What is the calculation formula for this circuit? How to calculate the value of VOUT？
The equation is correct. I assume you are using the ideal values of 200 mV/dec and 100pA for Vy and Iz, respectively?
Have you accounted for the following possible errors:
the current value of photodiode is 2.996 uA.,and the G is 2.5, The theoretical calculation is 2.23827V,But the actual output voltage is 2.2606V, Is the calculation formula incorrect?
Even an error of +/-10% of the Iz current could account for the difference in calculated value (with ideal values) and what you are measuring
I do not use the the Adaptive Biasing，I use the circuit diagram above .When I change light ，the VOUT has not changed, and I make the photodiode negative to ground ，the VOUT also has not changed.If I want to the photovoltaic mode ，how can I do？
I'm not sure how to do photovoltaic mode. But for most AD8304 applications, the PD needs to be either zero biased, or reverse biased. In the schematic above, the PD is forward biased, because the voltage at INPT pin is normally at +0.5V. To make the PD be zero-biased or reverse biased, the PD cathode must connect to +0.5V or higher, with respect to ground.
NOt using the adaptive biasing，is the photodiode negative connected to ground ？
Photodiode cathode should connect to +0.5 Volts or higher. Try connecting it to the VREF pin which should have +2 V.