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ADC Resolution Calculator

Find an analogue-to-digital converter's LSB size, levels, quantisation error and ideal SNR, the bits needed for a required resolution, or the effective bits from SINAD.

Formula

LSB=range2 n\mathrm{LSB} = \dfrac{\text{range}}{2^{\,n}}
quantisation error=±12 LSB\text{quantisation error} = \pm\dfrac{1}{2}\,\mathrm{LSB}
SNR=6.02 n+1.76 dB\mathrm{SNR} = 6.02\,n + 1.76\ \mathrm{dB}
ENOB=SINAD−1.766.02\mathrm{ENOB} = \dfrac{\mathrm{SINAD} - 1.76}{6.02}
bits=⌈log⁡2rangeresolution⌉\text{bits} = \left\lceil \log_2\dfrac{\text{range}}{\text{resolution}} \right\rceil
nn
number of bits
LSB\mathrm{LSB}
least significant bit: the smallest step the converter resolves
SINAD\mathrm{SINAD}
measured signal-to-noise-and-distortion ratio, in dB
ENOB\mathrm{ENOB}
effective number of bits

How it works

An n-bit converter divides its input range into 2ⁿ steps, and the size of one step, the LSB, is the range divided by that number. Rounding to the nearest step leaves a quantisation error of up to half an LSB, which for a full-scale sine wave gives an ideal signal-to-noise ratio of 6.02 n + 1.76 dB.

Real converters do worse, because of noise, distortion and offset and gain errors. The effective number of bits inverts the same relationship for a measured SINAD and says how many bits an ideal converter would need to have the measured performance. The resolution required is best chosen from the noise of the signal, with a margin, rather than from the datasheet bit count.

Worked example

A 12-bit converter with a 3.3 V range.

  1. Levels = 2¹² = 4,096.
  2. LSB = 3.3 V / 4,096 = 0.8057 mV.
  3. Ideal SNR = 6.02 × 12 + 1.76 = 74.0 dB.

One LSB is 0.806 mV, the quantisation error ±0.40 mV and the ideal SNR 74 dB.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • An ideal converter with a full-scale sine-wave input, for the SNR.
  • A fixed input range.

Common mistakes

  • Treating the bit count as the accuracy. Offset, gain and noise set the real accuracy.
  • Choosing the converter by bits when the sensor's noise is larger than one LSB.
  • Forgetting that the effective number of bits falls with input frequency.

Related tools

Sampling Frequency CalculatorSampling rate, record size and frequency resolutionOpen calculatorSignal-to-Noise Ratio CalculatorSNR in dB from amplitudes, powers or mean and standard deviationOpen calculatorDecibel CalculatorRatios to dB, dB to ratios, and dBm to powerOpen calculator

Related equipment

Service documentation, failure modes and parts for the instruments this calculation is used with.