CH11_非正弦周期电流电路和信号

i k r i 2 r 7 2 u 50 846 cos t 30

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Unformatted text preview: m ⋅ cos( kωt + Ψk ) k =1 = U 0 + U ( 1 )m ⋅ cos( ωt + Ψ1 ) + U ( 2 )m ⋅ cos( 2ωt + Ψ2 ) + .....U ( k )m ⋅ cos( kωt + Ψk ) + ..... 电流源: i s ( t ) = I 0 + I ( 1 )m ⋅ cos( ωt + Ψ1 ) + I ( 2 )m ⋅ cos( 2ωt + Ψ2 ) + .....I ( k )m ⋅ cos( kωt + Ψk ) + ..... 5 二、 有效值 ∞ 设 i ( t ) = I 0 + ∑ I km ⋅ cos( kωt + Ψk ) k =1 则: 2 I = I 0 + I (21 ) + I (22 ) + .... + I (kk ) + .... 其中 I ( k 为电流的 k 次谐波分量的有效值 ) 2 2 2 k 同理可得: U = U 0 + U ( 1 ) + U ( 2 ) + .... + U ( k ) + .... 例1: 有一非正弦周期电压 : u = 10 + 141.4 cos( ωt + 30° ) + 70.7 cos( 3ωt − 90° )V ,求电压的有效值。 解: 2 2 2 U = U 0 + U 1 + U 3 = 10 2 + ( = 10 2 + 100 2 + 50 2 = 112.2V 141.4 2 70.75 2 ) +( ) 2 2 6 三、平均功率 ∞ 设 i ( t ) = I 0 + ∑ I km ⋅ cos( kωt + Ψk ) k =1 ∞ u( t ) = U 0 + P = U0 I0 + ∑ U km ⋅ cos( kωt + Ψk ) k =1 ∞ ∑ U k I k cos ϕ k k =1 2 2 2 2 P = I 0 R + I1 R + I 2 R + ... + I k R + ... = I 2 R...
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