# ADC bit resolution (LSB) after a gain stage

If my signal path is as the following:

My input DR is 20mVpp and goes through the above path, and the ADC used is 16 bits. Would the LSB be 5V/(2^16)=76uV or the gain will be added to the LSB as (5V/(2^16))/90=0.84uV. If the gain is added I am having a hard time understanding why it improves the bit resolution.

• It depends whether you measure the LSB before or after the gain stage. Oct 14, 2021 at 16:00

The 90V/V gain stage reduces the effective LSB step size (from $$\ \frac{5~\text{V}}{2^{16}}=76~\mu\text{V} \$$ to $$\ \frac{5~\text{V}/90}{2^{16}}=0.84~\mu\text{V} \$$ as you suggest), and also reduces the dynamic range by the gain factor (from $$\ \pm2.5~\text{V} \$$ to $$\ \pm0.02778~\text{V} \$$ ).