Daqarta
Data AcQuisition And Real-Time Analysis
Scope - Spectrum - Spectrogram - Signal Generator
Software for Windows
The following is from the Daqarta Help system:

# Sound Card Harmonic Distortion

When a signal passes through a nonlinear system, it always generates harmonic distortion. A pure sinusoidal input signal yields additional output components at multiples ("harmonics") of the input frequency. If the distortion in the positive portion of the output is an exact mirror of the negative portion, the distortion will contain only odd-numbered multiples (odd harmonics). This is often the case with modern solid-state power amplifiers that clip symmetrically on positive and negative peaks.

If an amplifier with symmetrical clipping is driven hard enough, the flat tops and steep slopes of the output start to look like a square wave. See "Making Waves Via Sine Wave Synthesis" for hands-on experiments that show the odd-harmonic structure of square waves, using the Daqarta Generator.

You can also experiment with variable amounts of clipping by using the Generator. Create identical sine waves on two different streams of an output channel. You may want to use the Lines frequency step option to insure that the frequency is an exact integer submultiple of the sample rate so it will fall exactly on a spectral line with no leakage "skirts". Otherwise, you will need to use a window function to reduce them.

If one component is at 100% Level and the other is at zero, there will be no clipping. When both are at 100% they will add together to form the composite output, which will clip symmetrically at the 100% level whenever the total exceeds that. By increasing the second component Level from 0 to 100% you can control the amount of clipping and observe its effects on the waveform and spectrum.

Note that the true harmonic series will extend beyond the Nyquist frequency (which is the maximum unexpanded X-axis frequency and is half the sample rate), but the higher components will be "folded over" or "reflected" by aliasing and appear in the spectrum you see. If one of the reflected harmonics lands on one of the true lower harmonics, it will add to it or subtract from it depending on its polarity. (The spectrum display shows only absolute values, not polarities.)

If the positive and negative portions of a sine wave are not symmetrical, then even-harmonic components will also be produced. Old vacuum tube amplifiers (or those that don't use push-pull methods) tend to have even harmonics due to this phenomenon.

Using the above clipping setup, you can cause a sine wave to clip on only the positive or negative peaks by adding a positive or negative constant value. Toggle the second output stream off and just use the first sine wave. Adjust the DC Offset control to add a positive or negative constant, causing the total output to clip on only one polarity.

The distortion thus created will be more severe than that from a vacuum tube (which has a gentle saturation onset instead of an abrupt clipping point), but it will illustrate the presence of even harmonics due to asymmetery.

Harmonic distortion is typically measured as Total Harmonic Distortion (THD), which is the ratio of the energy in all harmonics divided by the energy in the original tone. More commonly, noise is usually included in the reported value, which is then shown as THD+N. This is the ratio of the energy in everything but the original tone, divided by the energy in the tone. Daqarta's THD_Meter and THD_Meter_LF macro mini-apps report both values.

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