There is potentially a lot to worry about driving such low sensitivity and low efficiency headphones.
One needs to be clear about terminology.
Gain is generally voltage gain. Volts on the input * gain = volts on the output. This makes some important assumptions, but in the systems we use, this is a good definition. We don't care about input impedance, and we consider power amplifiers as voltage sources. So it is OK. (We should pedantically, use power gain, but we don't define a known input impedance, so we can't. Expressed in dB we just define the gain as 20*log(voltage gain) instead of 10*log(power gain) and it all works out.)
A perfect voltage source has of course the ability to source infinite current, so when it can't, we have issues. We can probably break the problems into a few parts.
All amplifiers are usefuly modelled with their Thévenin equivalent, which places a notional resistor in series with the perfect voltage source output. So long as the Thévenin resistance is small relative to the headphone impedance it isn't a big issue. This resistance is for conventional amplifiers pretty much the resistance of the output devices + power supply impedance, all divided by the feedback factor. Poor output impedance can lead to frequency response issues. The output impedance and headphone impedance form a potential divider. Your useful voltage is the voltage seen out of this divider. Beware headphone amplifiers that put a real resistor on the output. They exist.
The linearity of output stages can be very sensitive to the load impedance. Transistors are not exactly linear devices at any time, and as the forward current increases the overall linearity of the output stage can suddenly start to become significantly non-linear. So much so that the performance of the amplifier starts to suffer. This is independent of the power supply capability. Feedback can only reduce the distortion by a fixed ratio. You can see this in Amir's stress measurements of any amplifier into low impedance loads. Such behaviour can mean much worse than expected distortion.
The power supply reserve can be depleted. Once the power rails start to sag everything can begin to go wrong. You can no longer be sure the amplifier is even operating correctly, and all manner of internals might have a transient failure. Distortion might rise to extraordinary levels until the rails recover.
A lot of headphone amplifiers will get into trouble driving a 40Ω load. Some will curl up and die, some will misbehave, and some will just sound bad. It isn't trivial to guess which ones will behave well. Proper performance measurements are a very useful guide. Marketing isn't.
One needs to be clear about terminology.
Gain is generally voltage gain. Volts on the input * gain = volts on the output. This makes some important assumptions, but in the systems we use, this is a good definition. We don't care about input impedance, and we consider power amplifiers as voltage sources. So it is OK. (We should pedantically, use power gain, but we don't define a known input impedance, so we can't. Expressed in dB we just define the gain as 20*log(voltage gain) instead of 10*log(power gain) and it all works out.)
A perfect voltage source has of course the ability to source infinite current, so when it can't, we have issues. We can probably break the problems into a few parts.
All amplifiers are usefuly modelled with their Thévenin equivalent, which places a notional resistor in series with the perfect voltage source output. So long as the Thévenin resistance is small relative to the headphone impedance it isn't a big issue. This resistance is for conventional amplifiers pretty much the resistance of the output devices + power supply impedance, all divided by the feedback factor. Poor output impedance can lead to frequency response issues. The output impedance and headphone impedance form a potential divider. Your useful voltage is the voltage seen out of this divider. Beware headphone amplifiers that put a real resistor on the output. They exist.
The linearity of output stages can be very sensitive to the load impedance. Transistors are not exactly linear devices at any time, and as the forward current increases the overall linearity of the output stage can suddenly start to become significantly non-linear. So much so that the performance of the amplifier starts to suffer. This is independent of the power supply capability. Feedback can only reduce the distortion by a fixed ratio. You can see this in Amir's stress measurements of any amplifier into low impedance loads. Such behaviour can mean much worse than expected distortion.
The power supply reserve can be depleted. Once the power rails start to sag everything can begin to go wrong. You can no longer be sure the amplifier is even operating correctly, and all manner of internals might have a transient failure. Distortion might rise to extraordinary levels until the rails recover.
A lot of headphone amplifiers will get into trouble driving a 40Ω load. Some will curl up and die, some will misbehave, and some will just sound bad. It isn't trivial to guess which ones will behave well. Proper performance measurements are a very useful guide. Marketing isn't.