As has been said, yes, you need a better DAC before you talk about headphone amplifiers. That being said, an audibly perfect DAC need not be very expensive. I would suggest, for a lapop, an emu 0404 USB. Since this is the sound section, and you want a scientific explanation, here are the RMAA tests for the emu 0404 USB:RightMark Audio Analyzer test : E-MU 0404 USB loopback unbal 16b 44k
All of those measurements are well, well beyond the threshold of audibility. If you're looking for a different card, make sure that they match these specs and you'll be fine:
Frequency response +/- 0.3db
Noise level < -80 db
Dynamic range < -80 db
THD < 0.05%
THD + Noise < -80 db
IMD + Noise < 0.05%
Stereo crosstalk < -20 db
IMD at 10 kHz < 0.05%
Now, these figures are good general guidelines for getting perfectly transparent sound coming out of your entire system, so it's a good idea to keep the values low on your source so your amplifier won't create additional distortion which additively will put you past the thresholds. That being said, the Emu 0404 is WELL below those points.
The Emu 0404 is pretty expensive for what it does (the PCI version is about half the price and the same performance - I verified this with testing that you can see here: RightMark Audio Analyzer test : [MME] E-DSP Wave [EC00]
), so you may want to look for other soundcards within your price range. That said, since you plopped down the cash for the 650's, you may as well spend the extra money on a good USB DAC that measures well, because the 0404 has a lot of other advantages to it as well.
If you're looking cheaper, there's a USB DAC called the Alien DAC that you can get for much cheaper, around 30 dollars in parts if you build it yourself, and I'd assume under 100 dollars if you got someone to build it for you. You can see the measurements here:RightMark Audio Analyzer test: Alien DAC 16b 44.1k USB power
It's not a stellar DAC, but it's pretty good, especially if you can find it at that 30 dollar price range - it'll be more than enough to get you started.
A lot of people on the forum will overestimate the importance of the source - while it is extremely important to get a transparent one, I find a lot of people overspend on sources - it doesn't take much to get an audibly perfect DAC.
Onto amps: this post is very informative and lets you understand, from a scientific standpoint, what a headphone amp's function is:Is a headphone amp needed? - Hydrogenaudio Forums
Notice how, when sufficient voltage is given, the clipping stops (as you can see from the scope readings). The headphones used there are beyerdynamic DT880's, and they're pretty inefficient, hard to drive phones. Even with worst-case scenario, heavily dynamic music driven at loud levels, only 3.90 VRMS is needed, but the rail voltages still need to be at around 16 volts. High impedance phones like the 650's need a lot of voltage swing, but not a lot of current output - you can see that through Ohm's law. So long as you have an amplifier with sufficient voltage, a low enough THD, and a flat frequency response (99% of properly designed amps), you'll also have an audibly perfect headphone amplifier - one that won't color the sound at all, and simply eliminate clipping/distortion.
Take a look here: Headphone Amps and Distribution | Sweetwater.com
Go through them, look at the spec sheets, and find one that's reasonably priced with enough rail voltage (you can't tell rail voltage just by looking at input voltage which will be what's listed, but it's a good rough guide that ~16V input voltage should be enough). One benefit of getting the emu 0404 as above would be that you can run 1/4" TRS cables from the headphone amp to the DAC, which in theory can reduce the noise of the cables, but in practice they're great cables because they're nearly impossible to break or destroy.
Good luck with your setup.