Difficulty: Easy
Correct Answer: Too many different values (and tight tolerances) of resistors are required
Explanation:
Introduction / Context:
Binary-weighted digital-to-analog converters (DACs) require precise element ratios to ensure linearity. As resolution increases, element values span wide ranges and matching becomes impractical. This question targets the key real-world limitation behind binary-weighted DAC implementations.
Given Data / Assumptions:
Concept / Approach:
For an n-bit binary-weighted DAC using resistors, the MSB path uses the smallest resistance (or largest current), and the LSB uses 2^(n-1) times that resistance. With growing n, resistor values span large ranges and must hold tight absolute and ratio tolerances, stressing process capabilities and layout area. Hence binary-weighted DACs are practical only at low resolutions; higher resolutions prefer R-2R ladders or segmented architectures.
Step-by-Step Solution:
Recognize binary weighting implies powers-of-two element ratios.Note that each extra bit doubles the value range.Understand IC resistor matching challenges across decades of values.Select the option emphasizing “too many different resistor values.”
Verification / Alternative check:
Compare a binary-weighted DAC to an R-2R ladder, which uses only two resistor values and scales easily to higher resolutions with better matching and smaller area.
Why Other Options Are Wrong:
Pins (A) and op amps (B) are not the core barriers.Capacitors (C) apply to switched-capacitor DACs, not classic resistor-weighted DACs.Reference stability (E) is not a 4-bit limitation.
Common Pitfalls:
Confusing binary-weighted resistor DACs with R-2R ladders, which specifically avoid the “many values” problem.
Final Answer:
Too many different values (and tight tolerances) of resistors are required
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