[ADUHF]

Quick follow up question- I understand the math and thanks for explaining it in this manner. Greatly appreciated. When we are talking about headphones being driven, is the mW value the most important thing to consider or must we also consider voltage? For example, do high impedance cans benefit from both a good amount of mW (such as 1/3 Watt or higher) and a certain minimum voltage? I am still curious if there's a standardized definition of "driven".

This is just my uninformed opinion on the subject. So take it with a grain of salt.

I think the power in watts or milliwatts is probably the better gauge though when comparing the sound levels of different headphone+amp rigs. That seems to be the figure that's most often focused on, in these kinds of discussions anyway.

I believe that dBs per volt is good for comparing the relative loudnesses of two different headphones. But that should tell you why volts are probably not as good for comparing the overall levels of different headphone+amp rigs. Because one headphone may sound quite a bit louder or quieter than another when receiving the same signal voltage. Due to their differences in sensitivity and impedance.

It is possible I have this all in reverse though. So I'd like to hear some other opinions, to see if others agree or disagree.

I think watts or milliwatts should give you a better idea of the overall output of the rig or system in decibels than voltage though.

 

[VNandor]

I was hoping there was a somewhat simpler answer to this question. Or maybe a general rule of thumb for listening to full dynamic range recordings on headphones. Like 1 watt, or 1/2 watt, for example. Maybe that's too simplistic a way of looking at it though.

IMO if you want to be pedantic about it, the impedance and sensitivity of the headphones should be checked first. Then you would have to know what's the loudest level you would ever want to listen to and also check how dynamic your music is. Do the math once to figure out how much power you need, get some amp that claims it can output that amount of power without distortion and you are set until your taste in music dramatically changes or you get a new headphone. Altough even with all of that, you might end up with something that doesn't sound good to you but in practice, it basically shouldn't happen.

Quick follow up question- I understand the math and thanks for explaining it in this manner. Greatly appreciated. When we are talking about headphones being driven, is the mW value the most important thing to consider or must we also consider voltage? For example, do high impedance cans benefit from both a good amount of mW (such as 1/3 Watt or higher) and a certain minimum voltage?

the mW value is linked to voltage, they depend on each other. Saying that an amp can output 1/3W power into a 300ohm headphone is the same as saying the output voltage of the amplifier with a 300ohm headphone is 10V. Once you plug a headphone in and raise the output voltage the power must raise with it as well. Does that make sense?

I am still curious if there's a standardized definition of "driven".

I don't know if there is a proper definition but that doesn't have to mean there isn't any.

 

[VNandor]

Another thing you may want to consider when looking at the RMS of wider dynamic range recordings is whether there's any headroom left in the recording itself. I think audio engineers (the good ones anyway) are normally supposed to a leave a few dBs on the top end, so that the transient peaks don't all hit 0 dBFS.

Yes, I checked the peak levels as well. Not all of them peaked near 0dBFS but I tried to take that into account. If I had measured a -3dBFS peak with -20dB RMS I would have reported a ~17.3dB RMS even though I measured -20. I guess I should have mentioned this in the other post. Anyways, this is because leaving that much headroom in a digital file is not a good practice as far as I know. The headroom is left there because otherwise the reconstructed analog signal might still get clipped (despite the digital signal not clipping at all) due to intersample peaks. With classical music, even a little bit of extra headroom should prevent intersample peaking and intersample peaking shouldn't clip the signal in the first place anyways, so I don't think there's any good reason to leave a big headroom.

Not sure about this though. (And perhaps this was the point you were tryin to make above re the full scale sine wave.)

The point I was trying to make is also explained in that wiki article. I'm familiar with the mathematical definition of RMS and not with the one that is defined by AES. Using the mathematical definition of RMS a sine wave would have a -3dB RMS if the peak was at 0dB but AES defined it in way that the RMS of that same sine wave would be at 0dB.

 

[skhan007]

Yes, it makes sense. Thank you.

My hope is that I'll be able to learn how to assess gear matching using these variables. For example, if I have headphone A that has a sensitivity of 97 dB and impedance of 300 Ohms, then I'll need to find an amp the that provides a minimum of X mW and Y volts to properly drive them. Something like that would be great. Of course, sound quality etc. will be subjective.

 

[ADUHF]

Retracted.

 

[bigshot]

I think we are talking about a different way of measuring dynamics. I've been talking about headroom as it is used in recording. Headroom is the safety buffer you maintain above the loudest sustained part of the music. The headroom is maintained to accommodate momentary transients that may pop up here and there. An example is the impact of a big kettle drum hit. It might spike up above the loudest part of the music for a fraction of a second and you wouldn't want that to clip and dull the dynamic impact. Generally, commercially recorded music has no more than 50-55dB dynamic range overall, because dynamics beyond that are difficult to listen to. Below -55dB it's nothing but room tone from the recording venue, and no one likes to jump up and adjust the volume all the time because the dynamics are too broad.

If you maintained a 30dB headroom buffer, that would push the loudest sustained part of the music down 8 times under zero. That would make the music very quiet overall compared to other CDs, because the top 30dB of the CD would be largely empty. Commercial engineers wouldn't allow a transient that big to exist in a sound mix, because the CD would have a non standard level when played back alongside other CDs. Generally, when recording, they reserve 20dB headroom to avoid clipping, which is a lot, but considering you never have any warning about what is going to be captured by the microphones, it keeps things safe, especially since they are recording with a high bit depth that gives them a very low noise floor. When they mix, the headroom they allow is much less, but it ranges depending on the expected audience for the music. Heavy Metal might have almost no headroom, normalized up near the top. And classical music might allow a bit more to allow for percussive sounds. But I can't imagine a momentary transient peak that would be more than double the sustained loudest part of the music. ...except maybe for the canon in the 1812 Overture.

When music is mixed, peak limiters are used to keep dynamics in line so the CD can play back at a decent level. That means for home equipment, you don't need that much headroom. For an amp, if you have the ability to reproduce a peak double the level of the loudest sustained part of the music without pushing into clipping, you should be safe to be able to reproduce just about any percussive transient you might find in commercially recorded music. Naturally, there are lousy engineers who don't maintain control over their recordings for one reason or another, but those non-standard CDs will likely be hard to listen to for more than one reason. You don't need to maintain headroom for gross negligence.

 

[VNandor]

I think you use headroom way more ambigously than I do. I mean it's not wrong, I've seen headroom being used in non-audio context as well so the word has a broad use. But by headroom, I mean specifically that if you want to play back something at given average level and the peak is 20dB above the average level, clearly, you need 20dB headroom above the average level to reproduce those peaks properly. This is why I think checking the average level of the recording and the peak of the recording makes sense, and the difference between them is the amount of headroom you need for playback.

 

[bigshot]

I'm using it in the sense that it is used in recording studios.

If you are saying that your figure is above average level, then we are saying the same thing. For a track with the maximum dynamics usually found in commercial recordings (55dB) that would be +27. I'm saying 10dB over the maximum sustained peaks. With a dynamic recording like Tchaikovsky, that would probably come out around +30 to +35 in your way of measuring. If an amp can do that, you are safe and don't need any more power to do the job.

Another way to look at it would be peak comfortable listening volume. For the loudest sustained peak level, that would be about 80dB. Add 10dB for a transient peak here and there and you are at 90dB. If an amp can produced 90dB, you should be fine. Anything over that would be overkill.

 

[VNandor]

Well, I'm using it in a way it makes sense for home playback. You can forget I mentioned headroom if you want to. All I'm saying is that if you have a recording which is at -25dB RMS and you want to play that back at a given SPL, you need to pick something that can go above the picked average SPL by 25dB. So saying that "oh this amp can drive the headphones to 120dB" could be a little bit misleading because people might automatically assume that the average SPL could get to 120dB with normal music especially if they don't understand how these measurements and calculations are being done.

 

[bigshot]

All recordings have the same maximum sustained peak level. That is the maximum comfortable volume you set it to with your amp. But not all recordings are as dynamic. So if you measure from the middle, a heavy metal song that is loud all the way through will have a quite different average level than a dynamic orchestral symphony with loud and quiet movements will. Using average level, heavy metal will come out loud. Using classical, it depends on whether it's Mozart or Wagner how it comes out. If you measure above the sustained peak, they will all measure the same way, because too loud for comfort is too loud for comfort. That is the max. With digital you have your zero level that defines the edge of clipping and the peak transient of your music. Dynamics all fall below that naturally. The top end is fixed. The middle floats depending on the recording.

I might not be explaining that clearly. But I'm trying.

 

[megabigeye]

Yes, it makes sense. Thank you.

My hope is that I'll be able to learn how to assess gear matching using these variables. For example, if I have headphone A that has a sensitivity of 97 dB and impedance of 300 Ohms, then I'll need to find an amp the that provides a minimum of X mW and Y volts to properly drive them. Something like that would be great. Of course, sound quality etc. will be subjective.

I can't tell if I'm completely missing the mark here, but it seems like people are getting a little carried away with the details and not really answering this question. Or maybe it was answered somewhere in this thread's seven pages and I simply missed/forgot it. Or maybe I'm misreading what you're saying and understand.

In all my years of poking around Head-Fi, I don't think I've ever come across a meaningful definition of "properly driven" according to most audiophiles. I even tried asking this question a few months ago, but I don't think it was ever answered at all. A lot of people seem to have a notion of some magical amount of power a headphone has to have in order to sound "good" or "its best" or "properly driven," but they never seem capable of answering how they arrived at that number. Those are all subjective terms, so definitions are subjective.

What it looks like you're asking, though, is how much power you need to get to a given SPL with a given headphone. That's easy to answer if you know how loud you want the loudest transients, and your headphone's impedance and sensitivity. I honestly have no idea how loud I listen and so I (almost arbitrarily) pick 120dB as the peak. I know that that's a lot louder than I'd ever want, but I figure it gives me plenty of leeway with my music and with my volume knob. In my (not 100% informed) opinion, it doesn't matter how dynamic your music is; you simply don't want to go above 120dB. So 120dB works as a concrete cutoff.

Each +10dB requires 10x power, so to determine how much power you need:
P_T = 10^(T-S)/10
Where P_T is target power, T is target volume, and S is headphone sensitivity.
Since headphone measurements are in milliwatts, this equation spits out milliwatts.

Using 120dB as T with your headphones:
P_T = 10^(120-93)/10
P_T = 10^2.7
P_T = 501mW

Then figure out the necessary voltage using Ohm's Law:
P = V²/R
where P is power, V is voltage, and R is impedance. In Ohm's Law, power is always in watts, so divide mW by 1,000.
Using your headphones again:
0.501W = V²/300Ω
V = √(0.501W*300Ω)
V = 12.3V

If you want to get technical, you should add the headphone's impedance (R_L = load impedance) to the amp's output impedance (R_S = source impedance), which would be important for an amp with very high output impedance, like an OTL.
P = V²/(R_L+R_S)

If your headphone's sensitivity is given in dB @ 1V (like some Sennheisers), use V_T = 10^(T-S)/20 to figure out target voltage, and then use Ohm's law to figure power.

 

[ADUHF]

Each +10dB requires 10x power, so to determine how much power you need:
P_T = 10^(T-S)/10
Where P_T is target power, T is target volume, and S is headphone sensitivity.
Since headphone measurements are in milliwatts, this equation spits out milliwatts.

Using 120dB as T with your headphones:
P_T = 10^(120-93)/10
P_T = 10^2.7
P_T = 501mW

Since you're ending up with milliwatts, then the above is computed from the headphone's "sensitivity" (really power efficiency, I think ) in dB/mW, rather than dB/V. Correct?

If your headphone's sensitivity is given in dB @ 1V (like some Sennheisers), use V_T = 10^(T-S)/20 to figure out target voltage, and then use Ohm's law to figure power.

Based on this comment, I assume the above is correct.

 

[bigshot]

I honestly have no idea how loud I listen and so I (almost arbitrarily) pick 120dB as the peak. I know that that's a lot louder than I'd ever want, but I figure it gives me plenty of leeway with my music and with my volume knob.

120dB is the threshold of pain and into the range where you incur serious hearing damage from short exposure. It's like laying down on the sidewalk next to a jackhammer. If you play Dark Side of the Moon at 120dB you'll be deaf before you get to the second track on the album. Most people listen to music below 80dB (80dB isn't pleasant). That is a much more reasonable target. The difference between 80 and 120dB is massive. I'd suggest arbitrarily picking 80dB. That will give you plenty of leeway.

I think the reason that a lot of discussion on Head-Fi goes in circles is because too much of it is based purely on arbitrary theory. I'm not criticizing you for that, it's the way things seem to work around here. Everyone talks about specs as arbitrary numbers on a page, and they don't translate them into real world listening with human ears. A lot of "experts" on yootoob make it worse by claiming to be able to hear numbers that only bats can hear. So everyone just grabs a worst case number out of the air and cites that. Then the next guy picks a slightly larger number "just to be safe" and uses that. The next person takes that number and makes it a little bigger "just to be safe"... and so on. Pretty soon you're at the threshold of pain and it isn't at all safe! There's no anchor in reality to give context to those numbers.

The truth is that home audio has pretty much achieved the goal of "perfect sound". Even cheap amps, DACs and players are audibly transparent (with the exception of tube amps). You have to really search hard to find anything that isn't. I've been patiently asking for years here for an example of a DAC that sounds different in a controlled listening test. I haven't found one yet. No one has bothered to do a controlled test, so they don't know.

All of this math and angst is thrown at us by the high end audio salesmen. They don't want us to know that their thousand dollar DAC sounds the same as a fifty dollar one. So they stir up the water and encourage normal forum members to propagate the confusion.

A controlled listening test is easy. I don't know why people avoid them so much. Maybe they really don't want to know.

There are things that matter, and getting a handle on how to quantify those things would be really handy for people. But they spend all their time chasing numbers that don't mean anything in the real world.

 

[skhan007]

Excellent, thank you!

If I did the math right, based on the above, 97dB sensitivity, 120dB, and 300 Ohms...I'm getting about 200mW and 7.7 volts needed. My DAC/amp currently does 310mW and 10v, so I'm operating well within a good range. I actually listen to my music at about 60-65dB, so not that loud, so I'm concluding I'm in good shape. Still very interested to hear my cans through various amps to hear for myself, however.

 

[ADUHF]

And it looks like I was probably wrong about the milliwatts being the most important factor. Because two headphones of different sensitivities/power efficiencies can apparently be driven to the same volume in dBs with different amounts of power. Very interesting!

I assume this is what VNandor was driving at in this post as well (with a bit less of the math spelled out)...

IMO if you want to be pedantic about it, the impedance and sensitivity of the headphones should be checked first. Then you would have to know what's the loudest level you would ever want to listen to and also check how dynamic your music is. Do the math once to figure out how much power you need, get some amp that claims it can output that amount of power without distortion and you are set until your taste in music dramatically changes or you get a new headphone. Altough even with all of that, you might end up with something that doesn't sound good to you but in practice, it basically shouldn't happen.

the mW value is linked to voltage, they depend on each other. Saying that an amp can output 1/3W power into a 300ohm headphone is the same as saying the output voltage of the amplifier with a 300ohm headphone is 10V. Once you plug a headphone in and raise the output voltage the power must raise with it as well. Does that make sense?

I don't know if there is a proper definition but that doesn't have to mean there isn't any.

So if you're trying to achieve similar amounts of headroom and volume on two different headphone+amp rigs, with differing impedances, then it looks like you have to go by the target in decibels, and work your way back from that. Rather than using either volts or milliwatts as a target.