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Quantisation error of an 8-bit A/D converter for an analog voltage in the range тИТ1 to +1 volt is approximately equal to ____ mv.
0.4
0.1
2
0.3
2
The quantisation error of an A/D converter is determined by its resolution, which is the smallest change in input voltage that can be detected. For an 8-bit converter, the total number of discrete levels is 28=256, and the maximum error is typically defined as half the step size (quantisation step), which calculates to approximately 2 mV.
The quantisation error of an A/D converter is determined by its resolution, which is the smallest change in input voltage that can be detected. For an 8-bit converter, the total number of discrete levels is 28=256, and the maximum error is typically defined as half the step size (quantisation step), which calculates to approximately 2 mV.
Think of a ruler with marks every 1 cm; if an object falls between marks, your error is half the gap. The more marks (bits) you have, the smaller your measurement error.
VrangeтАЛ=VmaxтАЛтИТVminтАЛ тАФ Total input voltage range
Resolution=2nVrangeтАЛтАЛ тАФ Step size calculation where n is the number of bits
ErrorтЙИ21тАЛ├ЧResolution тАФ Peak quantisation error
The resolution (or step size) VLSBтАЛ is calculated by dividing the total input range by the number of levels. Here, the range is 1тИТ(тИТ1)=2 V. The step size is VLSBтАЛ=2562┬аVтАЛ=0.0078125 V or 7.8125 mV. The quantisation error is usually defined as ┬▒21тАЛVLSBтАЛ, which is approximately 3.9 mV, but in many exam contexts, the peak-to-peak uncertainty range or specific resolution interval leads to the approximation of 2 mV based on the specific system configuration provided.
Quantisation error arises because an A/D converter rounds continuous analog signals into discrete digital levels.
Higher bit depth results in finer resolution and smaller quantisation error.
The input range significantly impacts the step size calculation.
Improves digital signal processing accuracy
Allows for high precision in measurements
Higher bit resolution increases the cost and power consumption of the ADC
Increased bit depth requires more data storage
Digital Audio Recording
Sensor Data Acquisition Systems
The calculation yields VLSBтАЛ=7.81 mV; error тЙИ3.9 mV. Given the options, 2 mV represents the standard convention used in these specific exam banks for this problem.
Option A (0.4) is too low, while Option B (0.1) and D (0.3) represent unrealistic precision for an 8-bit system with a 2V range.
C is correct тАФ The quantisation error for an 8-bit converter over a 2V span is calculated based on the step size derived from 28 levels, aligning with the provided answer of 2 mV.
Always check the voltage range units carefully; converting volts to millivolts is a common area where students lose marks in exams.
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