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The triplen harmonics of a distorted (non-sinusoidal) periodic signal are harmonics whose frequency is an odd integer multiple of the frequency of the third harmonic(s) of the distorted signal, resulting in a current in the neutral conductor. [4]
Simple examples are a half-wave rectifier, and clipping in an asymmetrical class-A amplifier. This does not hold true for more complex waveforms. A sawtooth wave contains both even and odd harmonics, for instance. After even-symmetric full-wave rectification, it becomes a triangle wave, which, other than the DC offset, contains only odd harmonics.
For example, if the fundamental frequency is 50 Hz, a common AC power supply frequency, the frequencies of the first three higher harmonics are 100 Hz (2nd harmonic), 150 Hz (3rd harmonic), 200 Hz (4th harmonic) and any addition of waves with these frequencies is periodic at 50 Hz.
In push–pull amplifiers and in CMOS, the even harmonics of both transistors just cancel. Experiment shows that a square wave can be generated by those amplifiers. Theoretically square waves consist of odd harmonics only. In a class-D amplifier, the output filter blocks all harmonics; i.e., the harmonics see an open load.
The ideal square wave contains only components of odd-integer harmonic frequencies (of the form 2π(2k − 1)f). A curiosity of the convergence of the Fourier series representation of the square wave is the Gibbs phenomenon. Ringing artifacts in non-ideal square waves can be shown to be related to this phenomenon.
Animation of the additive synthesis of a triangle wave with an increasing number of harmonics. See Fourier Analysis for a mathematical description.. It is possible to approximate a triangle wave with additive synthesis by summing odd harmonics of the fundamental while multiplying every other odd harmonic by −1 (or, equivalently, changing its phase by π) and multiplying the amplitude of the ...
Easy choices are to use an even function to generate even harmonics or an odd function for odd harmonics. See Even and odd functions#Harmonics. A full wave rectifier, for example, is good for making a doubler. To produce a times-3 multiplier, the original signal may be input to an amplifier that is over driven to produce nearly a square wave ...
A harmonic is any member of the harmonic series, an ideal set of frequencies that are positive integer multiples of a common fundamental frequency. The fundamental is a harmonic because it is one times itself. A harmonic partial is any real partial component of a complex tone that matches (or nearly matches) an ideal harmonic. [3]