Introduction
It's high time for me to start with such articles again, after 2 year-long pause and countless promises, meh!
In this article I'd like to give you a bit of insight into basic electronics and headphone specification. I've seen many people ask for headphone recommendations, and by the fact there's so much misinformation in the high-end audio, I decided to finally sit down and give you an idea of how things work.

Today, headphones come in various sizes and produce sound using different techniques.

• Dynamic drivers are most common. A coil is wound around permanent magnet which attract and repel membrane based on input signal, through which a sound is formed. This is notably the easiest way to produce sound waves.

• Planar magnetic (orthodynamic) drivers are similar to dynamic, but equip a large flat membrane and usually series of coils and magnets, which makes them quite heavy. They are not very common, and due to manufacturing costs, the price for such cans usually goes over $1000. One of such headphones is Audeze LCD series.

• Electrostatic drivers consist of a thin, electrically charged diaphragm, typically a coated PET film membrane, suspended between two perforated metal plates (electrodes). The electrical sound signal is applied to the electrodes creating an electrical field; depending on the polarity of this field, the diaphragm is drawn towards one of the plates. Such headphones however requires special amplifier, which applies voltage amplification to the input signal, usually in the range of hundreds or even thousands of volts.

For more info visit this article: http://headfonics.com/2011/05/dynamic-vs-orthodynamic-vs-electrostatic-which-is-which/

Headphone impedance
You can think of impedance as variable resistance across frequency. To put things simply, imagine a 100Ohm resistor. Ideally, such resistor would keep its value on 1kHz as well as on 20kHz. Magnetic coils suspended inside acoustic shell, however tend to put out different characteristics at various frequencies.

Fig. 1 - Impedance across baseband spectrum for DT990 - courtesy of headphone.com

Beyerdynamic DT990 are rated 250Ohm by the manufacturer, yet as you can see, there's big bump around 90Hz, which hits almost 400Ohm. This is caused by resonance inside the transducer, headphone shell construction, air pressure and also if you wear the headphone or not.
Most dynamic elements have similar characteristics, with such 'bump' being anywhere from 80-200Hz, except for balanced armature IEMs, where impedance vastly differs across the whole spectrum, and you can see jumps from 12Ohm to 80Ohm.

Impedance in relation to amplifier
To smoothen out those bumps, a headphone amplifier must have output impedance low enough to be 1/8 of the rated (lowest) headphone impedance. Turned around, headphone impedance must be at least 8 times higher than that of a headphone amplifier. This is mainly rule of a thumb, as 1:8 ratio produces less than 1dB difference in the resonant frequency, which is generally inaudible.
For example, DT990 250Ohm needs an amp with 30Ohm or lower output impedance.
This will ensure proper electrical damping and 'inaudibility' of this 'bump'.
Lower impedance headphones put more demands on the entire chain, ones such as Shure SE846 with 9Ohm impedance need an amp with just 1.1Ohm output impedance, but since the cable also add to this, it's best to use an amp that has less than 1Ohm.

Sensitivity
Each headphone comes also with rated sensitivity, usually in dB/mW or dBV units. This basically means how much volume you're getting for each miliwatt or volt respectively. DT990 are rated 96dB/mW, so they'll produce 96dB peak volume at 1mW. AKG K601 are rated 101dBV, so they'll produce 101dB at 1V RMS. Note that both values are usually measured only at 1kHz, so this is going to fluctuate across spectrum.
dBV is tied to rated impedance, so it's usually wildly used by manufacturers to claim 'higher numbers'.

Expected volume
This is probably what most of you are interested in most. To get an idea of how loud certain headphones will be using specific headphone amp, we need to know several specifics:

• Your preference of highest peak volume (most people agrees on 105dB, some audiophiles goes as far as 115dB, my recommendation is 100dB)
• Headphone impedance & sensitivity
• Amplifier output impedance
• Maximum undistorted voltage/current output from amplifier

I won't bother you with logarithmic calculations, instead you can download this spreadsheet to have it measured: https://robrobinette.com/images/Audio/Headphone_Power_Calculator.xls
Say I want an ideal amp for both of my VE Monks (32Ohm @ 110dB/mW) and AKG K240 Monitor (600Ohm @ 88dB/mW).

Monks need just 0.1mW (56mV, 1.77mA) to reach 100dB, while K240 need 16mW to reach the same level. What's more, K240 are rated 600Ohm, nearly 20 times more than Monks.
K240 thus need 16mW (3.08V, 5.14mA) to reach 100dB

High vs. low impedance
Today, manufacturers tend to favour lower impedance with the advent of portable players. Low impedance means you need more current and less voltage. It's easier to design and manufacture amplifiers that handles low impedance cans well. Such amplifiers tend to be more power efficient, as supply voltage doesn't have to be super high.

On the other hand, history favour higher impedance. Tube amplifiers generally outputs high voltage, but their distortion radically increases with more current required. Thus for tubes, high impedance cans are perfect choice, as they require more voltage but less current. Additionally, one can bridge loudspeaker amplifier with resistor and use it to drive high impedance headphones with no damping issues.

High impedance also has better electrical characteristics. With higher voltage and less current required to pull the membrane back and forth, the transducer react more precisely to fast transients, creating a better 'motor' system, which in turn may provide better audio quality. Furthermore, high impedance cans doesn't load the amplifier as much, which can lead to lower harmonic distortion, and effect of cabling on final sound is greatly diminished.

Ideal specs
Theoretically speaking, headphones with high impedance, but also high sensitivity should be perfect for every usage, as they don't need powerful amplifier, but are still loud enough and not susceptible to underdamping.
One of such pairs might be Sennheiser HD414 with overwhelming 2000Ohm impedance, yet still great sensitivity of 102dB/mW. But to be honest, even though the specs looks great, I ended up disliking the sound signature. Perfectly compatible on paper, but properly amped, the sound lacked weight. Just to give you an idea, that higher impedance may lead to better audio quality, but it's most certainly not a rule to lead by.

Too high sensitivity
Headphones with low impedance and high sensitivity lead with an advantage of not requiring any amplifier, as they play loudly on any system. But this has an adverse effect too. Such headphones may bring noise floor of your amp into audibility. With volume pot controlling the gain of the input stage, the noise you'll hear won't change even when you push the volume below 1.
There is a solution though. You can build yourself voltage divider acting as a 20dB pad to artificially decrease the sensitivity and thus shift the noise floor back into inaudibility.
https://diyaudioheaven.wordpress.com/headphones/headphone-attenuation-adapter/

Balanced wiring & amps
Some high-end manufactures of audiophool equipment, such as HiFiMan electronics are selling outrageously priced amplifiers and players with powered balanced output. There are several advantages to balanced wiring for headphones, but most of it is snake oil, more of that in next article.

In balanced setup, each transducer is amped separately, using two dual-mono amps, one with inverted phase. This configuration has an advantage of "seeing" half of the impedance of each driver, thus may provide better control over fast changes in dynamics. Voltage swing of op-amps used in balanced configuration is thus doubled.
However no audible advantage was proven (through blind tests) as of yet.

Improper power handling
Shit happens, be it DC offset at outputs, badly designed output stage, op-amp failure, bursting lots of DC directly into headphones, or accidentally turning the gain/volume knob too high. All this can easily fry the headphone drivers. High impedance in such cases play also a role of safeguard. To destroy high impedance transducer, you have to pump in lots of voltage, which rarely occurs accidentally. However to fry low impedance driver, all you need is couple of volts for the coil to overheat. Some amps, such as early version of Schiit Audio Lyr and Asgard do not implement output relay, so when you turn on the amp, there's nasty transient, easily reaching 2-3 volts. For 2kOhm HD414, this is no problem, but for 9Ohm Shure SE846, 2V equals almost 140dB. Suddenly your $1000 investment puffs up in smoke.
Not to mention the most important health aspect, low impedance high sensitivity headphones can very easily damage one's hearing, for that very same reason - it takes just millivolts to bring up the volume dangerously high.

Conclusion
Hopefully this article will help you better understand the topic. As always, numbers tell you only part of the story, what's important is ultimately that smile on your face. Each one of us has different standards and approaches to audio, by following the well-established facts about amping, you can get maximum out of your headphones by pairing it up with the right amp, no matter their impedance.
Each headphones sound different, just by shelling out lots of cash, one doesn't secure the clear winner. There's not such a thing. It's best to listen to your new pair, before you make the final decision to purchase it, as long as there's such chance.
If you're looking for great all-around headphones, trusted by audio engineers for tens of years, you can try AKG K240 or K271 line. For more contemporary styles, DT770-990 might be better suited. Perhaps ATH-m50x is the right choice for you.
Recommending headphones is a difficult task, as there are just so many variables that has to be taken into account, not just price. Still if you're in need of any advice, leave a comment.
Thanks for reading.

 

Last edited: Apr 13, 2016

Bravo Andrew!

Great to see something like this - nice reading!

 

Thanks for the time spent on this argument.
Maybe at the end I will understand why some high rated headphones sound like crap, and other sound like they came from heaven.

 

Last edited: Apr 13, 2016

pretty sure my headphones suffer from impotence.

 

Nothing like a good tech read

 

Glad you all liked it. It feels like I left so much info out.

 

edit edit edit
we want more!

 

Thanks for this @Andrew ! Very usefull and interesting stuffs

 

Thanks Andrew. I got a headphone-question for a long time: How is it possible that headphones can produce low frequencies (with such tiny drivers)? Does it have to do with our head, the fact that soundwaves can't 'escape', pressure building up?

 

Bass in headphones has to do with proper seal between transducer and ear canal. It's most apparent with earbuds that are hovering loosely inside one's outer ear - the bass in that case would be highly attenuated.

 

very youzfl

 

Great read Andrew. Thanks for sharing.

 

Very Nice Article My Friend! Very Informative!

 

Alright, thanks! Makes kind of sense.. Seal.. If you listen to a headphone close to, but not on the ear (no seal), there's no Low..

 

muchos gracias Andrew... you told me this was coming.. now it's here..

I'll finally get to understand a few things about my cans

 

@Andrew
Nice articel
You should add some headphones for the budget oriented people,the Samsons Sr850 and Superlux HD 681sound similar to Akg K240 and K702.
They are a just tad bit hyped in the mid/high freq,other than that they are superb for its price.(my testing)

 

Wow, extremely informative!

 

Missed it the first pass, caught it this time around and am smiles from ear to ear. Thanks for shining a light on my darkened ignorance.