Effective Number of Bits
ENOB = (SINAD − 1.76) / 6.02
Quick answer
This calculator solves ENOB = (SINAD − 1.76) / 6.02 for ENOB. With SINAD 20 dB, the result is 3.03. It solves in 2 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The effective number of bits measures the real-world performance of an ADC, accounting for all noise and distortion sources. An ideal N-bit ADC has SINAD = 6.02N + 1.76 dB. Working backward from a measured SINAD gives the ENOB, which is always less than the nominal bit count. For example, a 16-bit ADC might achieve only 13.5 ENOB at high input frequencies due to jitter, INL, and noise. ENOB is the single most important figure of merit for ADC dynamic performance and determines the actual useful resolution of the conversion.
Variables
- ENOB — Effective number of bits (dimensionless)
- SINAD — Signal-to-noise-and-distortion ratio (dB)
Practical Notes
The 6.02 comes from 20×log₁₀(2) and the 1.76 from 10×log₁₀(3/2) for a full-scale sine wave. ENOB decreases with input frequency due to aperture jitter (ENOB_jitter ≈ (−20×log₁₀(2πf×tj) − 1.76)/6.02). A 1 ps jitter clock limits ENOB to about 10.3 bits at 100 MHz input. Always check ENOB at your actual signal frequency, not just DC.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| ENOB | ENOB | — | — |
| SINAD | SINAD | dB | dB |
Step by step
- 1. What you know: SINAD 20 dB
- 2. The relation: ENOB = (SINAD − 1.76) / 6.02
- 3. Substitute: SINAD = 20 dB
- 4. Result: ENOB = 3.03
Worked examples
Minimum range
Given: SINAD 0.3 dB
Result: ENOB = -0.2425
Low range
Given: SINAD 3 dB
Result: ENOB = 0.206
Typical
Given: SINAD 20 dB
Result: ENOB = 3.03
High range
Given: SINAD 60 dB
Result: ENOB = 9.674
Maximum range
Given: SINAD 600 dB
Result: ENOB = 99.38
Solving for each variable
Solve for ENOB
SINAD 0.3 dB → -0.2425
Solve for SINAD
ENOB 0.025 → 1.911 dB
How ENOB changes with SINAD
| SINAD (input) | ENOB (result) |
|---|---|
| 2 dB | 0.03987 |
| 5 dB | 0.5382 |
| 10 dB | 1.369 |
| 15 dB | 2.199 |
| 20 dB | 3.03 |
| 30 dB | 4.691 |
| 40 dB | 6.352 |
| 80 dB | 13 |
| 140 dB | 22.96 |
| 200 dB | 32.93 |
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<p><a href="https://vbatpower.com/formulas/enob/">Effective Number of Bits</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Effective Number of Bits?
Use ENOB = (SINAD − 1.76) / 6.02. With SINAD 20 dB, ENOB works out to 3.03.
What is the formula for Effective Number of Bits?
The formula is ENOB = (SINAD − 1.76) / 6.02. The effective number of bits measures the real-world performance of an ADC, accounting for all noise and distortion sources.
How do you find SINAD when you know the other values?
Rearrange for SINAD: with ENOB 0.025, SINAD is 1.911 dB.
Related Concepts
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