What is the origin for the forumla:
\$ R= {1\over2}V_{LSB} ={1\over2}*{V_{inMax}\over2^n-1} \$
Where does the \$ {1\over2} \$ comes from?
Shouldn't it be just: \$ R={V_{inMax}\over{2^n-1}}\$ ?
Electronic – Origin of a Resolution formula for ADC/DAC
adcdac
Best Answer
If \$R\$ is the resolution as conventionally defined, then $$ R = \frac{V_{REF}}{2^N}$$ where \$R\$ is the resolution in volts, \$V_{REF}\$ is the internal reference voltage for the converter, and \$N\$ is the number of bits. The resolution is the smallest observable change in input voltage (for an ADC) or the smallest possible change in the output voltage (for a DAC). Note that the maximum observable/producible voltage is therefore $$V_{MAX} = R \times (2^N -1)$$ You need to be careful here, because the "maximum voltage" specification for an ADC may be the maximum input voltage that does not damage the ADC, not the maximum measurable voltage.
You can also talk about the uncertainty in an ADC input value, and the uncertainty is assumed to be plus or minus one-half of the resolution. I think perhaps you have mixed up the uncertainty and the resolution.