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Assistance with headphone DAC/AMP calculation

AudioBozo

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Joined
Sep 25, 2024
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Good afternoon ASR,

Goal: Calculate highest theoretical headphone loudness for a given AMP volume pot setting (assuming the source is maxed out), i.e 30% in low gain mode on an AMP.

I am trying to get my head around headphone calculations in regards to peak SPL at differing volume levels on the amplifier.

Headphones:
Sennheiser HD 600
Impedance: 300
SPL: 97dB (1V)

DAC/AMP: Aoshida Audio SMSL C200
Headphone output power: 2.6Wx2 into 16ohm and 1.3Wx2 intro 32ohm
Low gain mode: 0dB
Dynamic range: 123dB

So I have run into a few issues, there is no descriptor for headphone output power into 300ohms and I am unsure if it is possible to reliably calculate this. Amir's review of the SMSL C200 shows "Power versus distortion using 300ohm load" which states a max power of 153 milliwatts in high gain mode, but I use low gain. Even if I had the power into 300ohm I am still unsure if/how I could calculate peak potential loudness for a given volume setting of 30% for instance.

Is there anyway with the provided information to calculate a theoretical peak loudness with the SMSL C200 AMP set to 30% in low gain mode with the HD 600? If you are wondering why I am asking such an oddly specific request I had a noise incident in late October and have no reliable way of calculating the 'worst case scenario'. I generally max out my audio on the source and then set loudness with the amp, in a scenario where the source is blasting something as loud as it possibly can I would imagine the AMP would have the final say with peak loudness as if the power isn't there it will not be represented. If specifics are impossible then my only query would be, is upwards of 110db possible on the SMSL C200 at the 30% mark in low gain achievable if the source is boosted enough? Any misconceptions I have around this that can be cleared up would also be much appreciated as math was never my strong suit.

I have noticed for instance that Spotify maxed out is always louder than YouTube maxed out, likely due to compression which I have disabled in Spotify. This being the case could any application theoretically have drastically differing volume levels despite still being 'maxed out' and how loud could this go at a given setting... i.e 30% on the specified AMP? People who typically have 'blast' incidents maxed out the volume pot accidently or hooked up to the wrong line out, this wasnt the case with me it was the usual 24-30% setting on the AMP which works for almost everything just fine but this singular application however came out absurdly loud and it has me worried that I will not be able to control for this in future as the Windows sound limiter is bypassed with external DAC's.

If any of this seems unclear or its an impossible ask totally get it, I had no luck so thought I would ask prior to forgetting about it.
Thanks for reading and your time,
 
"30%" is not useful for calculating anything.

If you want to calculate Peak SPL, use a basic, cheapo multimeter and a 60Hz test tone to measure the headphone output voltage with the C200 set to your desired loudness.

For example, put on a track of your choosing, adjust the volume how you like it, then plug out one earcup end of the headphone cable and measure the AC voltage between the two pins while playing a 60Hz, 0dBFS test tone.

Say the multimeter reads 0.255Vrms, that means that the HD600 which has 103.7dB/Vrms according to Amir's measurements, will output 103.7+20*log10(.255/1)=91.8dB SPL Peak.

Say that the track you used to adjust volume is mastered to -0.5dBFS Peak, that reduces Peak SPL to 91.3dB.

You can use Room EQ Wizard to generate and export test tones and Audacity to inspect track levels.
 
"30%" is not useful for calculating anything.

If you want to calculate Peak SPL, use a basic, cheapo multimeter and a 60Hz test tone to measure the headphone output voltage with the C200 set to your desired loudness.

For example, put on a track of your choosing, adjust the volume how you like it, then plug out one earcup end of the headphone cable and measure the AC voltage between the two pins while playing a 60Hz, 0dBFS test tone.

Say the multimeter reads 0.255Vrms, that means that the HD600 which has 103.7dB/Vrms according to Amir's measurements, will output 103.7+20*log10(.255/1)=91.8dB SPL Peak.

Say that the track you used to adjust volume is mastered to -0.5dBFS Peak, that reduces Peak SPL to 91.3dB.

You can use Room EQ Wizard to generate and export test tones and Audacity to inspect track levels.
Hey Static,

Thanks for the reply, so it seems it isn't possible to hazard a guess without a more involved measurement. Given I do not make a habit of listening at the volume levels of the incident I will just proceed with more caution in future, thank you for providing the calculations as if it continues to bother me I will invest in a cheapo multimeter as suggested to see what the volume levels could have been.

Much appreciated,
 
Since the C200 in low gain mode is only good for 15 mW into 300 ohms or 2.12 Vrms, it'll barely hit 110 dB with the volume maxed out when using the HD600 at 103.7 dB SPL / 1 V. So the odds of that happening at any lower volume setting are zero. Should be sufficient either way.

I have noticed for instance that Spotify maxed out is always louder than YouTube maxed out, likely due to compression which I have disabled in Spotify.
Nope, that's probably not compression (which is only available for non-music long-format videos). Keep in mind that YT has rudimentary playback volume normalization which will pull down the level on anything hotter than -14 LUFS (but won't do anything for quieter material). You should find levels to be much the same after setting this up in Spotify as outlined here:
This has nothing to do with dynamic range compression, as relative dynamics within each track remain untouched. There is only a fixed volume adjustment that's being applied to the entire thing.

It be noted that -14 LUFS still is relatively hot. This does not provide enough headroom for '80s pop CDs, let alone classical. My preferred levels have slowly been going down over the years. I'm currently aiming for -23.9 LUFS (that's Foobar2000 preamp = -5.9 dB) or -25.9 LUFS, respectively. My default YT volume is 35%. I can't imagine there is very much out there that would require less than -25.9 LUFS, it covers the worst-case scenario in my collection (Mahler Symphony No. 4, Birmingham Symphony, Simon Rattle). I don't think I have more than one or two albums that even need the last 2 dB.

The good thing about having signal paths and gear with ample dynamic range is that you can easily afford this. If push comes to shove, you may need to enable high gain - big deal, the internal noise floor is still below 0 dB SPL even then (or about 20 dB lower than you need for headphones).
 
Since the C200 in low gain mode is only good for 15 mW into 300 ohms or 2.12 Vrms, it'll barely hit 110 dB with the volume maxed out when using the HD600 at 103.7 dB SPL / 1 V. So the odds of that happening at any lower volume setting are zero. Should be sufficient either way.


Nope, that's probably not compression (which is only available for non-music long-format videos). Keep in mind that YT has rudimentary playback volume normalization which will pull down the level on anything hotter than -14 LUFS (but won't do anything for quieter material). You should find levels to be much the same after setting this up in Spotify as outlined here:
This has nothing to do with dynamic range compression, as relative dynamics within each track remain untouched. There is only a fixed volume adjustment that's being applied to the entire thing.

It be noted that -14 LUFS still is relatively hot. This does not provide enough headroom for '80s pop CDs, let alone classical. My preferred levels have slowly been going down over the years. I'm currently aiming for -23.9 LUFS (that's Foobar2000 preamp = -5.9 dB) or -25.9 LUFS, respectively. My default YT volume is 35%. I can't imagine there is very much out there that would require less than -25.9 LUFS, it covers the worst-case scenario in my collection (Mahler Symphony No. 4, Birmingham Symphony, Simon Rattle). I don't think I have more than one or two albums that even need the last 2 dB.

The good thing about having signal paths and gear with ample dynamic range is that you can easily afford this. If push comes to shove, you may need to enable high gain - big deal, the internal noise floor is still below 0 dB SPL even then (or about 20 dB lower than you need for headphones).
Hi Steph,

A billion thanks for explaining, it has had a huge impact on my anxiety surrounding this.

Does this 110dB maxed out account for amplification on the source signal? i.e if you took every liberty to boost the source signal would this 110dB max still apply? If I hypothetically opened Audacity right now and blared a test tone on max amplification (in software) the worst case is still 110dB? Only reason I check is the volume was so loud for me at the time of the incident I was physically cringing, I must just be used to much lower sound levels as I was thinking I was hearing 110dB at least.... if its true there is no way I was hearing that at anything under 100% (was at 30) then my sound tolerance is lower than I thought and some peoples listening habits are truly mental. Maybe the fact it was distorted due to being through an in-game chat the heavily compressed nature made it sound way louder than it was, in addition to me having no real experience with louder sound levels in general. Given 20-24% is my standard listening level for modern mastered music in low gain I cant even imagine what 100 would be like.

Since the C200 in low gain mode is only good for 15 mW into 300 ohms or 2.12 Vrms, it'll barely hit 110 dB with the volume maxed out when using the HD600 at 103.7 dB SPL / 1

I would love to know how this was calculated/determined for low gain mode, as the specs page only shows 4VRMs for the TRS output. The calculations you used in general to make this determination would be useful for me as in combination with static's advice above I can cover all bases for both 'in use' and 'worst case scenario' sound levels. Apologies for the spoon-feeding, will be out of your hair after.

Appreciate your time,
 
Hi Steph,

A billion thanks for explaining, it has had a huge impact on my anxiety surrounding this.

Does this 110dB maxed out account for amplification on the source signal? i.e if you took every liberty to boost the source signal would this 110dB max still apply? If I hypothetically opened Audacity right now and blared a test tone on max amplification (in software) the worst case is still 110dB? Only reason I check is the volume was so loud for me at the time of the incident I was physically cringing, I must just be used to much lower sound levels as I was thinking I was hearing 110dB at least.... if its true there is no way I was hearing that at anything under 100% (was at 30) then my sound tolerance is lower than I thought and some peoples listening habits are truly mental. Maybe the fact it was distorted due to being through an in-game chat the heavily compressed nature made it sound way louder than it was, in addition to me having no real experience with louder sound levels in general. Given 20-24% is my standard listening level for modern mastered music in low gain I cant even imagine what 100 would be like.



I would love to know how this was calculated/determined for low gain mode, as the specs page only shows 4VRMs for the TRS output. The calculations you used in general to make this determination would be useful for me as in combination with static's advice above I can cover all bases for both 'in use' and 'worst case scenario' sound levels. Apologies for the spoon-feeding, will be out of your hair after.

Appreciate your time,
You can read low gain max power for 300 Ohm from the figure. Look at the X-value in the bottom right for the red line. That is indeed 15 mW. Since power is voltage squared divided by impedance, the max voltage is (14.99/1000*300)^.5 = 2.12 V. The highest possible voltage is sqrt(2) times bigger due to the test signal being a sine wave, i.e. 2.999 V and the highest possible power is 30 mW for the same reason. This gives a possible max SPL of around 115 dB SPL at full volume.
1735905812457.png


The output is limited by the digital format. Boosting the volume in programs can only increase the level so much and produces distortion when overdone. If the volume control on the C200 is programmed like that on the DL200, volume 30 is an attenuation of 34 dB, i.e. the highest possible peak is around 80 dB SPL. High distortion can sound quite loud compared to its level but at those levels should be unproblematic.
 
You can read low gain max power for 300 Ohm from the figure. Look at the X-value in the bottom right for the red line. That is indeed 15 mW. Since power is voltage squared divided by impedance, the max voltage is (14.99/1000*300)^.5 = 2.12 V. The highest possible voltage is sqrt(2) times bigger due to the test signal being a sine wave, i.e. 2.999 V and the highest possible power is 30 mW for the same reason. This gives a possible max SPL of around 115 dB SPL at full volume.
View attachment 418290

The output is limited by the digital format. Boosting the volume in programs can only increase the level so much and produces distortion when overdone. If the volume control on the C200 is programmed like that on the DL200, volume 30 is an attenuation of 34 dB, i.e. the highest possible peak is around 80 dB SPL. High distortion can sound quite loud compared to its level but at those levels should be unproblematic.

Thank you so much for taking the time and referencing the graph I needed to be looking at. I did check Amir's review in an attempt to answer my own question but my knowledge isn't close to being able to put the whole picture together myself. Appreciate you laying it out in layman's terms for me, this is more than sufficient.

Many thanks for assisting me and have a great year!
 
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