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奇谐函数

奇谐函数. f(t)=-f(t+T/2) 即波形移动 T/2 后，波形以横轴对称。其： a 0 =a 2 =a 4 = =b 2 =b 4 = =0 例 2 正弦函数 Esin( ω0t) 经全波整流和半波整流后波形为？见图 4.2-7 解： 全波整流 : f 1 (t)= E sin( ω 0 t) = Esin 为偶函数，则： b n =0 a n =4/T ſ E sin( ω 0 t) cos(nΩt)dt=4E/T ſ sin( ω 0 t)cos(nΩt)dt= ·

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奇谐函数

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  1. 奇谐函数 • f(t)=-f(t+T/2) 即波形移动T/2后，波形以横轴对称。其：a0=a2=a4= • =b2=b4= =0 • 例2正弦函数Esin(ω0t)经全波整流和半波整流后波形为？见图4.2-7 • 解：全波整流: f1(t)= E sin(ω0t) = Esin 为偶函数，则：bn=0 • an=4/Tſ E sin(ω0t) cos(nΩt)dt=4E/Tſ sin(ω0t)cos(nΩt)dt= · • (n=0,1,2)因此f(t)=2E/π[1-(2cos2ω0t)/3- (2cos4ω0t)/15+ 只含直流分量和偶次谐波。 • 半波整流： f2(t)= • f2(t)=f (t)+f (t)+f1(t)/2+ (Esin(ω0t))/2 图见4.2-8 • 所以,f2(t)=E/π[1+(πsin(ω0t))/2-(2cos2ω0t)/3-(2cos4ω0t)/15+ ] _ 2π ·t T (-2E) Hcosnπ T/2 T/2 n-1 0 π 0 Esin(ω0t) nt<t<(2n+1)T/2 0 (2n+1)T/2<t<(n+1)t

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