BrotherKathos
500+ Head-Fier
the "at least" 1/8 rule of thumb is like a crossroad where various ideas can coexist pretty well:
1) simply getting an efficient system. ideally you'd want the amp with as close to zero ohm as possible to achieve https://en.wikipedia.org/wiki/Impedance_bridging
2) limiting frequency response variations. when the lowest impedance of a headphone is already 8 times or more that of the amplifier, you get a stability within about 1dB in the response compared to another amp with a different impedance but also at least 1/8th of the headphone's impedance. obviously when I'm talking about 1dB or less, I'm assuming that the amps are identical in response into such load. this only help limiting the FR impact due to impedance.
here with the hd650, a high impedance amps will boost around 100hz a little compared to a low impedance amp. not really a big deal here thanks to the lowest impedance of the phone already being quite high. for multidriver IEMs, it can become very important and ruin the signature of an IEM(or make it subjectively better if we're super lucky).
2a) same idea when there are protective caps at the output of the amp. the caps will roll off the low end, and the smaller the impedance ratio(amp/headphone), the smaller the roll off. so getting a headphone at least 8 times the impedance of the amp will mitigate the roll off if protective caps are present at the output.
3) electrical damping. the movement of the driver is determined by mechanical damping(how stiff is the membrane, how heavy is the coil...). there is also how easily the air can flow when moved by the driver and how much air is being moved. and of course one hell of an important parameter is the electrical signal itself making the coil move ^_^.
http://hyperphysics.phy-astr.gsu.edu/hbase/oscda2.html in that link you can see the oscillating behavior for underdamped, critically damped, and overdamped conditions. you don't have to care about why or how,, just know that better electrical damping results in better control of the diaphragm. as I said, it's only one damping parameter for how the driver will move. but it still makes sense to avoid a massively underdamped behavior. unless you happen to like how it sounds. all those concepts are more or less important when it comes to fidelity of the signal reaching our ears, but they don't give the recipe for euphony or personal taste.
4) irrelevant for the HD650. looking at the amp this time, not all designs will be happy when a low impedance headphone is used. in an indirect way, sticking with the "at least 1/8th" rule, might on occasion help us stay within nominal use of the amp.
the 1/8th rule of thumb tends to increase our chances for stability and correct use of the gears. so it's a good rule as soon as we're not too sure about the gears we're using. of course audiophiles who constantly seek change might decide to take this the other way around. and to never follow the idea of impedance bridging for the opportunity to perhaps get bigger changes. ^_^
Thanks for posting this. It was very helpful to me in understanding impedance bridging. I’ve also been interested in whether or not bridging or matching is the best way to go. I know there is no way for this to work wih a hd650 since the impedance swings with frequency, but I think it might be possible with planar magnetics. Would they sound better if the amp matched their impedance, or should they still be bridged? My Audeze lcd 2c are 70 ohm flat so if i had a 70 ohm amp would that work better than a .1 ohm amp?