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Consider an N-bits ADC (Analog to Digital Converter) whose analog input varies from 0 to Vmax, then which of the following is not true?
- a)The least significant bit correspond to a change of Vmax/2N -1 in the analog signal
- b)The resolution of the ADC is Vmax/2N -1
- c)The maximum error in the conversion (or quantization error) is Vmax/2(2N -1)
- d)None of the mentioned
Correct answer is option 'D'. Can you explain this answer?
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Consider an N-bits ADC (Analog to Digital Converter) whose analog inpu...
None of the statements are true.
Most Upvoted Answer
Consider an N-bits ADC (Analog to Digital Converter) whose analog inpu...
The least significant bit correspond to a change of Vmax/2N -1 in the analog signal~> resolution of ADC
The resolution of the ADC is Vmax/2N -1~> resolution of ADC
The maximum error in the conversion (or quantization error) is Vmax/2(2N -1)
all are true so option (d)
The resolution of the ADC is Vmax/2N -1~> resolution of ADC
The maximum error in the conversion (or quantization error) is Vmax/2(2N -1)
all are true so option (d)
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Consider an N-bits ADC (Analog to Digital Converter) whose analog inpu...
Understanding ADC Basics
An Analog to Digital Converter (ADC) converts an analog signal into a digital representation. The specifications of an N-bits ADC are essential for understanding its performance.
Key Parameters of ADC
- Input Range: The analog input varies from 0 to Vmax.
- Resolution: This indicates the smallest change in input voltage that can be detected by the ADC.
Resolution Calculation
- The resolution of an N-bits ADC is calculated as:
\[ \text{Resolution} = \frac{Vmax}{2^N} \]
- This means that the smallest voltage change (the least significant bit or LSB) corresponds to \( \frac{Vmax}{2^N} \).
Quantization Error
- The maximum quantization error (the difference between the actual analog value and the nearest digital representation) is given by:
\[ \text{Max Error} = \frac{Vmax}{2 \times (2^N - 1)} \]
- This error is half of the LSB value, considering the ADC quantizes the input signal into discrete levels.
Analysis of the Options
- Option A: The least significant bit corresponds to a change of \( \frac{Vmax}{2^{N}-1} \) in the analog signal. (This is typically accurate for N-bits ADC.)
- Option B: The resolution of the ADC is \( \frac{Vmax}{2^{N}-1} \). (This is also correct as it describes the smallest detectable change.)
- Option C: The maximum error in conversion is \( \frac{Vmax}{2(2^{N}-1)} \). (This is true and reflects the quantization error.)
- Option D: None of the mentioned. (Since all previous options are true, this option is indeed correct.)
Conclusion
The correct answer is option D, meaning that all the described properties of the ADC are true, and thus there are no false statements among the other options.
An Analog to Digital Converter (ADC) converts an analog signal into a digital representation. The specifications of an N-bits ADC are essential for understanding its performance.
Key Parameters of ADC
- Input Range: The analog input varies from 0 to Vmax.
- Resolution: This indicates the smallest change in input voltage that can be detected by the ADC.
Resolution Calculation
- The resolution of an N-bits ADC is calculated as:
\[ \text{Resolution} = \frac{Vmax}{2^N} \]
- This means that the smallest voltage change (the least significant bit or LSB) corresponds to \( \frac{Vmax}{2^N} \).
Quantization Error
- The maximum quantization error (the difference between the actual analog value and the nearest digital representation) is given by:
\[ \text{Max Error} = \frac{Vmax}{2 \times (2^N - 1)} \]
- This error is half of the LSB value, considering the ADC quantizes the input signal into discrete levels.
Analysis of the Options
- Option A: The least significant bit corresponds to a change of \( \frac{Vmax}{2^{N}-1} \) in the analog signal. (This is typically accurate for N-bits ADC.)
- Option B: The resolution of the ADC is \( \frac{Vmax}{2^{N}-1} \). (This is also correct as it describes the smallest detectable change.)
- Option C: The maximum error in conversion is \( \frac{Vmax}{2(2^{N}-1)} \). (This is true and reflects the quantization error.)
- Option D: None of the mentioned. (Since all previous options are true, this option is indeed correct.)
Conclusion
The correct answer is option D, meaning that all the described properties of the ADC are true, and thus there are no false statements among the other options.
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Consider an N-bits ADC (Analog to Digital Converter) whose analog input varies from 0 to Vmax, then which of the following is not true?a)The least significant bit correspond to a change of Vmax/2N-1 in the analog signalb)The resolution of the ADC is Vmax/2N-1c)The maximum error in the conversion (or quantization error) is Vmax/2(2N-1)d)None of the mentionedCorrect answer is option 'D'. Can you explain this answer?
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Consider an N-bits ADC (Analog to Digital Converter) whose analog input varies from 0 to Vmax, then which of the following is not true?a)The least significant bit correspond to a change of Vmax/2N-1 in the analog signalb)The resolution of the ADC is Vmax/2N-1c)The maximum error in the conversion (or quantization error) is Vmax/2(2N-1)d)None of the mentionedCorrect answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Consider an N-bits ADC (Analog to Digital Converter) whose analog input varies from 0 to Vmax, then which of the following is not true?a)The least significant bit correspond to a change of Vmax/2N-1 in the analog signalb)The resolution of the ADC is Vmax/2N-1c)The maximum error in the conversion (or quantization error) is Vmax/2(2N-1)d)None of the mentionedCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider an N-bits ADC (Analog to Digital Converter) whose analog input varies from 0 to Vmax, then which of the following is not true?a)The least significant bit correspond to a change of Vmax/2N-1 in the analog signalb)The resolution of the ADC is Vmax/2N-1c)The maximum error in the conversion (or quantization error) is Vmax/2(2N-1)d)None of the mentionedCorrect answer is option 'D'. Can you explain this answer?.
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