What is the formula for THD + N?

The THD + N formula is THD+N = √(Σharmonics² + Σnoise²) / V1, where THD+N—Total distortion + noise ratio (fraction); Vharm—RMS sum of harmonic components (V); Vnoise—RMS noise (V); V1—Fundamental RMS amplitude (V).

What does THD+N mean in the THD + N formula?

THD+N is Total distortion + noise ratio (fraction).

THD + N

Q: How do you calculate THD + N?

Use the formula THD+N = √(Σharmonics² + Σnoise²) / V1. Total harmonic distortion plus noise combines all the harmonic distortion products and the broadband noise into a single fidelity figure, referenced to the fundamental. Enter the values you know in the calculator above and it solves for the remaining variable.

THD+N = √(Vharm² + Vnoise²) / V1

Calculator

THD + N

Harmonic RMS

Noise RMS

Fundamental RMS

Result

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Formula

THD+N = √(Σharmonics² + Σnoise²) / V1

Description

Total harmonic distortion plus noise combines all the harmonic distortion products and the broadband noise into a single fidelity figure, referenced to the fundamental. It is the most common audio and signal-chain quality metric because it captures everything that is not the wanted signal. Over the full bandwidth, THD+N is equivalent to SINAD expressed as a ratio rather than in decibels.

Variables

THD+N — Total distortion + noise ratio (fraction)
Vharm — RMS sum of harmonic components (V)
Vnoise — RMS noise (V)
V1 — Fundamental RMS amplitude (V)

Practical Notes

In dB, THD+N = 20·log10(ratio) and SINAD = −THD+N(dB). A 0.001% THD+N (−100 dB) is excellent audio performance; measurement bandwidth strongly affects the noise term.

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