ADC Theoretical SNR
SNR = 6.02 × N + 1.76 dB
Quick answer
This calculator solves SNR = 6.02 × N + 1.76 for SNR (dB). With Resolution (bits) 12 bits, the result is 74 dB. It solves in 2 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The theoretical maximum signal-to-noise ratio of an ideal N-bit ADC is determined by quantization noise alone. Each additional bit adds 6.02 dB of dynamic range (since each bit doubles the number of levels, and 20×log₁₀(2) = 6.02). The 1.76 dB term accounts for the relationship between the full-scale sinusoidal signal power and the uniformly distributed quantization noise. In practice, ADCs never achieve this theoretical limit due to thermal noise, clock jitter, nonlinearities, and other analog imperfections. The SINAD (signal-to-noise-and-distortion) specification measures the actual performance.
Variables
- SNR — Maximum signal-to-noise ratio (dB)
- N — ADC resolution in bits
Practical Notes
Theoretical SNR by resolution: 8-bit = 49.9 dB, 10-bit = 61.9 dB, 12-bit = 74.0 dB, 16-bit = 98.1 dB, 24-bit = 146.2 dB. Real-world ENOB = (SINAD - 1.76) / 6.02. A 12-bit ADC with SINAD of 68 dB has ENOB of 11 bits. High-resolution sigma-delta ADCs (24-bit) typically achieve 19-21 ENOB.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| SNR | SNR (dB) | dB | dB |
| N | Resolution (bits) | bits | bits |
Step by step
- 1. What you know: Resolution (bits) 12 bits
- 2. The relation: SNR = 6.02 × N + 1.76
- 3. Substitute: N = 12 bits
- 4. Result: SNR (dB) = 74 dB
Worked examples
Minimum range
Given: Resolution (bits) 0.8 bits
Result: SNR (dB) = 6.576 dB
Low range
Given: Resolution (bits) 8 bits
Result: SNR (dB) = 49.92 dB
Typical
Given: Resolution (bits) 12 bits
Result: SNR (dB) = 74 dB
High range
Given: Resolution (bits) 16 bits
Result: SNR (dB) = 98.08 dB
Maximum range
Given: Resolution (bits) 160 bits
Result: SNR (dB) = 965 dB
Solving for each variable
Solve for SNR (dB)
Resolution (bits) 0.8 bits → 6.576 dB
Solve for Resolution (bits)
SNR (dB) 0.3 dB → -0.2425 bits
How SNR (dB) changes with Resolution (bits)
| Resolution (bits) (input) | SNR (dB) (result) |
|---|---|
| 1.2 bits | 8.984 dB |
| 3 bits | 19.82 dB |
| 6 bits | 37.88 dB |
| 9 bits | 55.94 dB |
| 12 bits | 74 dB |
| 18 bits | 110.1 dB |
| 24 bits | 146.2 dB |
| 48 bits | 290.7 dB |
| 84 bits | 507.4 dB |
| 120 bits | 724.2 dB |
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<p><a href="https://vbatpower.com/formulas/adc-snr/">ADC Theoretical SNR</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate ADC Theoretical SNR?
Use SNR = 6.02 × N + 1.76. With Resolution (bits) 12 bits, SNR (dB) works out to 74 dB.
What is the formula for ADC Theoretical SNR?
The formula is SNR = 6.02 × N + 1.76. The theoretical maximum signal-to-noise ratio of an ideal N-bit ADC is determined by quantization noise alone.
How do you find Resolution (bits) when you know the other values?
Rearrange for Resolution (bits): with SNR (dB) 0.3 dB, Resolution (bits) is -0.2425 bits.
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