x1)=m{2/(x)em O Roi+L x,1)=m{20(x)2my} at 代入偏徼方程模型 ax ou+c Oh 0 at a(√20(x)em)=R(2(x)em)+L0Q(√21(x)2my) x℃ at (√2i(x)em)=G0(2(x)e)+C0(√2U(x)e) at U(x)=R01(x)+joL01(x) Ox I(x)=GoU(x)+jaCoB(x)
( , ) 2 ( ) ( , ) 2 ( ) j t m j t m i x t I I x e u x t I U x e = = 代入偏微方程模型 0 0 0 0 u i R i L x t i u G u C x t − = + − = + 0 0 ( 2 ( ) ) ( 2 ( ) ) ( 2 ( ) ) j t j t j t U x e I x R L x t e I x e − = + 0 0 ( 2 ( ) ) ( 2 ( ) ) ( 2 ( ) ) j t j t j t I x e U x G C x t e U x e − = + 0 0 U x I j I x ( ) ( ) ( ) x R L x − = + 0 0 I x U j U x ( ) ( ) ( ) x G C x − = +
dU(x) a=(R+j0L0)(x)=Z01(x) U(x) UZ dI(x (Go+jaCo(x)=Yu(x) dx (x)=1(x)∠v7(x) 20=1+101-单位长度阻抗 (x)=(x)∠(x) x=Gn+1C-单位长度导纳 由上式得:d2U ZU=y2U(电压相量沿线分布规律) dx r=√2010=B+-传播系数 B—衰减系数O—相位系数
( ) ( ) ( ) ( ) ( ) ( ) i u I x I x x U x U x x = = Z 1 1 ' 2 2 I x( ) U x( ) 0 0 0 U(0) 0 0 0 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) dU x R j L I x Z I x dx dI x G j C U x Y U x dx − = + = − = + = 0 0 0 0 0 0 Z R j L Y G j C = + = + 单位长度阻抗 单位长度导纳 -- -- 0 0 r Z Y j = = + ——传播系数 ——衰减系数 ——相位系数 2 2 2 0 0 d U Z Y U U dx 由上式得： = = （电压相量沿线分布规律）
dU(x)in (x) U(x) dx 方程解: U(x) yZ U(x=Ae+Ae U/(x) XXO 边值条件:1d(x少 求解出复常数1 dx 得:U(x)=Ae”+A2e=U(x)∠v(x) 实际电压(瞬时式):v(x,)=√2U(x)io+v(x)
Z 1 1 ' 2 2 I x( ) U x( ) U(0) 0 0 ( ) ( ) x x U x dU x dx 1 2 边值条件： 求解出 复常数 A A, ( , ) 2 ( )sin[ ( )] u 实际电压（瞬时式）: u x t U x t x = + 2 2 2 ( ) ( ) d U x U x dx = 1 2 ( ) rx rx U x A e A e − = + 方程解： 得： 1 2 ( ) ( ) ( ) rx rx U x A e A e U x x − = + =
电流求解为 U(=Ae+Ae (x)= 1 dU()=LAe-x-A2e'I y (x=-Ae -Ael 传输线特征阻抗 ∠C∠6
1 2 0 0 1 ( ) ( ) [ ] dU x rx rx I x A e A e Z dx r z − = − = − 电流求解为： Z 1 1 ' 2 2 I x( ) U x( ) U(0) 1 2 ( ) rx rx U x A e A e − = + Z Y0 0 = 0 0 C C Z Z Z Y = = 传输线特征阻抗： 1 2 1 ( ) [ ] C rx rx I x A e A e Z − = −
a)若已知始端电压电流, (x) 求沿线各点的电压电流值 UsO U(x)Z C(0)=U1 (0) A1+A2 (A1-42) → U(x)=Ae+A2e 2(1+Zl1) A1=(
1 1 2 1 1 2 1 ( ) C U A A I A A Z = + → = − 1 U U (0) = 1 I I (0) = a）若已知始端电压电流， 求沿线各点的电压电流值。 1 1 1 2 1 1 1 ( ) 2 1 ( ) 2 C C A U Z I A U Z I = + = − 1 2 ( ) rx rx U x A e A e − = + 1 2 1 ( ) [ ] C rx rx I x A e A e Z − = − Z 1 1' 2 2 I x( ) Us . U x( ) 0 x I x( )