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Home/1.8 When the square-wave signal of Fig. 1.5, whose Fourier series is given in Eq. (1.2), is applied to a resistor, the total power dissipated may be calculated directly using the relationship or indirectly by summing the contribution of each of the harmonic components, that is, P = P1 + P3 + P5 + …, 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 ω0 is the first, the one at 2ω0 is the second, etc.) 0.81; 0.93; 0.95; 0.96; 3

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1.8 When the square-wave signal of Fig. 1.5, whose Fourier series is given in Eq. (1.2), is applied to a resistor, the total power dissipated may be calculated directly using the relationship or indirectly by summing the contribution of each of the harmonic components, that is, P = P1 + P3 + P5 + …, 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 ω0 is the first, the one at 2ω0 is the second, etc.) 0.81; 0.93; 0.95; 0.96; 3

1.8 When the square-wave signal of Fig. 1.5, whose Fourier series is given in Eq. (1.2), is applied to a resistor, the total power dissipated may be calculated directly using the relationship or indirectly by summing the contribution of each of the harmonic components, that is, P = P1 + P3 + P5 + ..., 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 ω0 is the first, the one at 2ω0 is the second, etc.) 0.81; 0.93; 0.95; 0.96; 3

1.8 When the square-wave signal of Fig. 1.5, whose Fourier series is given in Eq. (1.2), is applied to a resistor, the total power dissipated may be calculated directly using the relationship or indirectly by summing the contribution of each of the harmonic components, that is, P = P1 + P3 + P5 + ..., 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 ω0 is the first, the one at 2ω0 is the second, etc.) 0.81; 0.93; 0.95; 0.96; 3

1.8 When the square-wave signal of Fig. 1.5, whose Fourier series is given in Eq. (1.2), is applied to a resistor, the total power dissipated may be calculated directly using the relationship or indirectly by summing the contribution of each of the harmonic components, that is, P = P1 + P3 + P5 + …, 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 ω0 is the first, the one at 2ω0 is the second, etc.) 0.81; 0.93; 0.95; 0.96; 3