Some comments regarding the possible origins of the "hump" in the ES9038 products:
- It appears to affect most of the ESS DACs (certainly the ES9028 and 9038 series).
- For the ES9038 that I was able to measure, the outputs are firmly biased at AVCC/2=1.65V
- The output impedance is indeed around 200ohm per output.
- When the I/V stage common mode voltage is set lower than the AVCC/2 bias voltage, then a DC current flows through the I/V resistor to account for the bias difference. Example: AVCC/2=1.65V Vcm=1V R=50ohm results in a current of (1.65-1)/200~3.2mA. For 8 outputs in parallel, this amounts for about 25mA.
- This current comes from the opamp negative supply, since it is sunk by the I/V opamp. It increases the I/V stage standby power dissipation by a significant margin.
- The displaced Vcm bias is used by ESS in their demo boards (at least for the ES9038 series).
- Essentially, we are dealing with two voltage sources, Vcm and AVCC/2 fighting, and the resulting current flows through the DAC output impedance.
- No idea on how the ESS output stages are designed, but the fact that such a current flow practically eliminates the distortion hump suggests a mechanism similar with displacing the gm "hump" in older op amps with bipolar outputs, by biasing the output with a current source. This method eliminates the gm doubling distortion "hump" generated by the op amp output stage.
- If this is correct, the "hump" is essentially because of the poor output impedance of the ESS outputs (200 ohm parallel, or the Thevenin equivalent series impedance). A poor output impedance is also typical for op amps that can be improved by biasing the output.
I am afraid that's all we can speculate and infer about the "hump" origin, lacking any information from ESS.