Question

Consider a half-wave rectified sine wave with a peak voltage of 100 V. It can be shown (GENT 3123) that the complex Fourier series coefficients are: 100 G-j25 n 13, t5, 7 C,- 100 2, P2 ,n 4, 6, a) Evaluate Dn , n-0, 「, 2 , 3, 4 for the polar Fourier series b) Evaluate φ, , n = 0, 1, 2 , 3, 4 for the polar Fourier series c) How many decibels (dB) is the second harmonic below the fundamental? d) How many decibels (dB) is the fourth harmonic below the fundamental?

Answer 1

Given data: c_0 = 100/pi c_1 = -j25 c_n = {0 n = plusminus 3, plusminus 5 ellipsis 100/pi(1- n^2) n = plusminus 2, plusminus 4 ellipsis a) D_n = Vertical-bar c_n Vertical-barD_0 = 100/pi D_1 = 25 D_2 = 100/pi(1- 2^2) = 100/3pi D_3 = 0 D_4 = 100/pi(1- 4^2) = 100/15pi b) phi_n = angle c_n phi_0 = 0 degree phi_1 = -90 degree phi_2 = -180 degree phi_3 = 0 degree phi_4 = -180 degree c) 2nd harmonic distortion A_2 = D_2 /D_0 =`100/3pi/100/pi = 1/3 harmonic distortion in dB A_2 = Vertical-bar 20log (1/3) Vertical-bar= 9.54dB hence 2nd harmonic is 9.54dB below fundamental d) 4th harmonic distortion A_4 = D_4 /D_0 = 100/15pi/100/pi = 1/15 distortion in dB A_4 = Vertical-bar 20log 1/15 Vertical-bar= 23.52dB hence 4th harmonic is 23.52dB below of fundamental