation. Of course you are right that to the consumer it ultimately does not matter why the difference is there. Then again, even if you find a statistical difference that exists for whatever reason, is it enough to cause the high impedance headphones to have statistically higher amount of frequency response variations with a realistic output impedance ? Because that is what really matters from a consumer's point of view in the end.