Tutorial - Interpreting THD and THD+N specifications and graphs

Discussion in 'Measurement Setups, Systems, and Standards' started by atomicbob, Sep 15, 2017.

  1. atomicbob

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    Typical audio device specifications include distortion specifications which are published as follows:

    THD less than 0.02%
    THD less than 0.02% at 1 KHz
    THD less than 0.02%, 20 Hz to 20 KHz, 0 dBu, 300R load

    The first specification is meaningless. It provides no information about the measurement conditions. The second is a little better acknowledging THD was measured at a single frequency with no level or load specified. It is not very useful unless you listen primarily to 1 KHz sinusoids. The third specification provides the frequency range over which the measurements were acquired, the voltage level and load used. This is a much more complete and honest specification. Yet greater insight may be derived from viewing the graph which produced that last specification.


    THD = Total Harmonic Distortion
    THD+N = Total Harmonic Distortion + Noise
    dBu = dB referenced to 0.775 Vrms

    Consider the following example:
    20170915-5 Project Sunrise III SE THD THD+N -14 dBu - w FFT 300 Hz - keysight annotated.png

    Points of interest

    1. Fundamental 300 Hz sinusoid at -26.55 dBu
    2. 2nd harmonic 600 Hz sinusoid at -96.22 dBu
    3. Calculated THD for 300 Hz both numeric display and point on graph
    4. Calculated THD+N for 300 Hz, numeric display and point on graph
    5. 60 Hz mains noise at -90 dBu
    6. 180 Hz mains noise at -105 dBu

    THD adds the dB levels of 2nd and higher harmonics of the fundamental input sinusoid found in the FFT, and compares the result to the fundamental in the FFT.

    THD+N adds dB levels of everything in the FFT except the fundamental, and compares to the fundamental, which typically results in a larger number due to inclusion of noise.

    Here are some useful equations.
    dB summing and distortion conversion equations - negative version.png

    To obtain the graph a sinusoid input to the device is swept from 20 Hz to 20 KHz, measuring and plotting the THD and THD+N results from the device output.

    Sample at 300 Hz :
    20170915-5 Project Sunrise III SE THD THD+N -14 dBu - w FFT 300 Hz - keysight.PNG

    Sample at 1000 Hz:
    20170915-6 Project Sunrise III SE THD THD+N -14 dBu - w FFT 1000 Hz - keysight.PNG

    Sample at 3000 Hz.
    20170915-7 Project Sunrise III SE THD THD+N -14 dBu - w FFT 3000 Hz - keysight.PNG
    The graphs for this device indicates a frequency neutral THD and THD+N. Residual noise observed is low as depicted in the spectrum with the primary residual noise being power supply mains related. However, given -90 dBu translates to 10 dB SPL for an HD800 this should remain inaudible.

    A graph for the same device using a SMPS power supply:
    20170908-1 Project Sunrise III SE THD THD+N -24 dBu - w FFT - meanwell.PNG
    The graph for this device indicates a frequency dependent THD with distortion rising as frequency falls. THD+N is frequency neutral but overall higher than the previous example. Also note the number of spikes in the spectrum. Residual noise (blackground) observed is noisier compared to the previous device measurement. (Please watch the y axis notation – this graph has different scales than the previous examples.)
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