Matching headphones and amps. Is it a scientific process?
Mar 17, 2021 at 7:35 PM Thread Starter

#### skhan007

I ask this question because I have recently acquired my first DAC/headphone amp combo and I'm using it with 300 Ohm headphones. To my ears, the unit (RME ADI-2) drives the headphones (ZMF Auteur) just fine. Perhaps the word "drive" needs to be defined and if I'm using it wrong, please correct me. I'm hearing full bass, crisp highs, my volume/output is nowhere near the maximum of what the unit puts out. I did an A/B between the RME unit and two different tube amps at the hifi shop and could hear little difference between them, in terms of how my headphones were driven.

I posted my experience in a thread and someone told me I was wrong and that I have no experience. Furthermore, I shouldn't post "absolute statements" such as my unit drives my headphones. I was told that an external headphone amp was necessary.

This made me curious. Is there math that says X impedance headphones require Y watts of power to be properly driven?

I can't imagine why RME would make a DAC/headphone amp (with a dedicated extreme power mode, specifically designed for high impedance headphones) if it was not capable of the task. Please share your thoughts, as I'm genuinely perplexed.

Mar 17, 2021 at 8:54 PM
Short answer: if you’re happy with the sound you’re hearing, and you can go as loud as you want, you’re good.
Someone giving you grief about a setup they have never heard is just giving an opinion, and it’s not worth that much.

Mar 17, 2021 at 8:58 PM
Mar 17, 2021 at 9:16 PM
Is there math that says X impedance headphones require Y watts of power to be properly driven?
It depends on how "properly driven" is interpreted. If it means "enough volume", it's fairly simple to calculate how loud a given headphone can get with a given amp if there's enough specs on them. If properly driven means "subjectively pleasing" then there's no easy way to tell if a headphone is properly driven because that has more to do with humans and perception than electronics.
If properly driven means "free of distortion", the best you can do with math is hope the manufacturers provided real-life specs instead of ideal ones and then make some educated guess that may or may not work out in the end.

Here's how I would do the math with your amp and headphone: checking RME's website, it looks like the amp's maximum output is 10V into 100ohms. We can use that to calculate how much power the amp can output into the headphone that is 300ohms using V^2/R which is 333mW. Looking at ZMF's site, the headphone's sensitivity is said to be 97dB/mW. We can use the output power and the sensitivity to determine how loud the headphone can get using sensitivity+10*log(output power) which is 122dB SPL.
Note that it doesn't imply anything about how "good" the sound is (which is completely subjective) or even about distortion (which could be measured at least).

I posted my experience in a thread and someone told me I was wrong and that I have no experience. Furthermore, I shouldn't post "absolute statements" such as my unit drives my headphones. I was told that an external headphone amp was necessary.
So right after telling you to not post "absolute statements" he says an external amplifier is necessary? That sounds hypocritical to me but whatever. People at headfi typically avoid trying to invalidate others' listening experiences, the moment someone tries to bring up controlled testing the thread usually erupts in flames, so maybe it's just a misunderstanding?

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Mar 17, 2021 at 9:28 PM
The short answer is 122dB is over the line for the threshold of pain and incurring hearing damage. Your amp is more than capable of doing the job.

Mar 17, 2021 at 9:32 PM
It depends on how "properly driven" is interpreted. If it means "enough volume", it's fairly simple to calculate how loud a given headphone can get with a given amp if there's enough specs on them. If properly driven means "subjectively pleasing" then there's no easy way to tell if a headphone is properly driven because that has more to do with humans and perception than electronics.
If properly driven means "free of distortion", the best you can do with math is hope the manufacturers provided real-life specs instead of ideal ones and then make some educated guess that may or may not work out in the end.

Here's how I would do the math with your amp and headphone: checking RME's website, it looks like the amp's maximum output is 10V into 100ohms. We can use that to calculate how much power the amp can output into the headphone that is 300ohms using V^2/R which is 333mW. Looking at ZMF's site, the headphone's sensitivity is said to be 97dB/mW. We can use the output power and the sensitivity to determine how loud the headphone can get using sensitivity+10*log(output power) which is 122dB SPL.
Note that it doesn't imply anything about how "good" the sound is (which is completely subjective) or even about distortion (which could be measured at least).

So right after telling you to not post "absolute statements" he says an external amplifier is necessary? That sounds hypocritical to me but whatever. People at headfi typically avoid trying to invalidate others' listening experiences, the moment someone tries to bring up controlled testing the thread usually erupts in flames, so maybe it's just a misunderstanding?
Thanks- if I’m understanding the math, my RME is indeed capable of driving my 300 Ohm headphones, correct? In a search, I noted a reviewer graphing results showing the RME it’s capable of 310 mW with a 300 Ohm Load, which he called “superb.”

Regarding the criticism I received, the member was clear in pointing out that I’m inexperienced and shouldn’t be stating the RME can drive my headphones. This is in an RME thread, so he’s an owner as well and seems set in the requirement of a separate amp. Pretty deflating, but I’ll get over it.

Mar 17, 2021 at 9:35 PM
You have to understand that an awful lot of people in audiophile internet forums (and other kinds of forums as well) aren't here to share information. They are here to pump up their egos. They aren't satisfied with who they really are, so they act like a pompous ass in forums and pretend to be more important than they really are. The really lame ones seem to think that tearing other people down builds themselves up. I seem to be a lightning rod for that kind of aggressive insecurity. I just blow past it. Don't let it bother you. It's the internet. Your amp and headphones are well matched.

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Mar 17, 2021 at 9:42 PM
You have to understand that an awful lot of people in audiophile internet forums (and other kinds of forums as well) aren't here to share information. They are here to pump up their egos. They aren't satisfied with who they really are, so they act like a pompous ass in forums and pretend to be more important than they really are. The really lame ones seem to think that tearing other people down builds themselves up. I seem to be a lightning rod for that kind of aggressive insecurity. I just blow past it. Don't let it bother you. It's the internet. Your amp and headphones are well matched.
Much appreciated. Thank you for the encouraging words and feedback on my amp/headphones question.

Mar 18, 2021 at 4:04 PM
It doesn't look like RME even makes a dedicated headphone amp. So if you want some RME goodness, a DAC or interface may be your best or only option there. RME generally makes pretty good stuff though. So you probably have one of the best DAC/headamp combos around with this unit. And it seems like your homey in the ZMF topic who was trying to steer you toward a separate amp might've been a tube fan.

That's not surprising btw. Because, as general rule, I believe tube amps tend to be higher impedance than alot of the more run o' the mill solid state amps. So they probably tend to be a pretty good fit with higher impedance headphones. So its an obvious go-to solution for alot audiophiles with higher impedance HPs. And might be somethin you'd want to try at some point in the future, for maybe a slightly different type of sound quality than your RME unit.

Any good solid state amp worth its salt though will have enough power to drive headphones with a variety of impedances. And the simple fact that your DAC has separate headphone outputs for both low and high impedance headphones (which is somewhat unusual) would certainly seem to indicate that it falls into that category.

If you have any lower impedance headphones or IEMs, or are planning on getting some, I would definitely give them a try on that IEM jack.

As others have already stated, there is indeed a bit of science that comes into play when trying to match up headphones and amps, in terms of the volumes, distortion levels, and also energy consumption (if that matters to you). Distortion is more of an issue though when driving a lower impedance headphone with a high impedance amp. So that would not be a concern in your situation. If you want to bone up a bit more though on the subject, here are a couple articles that may be worth a look...

https://en.wikipedia.org/wiki/Impedance_bridging
https://en.wikipedia.org/wiki/Damping_factor

Folks who subscribe to the damping factor/impedance bridging theory will generally suggest that your headphones should be at least 6 or 8 times the impedance of the amplifier's output, to keep the distortion level below the threshold of audibility. Most lower impedance headphones and amps will be well above that, because the amps are generally around 1 ohm, and the headphones are typically around 30-35 ohms.

Distortion will only start to become noticeable when you're using a lower impedance headphone with amplifiers above about 5 or 10 ohms. Which is not that unusual, especially on pro audio gear. So it can be helpful to know both the output impedance of your amp or audio gear, and the input impedance of your headphones when using lower impedance headphones, if you want to keep the audible distortion to a minimum.

Properly bridging the impedances can also save some energy as well. It is a common fallacy that higher impedance headphones require extra powerful amps. But that isn't really the case, if they are paired with a higher impedance amp that has an adequate (as opposed to insanely high) damping factor.

I do subscribe to the damping factor theory btw. And my headphone/amp combo does have an insanely high damping factor, which probably exceeds 250:1, since my headphones are 250 ohms, and my amp is only 1 ohm. So it's probably not the best combo from an energy consumption standpoint. The Bellari HA543 is one of the least expensive amps I could find though with a combination of XLR inputs, and enough power to sufficiently drive both high and low impedance headphones without distorting the sound on either one. For someone like me on a very tight budget.

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Mar 18, 2021 at 4:23 PM
As long as an amp is matched properly and is competently designed and manufactured, the only difference between one amp and another is features. Manufacturers throw tons of irrelevant "facts" at you to make you think their brand is better than the other, but all that stuff has no real impact at all on listening to music on the couch. All that blather boils down to inaudible sound and exceptions that don't apply to the definition of general use.

skahn007, your headphones sit right in the area that most headphone amps are designed to drive. In general, it's good to stick in the middle of the market like that. Either get a common impedance like yours, or get a set of cans like mine that don't need amping at all (32 ohm / 110dB sensitivity). When you start getting into non-standard designs, it gets complicated. Personally, I don't think it's worth it, because there's lots of great sounding stuff that isn't complicated like that.

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Mar 18, 2021 at 4:57 PM
Thanks- the best part of the Sound Science forum is that you all have great links to data, white papers, and other empirical information that is truly helpful and educational.

From the standpoint of sound quality (subjective), I think my RME DAC/amp combo sounds very good with my ZMF headphones. From the standpoint of power, sensitivity, dBr, and output (objective) all the numbers are indicative of more than adequate confirmation. I looked at Amir's data, which clearly indicated 310 mW was available on tap, which far exceeds what is required to run 300 Ohm headphones. He called this "superb" and given the math, I can see why. I'm quite perplexed at the guy who stated RME, which he also owns, is not sufficient to drive 300 Ohm headphones (he referenced Sennheiser HD800).

Out of pure curiosity, I may acquire/test drive/borrow (whatever works out) a solid state and tube headphone amp to see for myself. I did spend some time at the local HiFi shop with two high-end tube amps. I brought my RME and listened with my headphones to the DAC through each tube amp and then the DAC by itself, noting very little difference. The only thing I really picked up on was more presence in bass/sub-bass. Granted, I would like more time with a tube amp to listen further and take notes. I've been reading up on the THX 887, which some have paired with their RME. Many have stated it has resulted in some subjective improvements on their headphones.

Mar 18, 2021 at 5:02 PM
If you use computer as your source, it might be better to use a DSP to emulate a tube amp. Tube amps can very in sound a lot, and quite a few are designed to sound just like solid state. It's hard to know what you're getting. With a DSP, you can dial in each aspect of distortion exactly the way you want it. Much more flexible. The other advantage is that the sound is calibrated and consistent. Tubes can shift over long use.

I think a lot of the appeal of tubes has nothing to do with sound though. They look really nice glowing in the dark. I prefer clean solid state sound, so I put some christmas lights over my amp. It serves the same purpose.

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Mar 18, 2021 at 5:02 PM
As long as an amp is matched properly and is competently designed and manufactured, the only difference between one amp and another is features. Manufacturers throw tons of irrelevant "facts" at you to make you think their brand is better than the other, but all that stuff has no real impact at all on listening to music on the couch. All that blather boils down to inaudible sound and exceptions that don't apply to the definition of general use.

Fwiw, this was my take on the above from another related topic....

The differences in sound between amps should be minimal if not indiscernible though if the following criteria is met...

1. flat frequency response across audible spectrum
3. good power regulation
4. low noise (both internal and external)
5. low distortion
6. high damping factor with properly bridged impedance

So I'd agree that if the above factors are satisfied, and the unit is well-built using higher quality components that anything else is probably mostly just marketing hype and/or features and/or bells and whistles, and or design/cosmetic niceties... which some people care about. "Competent design and manufacture" is not a given though with the type of lower cost equipment that's currently within my budget. So it does make some sense for folks like me to pay attention to all the above details.

That RME unit looks like it has some pretty nice features btw. I'd love to have a dac/amp with some built-in parametric EQ functions like that! With a few more input options. Maybe someday when I'm a bit more well off.

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Mar 18, 2021 at 5:09 PM
I find competence across the board in home audio, at least for the past 20 or 30 years. Everything I've ever bought has been audibly transparent. That shouldn't be surprising because most gear is made from off the shelf components using standard designs. I don't buy the stuff advertised by fly by night Chinese sellers on eBay, or super high end boutique stuff that is deliberated designed to have a "house sound". Maybe that is what you're referring to. It seems to me, you could pretty much buy an amp or DAC at Amazon by throwing a dart at it and hit something competent.

Mar 18, 2021 at 5:56 PM
Yes, I'm using my computer as a source. You've piqued my curiosity about the DSP. Any names/recommendations off the top?