电子科技大学：《无线系统中的微波与射频 Microwave and RF Design in Wireless Systems》课程教学资源（课件讲稿）ch02 Transmission Lines and Microwave Network 传输线和微波网络

●●● 1.Lumped element model for a ●●●● ●●●●● ●●●0 transmission line ●●●●0 ●●●0 i(z.r) ●●●● ● ● z,) 42 i(z.) i(z+△x,) RAz L△x v(.) CAz viz+△z,) AZ R:2/m L:H/m ●Question1 G:S/m C:F/m 6

1.Lumped element model for a transmission line  Question 1 6 R m : /  L : / H m GSm : / CFm : /

i(z.0 iz+△x.) ●●● ●●●● ●●●●● RAZ ●●●0 v(z.) CAz ●●●● v(?+△z,功 ●●●● According to Kicrchoff's voltage and current law 基尔霍夫电压和电流定律 v(z,t)-RAzi(z,1)-LAz oi(=,1) 81 -v(z+Az,)=0 i(z,t)-G△zv(z+△z,t)-C△z v(2+A,0-i(z+△z,t)=0 8t Dividing by△z,and△z→0：ov(z,t)=v(z+△z,t)-(z,t) a(2,0=-Ri(z,t)-L di(z,t) 0z 8t l2.l-Ge,）-co2.0 0z Ot Differential equation for the voltage and current 电压和电流的微分方程 7

Differential equation for the voltage and current 电压和电流的微分方程 Dividing by z, and : vzt vz zt vzt (,) ( ,) (,)    According to Kicrchoff’s voltage and current law 基尔霍夫电压和电流定律 7 (,) (,) (,) ( ,) 0 ( ,) (,) ( ,) ( ,) 0 izt v z t R zi z t L z v z z t t vz zt i z t G zv z z t C z i z z t t                          z  0 (,) (,) (,) (,) (,) (,) C vzt izt Ri z t L z t izt vzt Gv z t z t                

●●● ●●●● ●●●●● ●●●0 ●●●●0 ●●●0 02,D=-R(e,0-Li2,0 ●●●● ● 0z 8t i(.D--GM=.)-C ov(=,1) 0z 8t For the sinusoidal steady-state condition: 正弦稳态条件 dV(=)=-(R+j@L)I(z) Telegrapher equation dz 电报方程 da)=-(G+joC)W(2） dz 8

(,) (,) (,) (,) (,) (,) C vzt izt Ri z t L z t izt vzt Gv z t z t                 For the sinusoidal steady-state condition: 正弦稳态条件 e j t  Telegrapher equation 电报方程 8 ( ) ( )() ( ) ( ) () dV z R j LI z dz dI z G j CV z dz           

●●● 2.Wave Propagation on a Transmission Line ●●●● ●●●● ●●●0 ●●●●0 dv( ●●●0 ●●●● dz )=-(R+j@L)I(z) ● dI()--(G+j0C)V(=) dz Wave equation dV2)-y2v(a)=0 dz2 波动方程 dI@-y21e)=0 dz2 where r=a+jB=/(R+j@L)(G+j@C) y:propagation constant传播常数 .:attenuation constant衰减常数 B:phase constant相位常数 9

2. Wave Propagation on a Transmission Line Wave equation 波动方程  : propagation constant传播常数  : attenuation constant衰减常数  : phase constant相位常数 ( ) ( )() ( ) ( ) () dV z R j LI z dz dI z G j CV z dz            where 9 2 2 2 2 2 2 ( ) () 0 ( ) () 0 dV z V z dz dIz I z dz                     j R jLG jC ( )( )

●●● ●●●● ●●●●● ●●●0 dV(2)-rV(=)=0 ●●●●0 ●●●0 d2 ●●●● ●● I)-1()=0 dz2 Solution of the wave equation: V(z)=Voe +Voe I(z)=Ioe+le direction propagation: 定向传播 e2→+Z erz>-Z 10

Solution of the wave equation: direction propagation: 定向传播 10 2 2 2 2 2 2 ( ) () 0 ( ) () 0 dV z V z dz dIz I z dz             0 0 0 0 ( ) ( ) z z z z Vz Ve Ve I z Ie Ie                - z e +Z   z e Z   