Tags: ADC, education, theory, Qe, quantization error

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          Quantization error Qe is defined as the difference between the analog input and the corresponding analog value of the ADC transfer curve [1] calculated as:

 

Q =  VIN  –  Vstaircase          [1]

 

where Vstaircase [1] is calculated as:

 

Vstaircase  =  number of a current step  •  LSB

 

          Fig. 38 presents the quantization error Qe for an ideal 3-bit flash ADC. Quantization error can be also expressed in LSBs. Knowing that 1 LSB = 0.5 V (see LSB), the quantization error in Fig. 38 is presented in LSBs in Fig. 39.

 

Quantization Error Qe in Volts

Figure 38: Quantization error Qe expressed in Volts for an ideal 3-bit ADC, where power supply VDD is equal to 4V.

 

Quantization Error Qe in LSBs

Figure 39: Quantization error Qe expressed in LSBs for an ideal 3-bit ADC, where power supply VDD is equal to 4V.

 

          The quantization error can be centered around x-axis by making the first step shorter, equal to 0.25 V or 0.5 LSB and by making the last step longer, equal to 1.5 V or 1.5 LSB. It is shown in Fig. 40. It is worth to notice, that the quantization error for VIN greater than 3.5 V has not changed.

 

Quantization Error Qe centered around x-axis

Figure 40: Quantization error Qe centered around x-axis.

 

 

References:

  1. Baker R. Jacob, CMOS Circuit Design, Layout, and Simulation, 3rd Edition, 2010, John Wiley & Sons