I have designed a sigma-delta AD converter,  and I am testing it on the user environment, but find the chip need a long time to be stable. please refer to the figure in attachment.

When the GND_module connected to GND_system,  data read out by mcu keeps on increasing and needs about 20~30 seconds to stablize. But the data can stablize in 3 seconds if GND_module doesn't connect to GND_system.

I can understand why the chip can work properly when GND_module floated. Although GND_module is floated, the capacitor(10uF) can be charged when SCL/SDA is low(through the ESD protection diode). The potential on this capactor is about (VDD-2*0.5) volt. So the chip can work(i.e. data read out by mcu stablizes in several seconds).

But it's really weird that the chip needs such a long time to be stable.

Some information on this chip may be important:
1. When GND_module floated, if VDD of 5V is applied the chip stablizes in 10 seconds while it need 30 seconds in 3V.
2. Substrate of the chip is P and not connected to GND_module(due to PCB design error). 0.35micron process.
3. the average current(when converting) is about 100uA
4. It seem to stablize quicker without exposure to light

I have been puzzled for couples of weeks and hope you can give me a hand.
Thank you very much!