The usual calculation formula for ADC output is

Therefore, the noise superimposed on the reference voltage will have a direct impact on the output voltage. The reference voltage noise can be transformed to the form accumulated on the output voltage:

• Divide the numerator and denominator by V_REF to get:
  Equation 14. $\mathrm{Output} \mathrm{Code}=\frac{{\mathrm{V}}_{\mathrm{IN}\left(\mathrm{RMS}\right)}}{{\mathrm{V}}_{\mathrm{REF}}}*\frac{2^{\mathrm{N}}}{1+{\displaystyle \frac{{\mathrm{V}}_{\mathrm{N},\mathrm{REF}\left(\mathrm{RMS}\right)}}{{\mathrm{V}}_{\mathrm{REF}}}}}$
• Simplify and obtain:
  Equation 15. $\mathrm{Output} \mathrm{Code}=\frac{{\mathrm{V}}_{\mathrm{IN}\left(\mathrm{RMS}\right)}*2^{\mathrm{N}}}{{\mathrm{V}}_{\mathrm{REF}}}*(1-\frac{{\mathrm{V}}_{\mathrm{N},\mathrm{REF}\left(\mathrm{RMS}\right)}}{{\mathrm{V}}_{\mathrm{REF}}})$
• Separate the above formula into summation form:
  Equation 16. $\mathrm{Output} \mathrm{Code}=\frac{{\mathrm{V}}_{\mathrm{IN}\left(\mathrm{RMS}\right)}*2^{\mathrm{N}}}{{\mathrm{V}}_{\mathrm{REF}}}-\frac{{\mathrm{V}}_{\mathrm{IN}\left(\mathrm{RMS}\right)}*2^{\mathrm{N}}*{\mathrm{V}}_{\mathrm{N},\mathrm{REF}\left(\mathrm{RMS}\right)}}{{{\mathrm{V}}_{\mathrm{REF}}}^2}$

  Therefore, the voltage form of the noise superimposed on the output voltage is:

  Equation 17. ${\mathrm{V}}_{\mathrm{N},\mathrm{REF}}=\frac{{\mathrm{V}}_{\mathrm{IN}\left(\mathrm{RMS}\right)}}{{\mathrm{V}}_{\mathrm{REF}}}*{\mathrm{V}}_{\mathrm{N},\mathrm{REF}\left(\mathrm{RMS}\right)}$

  It is related to the ratio of input voltage to reference voltage, which is the utilization rate at full-scale. The higher the full-scale utilization of the input, the greater the reference voltage noise superimposed on the ADC output.

Considering the impact of noise on the effective resolution of ADC, as Vin in the effective resolution is reduced from Vin in the reference noise, and the internal noise of ADC is usually constant and not related to the ADC input, an increase in ADC input voltage can improve the effective resolution under the influence of ADC noise, but cannot affect the effective resolution under the influence of reference voltage noise.

One way to reduce reference voltage noise is to add an RC filtering stage before adding the reference voltage to the ADC, filtering out some high-frequency noise. On the other hand, the influence of reference voltage noise can be reduced by selecting external or internal reference voltages reasonably.

Table 2-1 provides a comparison of the advantages and disadvantages of several different reference voltages.