@jk98 wrote:
It isn’t just about the impedance of the headphones though.
For mp3 players the output impedance is pretty small, so really only the headphone impedance matters. Most people tend to ignore it, although over at ABI we discussed this in detail a while back.
JK98 wrote:
Impedance total= output impedance of player * headphone impedance/(output impedance of player + headphone impedance)
Actually, for an mp3 player the way we talk about impedance you should be using the Thévenin model, not the Norton model (although your formula would work for other types of amplifiers, which is why i’m guessing it came up when you googled amplifiers). The Norton model won’t work so well because you can’t measure the short circuit current (the DAC will cut you off to prevent you from damaging it).
See:
http://en.wikipedia.org/wiki/Thévenin’s_theorem
http://en.wikipedia.org/wiki/Norton’s_theorem
Using the proper model, the impedance is actually calculated like so:
Impedance total= output impedance of player + headphone impedance
On ABI I calculated the output impedance of the Clip using dfkt’s measurements. Its about 1.6 ohms, quite small compared to the 16-64 ohms typically used in headphones, and so you can safely ignore it.
JK98 wrote:
The greatest amount of power is transfered when the headphone impedance matches the output impedance of the player.
This is a common misconception. Its actually completely wrong for these amplifiers, which is why the output impedance of the CLip is 1.6ohms and not 16 ohms :)
Instead you maximize power transfer by having the smallest possible output resistance. Ideally it would be zero, in which case the clip would transfer 100% of its power to the headphones. Instead, with headphones at 16 ohms it transfers 91% of its power to the load. Conversely, if it had 16 ohms output, and 16 ohm headphones, just 50% of its power would be transferred. Not very good at all!
Interestingly, efficiency actually increases for larger impedance headphones. For 32 ohm headphones, over 95% of the output power goes into the headphones (and at 64 ohms, nearly 98% goes)!
