So the buffer will be better equipped to supply the current the headphones require... how does this manifest sonically?

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That's a little hard to answer directly.

Basic theory (in my own words because I haven't read any books ):
Headphone amps usually do two things: amplify voltage (volume) and amplify current (uhm... think of power output ability). Opamp are used for voltage gain, they make things louder, but most opamps aren't good at driving low impedance loads at high current (like headphones which like some current). That's where the buffer comes in, it is used for current gain. It provides enough current to drive the headphones and takes the load off the opamp. Some opamps are good for both (like AD8397), but that limits you to the sound of this specific opamp. I like other opamps more than it, so I rather use different opamps (that usually don't do so well driving headphones directly) because of their sound signature and put a buffer in front of it to boost current and drive the headphones.

Buffers are another tricky thing, I personally don't mind the BUF634, it's not great (a little warm/thick) but it does sound nice. I also use LMH6321 for better clarity, but the current draw is huge and depending on the opamp, you might not want "more detail" as the opamp is already bright. It's a mix and match game and I like to play it instead of being stuck to one chip.

jh4db536 : Buffers run in series with the opamp (after it), not in parallel.

Looking at LMH6321's datasheet I would not use this buffer for anything battery powered, definitely not.

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How come? I use it and love it in my PPAS. Current draw is ~ 13mA / buffer, another ~ 15mA for opamps, total Iq 50-55mA - 5 hours off a $8 270mAh Accupower 9V. Of course in my main PPAS, I run it off 8x 800mAh Eneloop AAA.

Thanks for the explanation!

An ideal op amp will act as a voltage source. That is it will output a certain volatage regardless of how much current is being drawn.
In reality when an op-amp has to supply a lot of current its voltage gets pulled down.
A buffer does the job of supplying the necessary current and allows the op-amp to set the voltage. So there is no stress on the op-amp and it can perform closer to the ideal case.

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You just said why I'd never use it in a portable application. Five hours of battery life is pretty bad. Fine for day to day listening, but usually I do that straight out of my iPod without the amp. When I use the amp it generally means being away from convenient power outlets for a long period of time.

I guess YMMV, since it depends on how you use your amp.

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Perfect, thanks! I haven't used an opamp in ages... really need to review some of that stuff.

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This is a generalization that doesn't apply to some opamps that could indeed supply gobs of output current -- just as much or even more than some "buffers"...

Current draw will always pull down a source's voltage. A buffer is meant to minimize that.
Whether or not you consider the voltage drop negligible is a design decision.

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A buffer chip is nothing much more than some higher current output transistors in a package. Compare, say a BUF634 to the AD8397 opamp (which has a very stout output stage), you'll find that AD8397 can supply just as much current as a BUF634, while providing rail-to-rail swing capability that BUF634 cannot match.

This is not to mention some really high current opamps like OPA541...