Signal-to-Noise Ratio (SNR)
Signal-to-noise ratio formula, related measures (SINAD, ENOB), and Shannon capacity.
Reference
Formulas
- SNR (dB)
- = 10 · log₁₀(P_signal / P_noise) or 20 · log₁₀(V_signal / V_noise)
- SINAD
- Signal / (noise + distortion) — includes harmonics
- ENOB (ADC)
- = (SINAD − 1.76) / 6.02 — effective bits of resolution
- Ideal ADC SNR
- ≈ 6.02 · N + 1.76 dB (N = bits)
- Shannon capacity
- C = B · log₂(1 + SNR_linear) — bits/s for bandwidth B
Quick conversions
| SNR (dB) | Voltage ratio | Power ratio |
|---|---|---|
| 0 dB | 1:1 | 1:1 |
| 3 dB | 1.41:1 | 2:1 |
| 6 dB | 2:1 | 4:1 |
| 10 dB | 3.16:1 | 10:1 |
| 20 dB | 10:1 | 100:1 |
| 40 dB | 100:1 | 10 000:1 |
| 60 dB | 1 000:1 | 10⁶:1 |
| 96 dB | 63 000:1 | CD quality (16-bit) |
| 144 dB | 16 million:1 | 24-bit audio |
Typical SNRs
| System | SNR |
|---|---|
| Vinyl LP | ~65 dB |
| CD (16-bit) | 96 dB |
| 24-bit audio | 144 dB (theoretical) |
| Good CMOS camera | 40–50 dB |
| 4G LTE (typical) | 10–20 dB |
| WiFi (typical) | 25–40 dB |
| Analog FM radio | 50–60 dB |
Notes
- Higher SNR → more bits of data in the same bandwidth (Shannon).
- In photography, "SNR" often refers to per-pixel or per-shot; noise is dominated by shot noise at bright levels (√N).
Last updated: