SINAD from ADC Bits

SINAD = 6.02 × N + 1.76

Quick answer

This calculator solves SINAD = 6.02 × N + 1.76 dB for SINAD. With Number of Bits 0.5, the result is 4.77 dB. It solves in 2 directions, so you can enter the values you have and get the one you need.

Calculator

SINAD (dB)
—

Formula

SINAD = 6.02 × N + 1.76 dB

Description

This formula gives the theoretical maximum SINAD (signal-to-noise-and-distortion ratio) for an ideal N-bit ADC with a full-scale sine wave input. Each additional bit of resolution adds 6.02 dB of dynamic range. The 1.76 dB offset accounts for the sinusoidal signal being 1.76 dB above the quantization noise for a full-scale input. This represents the absolute best-case performance; real ADCs always achieve less due to thermal noise, clock jitter, nonlinearity, and other imperfections.

Variables

  • SINAD — Ideal signal-to-noise-and-distortion ratio (dB)
  • N — Number of ADC bits (dimensionless)

Practical Notes

Common ideal SINAD values: 8-bit → 50 dB, 10-bit → 62 dB, 12-bit → 74 dB, 14-bit → 86 dB, 16-bit → 98 dB, 24-bit → 146 dB. In practice, 24-bit ADCs rarely exceed 120 dB SINAD (about 19.7 ENOB) due to thermal noise limitations. Delta-sigma ADCs achieve high SINAD at low frequencies through oversampling and noise shaping.

Symbols and units

Symbol Meaning Default unit Accepted units
SINAD SINAD dB dB
N Number of Bits — —

Step by step

  1. 1. What you know: Number of Bits 0.5
  2. 2. The relation: SINAD = 6.02 × N + 1.76 dB
  3. 3. Substitute: N = 0.5
  4. 4. Result: SINAD = 4.77 dB

Worked examples

Minimum range

Given: Number of Bits 0.025

Result: SINAD = 1.911 dB

Low range

Given: Number of Bits 0.25

Result: SINAD = 3.265 dB

Typical

Given: Number of Bits 0.5

Result: SINAD = 4.77 dB

High range

Given: Number of Bits 0.8

Result: SINAD = 6.576 dB

Maximum range

Given: Number of Bits 8

Result: SINAD = 49.92 dB

Solving for each variable

Solve for SINAD

Number of Bits 0.025 → 1.911 dB

Solve for Number of Bits

SINAD 0.3 dB → -0.2425

How SINAD changes with Number of Bits

Number of Bits (input) SINAD (result)
0.05 2.061 dB
0.125 2.513 dB
0.25 3.265 dB
0.375 4.018 dB
0.5 4.77 dB
0.75 6.275 dB
1 7.78 dB
2 13.8 dB
3.5 22.83 dB
5 31.86 dB

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Frequently asked questions

How do you calculate SINAD from ADC Bits?

Use SINAD = 6.02 × N + 1.76 dB. With Number of Bits 0.5, SINAD works out to 4.77 dB.

What is the formula for SINAD from ADC Bits?

The formula is SINAD = 6.02 × N + 1.76 dB. This formula gives the theoretical maximum SINAD (signal-to-noise-and-distortion ratio) for an ideal N-bit ADC with a full-scale sine wave input.

How do you find Number of Bits when you know the other values?

Rearrange for Number of Bits: with SINAD 0.3 dB, Number of Bits is -0.2425.

Related Concepts

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