Oversampling SNR Improvement
SNR_eff = SNR + 10 × log10(N)
Quick answer
This calculator solves SNR_eff = SNR + 10 × log10(N) for Effective SNR. With Original SNR 44 dB, Oversampling Ratio 0.5, the result is 40.99 dB. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Oversampling an ADC by a factor of N and then averaging (decimating) improves the effective signal-to-noise ratio by spreading the quantization noise across a wider bandwidth. When the data is low-pass filtered and downsampled, only the noise within the signal bandwidth remains, effectively reducing the noise floor. Each 4x oversampling improves SNR by 6 dB, equivalent to gaining one bit of resolution. This technique is used in sigma-delta ADCs, digital audio, and precision measurement systems to achieve resolution beyond the native ADC capability.
Variables
- SNR_eff — Effective SNR after oversampling and decimation (dB)
- SNR — Original single-sample SNR (dB)
- N — Oversampling ratio
Practical Notes
This assumes the noise is white (uniformly distributed across the Nyquist bandwidth). If the noise is not white (e.g., 1/f noise), oversampling is less effective at improving SNR. For ADC applications, the input signal must contain dithering noise of at least 1 LSB amplitude for oversampling to work correctly. Without dither, quantization errors are correlated and do not average out properly.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| SNR_eff | Effective SNR | dB | dB |
| SNR | Original SNR | dB | dB |
| N | Oversampling Ratio | — | — |
Step by step
- 1. What you know: Original SNR 44 dB, Oversampling Ratio 0.5
- 2. The relation: SNR_eff = SNR + 10 × log10(N)
- 3. Substitute: SNR = 44 dB, N = 0.5
- 4. Result: Effective SNR = 40.99 dB
Worked examples
Minimum range
Given: Original SNR 0.66 dB, Oversampling Ratio 0.025
Result: Effective SNR = -15.36 dB
Low range
Given: Original SNR 6.6 dB, Oversampling Ratio 0.25
Result: Effective SNR = 0.5794 dB
Typical
Given: Original SNR 44 dB, Oversampling Ratio 0.5
Result: Effective SNR = 40.99 dB
High range
Given: Original SNR 132 dB, Oversampling Ratio 0.8
Result: Effective SNR = 131 dB
Maximum range
Given: Original SNR 1320 dB, Oversampling Ratio 8
Result: Effective SNR = 1329 dB
Solving for each variable
Solve for Effective SNR
Original SNR 0.66 dB, Oversampling Ratio 0.025 → -15.36 dB
Solve for Original SNR
Effective SNR 0.3 dB, Oversampling Ratio 0.025 → 16.32 dB
Solve for Oversampling Ratio
Effective SNR 0.3 dB, Original SNR 0.66 dB → 0.9204
How Effective SNR changes with Original SNR
| Original SNR (input) | Effective SNR (result) |
|---|---|
| 9.68 dB | 10.09 dB |
| 24.2 dB | 24.61 dB |
| 48.4 dB | 48.81 dB |
| 72.6 dB | 73.01 dB |
| 96.8 dB | 97.21 dB |
| 145.2 dB | 145.6 dB |
| 193.6 dB | 194 dB |
| 387.2 dB | 387.6 dB |
| 677.6 dB | 678 dB |
| 968 dB | 968.4 dB |
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<p><a href="https://vbatpower.com/formulas/averaging-snr/">Oversampling SNR Improvement</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Oversampling SNR Improvement?
Use SNR_eff = SNR + 10 × log10(N). With Original SNR 44 dB, Oversampling Ratio 0.5, Effective SNR works out to 40.99 dB.
What is the formula for Oversampling SNR Improvement?
The formula is SNR_eff = SNR + 10 × log10(N). Oversampling an ADC by a factor of N and then averaging (decimating) improves the effective signal-to-noise ratio by spreading the quantization noise across a wider bandwidth.
How do you find Original SNR when you know the other values?
Rearrange for Original SNR: with Effective SNR 0.3 dB, Oversampling Ratio 0.025, Original SNR is 16.32 dB.
How do you find Oversampling Ratio when you know the other values?
Rearrange for Oversampling Ratio: with Effective SNR 0.3 dB, Original SNR 0.66 dB, Oversampling Ratio is 0.9204.
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