ADC interfacing and sensor reading

Why it matters

Temperature, pressure, position, load and flow sensors mostly give an analog voltage or current. The ADC is where the physical world becomes a number, and its resolution, reference, sampling rate and the signal conditioning in front of it decide whether a controller sees 30.3 °C or noise. Converting raw counts back to engineering units correctly is a daily task for every mechatronics engineer.

Key ideas

What an ADC does. It samples an input voltage at discrete instants and quantises each sample into one of 2ⁿ integer codes, where n is the resolution in bits. Code 0 corresponds to 0 V (or V_ref−) and the full-scale code to V_ref.

Resolution and LSB. The step size (1 LSB) is V_ref/2ⁿ. A 10-bit ADC with 5 V reference resolves 4.88 mV. Quantisation error is at most ±½ LSB with ideal rounding (0 to −1 LSB if the converter truncates).

Code conventions. Microcontroller datasheets (e.g. AVR) define code = V_in × 2ⁿ / V_ref, truncated, with maximum code 2ⁿ − 1. Many textbooks instead use (V_in / V_ref) × (2ⁿ − 1). The two differ by less than 1 LSB; use the one your datasheet or question states.

Resolution is not accuracy. Offset error, gain error, non-linearity, reference tolerance and noise can make a 12-bit reading accurate to only 9–10 bits. A stable, low-noise reference matters as much as the bit count.

ADC types.

• SAR (successive approximation): a binary search using an internal DAC and comparator — one bit per clock, n clocks plus sampling. The standard on-chip MCU ADC (8–12 bits, up to a few MSPS).
• Flash: 2ⁿ − 1 comparators in parallel — fastest, but large and power-hungry, so low resolution.
• Sigma-delta: oversampling with noise shaping — 16–24 bits, slow; used for load cells and thermocouples.
• Dual-slope (integrating): very good noise rejection, slow; digital multimeters.

Sampling. The Nyquist criterion says the sampling rate must exceed twice the highest signal frequency (f_s > 2f_max), otherwise higher frequencies alias into false low-frequency readings. An analog low-pass (anti-aliasing) RC filter before the ADC removes noise above f_s/2. Sampling faster than needed does not improve resolution by itself, though averaging several samples reduces random noise.

On-chip ADC practice (ATmega example). 10-bit SAR, multiplexed input channels, reference selectable (AVCC, internal 1.1 V, external AREF). The ADC clock must be 50–200 kHz for full resolution, so a 16 MHz CPU uses prescaler 128 (125 kHz). A normal conversion takes 13 ADC clocks. Results are read from ADCL then ADCH.

Signal conditioning brings the sensor signal to the ADC range: amplification (op-amp, instrumentation amplifier for bridges and thermocouples), offset shifting, filtering, isolation and protection (series resistor, clamp diodes). Match the sensor's full range to V_ref to use all the codes.

Industrial signals. PLC and process instruments use 0–10 V and 4–20 mA. A 4–20 mA loop is converted to voltage with a precision shunt (250 Ω gives 1–5 V). The live zero at 4 mA lets the system detect a broken wire (0 mA) and powers two-wire transmitters.

Formulas

LSB = V_ref / 2ⁿ

• LSB = smallest voltage step (V); V_ref = reference voltage (V); n = number of bits.

D = int(V_in × 2ⁿ / V_ref) and V_in ≈ D × V_ref / 2ⁿ

• D = output code (dimensionless), 0 ≤ D ≤ 2ⁿ − 1 (datasheet convention).

Quantisation error = ±½ LSB (rounding)

f_s > 2 f_max

• f_s = sampling rate (samples/s); f_max = highest frequency in the input (Hz).

t_conv = N_clk / f_ADC

• Conversion time (s); N_clk = ADC clocks per conversion (13 for a normal ATmega conversion); f_ADC = ADC clock (Hz).

SNR_ideal = 6.02 n + 1.76 (dB)

• Ideal signal-to-quantisation-noise ratio for a full-scale sine wave.

x = x_min + (I − 4 mA) / (16 mA) × (x_max − x_min)

• Engineering value from a 4–20 mA signal I; x_min, x_max = transmitter range.

V = I × R_shunt

Worked examples

Example 1 (standard). An LM35 temperature sensor (10 mV/°C, 0 V at 0 °C) feeds a 10-bit ADC with V_ref = 5 V. The ADC reads 62. Find the temperature and the temperature resolution.

1. V_in = D × V_ref / 2ⁿ = 62 × 5 / 1024 = 0.3027 V.
2. T = V_in / (10 mV/°C) = 302.7 mV / 10 mV/°C = 30.3 °C.
3. LSB = 5 / 1024 = 4.883 mV → 0.49 °C per count.

Answer: T ≈ 30.3 °C, resolution ≈ 0.49 °C/count. (Using the internal 1.1 V reference would improve this to about 0.11 °C/count for temperatures up to 110 °C.)

Example 2 (GATE level). A 0–10 bar pressure transmitter gives 4–20 mA, read through a 250 Ω shunt by a 12-bit ADC with V_ref = 5 V. (a) The ADC reads 2458; find the pressure. (b) Find the pressure resolution. (c) The ADC's 125 kHz clock needs 13 clocks per conversion; what is the highest signal frequency that can be sampled without aliasing?

1. V = 2458 × 5 / 4096 = 3.0005 V.
2. I = V / R = 3.0005 / 250 = 12.002 mA.
3. P = 0 + (12.002 − 4) / 16 × 10 = 5.00 bar.
4. LSB = 5 / 4096 = 1.221 mV → current step = 1.221 mV / 250 Ω = 4.883 µA → pressure step = 4.883 µA × (10 bar / 16 mA) = 0.00305 bar.
5. t_conv = 13 / 125 × 10³ = 104 µs → f_s = 9615 samples/s → f_max < f_s / 2 = 4.8 kHz.

Answers: P ≈ 5.00 bar; resolution ≈ 0.003 bar per count; signals must stay below about 4.8 kHz. Note that only codes from about 819 (1 V) up to full scale are used, roughly 80 % of the range.

Common mistakes

• Mixing the 2ⁿ and 2ⁿ − 1 conventions mid-problem — pick one and state it.
• Treating resolution as accuracy; the reference tolerance alone can exceed 1 LSB.
• Leaving inputs above V_ref or below 0 V unprotected — readings clip and the pin can be damaged.
• Forgetting the 4 mA offset in 4–20 mA scaling.
• Sampling below 2f_max, or omitting the anti-aliasing filter, so noise aliases into the reading.
• Reading ADCH before ADCL on AVR (the result locks in the wrong order).
• Using a noisy supply (AVCC without filtering) as the reference.

For GATE ME

Expect numericals on resolution (LSB size), output code for a given input, input voltage for a given code, quantisation error, SNR from bit count, Nyquist sampling rate and sensor scaling (LM35, 4–20 mA, bridge outputs), plus MCQs on ADC types and their speed–resolution trade-offs. Practise keeping mV and V straight and stating which code convention you use.

Quick check

1. What is 1 LSB of an 8-bit ADC with V_ref = 3.3 V?
2. What code does a 10-bit ADC (V_ref = 5 V) give for 2 V input (datasheet convention, truncated)?
3. Which ADC type is fastest?
4. A 4–20 mA, 0–100 °C transmitter reads 8 mA. What is the temperature?
5. What is the ideal SNR of a 12-bit ADC?

Answers: 1. 12.9 mV 2. 409 3. Flash 4. 25 °C 5. ≈ 74 dB