Describe a binary-weighted DAC and why matching and offset are critical.

• A. It uses weighted binary currents or voltages to sum to an analog output; imprecise matching causes large gain error.
• B. It relies on a resistor ladder with equal values to approximate weights.
• C. It uses weighted binary currents or voltages to sum to an analog output; precise matching minimizes gain error and monotonicity issues.
• D. It converts digital bits by sampling a capacitor array.

Answer: (C)

A binary-weighted DAC relies on each bit steering a current or voltage that is scaled by a power-of-two factor, and all these weighted contributions are summed at a node to produce the analog output. The key point is that the output should be a precise, monotonic representation of the digital code, so every bit must contribute its exact intended amount.

Matching is critical because any mismatch between the bit weights—whether in current sources, resistors, or reference paths—shifts the overall transfer function. That causes gain error: the slope of the output versus code deviates from the ideal, making the steps not exactly the right size. If the mismatches are enough, you can even lose monotonicity, where increasing the code doesn’t guarantee a larger output or where some codes skip stepping altogether. Offset is the fixed bias that shifts the entire output up or down; even a small offset is amplified as more bits are used, distorting the relationship between code and output and reducing accuracy, especially at the lower codes.

That combination—precise matching and control of offset—keeps the DAC’s response linear and monotone, so the digital input reliably produces the expected analog value with correct step sizes.

The other choices either describe a different structure (not the direct binary-weighted approach), or miss the importance of monotonicity and offset in explaining why matching is essential.