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Default ADC distortion typical near 0dB??

Does anyone know if it is typical for an ADC to distort when driven near full
scale (0dB)?

I've got an Edirol UA5 USB audio interface. I put a 1600Hz sine wave in the
line input (played from the line out of a Creative Labs Nomad Jukebox 3),
turned the level up to just under 0dB and recorded a few seconds of audio.

When I looked at the spectrum (Adobe Audition 1.5!) I see several harmonics
(multiples of 1600Hz), and the largest one was only -40dB down or so. I
noticed these extra peaks went away once I lowered the input to say, -6dB.
So, it seems to exhibit some kind of clipping/overloading behavior, but the
input signal was not over. It was something like -1 or -2dB.

I looked at the circuit in this box. It is based on the AK4524 ADC. The
circuit seems to follow the standard design spec. The chip operates on +5V.
The driving opamps run on +/-5V. The input signal to the ADC seems to be
about 0.7V RMS at full scale.

So, could it be that these ADCs are really not very good? Or is the
supporting circuitry poor? Should I expect a more expensive box, like MOTU or
Presonus, to do it right? I guess it pays to check these things out.

Thanks for any help...
Richard