THD vs SINAD vs SNR: Key Differences Explained

This article compares Total Harmonic Distortion (THD), Signal to Noise and Distortion Ratio (SINAD), and Signal to Noise Ratio (SNR), highlighting the differences between them. We’ll also look at the formulas for each, showcasing the relationships between these important metrics.

THD, SINAD, and SNR are key parameters used to quantify the dynamic performance of Analog to Digital Converters (ADCs). They help us understand the distortion and noise present in A/D conversion. All three parameters are typically measured using FFT (Fast Fourier Transform) analysis.

Image Courtesy: Analog Devices, Inc.

Figure 1 depicts a fundamental signal and five harmonic components in a frequency spectrum. Notice that harmonic frequencies appear at integer multiples of the fundamental frequency. Spurious frequencies, on the other hand, show up at non-integer multiples of the fundamental signal frequency. Typically, the first five harmonic components are the most significant contributors to distortion.

SNR | Signal to Noise Ratio

• SNR stands for Signal to Noise Ratio.

• It’s the ratio of the amplitude of the fundamental signal to the amplitude of the noise signal.

• Noise includes all non-fundamental spectral components (e.g., spurious signals, harmonics, images) within the Nyquist range (0 to Fs/2, where Fs is the sampling frequency), excluding the DC component.

• Both the fundamental signal and its harmonics are considered for measurement.

• The bandwidth of the signal is a factor in SNR calculation.

• SNR is expressed as:

  $SNR = 20 * log_{10} \left[ \frac{Signal_{RMS}}{\sqrt{\sum{Noise_{RMS}^2}}} \right]$

  This can also be expressed in terms of power:

  $SNR(dB) = 10 * log_{10} \left[ \frac{Signal_{Power}}{Noise_{Power}} \right]$

The SNR formula calculates the ratio of the root mean square (RMS) of the signal to the RMS of the noise.

SNR can also be expressed in terms of SINAD and THD values, as shown in the equation above.

THD | Total Harmonic Distortion

• THD stands for Total Harmonic Distortion.
• It’s the ratio of the sum of the amplitudes of the harmonic components to the amplitude of the fundamental signal component. Usually, the first 5 to 6 harmonics are considered.
• Alternatively, it can be defined as the ratio of the RMS of the fundamental signal to the mean of the root-sum-square of its harmonics plus all noise components (excluding DC). In FFT analysis, the bandwidth typically extends from DC to Fs/2.
• THD can be expressed in dB, dBc, or as a percentage.
• THD quantifies the effect of high-frequency signal components.
• THD of an A/D converter is generally specified with an input signal close to full-scale, although it can be measured at any level.
• A THD analyzer, employing FFT methods, can be used for THD measurement.

The formula above considers the first five harmonic components (H1 to H5), where ‘F’ represents the fundamental frequency.

THD can be expressed as:

$THD = 20 * log_{10} \left( \frac{\sqrt{\sum_{i=1}^{5} H_i^2}}{F} \right)$

The equation above demonstrates the relationship between THD, SINAD, and SNR. It also expresses THD in decibels (dB).

SINAD | Signal to Noise and Distortion Ratio

• SINAD stands for Signal to Noise and Distortion Ratio.

• Its value is approximately equal to THD + noise.

• It’s the ratio of the signal amplitude (in RMS) to the sum of other spectral components (in RMS), including harmonic frequencies but excluding the DC component.

• SINAD is expressed in dB, and can be calculated as:

  $SINAD = 20 * log_{10} \left( \frac{Fundamental}{\sqrt{\sum{(Noise + Harmonics)^2}}} \right)$

  The above formula expresses SINAD as the ratio of the signal to the combined noise and distortion components.

The equation above shows the relationship between SINAD, THD, and SNR.

SINAD can also be expressed in terms of ENOB (Effective Number of Bits), as shown in the equation above.

Key Takeaways

From the descriptions above, we can conclude:

• SINAD is approximately equivalent to THD + Noise.
• SINAD value is typically greater than the SNR value.