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
- 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
Data conversion concept map
Data Conversion
Data conversion quiz
Data Conversion, quiz
1. The figure shows a smooth analogue signal and the stepped output of a converter. The steps arise because:
The converter can only output discrete levelsThe signal is being amplifiedThe sampling rate is above Nyquist2. An analogue to digital converter has a resolution of 8 bits. The number of discrete levels it can represent is:
25681283. A 12-bit analogue to digital converter can represent how many discrete levels?
409614410244. An 8-bit converter covers an input range of 0 to 10 V. Its resolution is approximately:
39 mV1.25 V390 mV5. According to the sampling theorem, an analogue signal containing frequencies up to 4 kHz must be sampled at a rate of at least:
8 kHz4 kHz2 kHz6. An 8-bit converter can resolve how many discrete levels?
2561285127. A 10-bit ADC spans 0-5 V. Its resolution is approximately:
4.9 mV49 mV0.5 mV8. Adding one bit to an ADC of a fixed input range:
Halves the step sizeDoubles the step sizeLeaves the step size unchanged9. The maximum quantisation error of a converter is:
Half of one stepOne full stepTwo steps10. A DAC is fitted at a system's output in order to:
Turn digital values into an analogue drive signalTurn a sensor voltage into digital dataFilter the supply rail