# ADC Total Harmonic Distortion plus Noise

The Total Harmonic Distortion Value (THD) is the Root-Sum-Square (RMS) value of the harmonics produced by the Analog-to-Digital Converter (ADC) relative to the RMS level of a sinusoidal input signal near full-scale. For example, assuming an input signal having frequency f, the harmonic frequencies are 2f, 3f, 4f, etc. The non-linearity in the converter will produce harmonics that were not present in the original signal. These harmonic frequencies usually distort the output, which degrades the performance of the ADC. This effect can be quantified as THD, which is the ratio of the sum of powers of the harmonic frequency components to the power of the fundamental/original frequency component (in terms of RMS voltage). In practice, only the first several harmonics of the input signal are included in the THD measurement because greater-order harmonics are insignificant compared to the noise floor in the measured Fast Fourier Transform (FFT) output. This ratio is specified in RMS decibels (dB) or RMS dBc. The formula describing THD is as follows:

(1)

The THD should have a minimum value for less distortion. As the input signal amplitude increases, the distortion increases. The THD value also increases with the increase in the frequency.

## Total Harmonic Distortion plus Noise (THD+N)

THD+N is the RMS value of the harmonics and noise produced by the ADC relative to the RMS level of a sinusoidal input near full-scale. THD+N does not necessarily include all data from the FFT analysis. For a valid THD+N specification, the noise bandwidth must be specified. If the noise bandwidth is taken over the entire usable bandwidth of the ADC (0 - fs/2), then the THD+N measurement provides the same results as Signal-to-Noise Ratio and Distortion (SINAD).