If V_ref is the output reference value and V_fs is the ideal full-scale output voltage when the digital inputs are all 1. Which of the following equation is correct?

Concept:

Output voltage = Resolution × Decimal equivalent of binary Data.

\({V_0} = K\;\mathop \sum \limits_{i = 0}^{M - 1} {2^i}{b_i}\)

K = Proportionality factor i.e. Resolution

b_n = 1: if n^th bit of digital input is 1

0 = If n^th bit of digital input is 0

Resolution: It is a change in the analog voltage corresponding to the LSB bit increment at the input.

\(R=\dfrac{V_r}{2^n-1}\)

\(\% \;R = \frac{{Resolution}}{{{V_{fc}}}} \times 100\)

\(\% \;R = \frac{1}{{{2^n} - 1}} \times 100\)

Explanation:

Refrence voltage (V_ref):

\({V_{ref}} = \frac{{{2^n}\left[ {{V_{FC}}(full\;save\;voltage} \right]}}{{\left( {{2^n} - 1} \right)}}\)

\({V_{FC}} = \frac{{{2^n} - 1}}{{{2^n}}}{V_{ref}}\)

^{\({V_{FC}} = {V_{ref}}\left[ {1 - \frac{1}{{{2^n}}}} \right]\)} 

Option 3 correct.

More information:

Error/Accuracy: Maximum error acceptance in ADC/DAC is 1 LSB bit which is equal to the resolution

Error ≤ resolution.

Full-scale voltage V_FC = Resolution × maximum decimal.

\(= \frac{{{V_r}}}{{{2^n} - 1}} \times {2^n} - 1\)