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Real Time Systems

Quantization and ADC Resolution

Converting an analog value to a finite number of levels introduces quantization error, and resolution in bits sets the floor on measurement precision.

From Continuous to Discrete Values

Sampling discretizes a signal in time; quantization discretizes it in amplitude. An analog-to-digital converter maps a continuous voltage to one of a finite set of numeric codes. The number of codes is set by the resolution: an N-bit converter has 2^N levels. Quantization is where analog precision meets digital finiteness.

Resolution and Step Size

Kronos motion — confinement time

The smallest distinguishable change is one least significant bit (LSB), equal to the full-scale range divided by 2^N. A 12-bit converter over a 10-volt range has a step of about 2.4 millivolts; a 16-bit converter over the same range resolves about 0.15 millivolts. Adding a bit halves the step and adds about 6 dB of dynamic range.

Quantization Error and Noise

Rounding a continuous value to the nearest level introduces an error of up to half an LSB. For busy signals this error behaves like added noise with a roughly uniform distribution. The theoretical best signal-to-noise ratio of an ideal converter is about 6.02N + 1.76 dB, which is the ceiling that resolution places on measurement quality before real-world imperfections are considered.

Choosing Resolution

Resolution should match the measurement need, not be maximized blindly. If sensor noise already exceeds several LSBs, more converter bits add data without information. The useful resolution is bounded by the entire chain: sensor noise, analog conditioning, reference stability, and the converter's own linearity. Specifying an ADC means matching its effective resolution to the smallest change the control loop actually needs to detect, while respecting the sample-rate demands set by Nyquist.