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In case you didn't see in that thread you linked everyone to, I'm a total noob at all this stuff. But from reading around I've learned that if you want good audio you need 4 things, headphones, DAC, amp, and a good source. Now I'm guessing if your source isn't from an MP3 player, then it's a computer most likely. But why doesn't an iPhone need a DAC? I would use Google but half of the links take me here anyway so I might as well ask for a more specialized answer for my situation. So is it bad that a DAC won't work with an iPhone or does the iPhone already take care of that conversion for me?
Not true: http://www.google.com.sg/search?sourceid=chrome&ie=UTF-8&q=dac
And Googling "iPhone DAC" would lead you to: http://www.google.com.sg/search?sourceid=chrome&ie=UTF-8&q=iphone+dac
The first link being: http://gadgetwise.blogs.nytimes.com/2011/01/05/a-dac-brings-hi-fi-to-the-iphone/
The point being that some people don't hear a difference with an external DAC. There is debate over whether this is because there is no audible difference or not.
In any case, however: the only DACs that can work with an iPhone have to be licensed/approved by Apple, and as a direct result of that (I suspect) they are more expensive than what you seem willing to pay right now. So it's a moot point. Get an amp, not a DAC/amp.
Also, it doesn't matter whether you're a noob at this or not--if you don't know why you should add something to your setup, you still probably shouldn't add it.
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If you use an LOD with the iPhone will you bypass the phone's own DAC? I thought that this was one of the purposes of an LOD - to significantly improve the sound quality from media players.
No, see above.
Regardless of the unique situation for iDevice LODs, "LOD" by definition is "Line Out Dock", and so we're really only talking about a line level signal being extracted from the player. As you will note, a line level signal is traditionally an analogue thing anyway...the idea of bypassing an internal DAC to extract the digital signal is a new, and different, thing.
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The E7 isn't that powerful, I'm don't think it would help much. Just wait until you can get a good amp.
OP, as he said. Your key concern with the HD600 is a good enough amp. The DAC is very much secondary--and you should be searching within Head-Fi for the answers, because discussion surrounding the HD600 and amping is well-documented.