Transcription of Chapter 16 Fourier Series Analysis
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Chapter 16 Fourier Series Analysis
- 257 - Chapter 16 Fourier Series Analysis Introduction Many electrical waveforms are period but not sinusoidal. For Analysis purposes, such waveform can be represented in Series form based on the original work of Jean Baptise Joseph Fourier . The application of Fourier - Series method includes signal generators, power supplies, and communication circuits. Fourier Series decomposes non-sinusoidal waveform into Series of sinusoidal components of various frequencies. With this property, frequency-domain representation or spectrum for periodic waveform is developed. The spectral concept ties the relationship between time-domain and frequency-domain properties of waveform.
A rectified half sine wave is defined over one period f(t) = Asin ωt for 0 < t < T/2 and f(t) = 0 for T/2 < t < T as shown in Fig. 16.1. Find the Fourier series of this wave form. Figure 16.1: A half-wave rectifier Solution The dc voltage shall be a 0 = ∫ ω + ∫ T T / 2 T / 2 0 0dt T 1 Asin tdt T 1 = π = − ω ω − A 1 2 T cos T A. The
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