MEASUREMENTS / MUSINGS: Headphone impedance, sensitivity, efficiency, and amplifier output impedance. (And a quick thought on Darko's "All You Need Is...")

Some people have walls of headphones. Well the other day I thought I'd take out my little collection accumulated over the last few decades around the house, some of them used by the kids, and let's dump them on the sound room ottoman to have a look :-).

The majority are based on dynamic drivers with a couple of balanced armatures (Etymotic ER-4, 1MORE Quad Driver). I'm actually missing a few there that were in use that evening by others around the home - the Dekoni Blue (an officially sanctioned "modded" Fostex T50RP Mk 3) planar-magnetic, the AKG K371, and Apple AirPods Pro (wireless) which my wife had brought to work and "forgot" to bring home that evening.

I was curious about the impedances of these devices and thought it would be good to put together a summary article looking at this along with the power needed to drive headphones and correlating these characteristics with amplification.

Although I have spoken of the importance of mobile audio in the past, I really have been remiss in not putting enough emphasis on this trend or the importance of headphones in these blog pages over the years. Despite this, some of the most common E-mails I've received over the years have actually been about headphones. So let's make sure to incorporate some "head-fi" in the days ahead!

I. Headphone Impedances

Behold, the "big graph" of headphone impedances - in total 24 headphones in my collection of all kinds of prices, both left and right drivers measured (click to have a close look!):

As you can see, headphone impedances cover a huge range of values compared to speakers. We use the term "impedance" (Z) rather than "resistance" (R) to denote that electrically, music exists as alternating current (AC) and there will be changes in the resistance of electrical flow depending on what frequencies are being sent through the circuit. Impedance is a result of the driver type, characteristics like the winding and wire gauge of the voice coils.

The "winner" of the lowest impedance device in my collection goes to the very inexpensive KZ ATE (~US$15) averaging around 18-19Ω, certainly not the best but a reasonable sounding headphone for the bottom-of-the-barrel bargain price. Notice that with most headphones, the impedance remains quite flat throughout the audible spectrum with a few exceptions. For example, the Polk Ultrafit 2000 dips below 18Ω from 1.5-5kHz to a minimum value of <16Ω at around 2.5kHz.

On the high end of impedance values in my "big graph" are devices that reach hundreds of ohms. The only truly high-impedance device I have here is the original Sennheiser HD800 which is rated as 300Ω (over the years has been succeeded by the 800S and closed-back 820, recently Drop announced their HD8XX to be released in November 2021) but we can see it going as high as 800Ω with the left earphone even though for much of the audio range, it hovers around 320-350Ω. The HD800 impedance peaks at 115Hz (resonant frequency). Similarly the Koss PortaPro left and right drivers show variation with a 105Hz resonance peak but lower overall impedance than the HD800.

Although not as common in domestic use, the higher impedance headphones are more popular in the pro audio world and companies like Beyerdynamic provide a range for some headphone models; for example, the DT 770 Pro comes in 16/32/80/250Ω variants. You can imagine in a studio there might be a need to plug in multiple parallel headphones to a source and this would be an example of why a higher impedance would be useful (as with resistance, the total impedance drops in a parallel circuit 1/Ztotal = 1/Z1 + 1/Z2 + ...).

One thing you'll notice about the graph is that we can grossly try to separate the groups of headphones into 3 categories: low, medium, and high-impedance devices. How we draw the dividing line is somewhat arbitrary, so here's how it looks to me:

Notice of all my headphones, the Sennheiser HD800 stands as an outlier of a clearly high impedance device. Let's zoom into the medium and low impedance headphones a bit more by plotting on a log scale:

We see many headphones straddle around or just below the 50Ω level. Thinking in round numbers then, let's categorize the impedance as:

Low Impedance: <50Ω

Medium Impedance: 50-150Ω

High Impedance: >150Ω

Headphone impedance is important when we think about how power is transferred between the amplifier and the transducer (headphone in this case).

To demonstrate the variability of headphone impedance, let's "zoom" in on a few to show you the various shapes the impedance takes across the audio spectrum:

Note that the Y-axis is set at 50Ω for comparison. Some generalizations we can make are that small IEMs and earbuds tend to be rather flat like the KZ ATE, Apple EarPod/EarBuds, and the 1MORE Quad Drivers. The unusual one showing more variability for an IEM is the Etymotic ER-4B based on a single balanced armature design dipping in the high frequencies.

Larger circumaural and supraaural dynamic headphones tend to have more impedance variability. The Grado SR60 and AKG Q701 headphones are typical examples but the Sony MDR-V6 is another along with the aforementioned Sennheiser HD800 and Koss PortaPro. Variability is not a bad thing, just something to be mindful of when matching amplifiers with high output impedance (we'll talk about this later).

Notice the Dekoni Blue / Fostex T50RP Mk 3 curve. While these are larger circumaural headphones, they're based on planar magnetic drivers which tends to be flat, almost resistive loads.

II. "But how loud does the headphone play!?" "How easy is it to drive?"

Okay, so now that we know different headphones have a wide range of impedances, and we can see from the graph that some are quite flat while others vary a bit, the idea of headphone "loudness" is an important one which we should consider.

Remember from high school physics that Power = Current x Voltage. Or rewritten as per Ohm's Law, Power = Voltage^2 / Resistance. 

Obviously, if an amplifier can provide huge current and unlimited voltage, we could use any headphone we want regardless of how "efficient" or "sensitive" (the only concern is that one must be careful not to damage the headphone with excess power!). Those are terms we've seen used with headphones, sometimes even interchangeably. Technically, to be precise, we can define:

Sensitivity: the amplitude produced in relation to a signal voltage provided by the amplifier measured as dB SPL/V.

Efficiency: the amplitude produced in relation to power - dB SPL/mW.

While related, the terms are technically different and both can say something about "how loud" the headphone can sound. These days, we see headphone specs published with both types of units depending on the manufacturer. If we know the impedance graph of the headphone, and either the efficiency or sensitivity, then we can work back and estimate just how "easy to drive" the headphone is.

Unlike the ideal infinite current/voltage amp, real-world headphone output jacks whether off your DAC, computer, DAP, phone, or a standalone headphone amp are limited on both accounts. The main shift over the last couple of decades with portable electronics is that we are typically limited by voltage that these devices can produce. Portable gear runs off batteries (particularly lithium rechargeables these days which have a nominal cell voltage of 3.6-3.85V) that have to power everything on the device, not just devoted to the headphone output.

Typically, mobile devices are limited to ~1Vrms output (many are down to just 0.7Vrms). There are exceptions of course, such as the LG V60 phone that can provide about 2Vrms for higher impedance devices - especially unique since many phones have already stopped featuring a headphone jack. Since maximum voltage is limited, if we need to transfer more power to the headphone, we need to draw more current, achievable by lowering impedance.

To provide just 1mW to a pair of 20Ω headphones, 0.14V and 7mA will do the job - within the limits of a small mobile device. As opposed to 600Ω headphones requiring 0.77V and only 1.3mA for 1mW which is getting really close to (if not exceeding) the maximum output voltage of many portable music players.

For low impedance headphones, amplifiers need to be able to provide more current.

For high impedance headphones, higher voltage is typically what is demanded of the amplifier.

A compromise would be a "medium impedance" headphone such as around 75Ω; 1mW can be delivered with 0.27V (and 3.7mA) which is not unreasonable with most mobile devices still with some headroom to play louder.

This is the reason why headphones these days meant for consumer audio are biased towards lower impedances. Going with a <50Ω headphone makes sense for voltage-limited mobile applications and one can potentially drive them louder by providing more milliwatts of power than their higher impedance brethren. [Historically, we could look at the Apple EarBuds hovering around 40Ω graphed above as an important landmark I suppose.]

We can convert between dB/mW [efficiency] and dB/V [sensitivity], quite easily - web calculator here, here, and an Excel spreadsheet. The calculation is nonlinear however, so it's not a simple mental correlation:

Sensitivity = Efficiency + 20 x log(sqrt(1000/Z))

Efficiency = Sensitivity - 20 x log(sqrt(1000/Z))

(Z = impedance in Ω) 

Note that for most headphones, the dB/V sensitivity value is typically a bigger number, so from an advertising perspective, this number looks better. An example is the Polk Ultrafit 2000 with a rated impedance of 32Ω. Polk's specs are rather nebulous, just claiming a "sensitivity" of "105dB" without specifying whether that's actually 105dB/V or 105dB/mW. Usually if in doubt, as in this example, 105dB/V are the correct units and is indeed a "sensitivity" value.

Assuming that one is using an amplifier that can output at least 1Vrms, and the impedance isn't extremely low (like say <15Ω) possibly demand more current than the device can provide, when comparing headphones, focus on the sensitivity (dB/V) value. Generally the higher this is, the louder it will go. For example, here are some of my headphones listed with measured impedance at 1kHz along with specified or measured sensitivities:

Apple EarPods (45Ω) - 118dB/V 

AKG K371 (35Ω) - 114dB/V 

Etymotic ER-4B (105Ω) - 108dB/V 

AKG Q701 (63Ω) - 103.8dB/V (measured here) 

Sennheiser HD800 (350Ω) - 103.77dB/V 

Dekoni Blue / Fostex T50RP Mk 3 (50Ω) - 99.7dB/V (measured here)

Guess which of those likely needs a headphone amplifier! (Yes, it's the Dekoni Blue / Fostex due to low sensitivity and at the same time low-moderate impedance sucking up current resulting in low efficiency of 86.7dB/mW only.)

Notice that the sensitivity values of the AKG Q701 and Sennheiser HD800 are almost the same. The big difference is the impedance. Due to the low impedance of the Q701, it'll need more current to hit the 1V mark, so overall it's a less efficient device at 91.8dB/mW compared to the HD800 of 99.2dB/mW.

In the days ahead, I'm sure we'll talk more about this as we consider specific headphones.

III. Sound quality and impedance...

In many articles, there is talk about lower impedance headphones being good for low-voltage mobile devices (makes sense as discussed above) but also mention that higher impedance headphones "sound better" (for example, here's an article). There are potentially a number of reasons this could be the case:

1. Higher impedance voice coils use thinner wiring with lower mass, this may result in better conveyance of nuances and temporal precision, possibly lower distortion characteristics.

2. Higher impedance headphones often require higher voltage to drive. The higher signal strength potentially improves signal-to-noise ratio.

3. Assuming the same output impedance from your amp, a higher impedance driver will improve damping factor. The effect of the small amount of cable resistance will also be lower when the driver has higher impedance. 

While there is a ceiling to how much damping is needed, the better the damping factor, the more flat the amplifier is able to maintain voltage output. With multi-way loudspeakers where there is greater bass driver mass, we can make a case that high damping in the bass frequencies could be useful to improve "tightness" - this is unlikely to be significant with small headphone drivers however.

So yeah, if you're into home audio listening, using a good headphone amp with clean output, and capable of larger voltage swings, those high impedance >150Ω headphones with lower sensitivity sound great! A good example of this that I heard recently was the Beyerdynamic DT 770 - 32Ω impedance model = 110.4dB/V, 250Ω model = 100.43dB/V. With the 250Ω model, it takes 1V to create the same loudness as only 0.32V with the 32Ω model. A good amplifier might exploit that 10dB difference with improved signal-to-noise (point 2).

By the way, despite the difference in sensitivity, both the Beyerdynamic DT770 32Ω and 250Ω versions have around the same power efficiency, 95.7dB/mW and 94.5dB/mW respectively; an example where it's more useful to look at the sensitivity rating rather than efficiency to determine "how loud" a pair of headphones sound.

As a demonstration of point 3, let's talk about the output impedance of amplifiers compared to headphone impedance. As a test subject, let's look at the little Polk Audio Ultrafit 2000 which I use when out jogging sometimes. Here are the impedance and phase curves:

These supra-aural, strap behind your head 'phones were selected because as you can see, their impedance profile isn't flat and this will allow us to see the effects that amplifier output impedances would have.

On my test bench, let's bring out a few devices to examine:

To the left, we see the Topping DX3 Pro DAC (LDAC V2) with small 3.5mm headphone jack (currently set at -6dB volume). Underneath is the ASUS Xonar Essence One which I've had since 2012. In the middle I dragged out my Pono Player. To the right on top of the Linear Audio AutoRanger is the RME ADI-2 Pro FS.

As you can see, I rigged a little test cable to tap the right and left channels to measure either dummy or actual headphone loads and currently have the Polk plugged into the 1/4" TRS end with appropriate adaptor. By the way, to the right edge of the table in white, green and blue are just some 10W resistor headphone "dummy loads" for use when I measure headphone amplifiers (20Ω as a "low impedance" load, 75Ω as "medium impedance", and 560Ω for "high impedance").

First, let's measure the output impedance of these headphone amplifiers:

At the bottom in blue is the RME ADI-2 Pro FS with a flat impedance curve of <0.3Ω across the spectrum (RME rates this device as 0.1Ω, there's a "floor" to how low I am able to measure). The Pono Player has an average of 4.65Ω, Stereophile measured it at around 3Ω and I've seen 5Ω elsewhere so my results are in line.

As for the Topping DX3 Pro V2 and ASUS Xonar, both have relatively high output impedance these days, measuring around 10Ω.

So, let's plug in the Polk Ultrafit 2000 headphone and see what the amplifier frequency responses look like:

As you can see, when an amplifier has a higher output impedance like the Topping and ASUS (red and green), the frequency response will vary with impedance of the headphone. In the case of the Ultrafit 2000, that means a peak up at 100Hz and a dip down to 2.5kHz. Since both the Topping and ASUS have similar output impedances, the curves correlate similarly. Notice that there's >1dB swing across the audible spectrum which could be audible.

In comparison, the RME ADI-2 Pro FS due to <1Ω output impedance demonstrates flat frequency response across the audible spectrum despite the Polk headphone's fluctuating load. This "load invariance" is something an audiophile who desires high fidelity reproduction should be looking for in a headphone amp.

Lest we become overconfident that we can always predict the amplifier frequency response based on the output impedance alone, remember that there will be "unorthodox" designs that dance to the beat of their own drummer. :-) We see this with the Pono Player plotted with dashed lines! My presumption is that this is a reflection of the Ayre output stage which the late Charles Hansen described as having zero feedback and implements their "diamond" buffer arrangement. There's a -2dB dip into 6kHz with this device for whatever reason! The frequency response looked so odd that I made sure to capture both the right and left channels to make sure this wasn't just an anomaly in one of my channels.

Clearly, if one is interested in accuracy, the RME ADI-2 Pro (and ADI-2 DAC with similar circuitry) is superior to the others. However, subjective opinions being what they are will produce various opinions. For example, while not by a huge amount, with a headphone that has the impedance profile of the Ultrafit 2000, some might find the bass/lower-mid accentuation that the Topping and ASUS DACs provide to be more pleasant along with a mild dip into 2-3kHz relieving a little bit of harshness. Likewise, the Pono Player results in an even more significant -2dB into 6kHz that might be interpreted as even better "smoothness" or "less fatiguing" especially with bright headphones like the Sennheiser HD800 that typically has a rise in this region.

Note that this is just the frequency response between the amplifier and headphone as affected by a low impedance load connected to a high impedance output. While it will affect the sound of the headphones, it's not the actual frequency response of the headphones themselves! For that we actually will need acoustic measurements like with this baby:

Yeah, I got the miniDSP EARS test fixture here to play with a little while back. We'll deal with that and talk about the trials and tribulations of headphone measurements with a $200 jig in future posts ;-). (Actually, there's a lot of variability when it comes to headphone testing regardless of expense for the measurement gear.)

IV. In Summary...

1. Objective analysis is cool because it tells us many things that could be of relevance! :-) Looking around headphone sites, there seems to be less resistance to the idea that measurements could be useful and it looks like there are more healthy discussions about what measurements mean and which might be more relevant. I don't think there's as much silliness or snake oil in the "head-fi" world compared to what we see in "high end" audiophilia.

2. Headphones/IEMs present a very wide impedance range to your headphone amplifier. Headphones can range from <10Ω up to >1kΩ. Some of the exotic headphones can be even higher like say the Stax SR-007 Omega II electrostatics with 170kΩ! Of course for those you'll be using special high-voltage amps as well.

3. General categories of low (<50Ω nominal), medium (50-150Ω), and high (>150Ω) impedance headphones can be considered when thinking about how well an amplifier can handle the device. Low impedance headphones need current while high impedance ones are more demanding of voltage for the same output power.

Portable electronics are typically voltage limited with outputs ~1Vrms. While they may provide more power to low impedance <50Ω headphones, there will be current limits that determine the maximum mW.

4. Remember the terms "sensitivity" and "efficiency". While "efficiency" in dB/mW is a common spec these days, "sensitivity" tells us directly how many dBs a 1V signal is able to produce with the headphone (typically at the 1kHz mid-range frequency). So if we know what voltage the amp is capable of, have an idea of current limits, understand the amp's output impedance, have a graph of the impedance response of the headphones, and we know the frequency response for the headphones themselves, we can appreciate in good detail how loud a particular headphone can be driven to and the tonality of the sound we expect to hear. :-)

5. Sure, potentially a higher impedance headphone might sound better for various reasons including flatter frequency response with high output impedance amps (better damping factor). This is just a minor factor among a multitude of variables when it comes to good-sounding headphones. Never make the mistake of simply saying that "high impedance sounds better".

6. As you can see in the frequency graphs comparing the Topping, ASUS, RME DACs, and Pono Player, output impedance does matter with variable low impedance headphones.

As a "rule of thumb", I like what NWAVGuy discussed a decade ago about headphone-to-amp impedance matching. Assuming a 1V signal, if we assume 1dB as a reasonable threshold of audible change, even a headphone with a wide variation in impedance like the Ultimate Ears SuperFi 5 (ranging from 10-90Ω) which he used, a headphone amplifier with output impedance 1/8th of the rated headphone "nominal" value will be in the ballpark of <1dB fluctuations. So, for the ASUS Xonar Essence One and Topping DX3 Pro (LDAC V2) with ~10Ω output impedance, it's best to pair these with medium impedance headphones of 80Ω or more for flatter frequency response. However, if you know that your headphone impedance is quite flat already, the frequency variation will actually be minimal anyways.

Okay audiophiles, I think that's enough for this post! We can talk about headphone testing in the days ahead with some of what I have along with various "experiments" :-).

Addendum [April 1, 2021]:
Since a number of us have been immunized now, with my small audiophile "bubble" buddies, I had a meeting the other night to listen to some headphones at my place:

Just add drinks and that's all ya need for a great evening of conversation, music and high fidelity. ;-)

A friend brought over a couple of his IEM's which I was able to quickly capture the impedance of given our discussion here:

A nice demonstration of the low impedance nature of some of the more sophisticated IEM's out there! The Noble Khan goes for ~US$2400. It sounds good, quite light weight with the stereolithography 3D plastic printed casing. There are 6 drivers inside that thing - 4 balanced armatures, 1 dynamic and 1 piezoelectric. Impedance down around 10Ω up at 10kHz. Measured sensitivity of 131dB/V.

Likewise the Shure SE846 (~US$900) is a nice sounding IEM again with multiple drivers and a complex impedance shape likely as a result of how this is all put together inside! Wowzers, 5.5Ω at 5kHz. Good thing we're looking at rated 135.6dB/V sensitivity.

No doubt, it would be good to use a low output impedance headphone amplifier with these.

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I don't see much happening in the audiophile world this week. As I mentioned last week, it has been a bit of a Spring Break "staycation" over the last few days for me.

For those who like superhero movies, Zack Snyder's Justice League on HBO Max is good. While it shares many of the same bits as the original 2017 release, it's amazing just how much the additions and dialogue changes have allowed the story to take on a different emotional tone. As usual, DC Comics movies tend to be a bit grittier, darker, with more adult themes. This version is certainly much more coherent while still adding bits of needed humor once awhile. Wonderful "remix" and "remaster"... Heck even my wife (who falls asleep in superhero movies) liked it despite the 4-hour length!

Hope you're all enjoying the music. Stay safe as it looks like we're in Wave 3 of the pandemic now.

Quick Addendum... :-)

Couldn't resist a comment after watching John Darko's "All You Need Is...?" video. I don't get his obsession about people calling others "idiots". Surely, audiophiles are more refined ladies and gentlemen than this.

There are parts of the video I do agree with although I dislike the way he's doing it and some of his implications. For example, I still think it's good to think about what constitutes "value" as discussed last week. Notice the lack of any kind of actual content as he gets on his soapbox and goes through the motions of a psychological plea to prepare readers/viewers for a "$7000 streaming DAC" review coming up. Interesting, even heart-warming, human-interest plea to you the dude with the credit card, when he supports you when you lay down $7Gs. What else is new?

By harping on the "idiot"-calling, he seems to believe there are many who insist the "Raspberry Pi is good enough for their streaming needs" (8:20) and if one disagreed, one is called an "idiot". I don't know if this is true... Maybe he has a bunch of low-quality trolls on his social media feed? Surely there's nothing wrong with wanting a more fancy, better looking, more full-featured, maybe easier to use, reliable, company-supported solution beyond a DIY Raspberry Pi.

Since he's bringing the Raspberry Pi into this discussion, I'm guessing in the days ahead he's not reviewing just DACs, but expensive network streamers that still need to be connected to a DAC. Reading between the lines, the issue that he's hinting at instead of confronting directly is the idea that a bit-perfect Raspberry Pi network streamer when delivering digital data to a good DAC is actually "all you need" for accurate sound quality. On that point, I agree, it will sound no different than a thousands-of-dollars digital network streamer or fancy computer. Just like you don't need an expensive Ethernet switch nor $$$ digital cables (so long as no incompatibility/defect of course). It's not "diminishing returns" we're talking about - it's basically no returns as far as sound quality is concerned!

Talking about cars, cameras, how much money a person earns (there's a hint of Michael Lavorgna's claim that naysayers are envious), etc. are just irrelevant tangents obscuring the central issue which is that as far as humans can hear with controlled listening tests, or find evidence for, "Bits Are Bits" when we're transmitting digital data. Differences like jitter are basically insignificant assuming you have a decent low-noise DAC these days.

For him to say "I know that my 7/8000€ streaming DACs sound better than $1000 streaming solutions and $500 streaming solutions - I know this!" (7:05) as reason for what he believes about sound quality without taking any other steps to detail or verify his "knowledge" clearly appears lacking if not scientifically implausible. By the way, how convenient that expensive stuff almost always sound better. Indeed, there are "linguistic tricks" (9:50) at play, and isn't making "his truth, your truth" (9:55) by mere words and claims, with nothing to back up the assertions somewhat empty?

Bottom line:

1. Whether the same DAC sounds different streamed through a Raspberry Pi versus something very expensive is not a matter of "my" or "your" truth. I do not believe the Pi, DAC, amplifier, cables, or speakers care about subjective beliefs/feelings when the electrical currents run through the circuits and sound waves are generated by the speakers or headphones. I have no problems with people spending big money on psychological thrills. Just be honest about it as there is a multitude of reasons to want something beyond needing to believe in sonic differences.

2. Darko's videos like these serve as advertising or perhaps preparation for advertising. Ultimately, advertising is about psychology (enhancing perceived value) as he demonstrates here, picking and choosing what to say with an aim to please a kind of audience, laying the seeds of what's to come; seemingly trying to soften the impact of a product he knows a certain set of audiophiles would have issues with. The content of this video is a play on pure emotions and not actually addressing or clarifying controversies.