D/A converter specifications: define linearity clearly In the context of a digital-to-analog converter (DAC), what is meant by “linearity”?

Introduction / Context:
DAC data sheets list several static accuracy terms: resolution, offset error, gain error, integral nonlinearity (INL), and differential nonlinearity (DNL). Distinguishing these terms is essential when selecting a converter for instrumentation, audio, or control applications.

Given Data / Assumptions:

• We consider static transfer behavior of an ideal versus a real DAC.
• “Linearity” here refers to the integral nonlinearity concept.

Concept / Approach:
Ideally, a DAC’s transfer function is a straight line relating code to output. Real devices deviate from this line due to resistor mismatch, current-source errors, and layout effects. Linearity quantifies the worst-case deviation of actual code points from a best-fit or endpoint straight line, independent of simple offset or gain shifts.

Step-by-Step Solution:
Define ideal relationship: V_out,ideal = slope * code + intercept.Measure actual V_out at each code.Compute error to the reference straight line; the maximum magnitude is the linearity error (often in LSBs).Therefore linearity corresponds to deviation from a straight line, not step count, accuracy comparison, or direction resolution.

Verification / Alternative check:
Data sheets specify INL in LSB; a low INL value means the transfer closely follows a straight line across codes.

Why Other Options Are Wrong:

• Reciprocal of steps: That is resolution (1/2^N of full scale).
• Comparison actual vs expected: That is overall accuracy (includes offset, gain, linearity).
• Ability to resolve forward vs reverse steps: That describes monotonicity/hysteresis behavior, not linearity.

Common Pitfalls:

• Equating precision (repeatability) with accuracy or linearity.
• Assuming high resolution guarantees good linearity—these are independent.

Final Answer:
It is the deviation between the ideal straight-line output and the actual output of the converter.