If vn_res represents the input-referred rms noise from all the resistors, vn_op represents the input-referred rms noise of OPA333-Q1, and vn_ADC represents the input-referred rms noise of ADS1015-Q1, the total input-referred noise of the entire system, vN, can be approximated by Equation 11.
It is important to note that the ADC noise contribution, vn_ADC, is attenuated by the non-inverting gain stage.
If the gain of the noninverting gain stage is high (≥ 5), a good approximation for vn_res2 is given by Equation 12. The noise contribution from resistors R2, R4, R5, and R6 when referred to the input is smaller in comparison to R1 and R3 and can be neglected for approximation purposes.
An approximation for the input impedance, RIN, of the application circuit is given by Equation 13. RIN can be modeled as a resistor in parallel with the shunt resistor, and can contribute to additional gain error.
From Equation 12 and Equation 13, a trade-off exists between vN and RIN. If R3 increases, vn_res increases, and therefore, the total input-referred rms system noise, vN, increases. If R3 decreases, the input impedance, RIN, drops, and causes additional gain error.