Question

Please solve all parts! THANK YOU IN ADVANCE!

Show all work, equations and how numbers plug into your equations to calculate answers Find the following: 1. Analyze the Fourier Spectrum of the full wave rectified sine wave. Let f(t) = sin(Wit) a) Find Fourier Series of f(t) b) Find the power in the DC component of the series c) What approx.. percentage of the total power remains in the harmonics of the rectified wave form? d) Design a low pass filter (find c) with a 3dB point at f3aB = . Now recalculate the number for part c). Use the following schematic, assume fo = 60 Hz f(t)- ww 512 → Filtered output f(t) C = ?

Answer 1

fit a) 1 t 0 RT gets | sint , To = π wo To = 2 - jowot dt Cn : fitse To To Co sint e - jant dt A jt - jt. Cn = ST ujant dt 2; jt (1-20 e - jt (172012 dt *] e CA 21 zry nt - jt (142n) jt11-20) e e 2 Cn (-20) D zaj jL1+2n) е -ja (1720) Co e jaC1-20) ; (1-20) j (1420) zaj - tn ja (1-2) Since e -jn (1+2n) e &n Cn zaj Lim jon] istite] 2 - (n = 25 1 -20 (1+2n) +-20) [ U Сл 7 (146) 2 Co - * (1-40² nato jnwot 2 e in folt= (1-462) na-00 j ant 2 T(1-40², n:- equivalent to 1r resistance 62 Power in DG Component that Power will be consumed in Vams p 2 R Um? P 2 R 2 . 'lim non (1-40?) . It P 2 4 Р X 2 2 T 2 p = 2 7C 0.2 W 2 Um 2 Total Power in tith 62 Vn sint since Vit) so Vm=1 1 / 2 w Total Power 0.2 w Fundamental Power (DL) Power Total Power) ² (Pc Power) Harmonic Power = (0.5) -(0.2) 2 0.458W 0.45) Percentage xloo 91.65% 0.5 d) Amm 52 ret) fit) | 3dB fo 2 - f3dB 2 2 t RC С TRfo C # x 5 x 2) c = 2.12 m F