7.08 Digital-to-Analog Converters (DAC Topologies & Proofs)
Related Concepts: 7.03 Digital-to-Analog Converters (DAC Topologies & Analysis) | 7.04 Analog-to-Digital Converters (ADC Topologies & Applications) | 7.09 Analog-to-Digital Converters (ADC Topologies & SAR Search)
7.08 Digital-to-Analog Converters (DAC Topologies & Proofs)
Overview: Nodal analysis proofs for Weighted-Resistor and R-2R ladder DACs, performance metrics (INL, DNL, settling time), and 2-decade BCD DAC design.
1. Weighted-Resistor vs R-2R Ladder DAC Matrix
| Metric | Weighted-Resistor DAC | R-2R Ladder DAC |
|---|---|---|
| Resistor Values | N different values (R, 2R, 4R, …, 2^{N-1}R). | Strictly two values (R and 2R). |
| Resistor Ratio Spread | 2^{N-1}:1 (High spread, e.g. 2048:1 for 12-bit). | 2:1 ratio (Low spread, easy IC tracking). |
| Monolithic IC Suitability | Poor due to resistance spread. | Excellent. |
2. R-2R Ladder Nodal Proof [PYQ: 2015, 2017, 2020, 2023, 2025]
Output voltage formula for N-bit input B_{N-1} … B_0:
V_o = - V_{ref} (R_f / R) * [ (B_{N-1} / 2^1) + (B_{N-2} / 2^2) + … + (B_0 / 2^N) ]