Binary-weighted DACs are often limited to about 4-bit resolution in practical IC form. What practical constraint primarily causes this limit?
-
AToo many pins are required on the IC package
-
BToo many operational amplifiers are needed
-
CToo many different values of capacitors are required
-
DToo many different values (and tight tolerances) of resistors are required
-
EThe reference voltage cannot be stabilized above 4 bits
Answer
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:
- Binary weighting doubles element value (or halves conductance) each bit.
- Linear output accuracy demands precise component ratios.
- IC process variation and mismatch grow problematic with large value spreads.
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