Electrical Engineering ⇒ Topic : Complex Waveforms

Sunita
 
Complex Waveforms So far we have considered sinusoidal waves. However, many electrical waveforms encountered in electrical and electronic equipment (e.g., square wave, sawtooth wave etc.) are not sinusoidal.Complex waves are those which depart from sinusoidal form i.e., they are nonsinusoidal. A *periodic nonsinusoidal wave of any form (complex waveform) can be considered to be made up of sinusoidal waveforms of various frequencies and amplitudes. The above statement is the basis of Fourier series. Accordingly, a square waveform can be considered to be made up from a combination of sinusoidal waveforms. Thus any nonsinusoidal quantity i can be expressed as the sum of a number of sinusoidal quantities i_{1}, i_{2},i_{3}.......... . The frequency of i_{1 }will be the same as that of i and the frequencies of i_{2}, i_{3}... will be integral multiple (2, 3, 4, 5...n) of that of i. In symbols, If we add **d.c. component I_{0} to equation (i), it is known as Fourier series. The term that has the same frequency as i, namely I_{m1 }sin (ωt + Φ_{1}) is called fundamental component;I_{m2} sin (2ωt + Φ_{2}) , whose frequency is twice that of i (or i_{1}) is called the second harmonic component; I_{m3} sin (3ωt + Φ_{3}) ) is the third harmonic.  
 
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