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ADC Bit Depth to Dynamic Range

Calculate the theoretical SNR and dynamic range of an audio ADC from its bit depth, and the improvement from oversampling.

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Formula

SNR = 6.02N + 1.76 dB, G_OS = 10·log₁₀(OSR)

N— Bit depth (bits)
OSR— Oversampling ratio (×)

How It Works

An ideal N-bit analog-to-digital converter (ADC) has a theoretical maximum SNR determined solely by quantisation noise: SNR = 6.02N + 1.76 dB. This formula arises because each additional bit halves the quantisation error and adds approximately 6.02 dB of SNR. The 1.76 dB offset accounts for the statistical distribution of quantisation error assumed to be uniformly distributed. For a 16-bit ADC the theoretical SNR is ~98 dB; for 24-bit it is ~146 dB. Oversampling — sampling at a multiple (OSR) of the Nyquist rate — spreads quantisation noise across a wider bandwidth, allowing a digital low-pass filter to remove noise above the audio band. The SNR improvement from oversampling is 10·log₁₀(OSR) dB, or approximately 3 dB per doubling of sample rate. Sigma-delta ADCs combine extreme oversampling (64–512×) with noise shaping to push quantisation noise to higher frequencies, achieving 24-bit resolution at audio frequencies from 1-bit or few-bit internal converters.

Worked Example

16-bit ADC, 1× oversampling (standard 44.1 kHz): SNR_ideal = 6.02 × 16 + 1.76 = 96.32 + 1.76 = 98.1 dB Dynamic range = 98.1 dB Oversampling gain = 10·log₁₀(1) = 0 dB 16-bit ADC with 4× oversampling (176.4 kHz): Oversampling gain = 10·log₁₀(4) = 6.0 dB Total SNR = 98.1 + 6.0 = 104.1 dB — equivalent to ~17 bits 24-bit ADC, 1× oversampling: SNR_ideal = 6.02 × 24 + 1.76 = 144.48 + 1.76 = 146.2 dB (Theoretical only — real 24-bit ADCs achieve 110–130 dB due to thermal noise and circuit imperfections) 24-bit ADC with 64× oversampling: Oversampling gain = 10·log₁₀(64) = 18.1 dB Total = 146.2 + 18.1 = 164.3 dB (theoretical limit of 24-bit + 64× OS)

Practical Tips

  • ✓For recording at 24-bit / 96 kHz, the effective dynamic range advantage over 16-bit comes not from the 48 dB theoretical improvement (which exceeds any analog chain's noise floor) but from the headroom it provides during gain-staging: record 10–20 dB below 0 dBFS to avoid digital clips without risking running out of dynamic range.
  • ✓ADC ENOB (effective number of bits) is the most useful single-number summary: ENOB = (SNR_measured − 1.76) / 6.02. An audio interface advertising '24-bit' with measured SNR = 118 dB has ENOB = (118 − 1.76) / 6.02 ≈ 19.3 bits — excellent but not 24.
  • ✓When comparing audio interfaces, compare A-weighted SNR specifications (often 3–6 dB better than unweighted) with the same input termination. Unweighted SNR is the more conservative and comparable figure.

Common Mistakes

  • ✗Expecting real ADC SNR to equal theoretical — a nominally 24-bit ADC rarely achieves 146 dB SNR in practice. Thermal noise, clock jitter, reference noise, and power supply noise limit most 24-bit audio ADCs to 110–130 dB (18–22 ENOB). Always check the datasheet for measured SNR/ENOB.
  • ✗Confusing oversampling with noise shaping — simple oversampling gains 3 dB per octave of OSR. Noise shaping (used in delta-sigma converters) provides much greater improvement by actively suppressing noise in the audio band at the cost of higher noise at supersonic frequencies.
  • ✗Using bit depth as the sole quality metric — jitter (timing uncertainty on the sample clock) converts to phase noise and degrades SNR at high frequencies. A 24-bit ADC with poor clock jitter can perform worse than a well-clocked 20-bit ADC in practice.

Frequently Asked Questions

Only if the ADC hardware genuinely resolves 32 bits, which is not achievable today with any analog circuit due to thermal noise (Johnson noise) limits. '32-bit float' recording is a digital processing format that provides 24-bit resolution with 8 bits of exponent for automatic gain control, preventing digital clipping. It does not add analog dynamic range beyond the ADC's measured SNR.
Sample rate affects bandwidth (Nyquist limit) and oversampling headroom, not the fundamental SNR within the audio band directly. Higher sample rates allow oversampling and noise shaping to be more effective, and reduce aliasing from analog-to-digital conversion above 20 kHz. For a given ADC bit depth, the within-band SNR improvement from doubling sample rate is approximately 3 dB.
100 dB A-weighted SNR is the minimum for professional-quality recording. 110+ dB is excellent (Focusrite Scarlett, Universal Audio Apollo range). 120+ dB is exceptional (Prism, Merging Technologies, RME). For typical home recording with ambient noise floors of 30–40 dBA, 100 dB SNR means the interface noise is 60–70 dB below the room noise — essentially inaudible.

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