Embedded Systems

ADC, DAC, and Analog Interfaces

The human body runs on analog signals: heart rhythm at 1 Hz, neural spikes at 1 kHz, muscle EMG at 500 Hz. Medical devices must digitize these with enough precision to detect a 50 µV ST-segment elevation (heart attack indicator) in the presence of 1 mV of 50 Hz power line interference. An ambulatory ECG monitor does this on a coin cell battery, sampling at 500 Hz with 16-bit resolution, for 14 days. The difference between a life-saving diagnosis and a missed alert is ADC resolution, sampling rate, and signal conditioning quality. This is what analog interfaces mean in practice.

**Automotive engine control**: crank and cam position sensors use ADC input capture to measure ignition timing to within 0.1 crankshaft degrees; fuel injector timing depends on 12-bit ADC readings of manifold pressure, coolant temperature, and oxygen sensor voltage
**Industrial IoT vibration monitoring**: Emerson AMS 9420 wireless transmitter samples vibration at 25.6 kHz with 24-bit ADC to detect bearing faults by frequency analysis; detects changes in vibration spectrum 6-8 weeks before mechanical failure
**Medical pulse oximetry (SpO2)**: reads two wavelengths of LED light through a fingertip with 16-bit ADC at 1 kHz, extracting 0.5% SpO2 changes; requires < 0.1% ADC linearity to distinguish critical saturation levels (94% vs 95%)

ADC Resolution and Quantization

A temperature sensor outputs 0-3.3V proportional to -40°C to 125°C. The microcontroller needs to read this as a number. The **Analog-to-Digital Converter** (ADC) maps a continuous voltage range to discrete integer values. Resolution is the number of bits: a 12-bit ADC produces integers from 0 to 4095. The **LSB** (Least Significant Bit) voltage is V_ref / 2^n. For a 12-bit ADC with 3.3V reference: LSB = 3.3 / 4096 = 0.806 mV. This is the minimum voltage change the ADC can detect.

**Quantization error** is inherent to all ADCs: the true analog value is rounded to the nearest integer multiple of LSB. Worst-case error is ±0.5 LSB. For a temperature sensor mapping 165°C range to 4096 steps: LSB = 165°C / 4096 = 40 millidegrees. Temperature measurement error from quantization alone: ±20 millidegrees - negligible for most applications. A 10-bit ADC: ±80 millidegrees - still acceptable. An 8-bit ADC: ±320 millidegrees - may matter for precision applications.

**Oversampling** improves effective resolution: averaging 4 samples gives 1 extra bit, 16 samples gives 2 extra bits, 256 samples gives 4 extra bits. A 12-bit ADC with 256-sample averaging achieves approximately 16-bit effective resolution. STM32 HAL includes oversampling hardware that performs this automatically without CPU overhead.

A 12-bit ADC with 3.3V reference reads a value of 2048. What voltage does this represent?

Sampling Rate and the Nyquist Theorem

Resolution determines accuracy; **sampling rate** determines what frequencies can be captured. The Nyquist-Shannon theorem states: to accurately reconstruct a signal with maximum frequency f_max, the sampling rate must be at least **2 × f_max**. Sample too slowly, and high-frequency content folds back into the measurement as false low-frequency components - **aliasing**. A 50 Hz power line interference sampled at 60 Hz appears as a false 10 Hz signal in the data.

**Nyquist theorem in practice:** - Audio (telephone quality): f_max = 4 kHz → sample at 8 kHz (ITU-T G.711) - Audio (CD quality): f_max = 20 kHz → sample at 44.1 kHz - ECG (medical): f_max = 150 Hz → sample at 500+ Hz - Vibration analysis (industrial): f_max = 10 kHz → sample at 25.6 kHz - Power quality monitoring: f_max = 2.5 kHz (50th harmonic) → sample at 6.4 kHz **Anti-aliasing filter** (low-pass analog filter before the ADC) must attenuate frequencies above f_sample/2 before sampling. Without it, aliasing is inevitable regardless of ADC resolution.

**Always use DMA for continuous ADC sampling**. CPU-polled ADC has jitter: interrupt latency varies by ±1-2 µs depending on what else the CPU is doing. At 25.6 kHz, ±2 µs jitter = ±5% timing error per sample. DMA transfers happen in hardware with deterministic timing. STM32 ADC + DMA + Timer trigger achieves < 10 ns sample timing jitter.

An ECG monitor samples at 250 Hz but the patient has a pacemaker artifact at 150 Hz. The digitized ECG shows a 100 Hz oscillation that was not present in the analog signal. What is happening?

Digital-to-Analog Conversion

The **DAC** is the inverse of the ADC: it converts a digital integer to an output voltage. Applications include audio output, waveform generation for signal generators, reference voltages for sensor excitation, and analog control signals to actuators. STM32 includes 12-bit DAC(s) capable of producing waveforms up to ~1 MHz. For higher-frequency output, an external DAC with SPI interface is used (e.g., MCP4922 at 2.4 Msps, or AD5791 at 1 Msps with 20-bit resolution).

**DAC key specifications:** - **Resolution**: bits (12-bit = 4096 levels, 16-bit = 65536 levels) - **Sample rate / update rate**: maximum samples per second - **Settling time**: time for output to reach final value after update (20 ns - 10 µs) - **Output impedance**: low impedance needed to drive loads without voltage sag - **Glitch energy**: unwanted output spikes during code transitions (minimized by deglitch circuits) - **INL/DNL**: Integral/Differential Non-Linearity - actual vs ideal transfer curve

A 12-bit DAC with 3.3V reference outputs voltage for code 1024. What is the output voltage?

Signal Conditioning

Real-world sensors rarely output 0-3.3V perfectly matched to the ADC input range. A thermocouple outputs 0-80 mV. A pressure sensor outputs 4-20 mA current loop. A piezoelectric vibration sensor outputs ±10V at high impedance. **Signal conditioning** adapts these diverse signals to the ADC's requirements through amplification, level shifting, filtering, and impedance transformation. Proper conditioning is as important as ADC selection.

Sensor Type	Output	Conditioning Needed	Common Circuit
Thermocouple	0-80 mV, ±µV accuracy	50-100x amplification, cold junction comp.	MAX31855, INA128
Current loop (4-20mA)	4-20 mA current	Shunt resistor (249Ω → 1-5V)	R + RC filter
Strain gauge	0.1-10 mV bridge differential	Instrumentation amplifier, 100-1000x gain	INA326, AD8220
MEMS microphone	Differential, 1V p-p	Differential-to-single-ended conversion	Low-noise op-amp
Piezo vibration	±10V, high impedance	Voltage divider + clamp to ADC range	Resistor divider + Zener

**Input protection** is critical: ADC inputs must not exceed V_ref (typically 3.3V) or go below 0V. Even 100 mV overvoltage can permanently damage the ADC input stage. Protection: Schottky diode clamps to VCC and GND, with a series resistor (1-10 kΩ) to limit current. Industrial sensors often have transients of ±50V from motor switching - protection networks are non-negotiable in industrial designs.

Higher ADC resolution always improves measurement accuracy

ADC resolution improves only the quantization floor; noise, offset errors, gain errors, and signal conditioning quality determine actual accuracy; a 12-bit ADC with good signal conditioning often outperforms a 24-bit ADC with poor conditioning

Real ADCs have multiple error sources: quantization noise (resolution-dependent), thermal noise (analog circuit property), integral non-linearity (INL, up to ±2 LSB even in 12-bit ADCs), offset and gain errors (up to ±1% without calibration). A 12-bit ADC with 0.1% total error gives 10-bit effective resolution (ENOB). Adding bits to the converter does not help if the analog front-end has 1% noise. Industrial measurements always start with signal conditioning quality, then choose resolution.

An exponential moving average filter with alpha=0.1 is used on a noisy ADC reading. The current filtered value is 100. A new noisy sample of 200 arrives. What is the new filtered value?

Key ideas

**ADC resolution** determines quantization granularity: LSB = V_ref / 2^n; oversampling (averaging 4N samples) adds 1 effective bit; 12-bit STM32 ADC with 3.3V ref: 0.8 mV/LSB
**Nyquist theorem**: sample rate must exceed 2 × f_max; frequencies above f_sample/2 alias into false lower-frequency components; always apply an analog anti-aliasing filter before the ADC
**DMA + Timer trigger**: the correct architecture for continuous ADC sampling; timer provides precise timing (< 10 ns jitter); DMA transfers to memory without CPU; CPU processes complete buffers via callbacks
**Signal conditioning** adapts real-world sensor signals to ADC input range via amplification (INA128 for thermocouples), level shifting, anti-aliasing filtering, and input protection (Schottky clamps + series resistor)

Вопросы для размышления

An audio recorder samples at 44.1 kHz. A guitar string produces harmonics up to 8 kHz. The anti-aliasing filter cutoff is 20 kHz. What is the minimum filter order needed to sufficiently attenuate a 25 kHz overtone before it aliases to 19.1 kHz (44.1 - 25)?
A pressure sensor has a 4-20 mA current loop output. The engineer uses a 100Ω shunt resistor instead of 249Ω to create 0.4-2V output, saving headroom. What problem does this create for the ADC dynamic range - and what is the minimum usable resolution now?
An industrial temperature controller needs ±0.1°C accuracy over a -40 to 125°C range (165°C span). What is the minimum ADC resolution required just for quantization to meet this spec - and what other error sources would make this harder to achieve in practice?

Связанные уроки

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