Question

Quantization error in ADC is due to

• A. Poor resolution
• B. Non-linearity of the input
• C. A missing bit in the output
• D. A change in the input voltage during the conversion time

Hint:

Quantization error is inherent in the ADC process due to the finite number of discrete output levels.
It is directly related to the resolution (number of bits) of the ADC. Higher resolution (more bits) means smaller quantization step size and smaller quantization error.
Maximum quantization error is typically \(\pm Q/2\), where \(Q\) is the quantization step size.

Answer 1

The Correct Option is A

Quantization is the process in an Analog-to-Digital Converter (ADC) where a continuous range of analog input values is mapped to a finite set of discrete digital output values. Quantization error is the difference between the actual analog input value and the digital output value that represents it (when converted back to an analog equivalent). This error arises because the continuous analog signal is approximated by a finite number of discrete levels.
(a) Poor resolution: Resolution is determined by the number of bits in the ADC. Fewer bits mean larger step sizes between quantization levels. A larger step size (poorer resolution) directly leads to a larger maximum possible quantization error. The quantization error is inherently linked to the step size Q, which is \(V_{FS}/2^N\) (Full Scale Voltage range divided by number of levels). The error is typically between \(-Q/2\) and \(+Q/2\). So, poor resolution (large Q) causes quantization error.
(b) Non-linearity of the input: If the ADC itself has non-linearity (e.g., differential non-linearity DNL, integral non-linearity INL), this introduces errors separate from the fundamental quantization error. Input non-linearity is not the cause of quantization error itself.
(c) A missing bit in the output: This would be a malfunction of the ADC (e.g., missing codes), leading to large errors, not the inherent quantization error.
(d) A change in the input voltage during the conversion time: This is known as an aperture error or error due to slew rate, and is typically addressed by using a Sample-and-Hold (S/H) circuit before the ADC. It's not the quantization error itself. Quantization error is a fundamental consequence of representing a continuous analog signal with discrete levels. The "fineness" of these levels is the resolution. Poor resolution means coarse levels, and thus a larger potential difference between the true analog value and its quantized representation. \[ \boxed{\text{Poor resolution}} \]