Data Conversion
Analogue and digital data; operation and application of analogue-to-digital and digital-to-analogue converters; resolution, quantisation error, sampling and the limits they impose.
Data conversion — summary notes
Free- Aircraft sensors are overwhelmingly analogue (a synchro angle, a thermocouple millivolt, a pressure transducer output) while the computers that use them are digital, so analogue-to-digital converters (ADCs) sit at the input and digital-to-analogue converters (DACs) at the output.
- An n-bit converter resolves 2ⁿ discrete levels. Adding one bit doubles the number of levels and halves the step size — resolution improves, quantisation error falls.
- Quantisation error is the rounding error inherent in representing a continuous value by the nearest step. It is bounded by ± half a step, and it can be reduced but never eliminated.
- Sampling must be fast enough to represent the signal: the sampling rate must exceed twice the highest frequency present (the Nyquist criterion), otherwise aliasing produces a false low-frequency signal that no downstream processing can remove.
- Conversion time (aperture) matters — a converter that is too slow smears fast-changing inputs. Successive-approximation ADCs are the common aviation compromise between speed and complexity.
- ⚠ Exam trap: resolution is set by the NUMBER OF BITS and the full-scale range, not by the sampling rate. More bits = finer steps; a faster clock only means more samples per second.
- Number of levels
- levels = 2ⁿ
- Resolution / step size
- Δ = full-scale range ÷ 2ⁿ
- Maximum quantisation error
- ± Δ ÷ 2
- Nyquist criterion
- fₛₐₘₚₗₑ > 2 × f𝗆ₐₓ
An 8-bit ADC spans 0–10 V. Find the number of levels, the resolution and the worst-case quantisation error.
Levels = 2⁸ = 256. Resolution = 10 V ÷ 256 ≈ 0.039 V, i.e. about 39 mV per step. The maximum quantisation error is half a step, roughly ±19.5 mV.
The same 0–10 V range is converted by a 12-bit ADC instead. What changes?
Levels = 2¹² = 4096, so resolution = 10 V ÷ 4096 ≈ 2.4 mV — sixteen times finer than the 8-bit converter, because four extra bits multiply the level count by 2⁴ = 16. The full-scale range is unchanged.
ADC resolution & quantisation
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FreeData Conversion
Data conversion quiz
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