Hey mate I'd appreciate if you'd give me your opinion on teh following: is it all about volume? in other words, if the volume is enough do i need an amp? otehrs have said no, that certain frequencies need higher voltage and therefore although i can't bare my volume on my macbook being more than 50% most of the time, when feeding into my dt880, i may not be driving certain frequencies as well as i could with a better amp. The Fiio x3 I just bougth for my partner to use her DT660s with at work and the 880/660 at home don't drive the 880 to a volume anywhere nearly as high as what the macbook does. Does this mean the macbooks amplifier is better?
If an amplifier has a flat frequency response, which is what we want, to work properly it should be able to to drive your cans equally across all audio frequencies. If the impedance of your cans change with frequency your amp will have to be able to drive the same voltages and supply different current levels to satisfy the imedance. This might a problem if impedances get lower and the amp can't supply enought current to drive to the same voltage and sustain volume levels. Generaly this shouldn't be the problem as for example some Sennheisers have impedances that rise somewhere around the mid-bass and the current deman is less not more. Low impedances require more current. A headphone has a sensitivity rating in dB per mW. to reach a level loud enough the amp has to supply enough power to drive the headphones to the dB level you want to listen to and have enought spare for headroom.
No you do not need higher voltages at certain frequencies. You will need higher voltages to drive cans at higher impedance for the same sensitivity. So if two cans have the same 89 dB/mW sensitivity and one is 50 Ohms and the other is 300 Ohms, the amp driving the 300 Ohm cans will need to have more gain and be able to drive the cans to a higher voltage.
P=E^2 / R
P = power
E = voltage so E^2 neans E squared
R = resistance or impedance of the cans.
So
E = sqrt(P x R)
So the 250 Ohm DT880's at 96 dB/mW ro reach lets say 117 dB would require 128 mA. That means the amp woud have to be able to reach approx 5.7V or about 16 Vp-p which is around the upper limit of a FiiO E12, not bad at all as do you need to reach the threshold of pain?
So basically higher impedance cans require more gain to reach higher voltages and lower impedance cans require more current at a lower voltage. Since amplifiers amplify the signal voltage by a constant set by the volume control, changing the load impedance with frequency does not change the expected voltage output of the amp. It only changes the output current required to meet that voltage. If the impedance gets too low and the amplifier cannot supply enough current to meet the required voltage you will get distortion. Also if the impedance drops to less than 8 or 10 times the Amp's output impedance you will lower the damping ratio a the quality of bass will suffer.
So your statement that certain frequencies require more voltage is not correct. If the volume/loudness is sufficient but the output impedance of the amp is not low enough the bass will suffer and you will need an amp with a lower output impedance to improve the damping factor. some say that the output impedance of your amp shoud be 1/8th the impedance of your cans, others say 1/10th. Don't forget that you need headroom to prevent distortion at high dynamics (the loud side of it).
So as I said previously, the Schiit Magni should drive you to pain with the 250 Ohm DT880's.