Decimation Resolution Gain
ENOB_gain = 0.5 × log2(OSR)
Quick answer
This calculator solves ENOB_gain = 0.5 × log2(OSR) for ENOB Improvement. With Oversampling Ratio 1.1, the result is 0.06875. It solves in 2 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Oversampling by the oversampling ratio (OSR) and then decimation (low-pass filtering and downsampling) improves the effective number of bits by half a bit per doubling of the sample rate. This is equivalent to the decimation-enob formula but uses OSR (oversampling ratio) as the input parameter. OSR = Fs_actual / (2 × Fsignal_max), the ratio of actual sampling rate to the minimum Nyquist rate. Sigma-delta ADCs combine extreme oversampling (OSR = 64 to 1024) with noise shaping to achieve 16-24 bit resolution from a simple 1-bit quantizer.
Variables
- ENOB_gain — Improvement in effective number of bits
- OSR — Oversampling ratio
Practical Notes
OSR of 4 = +1 bit, 16 = +2 bits, 64 = +3 bits, 256 = +4 bits. With noise shaping (as in sigma-delta converters), the gain is much higher: a first-order modulator gains 1.5 bits per doubling of OSR, a second-order gains 2.5 bits. This is why sigma-delta ADCs achieve very high resolution without extremely fast sampling rates.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| ENOB_gain | ENOB Improvement | — | — |
| OSR | Oversampling Ratio | — | — |
Step by step
- 1. What you know: Oversampling Ratio 1.1
- 2. The relation: ENOB_gain = 0.5 × log2(OSR)
- 3. Substitute: OSR = 1.1
- 4. Result: ENOB Improvement = 0.06875
Worked examples
Minimum range
Given: Oversampling Ratio 0.055
Result: ENOB Improvement = -2.092
Low range
Given: Oversampling Ratio 0.55
Result: ENOB Improvement = -0.4312
Typical
Given: Oversampling Ratio 1.1
Result: ENOB Improvement = 0.06875
High range
Given: Oversampling Ratio 1.76
Result: ENOB Improvement = 0.4078
Maximum range
Given: Oversampling Ratio 17.6
Result: ENOB Improvement = 2.069
Solving for each variable
Solve for ENOB Improvement
Oversampling Ratio 0.055 → -2.092
Solve for Oversampling Ratio
ENOB Improvement 0.025 → 1.035
How ENOB Improvement changes with Oversampling Ratio
| Oversampling Ratio (input) | ENOB Improvement (result) |
|---|---|
| 0.242 | -1.023 |
| 0.605 | -0.3625 |
| 1.21 | 0.1375 |
| 1.815 | 0.43 |
| 2.42 | 0.6375 |
| 3.63 | 0.93 |
| 4.84 | 1.138 |
| 9.68 | 1.638 |
| 16.94 | 2.041 |
| 24.2 | 2.298 |
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<p><a href="https://vbatpower.com/formulas/decimation-bits/">Decimation Resolution Gain</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Decimation Resolution Gain?
Use ENOB_gain = 0.5 × log2(OSR). With Oversampling Ratio 1.1, ENOB Improvement works out to 0.06875.
What is the formula for Decimation Resolution Gain?
The formula is ENOB_gain = 0.5 × log2(OSR). Oversampling by the oversampling ratio (OSR) and then decimation (low-pass filtering and downsampling) improves the effective number of bits by half a bit per doubling of the sample rate.
How do you find Oversampling Ratio when you know the other values?
Rearrange for Oversampling Ratio: with ENOB Improvement 0.025, Oversampling Ratio is 1.035.
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