Question

An 8 –bit D/A converter has step size of 20 mV. The full-scale output and the resolution will be nearly
1. 5.1 V and 0.3%
2. 4.6 V and 0.4%
3. 5.1 V and 0.4%
4. 4.6 V and 0.3%

Answer 1

Correct Answer - Option 3 : 5.1 V and 0.4%

Concept:

Resolution is defined as the smallest change in the analog output voltage corresponding to a change of one bit in the digital output.

The percentage resolution of an n-bit DAC is given by:

\(\%R = \frac{1}{{{2^n} - 1}} × 100\)

Also, the full-scale output for the given step size (Δ) is given by:

V_FS = (2ⁿ - 1) × Δ

where 2ⁿ - 1 = Number of levels

Calculation:

Given Δ = 20 mV and n= 8.

The full-scale output will be:

VFS = (28 - 1) × 20 mV

V_FS = 5.1 V

also, the percentage resolution will be:

\(\%R = \frac{1}{{{2^8} - 1}} × 100\)

%R = 0.4 %