Determining Headphone Driver Amp Requirements via Scientific Calculations

Discussion in 'Sound Science' started by WoodyLuvr, Jun 14, 2017.

1. I would be extremely interested in, and open to, hearing any/all thoughts regarding the determination of a headphone amp's driving potential & adequacy in meeting headphone driver requirements via equipment specs and scientific calculation.

A.) AudioQuest DragonFly Black - Power Output (Vmax) & Impedance: 1.15 Vrms (3.25 Vp-p) @ 0.3 ohms

B.) Nhoord Red v2 - Impedance & Sensitivity: 32 ohms @ 95 db/mW SPL (110 dB/V SPL)

i.) Best Amp Output Impedance for the Nhoord Red v2 by the “1/8th rule”: 1/8 * 32 ohms = <4 ohms

ii.) DragonFly Black Power Output with Nhoord Red v2: (1.15 Vmax * 1.15 Vmax)/32 ohms = 41.33 mW (Pmax)

iii.) SPL from Power for Nhoord Red v2 & DragonFly Black: 95 dB/mW + 10 * LOG (41.33 mW) = 111 peak dB SPL

iv.) SPL from Voltage for Nhoord Red v2 & DragonFly Black: 110 dB/V + 20 * LOG (1.15 Vrms) = 111 peak dB SPL
The DragonFly Black’s integrated headphone amplifier delivers a maximum voltage of 1.15 V per channel @ 0.3 ohms. This corresponds to a output power of 2×41.33 mW @ 32 Ohms driving the Nhoord Red v2s up to 111 peak db SPL.

If I am not mistaken the norm is to have around 105-110 dB SPL... unless, that is, one listens loudly (potentially unhealthy listening levels) to uncompressed audiophile recordings of dynamic classical pieces, then one may need up to 115-118 dB for headroom purposes correct? So, is 111 SPL sufficient? If not, where would the driver response be most effected? In the low end?

What other measurements and specifications should one take into account and why?

Frequency Response of Nhoord Red v2 Drivers "Alone - Outside of Cup"

Last edited: Jun 14, 2017
2. Contributor
as long as we're only talking power and nothing else, the problem lies really in the accuracy of the specs we get from the manufacturers.
a headphone can very well have a slightly different impedance and sensitivity.
the amp depending on how the specs are given might be for one channel or both, might be max power disregarding distortion levels, might give power into only one load significantly different from your headphone... here looking at the specs you provide, are those voltage values for a 32ohm load? if not your power estimates might not reflect reality. I see on the website that they effectively give a voltage without any more information. could mean that the voltage stays steady into most loads, or it could be a way to lose the consumer by avoiding to mentioning a more typical power into a given load because that value wouldn't impressive. I don't know which it is in this case.

so all that, and how music isn't always stuck to 0dB on the file, are already a few good reasons to consider some headroom beyond our own loudness needs when we can't confirm the measurements ourselves. but if you really get 1V into that headphone, it should be plenty loud.

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3. Gotcha on the specs.

Published power output for the DragonFly Black is 2 x 45 mW @ 32 ohms; however, my calculations come in a little lower at 41.33 mW???

If we go ahead and assume that the DragonFly and Nhoord specs are accurate at 2 x 45 mW @ 32 ohms @ 95 db/mW SPL (110 dB/V SPL) then a reasonable amount of headroom would be what? +30 db? From where, normal listening levels (60-80 db)?

Last edited: Jun 15, 2017
4. Contributor
sadly it depends on you and your habits. in my case I live in a rather quiet place and always listened to music quietly. I've tested myself over a period of time and never once did I set my amp to output more than 90db SPL(say more or less 3dB for my amateurish gears to estimate loudness). but beyond that, I use replay gain on my music and some pop songs end up with maybe 12dB attenuation to "feel" as loud as other more dynamic songs. and then I almost always use some EQ and will tend to attenuate the gain of my EQ by the same value as the boost I applied(clipping paranoia). over time I tend to check for clipping and adjust to my real needs, but still this mostly applies.
so all in all sometimes I will need my amp to go up to 90dB + up to maybe 18dB to compensate for various digital attenuation. but that's an absolute worst case scenario for me, not how loud I usually listen. in practice my amp is set for about 95dB into my hd650 and I adjust my preferred loudness in foobar, almost never reaching max level in it(yeah I'm a bit perfect multi murderer and not even ashamed of it ^_^).

but once I'm out in the street and cars pass next to me, if my IEM doesn't isolate a lot, I will be an idiot and boost the loudness a lot so that the cars stop covering my music. so ambient noise can also play a role in my final "needs". 110db is a lot already. most audiophiles are paranoid about lacking power and will ask for 115 or even 120dB, but IMO being able to reach 110db with less than 1%THD is already a lot.

now all this represents my views, be very sure that many others have different opinions. I remember someone saying that the amp being able to go much louder would result in the ability to follow faster transient response. and while it does kind of make sense, I don't tend to notice ultrasounds or a typical low pass on transients signals at 20khz, so I don't imagine that I should care about that with amps when they all go way beyond 20khz. but reasons like that will come from other people, like the idea that components made to handle higher voltages are just better, or ... I'm not super good at playing devil's advocate but just keep in mind that I don't express a consensus, just my opinion.

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5. No need to worry about a 0.4dB difference.
Normal "loud" listening is 85dB SPL, RMS with 20dB of headroom. But those are RMS figures, peaks can go 10dB higher, that would put you at 115dB SPL, Peak. And frankly, 85dB SPL is loud, louder than most of us would listen to.

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6. Really appreciate the thoughtful and/or lengthy replies... they have been great food for thought.

7. Here are some findings regarding an independent testing of the DragonFly 1.5 Black: https://archimago.blogspot.com/2017/06/measurements-audioquest-dragonfly-black.html

Vrms: 1.3 V
Vmax: 1.85V
Output Impedance: 0.61-ohms
Current Draw: <100mW (<90mA) @ 5V with a 16-ohm IEM at full volume... I find this particularly amazing!​

This blog/testing helped me discover an error on my part in my previous calculations... I always had assumed that Vmax and Vrms are one and the same and although they are close they are in fact not the same...

So I updated and corrected (all in bold text) my calculations as accordingly:

A.) AudioQuest DragonFly Black 1.5 - Power Output & Impedance: 1.3 Vrms (1.85 Vmax; 3.68 Vp-p) @ 0.61 ohms

B.) Nhoord Red v2 - Impedance & Sensitivity: 32 ohms @ 95 db/mW SPL (110 dB/V SPL)

i.) Best Amp Output Impedance for the Nhoord Red v2 by the “1/8th rule”: 1/8 * 32 ohms = <4 ohms

ii.) DragonFly Black Power Output with Nhoord Red v2: (1.85 Vmax * 1.85 Vmax)/32 ohms = 107 mW (Pmax)

iii.) SPL from Power for Nhoord Red v2 & DragonFly Black: 95 dB/mW + 10 * LOG (107 mW Pmax) = 115.3 peak dB SPL

iv.) SPL from Voltage for Nhoord Red v2 & DragonFly Black: 110 dB/V + 20 * LOG (1.85 Vmax) = 115.3 peak dB SPL​

Last edited: Jun 18, 2017
8. Just in case anyone missed the difference...Vrms is simply the RMS value of an AC waveform. The value will depend on amplitude and the shape of the wave. Vmax is half the peak-to-peak value, and will depend on wave amplitude only.

When referring to SPL, we mostly use RMS.
You've stated the output voltage, not power.
You need to work in RMS. Loudness perception relates closely to RMS values of waveforms, not their peak value. For example, a pulse waveform could have a peak value of 1.85, but RMS value of 1/10th of that or less. The perceived loudness will be approximately the same as the RMS value. Using Vmax (peak) values results in unrealistic results. For a sine wave, the peak and RMS values will be 3dB apart, but that's the only waveform where that is true, or even very predictable.

Peak based figures in SPL measurements apply only when measuring high level impulse sounds, things like gun shots.

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9. Raised above a normal living room noise floor, 85dB is an excessive volume level. Normal loud listening is between 55dB and 65dB. (accounting for an ambient 30dB noise floor)

Last edited: Jun 18, 2017
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10. Now I am thoroughly confused... why do electrical/audio formulas specific to calculating SPL from either Voltage or Power ask for and/or use Vmax values and not Vrms?

P (Pmax in mW) = (Vmax * Vmax) / Headphone Impedance
dB SPL = Sensitivity in dB/mW + 10 * LOG (Pmax in mW)
dB SPL = Sensitivity in dB/V + 20 * LOG (Vmax)

So if I substitute all Vmax values with Vrms as you have stated I get these results (look correct?):

ii.) DragonFly Black Power Output with Nhoord Red v2: (1.3 Vrms * 1.3 Vrms)/32 ohms = 52.8 mW (Pmax)

iii.) SPL from Power for Nhoord Red v2 & DragonFly Black: 95 dB/mW + 10 * LOG (52.8 mW Pmax) = 112.2 peak dB SPL

iv.) SPL from Voltage for Nhoord Red v2 & DragonFly Black: 110 dB/V + 20 * LOG (1.3 Vrms) = 112.3 peak dB SPL

Last edited: Jun 18, 2017
11. So if we say that the ceiling for normal loud listening is at ~65 dB or ~85 dB how much headroom is required to capture very dynamic recordings correctly? 20 dB or 30 dB?

Last edited: Jun 18, 2017
12. Don't know where you got that. Makes no sense, though, for reasons explained. Vmax/peak doesn't take into account loudness perception, heating, crest factor, etc. If you were concerned with damaging headphones, RMS would also be the important figure.
Yes, that's right.

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13. 20dB above 85dB SPL.

Most headphone listening, especially with open designs, will be louder than 65dB SPL.

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14. Ah, a good point regarding open backs... I hadn't consider that aspect at all. That 85 dB you gave is now making a lot more sense to me

15. Apologies for beating a dead horse but would someone please help me understand this... I am dying to figure out this whole headphone power amp'ing conundrum as I am missing something that would make sense of it all.

Forum members consistently state that the HD6XX will sound better with even more power (e.g. Schiit Magni 2)... the bass will be better... Why? How does more power (increased peak dB SPL) beyond let's say the Audioquest DFR's 14.7 mW @ 300 ohms (109.5 peak dB SPL) or even the Chord MOJO's 93.6 mW @ 300 ohms (117.5 peak dB SPL) make the HD6XX sound and perform better?

If we take the Schiit Magni 2's max power output of 260 mW @ 300 ohms (which is a tremendous amount of power) we find that it is capable of driving HD6XXs to a deafening 121.9 peak dB SPL!

SPL from Power = 97.8 dB/mW SPL + 10 * LOG (260 mW) = 121.9 peak dB SPL

Is this really necessary for better sound or is it well beyond what we can actually hear and benefit from? What I am trying to say or ask here is: why would we need anything more than 20 dB of headroom for even an extremely demanding and dynamic classical piece being listened at 85 dB with open backs or 65-75 db with closed backs??? Wouldn't anything under 105-110 peak dB SPL with less than 1%THD be more than enough to easily drive HD6XX and cover extremely demanding music pieces such as Mahler's Resurrection (Symphony No. 2)?

Where would one draw the line to represent that point of diminishing returns where a pair of headphones will no longer benefit from more power... 110-115 peak dB SPL or even lower?

Last edited: Jul 7, 2017