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Thd+n to Sinad Calculator

Reviewed by Calculator Editorial Team

Understanding the relationship between Total Harmonic Distortion plus Noise (THD+N) and Signal-to-Noise and Distortion (SINAD) is crucial for evaluating the performance of audio systems, power amplifiers, and communication equipment. This calculator helps you convert THD+N values to SINAD ratios and interpret the results.

What is THD+N?

Total Harmonic Distortion plus Noise (THD+N) is a measure of the quality of a signal in an audio system or electronic circuit. It combines two important metrics:

  • Total Harmonic Distortion (THD): Measures the distortion caused by nonlinearities in the system, expressed as a percentage of the fundamental signal.
  • Noise: Measures unwanted electrical signals that degrade the signal quality.

THD+N is calculated as the square root of the sum of the squares of THD and noise, providing a single metric that represents both distortion and noise.

What is SINAD?

Signal-to-Noise and Distortion (SINAD) is another important metric that combines signal strength, noise, and distortion. It is expressed in decibels (dB) and represents the ratio of the desired signal to the sum of noise and distortion.

A higher SINAD value indicates better signal quality, as it means the signal is stronger relative to the unwanted noise and distortion components.

THD+N to SINAD Formula

The relationship between THD+N and SINAD can be expressed using the following formula:

SINAD (dB) = 20 * log10(1 / √(THD+N² + Noise²))

Where:

  • THD+N is the total harmonic distortion plus noise, expressed as a decimal (e.g., 0.05 for 5%).
  • Noise is the noise level, expressed as a decimal (e.g., 0.02 for 2%).

This formula converts the combined THD+N and noise values into a SINAD ratio in decibels, which is a more intuitive measure of signal quality.

How to Use This Calculator

  1. Enter the THD+N value as a percentage (e.g., 5 for 5%).
  2. Enter the noise level as a percentage (e.g., 2 for 2%).
  3. Click the "Calculate" button to compute the SINAD ratio.
  4. Review the result and interpretation.

Note: THD+N and noise values should be entered as percentages (e.g., 5 for 5%). The calculator will convert these to decimal form for the calculation.

Example Calculation

Let's say you have a system with:

  • THD+N = 5%
  • Noise = 2%

Using the formula:

SINAD (dB) = 20 * log10(1 / √(0.05² + 0.02²)) = 20 * log10(1 / √(0.0025 + 0.0004)) = 20 * log10(1 / √0.0029) = 20 * log10(1 / 0.05385) = 20 * log10(18.59) ≈ 20 * 2.56 ≈ 51.2 dB

So, the SINAD ratio for this system is approximately 51.2 dB.

FAQ

What is the difference between THD+N and SINAD?

THD+N is a measure of distortion and noise combined, while SINAD is a ratio that combines signal strength, noise, and distortion. SINAD is expressed in decibels and provides a more intuitive measure of signal quality.

How do I improve SINAD in an audio system?

To improve SINAD, you can reduce noise sources, use high-quality components, and minimize distortion through proper circuit design and amplification techniques.

What is a good SINAD value?

A good SINAD value depends on the application. For high-fidelity audio systems, values above 90 dB are desirable, while communication equipment may require values above 60 dB.