Question

Determine the resolution and the quantization error in volts for a 4-bit A/D converter that has a full scale range of EFSR =5 V . If the desired quantization error should be within 1 mV, how many bits are needed?

Answer 1

Answer:

minimum of 12 bits is required

Explanation:

Full scale range Ef = 5v = L

Resolution $R_{ADC} = \frac{L}{2^n -1}$

n = 4 bit

$R_{ADC} = \frac{5}{2^4 -1} = 0.333 VQuartization error is[tex] \epsilon = \frac{1}{2} R_{ADC}$

               $= \frac{1}{2} 0.333 = 0.166 V$

we know if error is less than 0.001 V then we have

$1/2 R_{ADC} \leq 0.001$

$R-{ADC} \leq 0.002$

$0.002\geq \frac{L}{2^n -1}$

$\frac{L}{2^n -1} \leq 0.002$

$\frac{L}{0.002} \leq 2^n -1$

Solving for n we get

$n\geq 11.288$

n = 12

Therefore minimum of 12 bits is required