How to understand the impedance and efficiency of a headphone vs volume

[uppsju]

I have a Topping DX3 Pro, and for over a year I've been using it to power my Monoprice M1060 (v2). I recently bought Hifiman Sundara to see how they differ in sound. One thing puzzles me though. As far as I see the M1060 has an impedance rating of 50 ohms and sensitivity of 96db, vs the Sundara's 37 ohms and 94db.
When I use my M1060 it is comfortable around -20 dB on the amp. However, to get the same sense of volume on the Sundara, I have to increase to -10 dB.
I would have thought it should be the other way around. What am I missing or not understanding?

Thanks.

 

[majingotan]

You should look for efficiency in dB/mw and add that as a factor. Keep in mind dB is in log scale and as such to increase the loudness by 2 dB, your amplifier requires 10x the power. Sundara is rated at 94 dB/mw while Monolith is rated at 96 dB/mw hence the more power required by DX3 to match the level with Monolith

 

[uppsju]

I see. So the efficiency in dB/mw in this case matters more than the impedance.

 

[Fluffy]

The units of sensitivity here are important – 94 dB/1mW in the case of Sundara. That means that when 1 milliwatts of power is put into it, it produces sound at a loudness of 94 db spl. In the m1060, the same milliwatt of power will drive them to 96 db spl. Meaning, the m1060 driver is more efficient than the sundara, therefore requires less power to reach the same volume level.

50 and 37 ohm are virtually the same in terms of the resistance they apply to the current from the amplifier, so they are not the major contributor here.

 

[solderdude]

The efficiency in dBV is what counts because headphone amplifiers provide an output voltage.
dBmW says nothing when comparing loudness unless you also include the impedance.
That is why one should only compare dBV and calculate dB/mW values to dB/V

HERE is a handy chart showing both dB/mW and dB/V for a lot of headphones.
I made a chart myself but isn't up to date anymore

Here is some reading material about it.

Some manufacturers specify dBmW other dBV and more often then not they just say 'efficiency' and give a number and leave out what it really is.

Sundara: Efficiency: 94 dB/1mW (108 dB/1V)
M1060 Efficiency: = 98dBmW (111dB/V) (Tyll's measurements)

Basically the M1060 will play 3 dB louder on the same volume setting.
No idea where the 10dB difference comes from, maybe the v2 differs, maybe the frequency or way the numbers are created account for differences.

 

[RayDunzl]

You should look for efficiency in dB/mw and add that as a factor. Keep in mind dB is in log scale and as such to increase the loudness by 2 dB, your amplifier requires 10x the power.

With the 2dB mentioned above, was "twice as loud" the intended meaning?

"Twice as loud" is generally recognized as a 10dB change in SPL, and a 10x increase in power.

 

[majingotan]

With the 2dB mentioned above, was "twice as loud" the intended meaning?

"Twice as loud" is generally recognized as a 10dB change in SPL, and a 10x increase in power.

Yep. Thanks for the correction

 

[clemenules]

I was going to ask this in a new thread but this seems like a better place. Help me with my paralysis by analysis by making me understand amp power and (potential) volume and therefore making amp choice easier. Currently on Fiio E10 (non K).

I'm trying to figure out how loud I usually listen, what I'd need in power from an amp now and what I'd need in future (if I get more 'difficult' headphones) to provide this listening volume. My confusion comes from emphasis on raw power (it seems) in reviews of headphone amps. 1W powerful... 2W better! Looking at how I listen and solderdude's chart I can't imagine who would need that much power for the vast majority of headphones out there (also quality ones).

Info sources:
Amp specs I got from here: http://nwavguy.blogspot.com/2012/01/fiio-e10-dac.html
Headphone Beyer dynamic DT770 250Ohm specs here: https://reference-audio-analyzer.pro/en/user-report.php?id=563
Calculation sheet that I don't understand: https://reference-audio-analyzer.pro/en/amp-spl.php (dont understand what Average RMS power for music signal is supposed to be (2V?), same for peak factor and dBFS (0 if at 100% in windows?) )

Specs:
DT 770 250 Ohm: 254 Ohm average impedance, sensitivity 100.43 dB/V SPL (or 94.48 dB/mW SPL)
E10 (non K!): 2,7 Vrms, 130mA max output current, 0,5 Ohm output impedance

Volume knob on the E10: 2,5 = comfortable, 3 = seldom go above this, 4-5 if I want to listen loud but this already feels like it is unsustainable for more than a couple of songs.

So.... how do I estimate how loud I usually listen? Can I assume that volume at 2,5 = 2,5 / 10 * 2,7 Vrms = 0,675 Vrms ? Where do I go from there?

EDIT: Hope everyone is safe and healthy!

 

[solderdude]

To reach impressive levels (that can only be sustained for a duration less than 2 mins or so you will need to reach 120dB peak level.
All levels lower than that automatically are distortion free.
Those that only need long duration background music will have more than enough with your typical phone or portable player.
reaching 100dB SPL (= not equal to 100 Phon nor the average levels one sees in the tables mentioning street sound, sirens at x meters etc.)

The max output voltage = 2.7V rms so 108dB peaks can be reached using the E10.
That may be sufficient for most occasions and most people.

It may not be enough for those that also want 'impressive' levels to sound great. The DT770 isn't going to do this without distortion anyway. You would need a planar or other headphone for that.

To reach 120dB peak (which the DT770 doesn't handle that well) you would need an amp with 10Vrms output (or close to it)
As said, the DT770 already distorts already at that point.

The only way to tell if your amp is clipping is to actually look at the output voltage using a scope. Mild clipping is usually not heard as 'clipping' but rather a 'rougher' sound. When going further people find 'dynamics' to be lacking and beyond that the sound turns 'harsh' and unpleasant.

Moral of the story is: When you only listen to music at low levels you don't need much power at all. When every now and then you like to crank it up to impressive levels (for short durations) for instance to hear impressive bass it is best to use an amplifier that has enough power.
For MOST headphones out there this means 0.2 to 0.5W but some rare ones need more. Usually the owners buy specialised amps anyway, fitting the price of their expensive headphones. Most of the more expensive amps pack more than enough power.


When you want to find out how loud one listens one would have to record the output voltage of the source and know/measure the peak voltages and average voltages or use a dB meter that is very slow (long integration time) to measure average levels or measure peak levels (A-weighting) and look up the DR value of the used song.
Most people listen to music with average levels between 60 and 75dB average levels (around 60dB for long duration)
The average SPL and peak SPL differs per song/recording.

 

[clemenules]

Thank you Solderdude!

I think I get the first half of the amp reviews here (distortion, noise floor), however I remain confused about the power part.

Above mentioned link on the E10 mentions max load:
Low gain into 300 ohms: 1.55 Vrms 8 mW
High gain into 300 ohms 2.52 Vrms 21 mW

Amir mentions a 100 mW he likes to see as an appropriate value to determine suitability for a certain ohm. There are plenty of amps reviewed here that push 250 mW into 300 Ohm.

What does that mean and how do I compare that to my E10 specs? Because you also mention Vrms is more important to determine loudness? Then why all the graphs on x mW into y Ohm? If 1.55 Vrms 8 mW at 3/10 of the volume setting is already loud enough for me, why would I ever need an amp that can push 250 mW into my headphone, even after taking into account power doesnt scale linearly with loudness?

 

[solderdude]

The 'problem' is that headphone amplifiers have a voltage limit and a current limit.
because of this power levels at lower and higher impedances may differ (but can be calculated).

In this case it looks like the max output voltage = 2.5V in high gain setting.
It is usually no problem to maintain such a voltage to at least 120 Ohm loads.
Calculating for 250 Ohm: 25mW in high gain mode and 9.6mW in 250mW on low gain mode.
That is short of the 100mW Amir regards as sufficient.
This number actually depends on the efficiency of the headphone itself.
These can easily vary between 66dB/mW and 145dB/mW.
When we look at the more realistic dB/V then we have variances between 80 and 145dB/V.

At 100dB/V efficiency this means: At high gain setting = 108dB peak level, at low gain setting = 104dB peak level.
Depending on the DR rating of the recording average SPL (without going into clipping) could vary between 5dB to 20dB below the peak levels (depending on the recording)

Then there can be a gain setting that 'limits' the output power when a maximum input voltage level is present (from A DAC for instance)
This means that in low gain mode for instance 2x gain and connected to a phone that has 1Vrms output voltage the max output voltage could not reach above 2V rms (not clipped) where the amp itself can reach 7Vrms output voltage.
In high gain mode that amp could well have 8x gain and clip with the same input voltage.

Then there is the 'volume setting' which usually has linear scale on the front panel (say 1 to 10) or no scale at all.
because a potmeter has a (semi)log type behavior and not all pots and volume controls are created equal nor are gains, output levels and recording levels always the same one cannot make predictions about SPL levels based on volpot 'setting'.
Only when one really is into this and knows what taper and gains are used, what efficiency a headphone has (and how that was determined) and knows what DAC and or software volume settings are used one can say something about actual levels.

To be sure one has to actually measure.

 

[AnalogSteph]

This number actually depends on the efficiency of the headphone itself.
These can easily vary between 66dB/mW and 145dB/mW.
When we look at the more realistic dB/V then we have variances between 80 and 145dB/V.

That range seems a bit extreme even to me. What is there with 145 dB/V? The most sensitive grass growing detectors in IEM form I can think of were in the 130s dB/V (with impedance in the low double-digit ohms, efficiency rating 115-119 dB/mW). On the bottom end, K1000s were rated at 83.5 dB / V (120 ohm, so 74 dB/mW), and the well-known "amp crusher" HE-6 comes out at almost exactly 90 dB for 1 V (53 ohms, so 77 dB/mW).

NwAvGuy used a target max SPL of 110 dB, and he apparently wasn't exactly a quiet listener either. Amplifier power recommendations for speakers generally seem to aim for the 103-110 dB range.

For me personally (a ca. 10 dB quieter than average listener), it took loud playback of dynamic classical music to drive a little Clip+ (800 mV max) to its limits with a ~102 dB/V HD580, and even then it was more a question of running out of gain (album gain probably was around -4 or -5 dB, plus I generally have another -3 dB in, so RG around -8 dB total, while the Clip+ will reach max output for 0 dBFS at volume setting +3 dB and tops out at +6 dB, so chances are we still were ~4-5 dB below max output at this point).

Chances are, if you're young and have not done your best to ruin your hearing e.g. by going to concerts and clubs without protective measures, maximum output power won't be a primary concern. Noise might though.

 

[solderdude]

That range seems a bit extreme even to me. What is there with 145 dB/V?

My reply is based on actual measurements.

Noise will be a problem when using high sensitivity IEM's for certain.

 

[AnalogSteph]

My reply is based on actual measurements.

That one sure beats the spreadsheets we used to be passing around in the olden days, a decade ago.

Hmm, so K1000s were actually more sensitive than spec. HE-6s, less so. At 2 Vrms for 94 dB SPL (that sample was even less sensitive than Headroom's), it's hardly surprising that these can take a small speaker amp, like 25 wpc.

I think they may have a bit of a problem getting good seal with closed headphones on their setup. HD212Pros should be super bassy for one, and several other models are looking a bit lean <100 Hz.

Noise will be a problem when using high sensitivity IEM's for certain.

At least a few of these would actually seem to benefit from some extra output impedance, like 10 ohms, lessening the problem - others wouldn't though. It's pretty nuts if you come up with a required output noise level under 2 µV (that's at least 88 dB SNR re: 50 mV for ya, or a mere handful of the amplifiers Amir has tested).

These old Beyers like the DT831 must have been optimized for high-impedance integrated amp headphone outputs - according to my calculations it would take something like 300 ohms upwards to restore some half-decent balance to their frequency response, and then they're still rather bright.

 

[solderdude]

Noise issues can easily be solved using a passive attenuator.

I usually do not look at their FR measurements. I feel they use the incorrect 'compensation' but the efficiency and impedance comparison chart is very handy.

a 25W (4 Ohm) speaker amp puts out 10V. For a K1000 this is 'just' 0.6W for a HE-6 = 2.2W = about 108dB for both.
a 25W (8 Ohm) speaker amp puts out 14V. For a K1000 this is 1.2W for a HE-6 = 4.4W = about 111dB for both.

The HE6 needs quite a lot of power (100000 x more) compared to the Campfire Audio Andromeda to reach the same SPL