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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 STIM3A Advanced Stimulus Signal Generator and the DEMO.ADC board driver.
You can also experiment with variable amounts of clipping by using the STIM3A/DEMO setup. Create identical sine waves on two different DAC tone component pages. You may want to use the STIM3A StepN 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", or else you will need to use a window function to reduce them.
If one component is at 100% Level and the other is at zero or Off, there will be no clipping. When both are On they will add together to form the composite output, which will clip symmetrically at the 100% level when 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 magnitude or power spectrum 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 others 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. Just change the second sine wave frequency to 0 (DC) and change the phase to +90 or -90 degrees. The Level control will then add a positive or negative constant to the first sine wave, 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.
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