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

minimum of 12 bits is required

Step-by-step explanation:

Full scale range Ef = 5v = L

Resolution
`R_(ADC) = (L)/(2^n -1)`

n = 4 bit

`R_(ADC) = (5)/(2^4 -1) = 0.333 V</p><p>Quartization error  is</p><p>[tex] \epsilon = (1)/(2) R_(ADC)`

`= (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 (L)/(2^n -1)`

`(L)/(2^n -1) \leq 0.002`

`(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