Consider the following statements regarding ADC characteristics:
1. Resolution of an ADC is defined as the smallest change in analog input that can be detected and is inversely proportional to number of bits.
2. Quantization error is inherent in ADC and cannot be completely eliminated but can be minimized by increasing resolution.
3. Sampling rate has no effect on signal reconstruction quality in digital systems.
Which of the above statements is/are correct?
Answer & step-by-step solution
An ADC discretizes both amplitude and time. Bit depth controls amplitude resolution; sampling frequency controls temporal/spectral resolution and aliasing. Key relation: LSB ≈ VFS/2^n (or VFS/(2^n−1), depending convention); ideal quantization error ≈ ±0.5 LSB; sampling theorem requires fs > 2fmax for ideal band-limited reconstruction.
Exam focus: Bits → amplitude resolution. Sampling rate → aliasing/reconstruction. Common trap: Saying “more bits means resolution is 1/n”; it is approximately one part in 2^n.
Statement-wise Verification
- Statement 1 - Incorrect.
Resolution of an ADC is defined as the smallest change in analog input that can be detected and is inversely proportional to number of bits.
As worded: the smallest quantization step decreases exponentially with bit count, approximately as 1/2^n, not as 1/n. The definition part is reasonable, but the stated proportionality makes the full statement false. - Statement 2 - Correct.
Quantization error is inherent in ADC and cannot be completely eliminated but can be minimized by increasing resolution.
Finite quantization creates unavoidable quantization error; more bits reduce LSB size and therefore reduce ideal quantization uncertainty. - Statement 3 - Incorrect.
Sampling rate has no effect on signal reconstruction quality in digital systems.
Sampling rate determines whether spectral replicas overlap (aliasing) and therefore directly affects reconstructability.
Core Concept
An ADC discretizes both amplitude and time. Bit depth controls amplitude resolution; sampling frequency controls temporal/spectral resolution and aliasing. These are separate limitations and should never be mixed.
Formula / Key Relationship
LSB ≈ VFS/2^n (or VFS/(2^n−1), depending convention); ideal quantization error ≈ ±0.5 LSB; sampling theorem requires fs > 2fmax for ideal band-limited reconstruction.
Step-by-Step Check
Mathematical dependence 2^n disproves the “inverse to number of bits” wording. Nyquist reasoning disproves statement 3. Only statement 2 survives, so B.
Why the Other Options Are Wrong
Option A is incorrect because it includes incorrect statement(s) 1. Option C is incorrect because it includes incorrect statement(s) 1, 3 and omits correct statement(s) 2. Option D is incorrect because it includes incorrect statement(s) 1, 3.
Answer-Key Verification Note
The uploaded provisional key marks D . After independent technical verification, the defensible answer is B . This discrepancy is stated explicitly rather than silently copying the provisional key.
Exam Shortcut / Approach
Bits → amplitude resolution. Sampling rate → aliasing/reconstruction.
Common Mistake
Saying “more bits means resolution is 1/n”; it is approximately one part in 2^n.
Quick Revision
ADC Resolution Quantization and Sampling is linked with Analog-to-Digital Conversion, Data Converters and Digital Electronics. Bits → amplitude resolution. Sampling rate → aliasing/reconstruction.
ADC विशेषताओं के संबंध में निम्नलिखित कथनों पर विचार कीजिए:
1. ADC का रेज़ोल्यूशन एनालॉग इनपुट में वह सबसे छोटा परिवर्तन है जिसे पहचाना जा सके और यह बिटों की संख्या के व्युत्क्रमानुपाती है।
2. क्वांटाइज़ेशन त्रुटि ADC में अंतर्निहित है, इसे पूरी तरह समाप्त नहीं किया जा सकता पर रेज़ोल्यूशन बढ़ाकर कम किया जा सकता है।
3. डिजिटल सिस्टम में सैंपलिंग दर का सिग्नल पुनर्निर्माण गुणवत्ता पर कोई प्रभाव नहीं पड़ता।
उपरोक्त में से कौन-सा/से कथन सही है/हैं?
उत्तर और चरणबद्ध हल
ADC आयाम और समय दोनों को असतत करता है। बिट संख्या आयाम रेज़ोल्यूशन तय करती है; सैंपलिंग आवृत्ति एलियासिंग और पुनर्निर्माण तय करती है। मुख्य संबंध: LSB ≈ VFS/2^n; आदर्श क्वांटाइज़ेशन त्रुटि ≈ ±0.5 LSB; fs > 2fmax।
परीक्षा फोकस: बिट → आयाम रेज़ोल्यूशन; सैंपलिंग दर → एलियासिंग। सामान्य गलती: रेज़ोल्यूशन लगभग 2^n में एक भाग है, 1/n नहीं।
विस्तृत हल (मूल भाषा में)
Statement-wise Verification
- Statement 1 - Incorrect.
Resolution of an ADC is defined as the smallest change in analog input that can be detected and is inversely proportional to number of bits.
As worded: the smallest quantization step decreases exponentially with bit count, approximately as 1/2^n, not as 1/n. The definition part is reasonable, but the stated proportionality makes the full statement false. - Statement 2 - Correct.
Quantization error is inherent in ADC and cannot be completely eliminated but can be minimized by increasing resolution.
Finite quantization creates unavoidable quantization error; more bits reduce LSB size and therefore reduce ideal quantization uncertainty. - Statement 3 - Incorrect.
Sampling rate has no effect on signal reconstruction quality in digital systems.
Sampling rate determines whether spectral replicas overlap (aliasing) and therefore directly affects reconstructability.
Core Concept
An ADC discretizes both amplitude and time. Bit depth controls amplitude resolution; sampling frequency controls temporal/spectral resolution and aliasing. These are separate limitations and should never be mixed.
Formula / Key Relationship
LSB ≈ VFS/2^n (or VFS/(2^n−1), depending convention); ideal quantization error ≈ ±0.5 LSB; sampling theorem requires fs > 2fmax for ideal band-limited reconstruction.
Step-by-Step Check
Mathematical dependence 2^n disproves the “inverse to number of bits” wording. Nyquist reasoning disproves statement 3. Only statement 2 survives, so B.
Why the Other Options Are Wrong
Option A is incorrect because it includes incorrect statement(s) 1. Option C is incorrect because it includes incorrect statement(s) 1, 3 and omits correct statement(s) 2. Option D is incorrect because it includes incorrect statement(s) 1, 3.
Answer-Key Verification Note
The uploaded provisional key marks D . After independent technical verification, the defensible answer is B . This discrepancy is stated explicitly rather than silently copying the provisional key.
Exam Shortcut / Approach
Bits → amplitude resolution. Sampling rate → aliasing/reconstruction.
Common Mistake
Saying “more bits means resolution is 1/n”; it is approximately one part in 2^n.
Quick Revision
ADC Resolution Quantization and Sampling is linked with Analog-to-Digital Conversion, Data Converters and Digital Electronics. Bits → amplitude resolution. Sampling rate → aliasing/reconstruction.
ADC ની લાક્ષણિકતાઓ સંબંધિત નીચેના વિધાનો ધ્યાનમાં લો:
1. ADC નું રેઝોલ્યુશન એનાલોગ ઇનપુટમાં ઓળખી શકાય તેવો સૌથી નાનો ફેરફાર છે અને તે બિટની સંખ્યાના વ્યસ્ત પ્રમાણમાં છે.
2. ક્વોન્ટાઇઝેશન ત્રુટિ ADC માં સહજ છે, તેને સંપૂર્ણ દૂર કરી શકાતી નથી પરંતુ રેઝોલ્યુશન વધારીને ઘટાડી શકાય છે.
3. ડિજિટલ સિસ્ટમમાં સેમ્પલિંગ દરની સિગ્નલ પુનઃરચનાની ગુણવત્તા પર કોઈ અસર થતી નથી.
ઉપરોક્તમાંથી કયું/કયા વિધાન સાચું/સાચા છે?
જવાબ અને પગલાવાર ઉકેલ
ADC કંપવિસ્તાર અને સમય બંનેને અલગ-અલગ બનાવે છે. બિટની સંખ્યા કંપવિસ્તાર રેઝોલ્યુશન નક્કી કરે છે; સેમ્પલિંગ આવૃત્તિ એલિયાસિંગ અને પુનઃરચના નક્કી કરે છે. મુખ્ય સંબંધ: LSB ≈ VFS/2^n; આદર્શ ક્વોન્ટાઇઝેશન ત્રુટિ ≈ ±0.5 LSB; fs > 2fmax.
પરીક્ષા મુદ્દો: બિટ → કંપવિસ્તાર રેઝોલ્યુશન; સેમ્પલિંગ દર → એલિયાસિંગ. સામાન્ય ભૂલ: રેઝોલ્યુશન આશરે 2^n માં એક ભાગ છે, 1/n નહીં.
વિગતવાર ઉકેલ (મૂળ ભાષામાં)
Statement-wise Verification
- Statement 1 - Incorrect.
Resolution of an ADC is defined as the smallest change in analog input that can be detected and is inversely proportional to number of bits.
As worded: the smallest quantization step decreases exponentially with bit count, approximately as 1/2^n, not as 1/n. The definition part is reasonable, but the stated proportionality makes the full statement false. - Statement 2 - Correct.
Quantization error is inherent in ADC and cannot be completely eliminated but can be minimized by increasing resolution.
Finite quantization creates unavoidable quantization error; more bits reduce LSB size and therefore reduce ideal quantization uncertainty. - Statement 3 - Incorrect.
Sampling rate has no effect on signal reconstruction quality in digital systems.
Sampling rate determines whether spectral replicas overlap (aliasing) and therefore directly affects reconstructability.
Core Concept
An ADC discretizes both amplitude and time. Bit depth controls amplitude resolution; sampling frequency controls temporal/spectral resolution and aliasing. These are separate limitations and should never be mixed.
Formula / Key Relationship
LSB ≈ VFS/2^n (or VFS/(2^n−1), depending convention); ideal quantization error ≈ ±0.5 LSB; sampling theorem requires fs > 2fmax for ideal band-limited reconstruction.
Step-by-Step Check
Mathematical dependence 2^n disproves the “inverse to number of bits” wording. Nyquist reasoning disproves statement 3. Only statement 2 survives, so B.
Why the Other Options Are Wrong
Option A is incorrect because it includes incorrect statement(s) 1. Option C is incorrect because it includes incorrect statement(s) 1, 3 and omits correct statement(s) 2. Option D is incorrect because it includes incorrect statement(s) 1, 3.
Answer-Key Verification Note
The uploaded provisional key marks D . After independent technical verification, the defensible answer is B . This discrepancy is stated explicitly rather than silently copying the provisional key.
Exam Shortcut / Approach
Bits → amplitude resolution. Sampling rate → aliasing/reconstruction.
Common Mistake
Saying “more bits means resolution is 1/n”; it is approximately one part in 2^n.
Quick Revision
ADC Resolution Quantization and Sampling is linked with Analog-to-Digital Conversion, Data Converters and Digital Electronics. Bits → amplitude resolution. Sampling rate → aliasing/reconstruction.
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