Ampliefiers, distortion, headroom - help understanding

[oogabooga]

Hi everyone,

Been having a hard time understanding distortion and headroom for headphone amps and wanted to ask for some help to see if I have things right.

Consider a hypothetical amp and headphones. When a 1 kHz test signal is played, the combination has audible distortion when set to 80% of maximum volume, and no audible distortion when set to 70% of maximum volume. The 1 kHz test signal is a 'full scale' sine wave; the digitally-encoded sine wave amplitudes goes all the way from the minimum to maximum allowed values.

For the sake of this question, let's assume that this distortion threshold is the same for a sine-wave test signal at any audible frequencies: distortion at 80%, no audible distortion at 70%.

Does this mean that, when set to 70%, the amp and headphones will also have no audible distortion for ANY music/audio file? The internet mentions things like "crests" and "dynamic range" of music - I get that music has a wide range of output intensity but I would expect all those intensities to be lower or equal to that from the sine-wave test signals. Thus, the combination could never have any audible distortion with the volume at 70%, but may have audible distortion with the volume at or above 80% depending on the music.

Looking forward to hearing thoughts and learning if/where I've made a wrong assumption above!

Thanks in advance

 

[DVDdoug]

It's the peaks that clip.

when set to 80% of maximum volume,

The percentage of rotation with an analog volume control isn't calibrated to anything... Feed a louder signal into the amp and it will clip at a lower setting. Most amplifiers have enough extra gain so can go full volume (or more into distortion) with a slightly lower-than-normal signal.

With digital "100%" usually means the digital maximum of 0dBFS. Nothing bad happens when you get close to 0dB digitally but it can't go over. Usually you only get digital clipping if the recording is clipped. But a few media players can go over 100% and digital EQ can also push the digital peaks into digital clipping.

The difference with a sine wave and music is also only important on the analog side. Often an amp can put-out more power on an occasional peak than with sine waves.

 

[rdenney]

What it means is that the amplifier runs out of the ability to supply current to the speakers. What moves speakers is voltage--the voltage is what charges the voice coil to achieve the required magnetic flux to move in the prescribed way. But that motion, and the accelerations required to create the back-and-forth of the frequency domain, consume power. The amplifier has to be able to supply the current being drawn by the speaker voice coil when it attempts to respond to the change in voltage. If the amplifier runs out of the ability to provide current, the voltage will sag and the speaker will not move in the prescribed way (which clips off the top of the waveform). That's distortion.

It happens at lower levels, too. If a preamp is attempting to drive an amplifier's input load (and amplifiers have very low input input impedance to exert control, so the preamp has to be able to control itself) and can't supply the current necessary to create the voltage waveform, the waveform will clip even down in the single digits of volts involved. This comes across as crackling distortion, loud parts being compressed into ugly sounds.

Setting the gain of each stage that amplifies the previous fully without clipping is called the "gain structure".

The full-size waveform of your hypothetical sine wave might clip at the 75% setting on the amp, but you might want to be able to make a signal louder that never gets to 100% in the first place, and it might need 85% on the amp before it would clip. So, amps are designed so that zero attenuation from the volume control allows a higher voltage than the amp can supply, so that it can be cranked up with smaller input signals.

Headroom colors the whole above discussion, because there's not a hard point where the amp clips, but rather a range of points depending on how long the peak persists. Traditional amps store temporary boosts of power in the transformer and capacitors in the power supply, and can fill out waveforms beyond their continuous capability if the request is short enough. That's headroom. Amps with switched and regulated power supplies don't have headroom like traditional amps, but it's easy for them to be designed with higher power in the first place to overcome that limitation. But the relationship between peak duration and ability to supply the required current confounds lots of power comparisons, particularly with dynamic music.

Rick "is a 200WPC amp with no headroom more powerful than a 100WPC amp with 3dB of additional headroom? It depends on the music" Denney

 

[oogabooga]

It's the peaks that clip.


The percentage of rotation with an analog volume control isn't calibrated to anything... Feed a louder signal into the amp and it will clip at a lower setting. Most amplifiers have enough extra gain so can go full volume (or more into distortion) with a slightly lower-than-normal signal.

With digital "100%" usually means the digital maximum of 0dBFS. Nothing bad happens when you get close to 0dB digitally but it can't go over. Usually you only get digital clipping if the recording is clipped. But a few media players can go over 100% and digital EQ can also push the digital peaks into digital clipping.

The difference with a sine wave and music is also only important on the analog side. Often an amp can put-out more power on an occasional peak than with sine waves.

Thanks @DVDdoug for the reply. So if I've understood correctly, as long as there's no digital clipping in the audio file, and staying at 70% on the volume pot in this hypothetical amp, then no audible distortion?

I also agree the volume control isn't calibrated to anything, only that 70% < 80% and the test signal was already the max 0 dBFS.

 

[oogabooga]

What it means is that the amplifier runs out of the ability to supply current to the speakers. What moves speakers is voltage--the voltage is what charges the voice coil to achieve the required magnetic flux to move in the prescribed way. But that motion, and the accelerations required to create the back-and-forth of the frequency domain, consume power. The amplifier has to be able to supply the current being drawn by the speaker voice coil when it attempts to respond to the change in voltage. If the amplifier runs out of the ability to provide current, the voltage will sag and the speaker will not move in the prescribed way (which clips off the top of the waveform). That's distortion.

It happens at lower levels, too. If a preamp is attempting to drive an amplifier's input load (and amplifiers have very low input input impedance to exert control, so the preamp has to be able to control itself) and can't supply the current necessary to create the voltage waveform, the waveform will clip even down in the single digits of volts involved. This comes across as crackling distortion, loud parts being compressed into ugly sounds.

Setting the gain of each stage that amplifies the previous fully without clipping is called the "gain structure".

The full-size waveform of your hypothetical sine wave might clip at the 75% setting on the amp, but you might want to be able to make a signal louder that never gets to 100% in the first place, and it might need 85% on the amp before it would clip. So, amps are designed so that zero attenuation from the volume control allows a higher voltage than the amp can supply, so that it can be cranked up with smaller input signals.

Headroom colors the whole above discussion, because there's not a hard point where the amp clips, but rather a range of points depending on how long the peak persists. Traditional amps store temporary boosts of power in the transformer and capacitors in the power supply, and can fill out waveforms beyond their continuous capability if the request is short enough. That's headroom. Amps with switched and regulated power supplies don't have headroom like traditional amps, but it's easy for them to be designed with higher power in the first place to overcome that limitation. But the relationship between peak duration and ability to supply the required current confounds lots of power comparisons, particularly with dynamic music.

Rick "is a 200WPC amp with no headroom more powerful than a 100WPC amp with 3dB of additional headroom? It depends on the music" Denney

Thanks for the detailed explanation, Rick! That helped me understand distortion and amplifier headroom more broadly. I was hoping to clarify something a bit more specific though — does the absence of distortion at 70% volume with a full-scale sine wave imply that any real-world music played at the same volume would also be distortion-free on that specific (hypothetical) amp/headphone combo? Or is there something else I'm not considering here?

 

[kemmler3D]

Does this mean that, when set to 70%, the amp and headphones will also have no audible distortion for ANY music/audio file?

Could be, but not necessarily - a sine wave has RMS power equal to Peak/sqrt(2) but a square wave has RMS = peak. In other words, some stuff takes more power even at the same peak amplitude and fundamental frequency. If there is a big difference between peak and continuous power for a given amp, it might be a factor.

 

[Scytales]

Could be, but not necessarily - a sine wave has RMS power equal to Peak/sqrt(2) but a square wave has RMS = peak. In other words, some stuff takes more power even at the same peak amplitude and fundamental frequency. If there is a big difference between peak and continuous power for a given amp, it might be a factor.

Add to that fact that digital sine test signals encoded in PCM are mostly designed such that the peak amplitude of the sine wave is at or slightly lower or above the levels corresponding respectively to the maximum (in the positive direction) as well as the minimum (in the negative direction) digital code, whereas there are no certainty that the various peaks of a musical waveform will always match exactly with the maximum or minimum digital code. Consequently, when converted to analogue, the peaks of the musical waveform might exceed the analogue peak level measured with sine test signals. As demonstrated by John Siau and, before him, by Nielsen and Lund, it can happen more frequently than anyone think of, especially when PCM signals are digitally processed in the playback chain.

And for those who play SA-CDs, there is the fact that the 0 dB SA-CD has been defined by Sony and Philips as the peak level of a sine wave at only 50% modulation index of the DSD signal, with provision for peaks to briefly exceed that level up to +3.1 dB SA-CD (about 70% modulation index). Moreover, there are some SA-CDs that have been produced before accurate digital level metering for DSD has been available and therefore some SA-CDs can even exceed the allowable maximum signal level permitted by the standard (I have one such disc).

For all these reasons, it seems to me that to get the more accurate waveform reproduction in all conceivable use cases, it might be useful to incorporate into the gain staging of the system an additional headroom above the maximum unclipped signal measured with digitally encoded sine waves (be them in PCM or DSD).

Considering that the dynamic range attainable by modern amplifier systems is so huge that audible noise levels are seldom a problem nowadays, I think it is a good trade-off to sacrifice a bit signal to noise-ratio to avoid potential clipping, however brief, in the analogue domain.

Others might disagree and favor the opposite: maximising the signal to noise ratio and let brief signal clipping happens, on the behalf that if the clipping is very brief or unfrequent, it may be unoticed.

The controversy could only be resolved by properly conducted listening tests.

 

[rdenney]

Could be, but not necessarily - a sine wave has RMS power equal to Peak/sqrt(2) but a square wave has RMS = peak. In other words, some stuff takes more power even at the same peak amplitude and fundamental frequency. If there is a big difference between peak and continuous power for a given amp, it might be a factor.

Yes, but there is nuance there, too. If the problem is that the amp is being asked to supply voltage above its voltage rails, it will clip no matter what the RMS power requirements. So, calibrating the gain structure to avoid clipping using sine waves will prevent that fault. But it won't prevent running out of current or power if the RMS envelope requires more than it can supply for a given peak voltage. RMS is the area under the waveform curve, while voltage is its amplitude only.

Another nuance: The lower the load impedance, the more current a given voltage will demand.

Rick "amps are limited by voltage and also by current" Denney

 

[oogabooga]

As demonstrated by John Siau ...

Hi @Scytales

Thanks for the reply and the links. I watched that Youtube video and found it very interesting! I think it nicely illustrated @DVDdoug 's point that "It's the peaks that clip".

I don't know if my specific DAC/AMP has that exact issue or not, but it makes a convincing case to lower the volume in my Mac by 3 dB to avoid issues.

 

[Scytales]

Hi @Scytales

Thanks for the reply and the links. I watched that Youtube video and found it very interesting! I think it nicely illustrated @DVDdoug 's point that "It's the peaks that clip".

I don't know if my specific DAC/AMP has that exact issue or not, but it makes a convincing case to lower the volume in my Mac by 3 dB to avoid issues.

You're welcome!

ASR member NTTY has designed a test-CD with some specific signals to test inter-sample overs: https://www.audiosciencereview.com/...test-cd-for-measurements-of-cd-players.58046/