向量法电路总结 第1篇

1、VCR相量形式

电阻相量形式

时域形式

i(t) = \sqrt{2}Icos(wt+\theta)

u_{R} = \sqrt{2}Icos(wt+\theta)R

相量形式

\bar{I} =I\angle\theta_{i}

\bar{U} =RI\angle\theta_{i}

相量关系 \bar{U} =R\bar{I}

电容相量关系

时域形式

u(t) = \sqrt{2}ucos(wt+\theta_{u})

i_{c} = Cdu/dt = \sqrt{2}WCUcos(wt+\theta_{u}+\Pi/2)

相量形式

\bar{I} =WCU\angle\theta_{u}+\Pi/2

\bar{U} =U\angle\theta_{u}

相量关系 \bar{U} =-j1/wc\bar{I} = jX_{c}\bar{I}

有效值关系： I_{c} = WCU

相位关系： \theta_{i} = \theta_{u} +\Pi/2

电感相量关系

时域形式

i(t) = \sqrt{2}Icos(wt+\theta_{i})

U_{L} = Ldi/dt = \sqrt{2}WLIcos(wt+\theta_{i}+\Pi/2)

相量形式

\bar{U} =WLI\angle\theta_{i}+\Pi/2

\bar{I} =I\angle\theta_{i}

相量关系 \bar{U} =jWL\bar{I} = jX_{L}\bar{I}

有效值关系： U_{c} = WLI

相位关系： \theta_{u} = \theta_{i} +\Pi/2

向量法电路总结 第2篇

di/dt =dRe(\sqrt{2}\bar{I}e^{jwt})/dt=Re(\sqrt{2}jw\bar{I}e^{jwt}) = jw\bar{I}

\int_{}^{}idt =\int_{}^{}Re(\sqrt{2}Ie^{jwt})dt=Re(\sqrt{2}\bar{i}/jwe^{jwt}) = \bar{I}/jw

正弦函数 \Leftrightarrow 相量

时域 \Leftrightarrow 频域

正弦图\Leftrightarrow相量图

范围：实用同频率正弦量时不变线性电路

分析正弦稳态电路

向量法电路总结 第3篇

W = RI^{2}T =\int_{0}^{T}Ri^{2}(t)dt

I = \sqrt{\int_{0}^{T}i^{2}(t)dt}/T

I=1/\sqrt{2}I_{m}

正弦量 \Leftrightarrow 复数

F(t) = \sqrt{2}Ie^{j(wt+\theta)}

F(t) = \sqrt{2}Icos(wt+\theta)+j\sqrt{2}Isin(wt+\theta)

Re(F(t)) =\sqrt{2}Icos(wt+\theta)

F(t) = \sqrt{2}Ie^{j(wt+\theta)} = \sqrt{2}Ie^{j(wt)}*e^{j(\theta)}

\bar{I} = I\angle\theta

\sqrt{2}Icos(wt+\theta)\Leftrightarrow I\angle\theta

向量法电路总结 第4篇

复数表示形式

F = a+jb

F = |F|(cos\theta+jsin\theta)

F = |F|e^{j\theta}

F = |F|\angle\theta

|F| = \sqrt{a^{2} + b^{2}}

旋转因子

e^{j\theta} = cos\theta + jsin\theta

\theta = \Pi/2

e^{j\Pi/2} = j

\theta = -\Pi/2

e^{j-\Pi/2} = -j

\theta = \Pi

e^{j\Pi} = -1