📖 The lesson
Analogue data and digital data
Analogue data varies continuously and can take any value within its range: the voltage from a pressure transducer, the AC output of a tachometer generator, a thermocouple's millivolts, the position of a potentiometer, a synchro's three wires or an LVDT. Digital data takes only discrete values, coded as binary words — a pulse train on a data bus, or a discrete that is simply 28 V or open.
- Digital data has big advantages: it can be stored, processed by computers and multiplexed onto one data bus; it is immune to noise as long as a 1 can still be told from a 0; and its accuracy does not degrade with cable length, temperature or the number of receivers. Accuracy is set by the number of bits, not by the quality of the wiring.
- But the physical world is analogue. Sensors measure analogue quantities, and many indicators, servo motors and audio outputs need analogue drive. Converters join the two worlds.
An analogue-to-digital converter (ADC) turns an analogue voltage or current into a binary number. A digital-to-analogue converter (DAC) turns a binary number back into a voltage or current proportional to it.
How an ADC works
- Sampling: the input is measured at regular intervals. A sample-and-hold circuit captures the input and holds it steady while the conversion takes place.
- Sampling rate and Nyquist: to represent a signal faithfully, it must be sampled at more than twice its highest frequency (the Nyquist criterion). Sampling too slowly causes aliasing — the samples describe a false, lower frequency. An anti-aliasing low-pass filter before the ADC removes frequencies the converter cannot follow.
- Quantisation: the sample is rounded to the nearest of the converter's 2n levels, where n is the number of bits.
- Resolution: the smallest change the converter can show — one step, or 1 LSB = full-scale range ÷ 2n. An 8-bit converter resolves 1 part in 256 (about 0.4%); on a 10 V range that is about 39 mV per step. A 12-bit converter resolves 1 part in 4 096 (about 2.4 mV on 10 V).
- Quantisation error: the rounding error, at most ±½ LSB. It is reduced only by using more bits.
- Encoding: the level is output as a binary word — in parallel (one wire per bit) or serially — in straight binary, two's complement for bipolar inputs, or BCD for displays.
- Conversion time: how long one conversion takes. It limits the maximum sampling rate.
Types of ADC
Every ADC compares the input with a known reference using one or more comparators — circuits whose output switches to 1 when one input is higher than the other. The types differ in how many comparisons they make and how.
- Flash (parallel): 2n − 1 comparators, each with its own reference from a resistor divider, all working at once. The fastest type, but the comparator count doubles with every bit (255 for 8 bits), so it is costly, power-hungry and limited to low resolution. Used for very fast signals such as radar and video.
- Successive approximation (SAR): a binary search, one bit per clock pulse, MSB first, using an internal DAC and one comparator. Conversion takes n clock cycles regardless of the input. The most common general-purpose ADC.
- Ramp, counter or staircase: a counter drives a DAC upwards from zero until its output passes Vin, then the count is read. Simple and cheap, but slow, and the conversion time varies with the input (up to 2n clocks). A tracking version counts up or down to follow the input.
- Dual-slope (integrating): a capacitor is charged by Vin for a fixed time, then discharged by a reference while a counter measures how long it takes. The count is proportional to the average input. Slow but very accurate, and it rejects noise and mains hum, so it is used in digital multimeters.
- Sigma-delta: a very fast 1-bit converter plus digital filtering, giving high resolution at moderate speed — used for audio and precision sensors.
Digital-to-analogue converters
A DAC adds together currents or voltages weighted by each bit, so that the output is proportional to the binary input: Vout = Vref × (code ÷ 2n).
- Binary-weighted resistor DAC: each bit switches a resistor into an op-amp summing amplifier, with values R, 2R, 4R, 8R… so each bit contributes half as much as the one before. Simple, but for many bits it needs a very wide range of very precise resistors, which is hard to make — so it is used only for a few bits.
- R-2R ladder DAC: uses only two resistor values, R and 2R, repeated for every bit. It is easy to make accurately on a chip and is the most common DAC.
- The DAC output is a staircase, one step per code. A low-pass (smoothing) filter after it removes the steps when a smooth signal such as audio is needed.
- Resolution: one step = Vref ÷ 2n. Settling time: how long the output takes to settle within ±½ LSB of its new value after the code changes. A DAC is monotonic if its output never falls when the input code rises.
- Errors include offset (output not zero for code 0), gain (wrong full-scale value), non-linearity, and short glitches when many bits change at once (for example 0111 → 1000).
Inputs, outputs and limitations
| ADC | DAC | |
|---|---|---|
| Input | Analogue voltage or current within a set range — unipolar (for example 0–10 V) or bipolar (±10 V); a reference voltage; a clock and a start-conversion signal | Binary word (parallel or serial), a reference voltage, a load/latch signal |
| Output | Binary word, plus an end-of-conversion (data-ready) signal | Analogue voltage or current proportional to the code |
| Limitations | Resolution and quantisation error; conversion time and maximum sampling rate; aliasing; input over-range (the output saturates at all 1s); offset, gain and linearity errors; temperature drift; noise | Resolution; settling time; glitches; offset, gain and linearity errors; monotonicity; reference accuracy and drift |
The trade-off to remember
More bits give finer resolution but cost conversion time, price and power. Faster converters (flash) have fewer bits; the most accurate (dual-slope) are the slowest.
Aircraft applications
- Air data computers: pressure transducers produce analogue signals that are digitised, corrected and sent as altitude, airspeed and Mach on ARINC 429 or other buses.
- FADEC / EEC: thermocouple, pressure, speed and position inputs are digitised for the engine control computer; its outputs drive torque motors through DACs and drivers.
- Flight data acquisition: the (D)FDAU converts analogue parameters, synchros and discretes into digital data for the flight data recorder and quick-access recorder.
- Synchro-to-digital and resolver-to-digital converters read older synchro transmitters into digital systems; digital-to-synchro converters drive legacy electromechanical indicators from digital data.
- Audio and video: the cockpit voice recorder, digital audio management systems and cabin entertainment digitise sound and pictures.
- Fuel quantity, hydraulic pressure and many other sensors feed data concentrators (for example Airbus SDACs) that digitise them for the displays.
Maintenance view
Converters live inside LRUs, so they are not adjusted on the aircraft. But their analogue inputs are sensitive: a poor sensor ground, a damaged shield or a high-resistance connector pin can show up as an offset or noisy reading in an otherwise healthy digital system.