When the square-wave signal of Fig. 1.5, whose Fourier series is given in Eq. (1.2), is...

 

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When the square-wave signal of Fig. 1.5, whose Fourier series is given in Eq. (1.2), is applied to a resis- tor, the total power dissipated may be calculated directly using the relationship P = 1/T J% (/R) dt or indirectly by summing the contribution of each of the harmonic components, that is, P P, + P,+ P.+...., which may be found directly from rms values. Verify that the two approaches are equivalent. What fraction of the energy of a square wave is in its fundamental? In its first five harmonics? In its first seven? First nine? In what number of harmonics is 90% of the energy? (Note that in counting harmonics, the fundamental at w, is the first, the one at 2@, is the second, etc.) Ans. 0.81; 0.93; 0.95; 0.96: 3 %3! 4V %3D v(1) (sin w,t + sin 3 a,t + sin 5 w,t + ...) (1.2) When the square-wave signal of Fig. 1.5, whose Fourier series is given in Eq. (1.2), is applied to a resis- tor, the total power dissipated may be calculated directly using the relationship P = 1/T J% (/R) dt or indirectly by summing the contribution of each of the harmonic components, that is, P P, + P,+ P.+...., which may be found directly from rms values. Verify that the two approaches are equivalent. What fraction of the energy of a square wave is in its fundamental? In its first five harmonics? In its first seven? First nine? In what number of harmonics is 90% of the energy? (Note that in counting harmonics, the fundamental at w, is the first, the one at 2@, is the second, etc.) Ans. 0.81; 0.93; 0.95; 0.96: 3 %3! 4V %3D v(1) (sin w,t + sin 3 a,t + sin 5 w,t + ...) (1.2)