No.
The power of an amplifier basically tells you how loudly it will play, if you have hard to drive headphones. Headphones with low impedance need more current than headphones with higher impedance. BUT the sensitivity of the headphones is an important number.
For example lots of IEMs have very low impedance, but they are also very sensitive. That means the voltage can be low. So IEMs normally sound loud with a much lower volume setting than full sized headphones.
So the low impedance of IEMs doesn't matter very much.
There are full size headphones that are low in impedance and also low in sensitivity. So you have to turn the volume control much higher. And because they have low impedance, that requires the amplifier to deliver more power. There are two simple formulae:
power = volts x amps
volts = impedance x amps
So a bit of algebra gives you this formula:
power = impedance x amps x amps
or:
power = volts x volts / impedance.
So if we use the second formula we know that 300 ohm headphones can be driven at 4.49V by Hugo:
4.49 x 4.49 = 20.1601
Divide that by 300 ohms:
= 0.0672 watts.
Which is the same as 67.2 milliwatts (thousandths of a watt). Which is very close to the number that is reported: 67.28 milliwatts.
If the amplifier can't deliver the power it will crackle and make other horrible noises.
In the end you have to know the sensitivity specification for a headphone and the impedance, to get an idea of how hard it is to drive. If the sensitivity is really really low then something like Hugo won't have enough volts. In that case Hugo isn't running out of power, instead the volume control just doesn't go far enough! It will also sound crackly though when you reach the maximum loudness.
No these numbers are from a site that did some testing.
If we use the formula above you can see that at 199 ohms:
power = volts x volts / impedance
0.10131 = 4.49 x 4.49 / 199
everything is fine (the measured number is 0.10149 watts). With lower impedance at the same voltage, more power is required, 101 milliwatts at 199 ohms compared with 67 milliwatts at 300 ohms.
That's the same as saying "a lower impedance headphone needs more power at the same volume control position."
Less impedance is like a fat water pipe. More impedance is like a narrow water pipe. The amount of water that can flow through the pipe depends on how fat the pipe is. So if the water pressure is the same, more water flows through the pipe that impedes less. The pipe on your toilet where all the **** goes is FAT. It needs to be fat because lots of water wants to travel through it very quickly in 3 or 4 seconds (and you might have done a fat ****!). But the pipe that puts water into the tank is much thinner, because it's OK to fill the tank slowly in a minute or two. So the fat pipe has low impedance and the thin pipe has high impedance.
Back to the measurements for Hugo, when you look at 100 ohms you see something has gone wrong:
0.201601 = 4.49 x 4.49 / 100
but the measured power is only 0.12718 watts - quite a lot of power is missing: 0.201601 - 0.12718 = 0.074421. That's about 74 milliwatts that's gone missing. That's because Hugo isn't very powerful. And the numbers get worse as the impedance falls lower.
The lack of power only matters if the headphone needs lots of volts (water pressure). If the headphone is an IEM, which doesn't need lots of volts, then the formula is fine. For example, Shure SE 535:
http://reference-audio-analyzer.pro/en/report/hp/shure-se-535.php
has 26 ohms impedance. In the table for Hugo at 25 ohms there's 20.51 milliwatts of power available. According to that page, for 94dB SPL (that's quite loud) you need 4 milliwatts of power. So Hugo has plenty of power. You can turn it up even louder as there's more voltage range left and more power available.
Eventually you'll get crackling distortion from Hugo if you keep on increasing the volume. But you might kill the IEMs by playing them too loudly first.
