Index DigitalTHD, SINAD & ENOB

THD, SINAD & ENOB

Combine harmonic levels and noise into the figures printed on spec sheets.

THD0.00187%−94.6 dB

THD in dB−94.6dB

THD+N0.00191%

SINAD94.4dB

ENOB15.4bit

DominantH2

Spectrum of a 1 kHz test tone

Fundamental
Harmonics
Noise floor per bin

The noise floor is drawn as a 32k-point FFT would show it: about 42 dB below the total noise, because the noise is spread across many bins.

Input

Harmonic 2

H_2

dBc

Harmonic 3

H_3

dBc

Harmonic 4

H_4

dBc

Harmonic 5

H_5

dBc

Noise, 20 kHz band

N

dBc

Total noise relative to the 1 kHz fundamental.

How it works

Total harmonic distortion

THD compares the combined level of the harmonics a device adds to the level of the tone you fed it. With each harmonic given in decibels relative to the fundamental (dBc), powers are summed:

\mathrm{THD} = \sqrt{\sum_{k \ge 2} 10^{H_k/10}}

\mathrm{THD}_{dB} = 20\log_{10}\mathrm{THD}

Multiply the ratio by 100 for the percentage. A figure of 0.001% is the same as −100 dB.

Adding the noise

\mathrm{THD{+}N} = \sqrt{\sum_{k \ge 2} 10^{H_k/10} + 10^{N/10}}

SINAD is the same quantity turned upside down and expressed as a positive number of decibels. It is the single most compact summary of how clean a converter or amplifier is.

Effective number of bits

\mathrm{ENOB} = \frac{\mathrm{SINAD} - 1.76}{6.02}

This asks how many bits an ideal converter would need to match the measured SINAD. A DAC with 120 dB SINAD resolves about 19.6 bits, whatever the word length on its label.

What the number hides

One figure cannot say which harmonics dominate. Low-order harmonics (second, third) are largely masked by the tone itself; the same THD made of high-order products is more audible. The spectrum tells you more than the percentage.