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Additionally, I think it might be useful information (especially for relatively new hi-fiers like myself) to know what headphones that seem to have a low impedance rating actually require much more power to be driven properly. If we could start compiling a list of these "deceptive imdepance rating" headphones, that would be very cool.
Have a look at the PDF files
here, in particular the "Volts RMS required to reach 90 dB SPL" spec at the bottom right. The higher it is, the harder to drive the headphone is in terms of voltage requirement; the most extreme examples are the Hifiman HE-6 (~50 Ohm, 1.018 Vrms) and the Beyerdynamic T70 (250 Ohm, 0.099 Vrms) - the HE-6 needs 10 times higher voltage despite having 5 times lower impedance. Note that it is common for a source to be able to output less voltage into lower impedance than into high impedance, so take that into account as well (see
this graph of the FiiO E11 for an example).
However, voltage requirement is not the only parameter that determines how well a headphone works from a particular source. In fact, it is the only one where low impedance is inherently better, but is worse in some other aspects. If you check the E11 graph again, you can see that the higher the load impedance is, the lower the distortion becomes. Also, the frequency response of the headphone can be changed due to interaction between the impedance of the source and the drivers: a frequency dependent variation in the impedance of either will cause this effect. Therefore, the flatter the "Electrical Impedance and Phase" graph is for a headphone, the less its frequency response will change from different sources; compare the Sennheiser HD598 and the Audio Technica ATH-M50, for example. The HD598 is prone to having boomy bass when driven through high output impedance - typically, this happens with computer sources (both onboard and internal sound cards) and old receivers. Variations in the output impedance of the source are usually the result of capacitor coupled outputs, which is common with portable devices and sound cards; the effect on the audio is rolled off sub-bass. All these frequency response anomalies are less likely to occur with a high impedance headphone. The ratio of the headphone impedance and source impedance is called the
damping factor, and it also affects the sound in other ways (e.g. distortion); in most, but not all cases, a higher damping factor is better, so you want either low output impedance or high headphone impedance to maximize it. Finally, a higher voltage sensitivity is not always a good thing, since you may not need the extra headroom for more SPL anyway, and the source may perform worse (audible hiss, channel imbalance, etc.) if you have to turn down the volume too much.
To summarize, an amplifier is not only useful to increase the maximum SPL, but it also fixes some problems that affect
low impedance headphones when driven from cheap sources. For example, the
Ultimate Ears UE700 IEM has low impedance and very high sensitivity, so it should be easy to drive if you only consider those parameters. But if you connect it to an onboard audio jack with 75 Ohm output impedance, it would have audible noise, and resonance in the upper midrange. An external amplifier would fix the resonance, and improve the noise as well at not very high listening volume.
