Chain cireuit Transmission Line -Uniform trans Definition of warelength: A v(z)=ve*+v-e*kat lp(x)=3-2sg am=(Ole+e(O)e 8aa HI(z)=V. The velocity of wave =V(R+joL)(G+joc) =[1+p(x)em [1+P(O)e2p]velox in transmission line: Definition 2: natural imped R+JOL 工1=2+21-p(x)em=221-p(o)e1em B=2 G+joC Uniform lossless transmission line: reflection on the ling um Uniform lossless transmission line jB lected wave z absorption cident way V=Z I2 (t) incident gave in z shox eflected wave reflected wave r( z-shkx chkx人x2 Voltage/current reflection coefficient Zshkx +Z chkx jz,tgB P, (x)=relected wave=-P, (x incident wave Zin changes along the transmission line by half wavelength. V and I change along the transmission line by one w北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 kx - ZC + V1 - + V2 I1 I2 ZL Zin *** x - + V1 - + V2 I1 I2 k, Zc ZL Zin x 0 β β β β ββ + + + + LC LC j x -j2 x j x 1 V2 V 2 L L LC LC j x -j2 x j x 1 V2 V 2 c c ZZ ZZ V = [1+ρ (x)]V e = [1+ρ (0)e ]V e 2Z 2Z ZZ ZZ I = [1-ρ (x)]I e = [1-ρ (0)e ]I e 2Z 2Z φ β β − = = + − = = + L C j V V L C L C -j2x -j2 x V V L C Z Z ρ (0) ρ (0) e Z Z Z Z ρ (X) e ρ (0)e Z Z v v β β β β ρ ρ + = = + + = 1 L C in C 1L C -j2 x C -j2 x V Z jZ tg x Z Z I jZ tg x Z 1 (0)e Z 1- (0)e Uniform lossless transmission line: reflectance = reflection/incidence 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 Z Assuming R,G,L,C are the parameters of unit length *** -kZ kZ -kZ kZ e Z V e Z V I(z) V(z) V e V e + + − + − + = − = + C C (R j L)(G j C) k α jβ = + ω + ω = + attenuation constant Phase constant 2 Definition of wavelength : π λ β = Summary 1 v ω β = = LC The velocity of wave in transmission line: Chain circuit → Transmission Line →Uniform transmission line Wavelength: The unit length of wave which is transmits on the transmission line. Definition 1: transfer constant G j C R j L - I V I V ZC ω ω + + = = = − − + + Definition 2: natural impedance 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 Uniform lossless transmission line: reflection on the line *** ZL x x k ZC k ZC x k ZC k ZC x V(t)+ - incident wave reflected wave incident wave reflected wave absorption Transmissive wave incident wave reflected wave Transmissive wave incident wave reflected wave Voltage/current reflection coefficient: reflected wave incident wave ρV I (x) = =−ρ (x) Summary 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 北京大学 V2 = ZLI2 kx - ZC + V1 - + V2 I1 I2 ZL Zin ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ =⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − 2 2 1 C C 1 1 I V Z shkx chkx chkx Z shkx I V *** k = jβ Uniform lossless transmission line x - + V1 - + V2 I1 I2 k, Zc ZL Zin x 0 L C L C C L C L C C 1 1 in jZ tg x Z Z jZ tg x Z Z shkx Z chkx Z chkx Z shkx Z I V Z + + = + + = = β β Zin changes along the transmission line by half wavelength. V and I change along the transmission line by one wavelength Summary