Weighted Resistor DAC Comparison (Optional)

Key Concepts

• Binary Weighting: The fundamental concept behind both DAC types, where each bit contributes a value proportional to $2^i$.

• Resistor Range (Weighted): The need for vastly different resistor values ($R$ to $R/2^{N-1}$) is the main drawback.

• Resistor Range (R-2R): Only needs R and 2R, simplifying manufacturing and improving matching.

• Accuracy vs. Tolerance: DAC accuracy relies heavily on precise ratios of resistors, not just individual absolute values.

• Scalability: R-2R is highly scalable to more bits; Weighted Resistor is not.

• Linearity & Monotonicity: Improved in R-2R due to better resistor matching.

• IC Fabrication: R-2R is far more practical for integrated circuits.

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• Examples

• Imagine a 10-bit DAC:

• Weighted Resistor: Would require resistors from $R$ (e.g., 10kΩ) down to $R/512$ (e.g., \~19.5Ω). Trying to get these 10 resistors (and their ratios) precise to 0.1% is nearly impossible.

• R-2R Ladder: Would only need 10kΩ and 20kΩ resistors. Manufacturing many of these two values, with a highly precise 1:2 ratio, is much more feasible and leads to higher accuracy.

• Building with Discrete Components: If you tried to build a high-resolution Weighted Resistor DAC, you'd find it extremely hard to even buy discrete resistors with the necessary precise values and tolerances. For R-2R, you could buy common 1% or 0.1% R and 2R resistors and get much better results.

• Audio Applications: In high-fidelity audio, where resolution of 16-bit, 24-bit, or even 32-bit is common, R-2R or more advanced architectures (like Sigma-Delta) are used. A Weighted Resistor DAC would be completely unsuitable due to its inherent linearity limitations at such resolutions.

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• Flashcards

• Term: Weighted Resistor DAC Limitation

• Definition: Requires a wide range of highly precise, binary-weighted resistor values, making high-resolution implementation impractical.

• Term: R-2R Ladder DAC Advantage

• Definition: Uses only two resistor values (R and 2R), simplifying manufacturing and allowing for superior resistor matching and linearity in high-resolution DACs.

• Term: Resistor Ratio Matching

• Definition: The ability to maintain precise proportionality between resistor values, which is critical for DAC linearity; much easier with R-2R.

• Term: DAC Linearity

• Definition: How accurately the analog output follows the ideal linear relationship with the digital input; directly impacted by resistor precision.

• Term: Monotonicity

• Definition: A DAC characteristic where output voltage never decreases as digital input increases; easier to achieve with R-2R.

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• Memory Aids

• "Weighted is Widely Woeful": The Weighted resistor DAC requires Widely different resistor values, leading to Woeful accuracy at high resolutions.

• "R-2R Rules for Resolution": The R-2R ladder Rules the DAC world for high Resolution because it only needs R and 2R.

• "Ratio is Royalty": In R-2R, it's the precise ratio between R and 2R that matters most, which is easy to maintain, making it the "royalty" of DACs.

• "W for Wide, R for Right": Weighted DAC needs a Wide range of resistors. R-2R DAC uses only R and 2R, which is the Right way for precision.

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Examples & Applications

Memory Aids

Interactive tools to help you remember key concepts

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