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HW#4_solution

# HW#4_solution - HW4 1 vin(t = 2 cos(2 t 1 cos(4 t 2 = 10...

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HW4 1. ( ) 2cos(2 ) in v t t π = a) 2 ( ) 10cos(2 ) 0.1cos (2 ) out v t t t π π = + 2 2 4 4 2 2 4 4 2 2 5 2 2 2 1 cos(4 ) ( ) 10cos(2 ) 0.1 2 1 1 10 ( ) 0.05 0.05 ( ) 2 2 0.05 5 5 0.025 0.025 | [ ]| (0.025) 2.5 10 46.02 | [1]| 5 out j t j t j t j t j t j t j t j t out k out t v t t e e e e e e e e V k THD dB V π π π π π π π π π π = + = + = + + + + = + + + + = = = b) 0 1 ,0 0.5 ( ) 1 1 ,0.5 1 out t v t T t < = = < 0 1 2 0 0 0 0.5 1 2 2 0 0.5 2 0.5 2 1 0 0.5 1 [ ] ( ) ( ) 0, 1 1 [ ] | | 2 2 1 1 1 (( 1) 1) (1 ( 1) ) (1 ( 1) ) 2 2 0 , 2,4,6... [ ] 2 o T jk t jk t out out out jk t jk t jk t jk t out k k k out V k v t e dt v t e dt T e e dt when k V k e e jk jk jk jk jk k V k jk ω π π π π π π π π π π = = = = + = + − − = − − = = 2 2 2 2 2 1 2 1 2 , 1, 3, 5... 4 1 | [ ]| ( ) 1 2 1 ( ) ( ) 4 | [1]| 2 1 0.234 6.31 out k k k out k V k k THD Use Matlab to culculate V k dB π π π = = = = + = = = + = = −

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