Quantization Noise Calculator Formula

Understand the math behind the quantization noise calculator. Each variable explained with a worked example.

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Formulas Used

Ideal SNR

snr_ideal = 6.02 * num_bits + 1.76

LSB Voltage (1 step)

lsb_voltage = lsb_v

LSB Voltage

lsb_mv = lsb_v * 1000

Quantization Noise RMS

quant_noise_rms = lsb_v / sqrt(12)

Quantization Levels

num_levels = pow(2, num_bits)

Variables

VariableDescriptionDefault
num_bitsADC Resolution (bits)12
full_scale_vFull Scale Voltage(V)3.3
lsb_vDerived value= full_scale_v / pow(2, num_bits)calculated

How It Works

Quantization Noise in ADCs

When an analog signal is digitized, the rounding to discrete levels introduces quantization noise uniformly distributed over one LSB.

Formulas

Ideal SNR = 6.02 x N + 1.76 dB (for a full-scale sine wave)

LSB = V_full_scale / 2^N

Quantization Noise RMS = LSB / sqrt(12)

Each additional bit of resolution adds approximately 6 dB of SNR. Real ADCs achieve slightly less due to thermal noise, linearity errors, and timing jitter.

Worked Example

A 12-bit ADC with 3.3 V full-scale range.

num_bits = 12full_scale_v = 3.3
  1. 01Ideal SNR: 6.02 x 12 + 1.76 = 74.0 dB
  2. 02LSB: 3.3 / 4096 = 0.000806 V = 0.806 mV
  3. 03Quantization noise RMS: 0.806 / sqrt(12) = 0.233 mV
  4. 04Quantization levels: 2^12 = 4096

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