Analog Input and Signal Processing

What the ADC does

An analog-to-digital converter (ADC) turns a voltage into an integer. An n-bit ADC divides its reference voltage into 2ⁿ steps; the size of one step is the LSB (least significant bit). Most microcontrollers use a successive-approximation ADC: a sample-and-hold capacitor captures the input, and a comparator and a digital-to-analog converter home in on the value one bit at a time, in a few microseconds. Others (sigma-delta) trade speed for resolution and noise rejection, and external ADC chips offer 16 to 24 bits for precision sensing.

LSB = V_ref ÷ 2ⁿ    counts = floor(V_in ÷ LSB)    V_in ≈ counts × LSB

Resolution, accuracy and noise

Resolution	Reference	Steps	LSB	Ideal signal-to-noise (6.02 n + 1.76)
8 bits	3.3 V	256	12.891 mV	49.9 dB
10 bits	5.0 V	1 024	4.883 mV	62.0 dB
10 bits	3.3 V	1 024	3.223 mV	62.0 dB
12 bits	3.3 V	4 096	0.806 mV	74.0 dB
16 bits	3.3 V	65 536	0.050 mV	98.1 dB

Resolution is not accuracy. Resolution is the number of steps; accuracy is how close each step is to the true value. The real errors are: offset (a reading that is the same amount off at every input), gain error (a slope that is slightly wrong), INL (integral non-linearity: a curve that bends from the straight line) and DNL (steps of unequal size, which can leave missing codes), and noise. Together they usually cost one to three bits: a “10-bit” ADC on a noisy board is good to about 8 or 9 bits. The number of bits that are actually meaningful is the effective number of bits (ENOB), found from the measured noise: ENOB = (SINAD − 1.76) ÷ 6.02.

The reference voltage

Counts are a ratio to the reference voltage, so the reading is only as good as the reference. The choices are the supply (simple, but it moves with the supply), an internal reference (typically 1.1 V, 2.048 V or 2.5 V, accurate to 1 to 2 %) or an external precision reference (0.05 % or better). Where the sensor is ratiometric (a potentiometer, a bridge or a thermistor divider powered from the same supply) use the supply as the reference: the supply error cancels. Where the sensor has its own fixed output (a temperature sensor with 10 mV/°C), use a stable reference.

The source impedance and the sample capacitor

The ADC input charges a small sample-and-hold capacitor (typically 10 to 20 pF) through the sensor’s output impedance and the internal switch. If the source impedance is too high, the capacitor does not charge to the final value in the sample time, and the reading is wrong and depends on the previous channel.

Battery divider. To read a 4.2 V battery with a 3.3 V ADC, a divider of R1 = R2 = 100 kΩ halves the voltage to 2.10 V but draws 21 µA continuously from the battery (enough to flatten a small cell in a few months) and presents a 50 kΩ source to the ADC. Add a 100 nF capacitor at the ADC pin, or switch the divider on only while measuring.

Sampling rate and aliasing

A signal can be reconstructed only if you sample at more than twice its highest frequency (the Nyquist rate). Frequencies above half the sampling rate are not lost: they fold back (alias) into the band as false lower frequencies. The only cure is to remove them before the ADC with an analog anti-aliasing filter (an RC low-pass), because once sampled the aliases cannot be told from real signals.

• RC anti-alias filter: f_c = 1 ÷ (2π R C): for a 100 Hz cut-off with 1.6 kΩ and 1 µF; set it below half the sample rate and above the signal you want.
• Sample at a steady rate from a timer interrupt (see Timers, PWM and Timing), not a loop whose speed varies.
• Take readings in a quiet moment: not while a motor, relay or radio switches.

Averaging, oversampling and filtering

Filter	What it does	Cost	Best for
Moving average (N samples)	Mean of the last N readings; noise falls as 1 ÷ √N	N values of memory; lag of about N ÷ 2 samples	Steady signals with random noise
Exponential (first-order IIR)	y += α (x − y)	One variable; a few instructions	The standard choice; tune α to the speed you need
Median (3 or 5 samples)	Takes the middle value	A small sort	Removes spikes and outliers without blurring edges
Oversampling and decimation	Adds resolution: 4k samples give k extra bits	Time and the right kind of noise	Squeezing 12 bits out of a 10-bit ADC
Median then average	Reject the spikes, then average the rest	Slightly more code	Noisy industrial signals

// Exponential filter in integers: y keeps 4 extra fractional bits
static int32_t y16 = 0;                       // filtered value, scaled by 16
int16_t filter(int16_t x) {                   // x is a raw ADC count
  y16 += ((int32_t)x * 16 - y16) >> 3;        // alpha = 1/8
  return (int16_t)((y16 + 8) >> 4);           // round and drop the fraction
}

Calibration and scaling

The raw count is not yet a measurement. Convert it to engineering units with a straight line, ideally calibrated against two known points to remove the offset and gain errors of the ADC, the reference and the sensor together.

Integer scaling without floating point

Multiply first, then divide, in a wide enough type: millivolts = counts × 3 300 ÷ 4 095 needs counts × 3 300 up to 13 513 500, which overflows 16 bits but fits a 32-bit integer, so declare the product uint32_t (on an 8-bit chip, write 3300UL). Round by adding half the divisor first: (counts * 3300UL + 2047) / 4095.

Worked sensor examples

Getting a quiet ADC reading

• Separate analog from digital: keep analog traces short and away from clocks, PWM and switching supplies; use a ground plane; join analog and digital grounds at one point.
• Decouple the analog supply and reference with 100 nF and 10 µF capacitors close to the chip, and a ferrite bead or small resistor from the digital supply on chips with a separate AVCC pin.
• Use ADC noise reduction modes where available: the CPU sleeps during the conversion, removing its digital noise.
• Avoid changing digital outputs near an ADC pin during a conversion.
• Shield and twist the wires of sensors that are more than a few centimeters away (see Sensor Outputs and Wiring) and filter at the input.
• Use a differential input or an external ADC for small signals (bridges, thermocouples): an instrumentation amplifier or a 24-bit sigma-delta chip is the right tool.

Related

• Embedded Systems: the overview of this guide.
• Timers, PWM and Timing: steady sampling from a timer.
• Memory, Number Formats and Reliability: fixed-point math and storing calibration.
• Analog Circuits and Sensing and Sensors and Field Devices: dividers, filters, op-amps and the sensors themselves.
• Data Logging: sampling, storage and timestamps.

FAQ

Why is my 10-bit ADC not accurate to 10 bits?

Resolution is the number of steps; accuracy is how close each step is to the true value. Reference error, offset, gain error, non-linearity and noise typically cost the last one to three bits. Averaging helps noise but not a drifting reference.

Should I average or use a median filter?

Averaging reduces random noise; a median removes isolated spikes. For a signal with both, take a median of three or five samples, then average the results.

Can I get more bits by oversampling?

Yes, if there is enough noise to dither the readings (at least about 1 LSB): 4 times the samples gives 1 extra bit. It does not help if the ADC is quiet, because the readings are then the same code each time.

Why do my readings change when I switch to another channel?

The sample capacitor has not settled from the previous channel because the source impedance is too high. Lower it with a buffer or a capacitor, discard the first reading after a channel change, or lengthen the sample time.

References

• Microcontroller datasheets and application notes on ADC accuracy, sample time and oversampling (for example Microchip AN-1152 / AVR121 “Enhancing ADC resolution by oversampling”).
• Horowitz, P. and Hill, W., The Art of Electronics, Cambridge University Press (sampling, aliasing and filters).
• Texas Instruments and Analog Devices ADC application notes (ENOB, INL and DNL).

Last reviewed: October 2026. Values use common parts and typical specifications: check your own datasheet.