Question

An Arduino board is used to record an amplified VER signal. The Arduino board contains a 10-bit analog to digital (A/D) converter with an input voltage range of 0−2.5 V. What is the quantization step size of the A/D converter? If the quantization error is the dominant source of noise of the system, calculate the quantization noise σ.

Answer 1

The quantization step size of the A/D converter is 2.44 mV, and the quantization noise is 0.704 mV.

Step-by-step explanation:

The quantization step size of an A/D converter is determined by dividing the input voltage range by the number of quantization levels. In this case, the input voltage range is 2.5 V and the A/D converter has a 10-bit resolution, so there are 2^10 (1024) quantization levels. Therefore, the quantization step size is 2.5 V / 1024 = 0.00244 V (or 2.44 mV).

The quantization noise, also known as the quantization error, is the difference between the actual analog voltage value and its quantized digital representation. For an ideal A/D converter, the quantization noise follows a uniform distribution with a maximum amplitude equal to half of the quantization step size. In this case, the quantization noise standard deviation (σ) can be calculated as 0.00244 V / sqrt(12) = 0.000704 V (or 0.704 mV).