Impedance in headphones vs. speakers - confused

My head is still swimming!!!!!!

So my new integrated amplifier states in the manual that only headphones with a minimum of 50 ohms should plugged into the headphone jack. So I take it this means that there is not a lot of current available through the amp powering the headphones? But an acceptable power supply?

Thanks, glad that I could help some. It's not really too hard to understand once you realize that you have to think in terms of voltage/current & power into the load.

what the int. amp manuf. is telling you is that do not apply a heavy (current) load than a 50 Ohms headphone or else the headphone will ask for too much current that will stress the internal headamp. Nothing's going to happen if you drive a less-than-50 Ohms headphone occasionally but over time, the electronics in the headamp will fatigue. You can go higher in the headphone impedance - 100 Ohms, 120 Ohms, 220 Ohms & keep checking how the headphones sound. As the headphone impedance increases, the current pulled from the int. amp headamp will go down & down but the voltage swing will go up & up. At some headphone impedance, your ears will let you know that it's not longer sounding dynamic enough. Once you find that, you've found the upper limit of your headphone impedance.

The one thing that I find confusing though is that most home amplifiers that can handle lots of current are usually expensive. My guess would be because of dealing with the heat generated.

yes, this is one reason - larger heatsinks get very expensive. There are many other reasons: the transformers get very heavy & physically very large in diameter to accomodate very large amounts of current. Thus, they become very expensive. To accomodate a larger xformer, the chassis becomes bigger. More machined metal, more expense. To handle large current, you need higher amperage recitifier diodes - these are also expensive. Then, you have to heatsink these rectifier diodes really well otherwise their performance derates very rapidly. Again, internal heatsinking takes space & money. This is passed onto the customer.
It's a snowball effect when you make a high current amp.... ;-)

But in terms of headphones, an iPhone can easily muster enough current to power a lower impedance headphone such as 16 or 32 ohms. Is it because the amount of current is so small at that point thats not really a big deal? But voltage is because its battery powered?

That's right. The diaphragm of the ear-bud headphone takes that kind of current that can be supported by a micro-electronics circuit inside the iPhone. As you correctly stated, the voltage peak-peak swing is limited by the battery which can be 4.5V when fully charged & then decays to 3.5V when discharged & everything stops working. The electronics inside an iPhone or iPod Classic is just about good enough to drive the Apple-provided ear-buds but try to drive, say, an integrated amp line-in input (I did that before I got my iPod dock) & it sucked big time! No umph at all & a very flat/flacid playback. If I went a little above 75% of the volume, I'd get distortion thru my speakers (I was clipping that internal headamp) as it was struggling to drive the line-in of my int. amp.

Ok. This is all starting to make sense to me now and I really appreciate your very clear and helpful answers. This has been bothering me for quite a while so it feels good to start to understand it :) Thanks!

Theres's only one thing that I still don't understand. Why is it that an iPod or iPhone won't get stressed out delivering the current required for 32 ohm headphones (apple earbud's or a pair of Grado's for example) but my $3000 integrated amplifier which requires a minimum of 50 ohms has a problem with it? Yet the integrated amp can apparently supply enough current to power 4 ohm home speakers with no problem.

Excellent explanations by Bombaywalla.

A couple of additional points:

1)Another possible reason for the recommendation by your integrated amp manufacturer to use headphones having impedances of 50 ohms or more is that while its headphone amplifier circuit might have no trouble providing the voltage, current, or power required by low impedance headphones, its output impedance may be too high, and vary too much as a function of frequency, to provide good sonics when driving low impedances. That same problem sometimes arises in interfacing preamp outputs to power amp inputs.

If the headphone amp within the integrated amplifier has an output impedance that is a substantial fraction of the impedance of the headphones, and if that output impedance varies significantly over the audible frequency range (as may often be the case), the resulting frequency response will be significantly non-flat, as a result of the voltage divider effect. The voltage that the headphone amp "tries" to put out being divided between the headphone's impedance and its own output impedance. For a given output impedance, the higher the impedance of the headphones the less significant that effect will become.

2)Keep in mind that to produce a given volume level at the listener's ears, the power required by a set of headphones is VASTLY less than the amount of power required by a pair of speakers. Perhaps 100,000 times less, or thereabouts. Headphones commonly produce sound pressure levels of around 100 db in response to an input of 1 milliwatt (0.001 watts). Speakers having typical efficiencies that are listened to at typical distances will require, as a rough order of magnitude, something like 100 watts to produce that same spl.

So a hypothetical 32 ohm speaker, were such a thing to exist, would require vastly more current, voltage, and power to produce a given volume at the listener's ears than a 32 ohm headphone.

Regards,
-- Al

Theres's only one thing that I still don't understand. Why is it that an iPod or iPhone won't get stressed out delivering the current required for 32 ohm headphones (apple earbud's or a pair of Grado's for example) but my $3000 integrated amplifier which requires a minimum of 50 ohms has a problem with it? Yet the integrated amp can apparently supply enough current to power 4 ohm home speakers with no problem.

The electronics for the integrated amp to drive 4 Ohm speakers should be totally different & separate from the electronics that is the headamp. There should be 2 separate circuit boards for these 2 separate functions. The electronics that is driving your 4 Ohm loudspeaker is NOT the circuit driving your headphone. Once you have switched off your int. amp & let is sit for several hours to let the power supply caps discharge, pop open the top lid & take a look inside. You should see a separate circuit board for the headamp.
All the money was spent in making a much better int amp to drive a loudspeaker than a headamp to drive headphones. The headamp was thrown in there as a feature with minimal cost & effort. People who are serious about headphone listening more often than not have a dedicated/separate headphone amp.