How much power is enough?

Discussion in 'Sound Science' started by ToTo Man, Aug 1, 2018.

1. Apologies if this question has been asked ad nauseam, this is my first post in the Sound Science section so please be gentle with me!

I've been into headphones for a few years now but am still somewhat mystified by how much power / headroom is required to obtain optimum performance.

With loudspeakers, things are somewhat easier. You look at their impedance (which is typically between 4 and 8 ohms nominal) sensitivity (Xdb for 1w at 1m), consider the manufacturers recommended power range (i.e. use with amplifiers between Y and Z watts per channel RMS), and depending on how loud you listen at and how much headroom you want above that, you go shopping for an amp that at least meets or preferably exceeds those minimum specs. (OK I'm oversimplifying things but you get the idea).

With headphones, things seem a bit more ambiguous. With such a wide range of nominal impedances (from below 16 ohms to above 600 ohms), sensitivity sometimes expressed in Watts and other times expressed in Volts, the fact that some headphone amp manufacturers provide maximum wattage specs whilst others provide RMS wattage specs into a small sample of loads, and some expressing it in terms of max or RMS Volts instead of mW. I find it very confusing to figure out just how much power and headroom a particular headphone requires to perform optimally with full dynamic range, and exactly how much power and headroom a particular headphone amp can provide into a specific load.

To give some examples, let's compare
two Class A designs, the Schiit Asgard and the Arcam rHead:

Asgard 2:
Maximum Power, 32 ohms: 1.0W RMS per channel
Maximum Power, 50 ohms: 1.0W RMS per channel
Maximum Power, 300 ohms: 380mW RMS per channel
Maximum Power, 600 ohms: 190mW RMS per channel

Maximum power (both channels driven)

As the rHead quotes an RMS voltage figure, I am assuming the Watts figure is also RMS, or might it be peak value? The rHead doesn't quote a figure for 600 ohms, but since the trend seems to be half the power for double the impedance, it will probably be around 65mW. So into a 32 ohm load the Asgard and rHead have near identical power outputs, but into 600 ohms the Asgard is 3x more powerful than the rHead.

Let's take another example, the Schiit Vali 2 and the Audio-Technica AT-HA5050H. Not exactly an apples to apples comparison because one costs <\$149 and the other costs >\$5k, but it's the power specs I'm most interested in:

Vali 2:
Maximum Power, 16 ohms: 1300mW RMS per channel
Maximum Power, 32 ohms: 1000mW RMS per channel
Maximum Power, 50 ohms: 650mW RMS per channel
Maximum Power, 300 ohms: 270mW RMS per channel
Maximum Power, 600 ohms: 140mW RMS per channel

AT-H5050H:
Rated Output (20 Hz – 20 kHz):
125 mW + 125 mW (16 ohms load)
62 mW + 62 mW (32 ohms load)
31 mW + 31 mW (64 ohms load)
3.3 mW + 3.3 mW (600 ohms load)

So into a 600 ohm load, the Vali 2 provides more than 40x the power of the AT-H5050H. If I compare the AT-H5050H to the Valhalla 2 or Mjolnir 2, the differences gets even bigger, as these two Schiit amps put out 125x more power into 600 ohms than the AT-H5050H.

So, if we have 3.3mW RMS provided by one headphone amp and 450mW RMS provided by another headphone amp, just how much power and headroom is really required to drive a typical 300 to 600 ohm dynamic headphone cleanly with no distortion? This is something I'd really like to understand. (I'm referring to headphones such as the 300 ohm Sennheiser HD600/HD650, 300 ohm Sennheiser HD800/HD800S, 420 ohm Audio-Technica AT-ADX5000, and 600 ohm Beyerdynamic DT880).

Many thanks.

Last edited: Aug 1, 2018
ZenErik likes this.
2. I’m curious about this as well as I feel like more power is often not as important as some make it out to be.

Most amps I’ve used over the years I can’t even turn past 9 o’clock on low gain. Some of the more powerful ones I could barely get to 8 o’clock at normal listening levels. Do I really need all that power? Something tells me ‘probably not’.

Personally, I’d like to be able to turn more amps closer to 12 o’clock while still feeding them a line level signal.

Last edited: Aug 1, 2018
3. I get what you mean about the volume position problem, however this can often be a separate issue that's not necessarily related to the amp's power output capabilities (at least this is my experience with loudspeaker amplifiers, but I assume it also applies to headphone amps).

The volume pot is typically calibrated to reach a defined level of output at a defined position on the dial with a defined level of input signal. For example, if the volume pot is calibrated to reach the amp's full output capability at 3 o'clock position with 150mV input signal (as was common before the digital revolution), then feeding the amp with a 2V input signal will cause it to reach its full output capability much earlier on the pot, e.g. at 9 o'clock instead of 3 o'clock.

You can therefore
have a situation where a low-powered amp sounds "more powerful" than a high-powered amp simply because the volume pot has been calibrated to reach maximum volume much sooner on the dial, but it really isn't more powerful, because once it reaches full output, turning the volume pot up higher will just cause the amp to go into clipping/distortion.

I suspect some manufacturers do this intentionally to fool consumers into thinking their amp is more powerful than it is, and it drives me nuts because it is very impractical when you are restricted to such a narrow range on the volume pot. That's why I like amps that have a separate gain switch. That way, if you have sensitive headphones, you can use Low Gain mode and be able to use a wide range on the volume pot without it becoming too loud too soon. And if you have hard-to-drive headphones, you can use High Gain mode and not have to worry about running out of range at the top end of the volume pot before it gets loud enough.

Last edited: Aug 1, 2018
4. You would probably find people willing to do the math for you if you gave one specific example and asked about that. You put so many words and numbers in your post, I think it's making people think it isn't worth the time to answer. By the way, there was a thread a little while back about impedance. You might want to check that. It listed the mathematical formula for calculating the amping requirements.

Last edited: Aug 1, 2018
robert766, ToTo Man and ZenErik like this.
5. Contributor
thing is, you're not asking a lot of specific questions, instead you sort of hope for the answer about life and everything, so it's a little overwhelming ^_^.
that one is simple, go for P=V²/R and you can see if you come close or not, in this case we do so RMS it is. most of the time, those specs should specify that they're values at 1%THD or 0.1%THD for some products. it's more relevant because you won't really care to have up to 50W if the sound is actually audible crap since a little over 1W into that given load. ^_^

all in all it's really difficult to be sure about much of anything and I'm pretty confident that many manufacturers do it on purpose. using different or incomplete nomenclatures, giving references into a different load, anything goes. and as you said it's the same for headphone specs with sensi given for 1volt or 0.1V or 1mW. if the all information is reliable and clearly expressed, then we can always convert everything into almost everything else, but it's a PITA and not something that the typical audiophile will do.
and that leads us to said audiophiles having a tendency to go for way more power than they will ever use. basically because they have no idea, so insecurity pushes them to get always more. understandable, but it leads to the same audiophiles posting a lot of garbage claims about power requirements on forums. added to how any subjective impression can be falsely correlated with power, and it's a mess.

I'll do one headphone with you, the hd600 is given as 102db/V meaning that if your amp sends a 1V 1khz tone into the 300ohm hd600, you'll get a 102dB SPL, 1khz tone. want to know how many mW that is, again P=V²/R=1/300=0.00333W so 3.33mW.
you can go the other way around, you want to know how loud it would be into 1mW to have the sensitivity in dB/mW? 1mW, or in W for the formula, 0.001=V²/300. V=0.55. if 1V is 102dB, how loud would 0.55V or 1mW be? hocus pocus lazy magic http://www.sengpielaudio.com/calculator-gainloss.htm . we learn using the third calculator thingy on the page that we would lose 5.19dB going from 1V down to 0.55V(which is normal, as half the voltage is -6dB). so 102-5.19=96.81dB. all that crap to say that the sensitivity of the hd600 is about 97dB/mW. ^_^

now more interesting, you take your Asgard specs into 300ohm, which is 380mW, and want to know how loud the hd600 would go when feed that much power?
0.38=V²/300
V= 10.67
going from 1V to 10.67V I once again cast the lazy man spell http://www.sengpielaudio.com/calculator-gainloss.htm and get a 20.56dB variation. I just have to add that to the sensitivity of the headphone at 1V: 102+20.56=122.56dB SPL. that's how loud you could expect your 1khz tone to get with the Asgard turned up to the max or up to reaching 1%THD(whichever came first in their measurements).

now the AT-H5050H: well you don't have the output into 300ohm. so you have to sort of guess. and while it usually works out to expect linear progression for power vs impedance of the load, on some designs, the assumption is wrong. so I would personally try to contact the manufacturer to get the power into 300ohm if that's the load I'm interested in for my headphone. from our little conversion games before, we already know what we get with 3.33mW as that's 1V into 300ohm which is the sensitivity specs for the hd600: 102dB for 1V. so worst case scenario, you could still probably expect at least a 102dB loud 1khz tone. but that's really no more than the vague estimation I gave. I would personally forget about that amp or contact the manufacturer or whoever can tell me what happens into 300ohm.

and basically you have to go for this kind of annoying process all the time or hope that someone else already went for it somewhere. those are only estimations, I don't care about possible phase issues, variability between pairs of the same headphone, how the headphone isn't 300ohm at all frequencies... and it's sort of pointless to wonder about all that because we usually don't have much data outside of 1khz. so you basically accept that you're only getting a superficial indication where you make sure you'll have enough power to go as loud as you like with a given headphone(usually people aim for 110 or 115dB as loudest they need to go). and maybe pick the amp with a little extra headroom beyond that, just in case for all the stuff you don't know.
beyond that is IMO it is rarely beneficial and sometime detrimental to aimlessly seek power. if I had a hd600, I wouldn't go buy an amp that can do 20W into 300ohm. I also probably wouldn't go for the AT-H5050H.

all right. I made a mess, not sure if I cleared up anything ^_^.

ZenErik and ToTo Man like this.
6. Contributor
Just a thought - you're approaching things from the wrong direction IMO. Lets look first of all at your HD800S.

300 ohm, SPL 102 db (1 kHz, 1 Vrm)

So go to this site, and enter the appropriate specs : http://www.digizoid.com/power.php

Gets you this:

So now lets look at the Asgard 2.

Into 300 ohms it will push 270 mW - which puts you far beyond the realms of pain. Unfortunately Schiit doesn't list voltage or current, but given the total power output - there won't be any issues.

Looking at the rHead - into 300 ohms it will push 0.13 W (or 130 mW). It will fall slightly short of the Asgard 2 - but still reach 115-120 dB with the HD800S

Now I'm going to show you something pretty simple which a lot of people would turn up their noses at - but it illustrates my point nicely. FiiO's A5 portable amp (http://www.fiio.net/en/products/59/parameters).
150 mW into 300 ohm
250 mA peak output current
14.96 Vp-p (5.28 Vrms) peak output voltage

Again using the power calculator for the HD800s - doesn't quite get to painful (7.94 Vrms) but will easily drive past "very loud" (4.47 Vrms)
Easily meets current requirements
Doesn't quite get to painful (210 mW)) but will easily drive past "very loud" (67 mW)

Most people will laugh at driving an HD800S with a portable amp - but guess what, it manages very well with no distortion. My usual ave listening never goes past 80 dB. I'd deafen my self if I turned up to full volume.

If you're driving the Senns (HD800, HD650 etc) you need moderate power and decent voltage. If it was something like an AKG or a Planar - you don't need the voltage, but you do need current. Calculate the power required for your most demanding headphone, then choose an amp which meets the power requirements and has the features and aesthetics you want. The constant chase for higher numbers is pretty silly. On a lot of amps - unless you're driving an HE6 or similar, you'll never use the power which is available.

Last edited: Aug 2, 2018
castleofargh, ToTo Man and ZenErik like this.
7. this helps my understanding quite a bit. Thanks.

So do the other posts, but this one seems a bit easier for my simple mind to grasp.

8. https://en.m.wikipedia.org/wiki/Damping_factor

Damping Factor is one of the most under-talked about concepts at Head-Fi. It’s a concept where control of the headphone diaphragm both excursions and halting effects the control and audio quality of the bass. It also effects other sonic attributes.

When the damping factor has been corrected many times it adds only 1bB of bass. Though due to control, the bass is better defined and actually can be perceived as more bass. This single issue and the proliferation of low output amps mismatched or closely but not perfectly matched with headphones on review, has been a source of endless confusion. Many folks just don’t know what the correct amp for their headphones could sound like.

Even finding powerful home amplifiers can increase the quality of sensitive multiple BA array IEMs, taking them to a place no one would have thought possible. Obvious here we are also hearing the amplifier build and not just the amplifier power. As a home amplifier for IEMs can have a better placed separation of circuits and better materials. Obviously a high power amp could cause low level noise with ultra sensitive IEMs, but quality equipment can be built dead quite, as long as your grounded right; and/or have power conditioning.

This has been the biggest thing I have learned here in 10 years.

And it just keeps getting more complicated when you realize just how deep the rabbit hole goes.
https://www.innerfidelity.com/conte...ents-explained-electrical-impedance-and-phase

Last edited: Aug 2, 2018
9. Thank you all for your answers and links to external articles and calculators, they are extremely helpful and I am in the process of studying them all carefully so that I fully grasp the concepts.

I apologise for my rambling OP, upon reflection it was quite a barrage of musings to wade through, but if nothing else it demonstrated the extent of my confusion over these issues.

I mentioned the AT-HA5050H because this is what I was sent by A-T to demo the ATH-ADX5000 headphones with, which are 420 ohms nominal impedance (with a peak impedance of 950 ohms at driver resonance) and 100dB/mW sensitivity. The amp likely wasn't built with those particular headphones in mind, but I find it curious that would provide me with an amp that puts out what I guesstimate to be around 5mW RMS per channel into 420 ohms.

EDIT - According to the digizoid calculator, the ADX5000 requires 0.65Vrms or 1.01mW to reach 100dB and 2.05Vrms or 10.01mW to reach 110dB. This is approximately half the power required for the 97dB/1mW HD600 and HD800S, but only 15% less voltage. If I use the ADX5000's peak impedance of 950 ohms, the mW requirements of course remain the same, but the required voltage increases to 0.97Vrms for 100dB and 3.08Vrms for 110dB. The HA5050H doesn't provide voltage output specs, but the mW specs provided suggest this amp probably doesn't have enough power in reserve for high impedance headphones if you want peaks of over 100dB and want to retain full dynamics across all frequencies.

Last edited: Aug 2, 2018
10. Amplifier output impedance is another very interesting topic which I am fortunately not quite as ignorant about, almost but not quite! . However until reading the GoldenEars article above I didn't realise quite how much impact it can have on higher frequencies. Most of the discussions tend to focus on bass and control around the driver resonance frequency, as this is where the impedance peak of most open back headphones tend to be. By luck, all of the headphones I own have fairly level impedance curves through the mids and high frequencies, which is likely why I haven't noticed much impact on these frequencies by changing the output impedance.

11. It’s a subject that goes on and on. We have physical damping from the diaphragm along with electrical damping from the coil.......and it all goes on to affect the movement of the driver. But your saying that all your heqdphones seem to have level impedence curves which means the load does not alter depending on the frequency?

What’s interesting is there is not talk ever of over damping. So as long as the noise floor is fine, basically the more power the better. At least that’s always been my saying.

12. There's a point where more power is just more power. "More is Better" is one of the biggest myths in home audio.

Tsukuyomi likes this.
13. And......the most misleading event with my subjective listening has been the more expensive amps not only had more power, but most likely were built better and better designed which added to the sonic benefits at hand.

Last edited: Aug 2, 2018
14. Contributor
your lazy man magic is much more powerful than mine. 10points for gryffindor!

15. I think the green from the money the amps cost made them sound better... that or the green marker.