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V 1, V 2, and V 3 are the peak values of the harmonic components that comprise the composite waveform, which also has a frequency of f. The second harmonic undergoes two complete cycles during one cycle of the fundamental frequency, and the third harmonic traverses three complete cycles during one cycle of the fundamental frequency. The significance of harmonic frequencies can be seen in Fig. If the fundamental frequency is 60 Hz (as in the U.S.), the second harmonic frequency is 120 Hz, and the third harmonic frequency is 180 Hz.
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The fundamental (or first harmonic) frequency has a frequency of f, the second harmonic has a frequency of 2 x f, the third harmonic has a frequency of 3 x f, and the nth harmonic has a frequency of n x f. The terms are known as the harmonics of the periodic waveform. V 1, V 2, V 3, …, V n are the peak values of the successive terms of the expression. In this equation, V 0 represents the constant or the DC component of the waveform. The Fourier expression is an infinite series. 4.2, the simplified Fourier expression states. (4.1) and (4.2) and which by definition are pure sinusoids.įor the periodic non-sinusoidal waveform shown in Fig. The sign of phase angle θ is positive if the current leads the voltage and negative if the current lags the voltage.įigure 4.1 contains voltage and current waveforms expressed by Eqs. Where, ω = 2πf is known as the angular velocity of the periodic waveform and 0 is the difference in phase angle between the voltage and the current waveforms referred to as a common axis.