# ADC Quantization Error

## Quantization

Quantization is the process where the Least Significant Bit (LSB) is determined if the input analog voltage lies in the lowest sub-range of the input voltage range. For example, consider an ADC with VREF = 2 V and the resolution is 3-bit. The 2 V is divided into eight sub-ranges, so the LSB voltage is within 250 mV. Now, an input voltage of 0 V, as well as 250 mV, is assigned to the same output digital code 000. The input analog voltage range from 251 mV to 500 mV will be assigned the digital code 001 and so on. To define a perfect ADC, the concept of quantization must be used. Due to the digital nature of an ADC, continuous output values are not possible. The perfect ADC performs the quantization process during conversion. This results in a staircase transfer function where each step represents one LSB. This figure below shows the transfer function of a perfect 3-bit ADC operating in Single Ended mode.

## Quantization Error

From the figure above, we can see that an input voltage of 0 V produces an output code 000. At the same time, an input voltage of 250 mV also produces the same output code 000. This is the quantization error due to the process of quantization. As the input voltage rises from 0 V, the quantization error also rises from 0 LSB and reaches a maximum quantization error of 1 LSB at 250 mV. Again, the quantization error increases from 0 to 1 LSB as the input rises from 250 mV to 500 mV. This maximum quantization error of 1 LSB can be reduced to ±0.5 LSB by shifting the transfer function towards left through 0.5 LSB.

The figure below shows a quantization-adjusted perfect transfer function together with an ideal transfer function. The perfect ADC equals the ideal ADC on the exact midpoint of every step. This means that the perfect ADC essentially rounds input values to the nearest output step value.