Decimation ENOB Gain
ENOB_gain = log2(N) / 2
Quick answer
This calculator solves ENOB_gain = log2(N) / 2 for ENOB Improvement (bits). 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 followed by decimation (averaging and downsampling) increases the effective number of bits of an ADC. Each quadrupling of the sample rate gains one additional bit of resolution. This technique spreads the quantization noise across a wider bandwidth, then the decimation filter removes the out-of-band noise, leaving a cleaner signal at the original Nyquist rate. Sigma-delta ADCs exploit this principle with very high oversampling ratios (64x to 256x) combined with noise shaping to achieve 24-bit resolution from a simple 1-bit comparator.
Variables
- ENOB_gain — Additional effective bits of resolution
- N — Oversampling ratio (sampling rate / Nyquist rate)
Practical Notes
To gain 1 bit, oversample 4x. To gain 2 bits, oversample 16x. To gain 4 bits, oversample 256x. This assumes white noise and a proper decimation filter (not just averaging). Sigma-delta ADCs add noise shaping which pushes more quantization noise out of band, allowing much greater ENOB gain per octave of oversampling.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| ENOB_gain | ENOB Improvement (bits) | — | — |
| N | Oversampling Ratio | — | — |
Step by step
- 1. What you know: Oversampling Ratio 1.1
- 2. The relation: ENOB_gain = log2(N) / 2
- 3. Substitute: N = 1.1
- 4. Result: ENOB Improvement (bits) = 0.06875
Worked examples
Minimum range
Given: Oversampling Ratio 0.055
Result: ENOB Improvement (bits) = -2.092
Low range
Given: Oversampling Ratio 0.55
Result: ENOB Improvement (bits) = -0.4312
Typical
Given: Oversampling Ratio 1.1
Result: ENOB Improvement (bits) = 0.06875
High range
Given: Oversampling Ratio 1.76
Result: ENOB Improvement (bits) = 0.4078
Maximum range
Given: Oversampling Ratio 17.6
Result: ENOB Improvement (bits) = 2.069
Solving for each variable
Solve for ENOB Improvement (bits)
Oversampling Ratio 0.055 → -2.092
Solve for Oversampling Ratio
ENOB Improvement (bits) 0.025 → 1.035
How ENOB Improvement (bits) changes with Oversampling Ratio
| Oversampling Ratio (input) | ENOB Improvement (bits) (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-enob/">Decimation ENOB Gain</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Decimation ENOB Gain?
Use ENOB_gain = log2(N) / 2. With Oversampling Ratio 1.1, ENOB Improvement (bits) works out to 0.06875.
What is the formula for Decimation ENOB Gain?
The formula is ENOB_gain = log2(N) / 2. Oversampling followed by decimation (averaging and downsampling) increases the effective number of bits of an ADC.
How do you find Oversampling Ratio when you know the other values?
Rearrange for Oversampling Ratio: with ENOB Improvement (bits) 0.025, Oversampling Ratio is 1.035.
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