●●● Microwave and RF Design of ●●●● ●●●●● ●●●● ●●●●0 Wireless Systems ●●●0 ●●● ● ● Chapter 2 Transmission Lines and Microwave Network 传输线和微波网络 Dr.Xian Qi Lin 1
Microwave and RF Design of Wireless Systems Transmission Lines and Microwave Network 传输线和微波网络 Chapter 2 Dr. Xian Qi Lin 1
●●● ●●●● ●●●● ●●●0 2.1 Transmission line ●●●●0 ●●●0 ●●●● 传输线 ● §2.2 The Smith Chart 史密斯圆图 2.3 Microwave Network Analysis 微波网络分析 S 2.4 Impedance Matching 阻抗匹配 2
§2.1 Transmission line 传输线 §2.2 The Smith Chart 史密斯圆图 §2.4 Impedance Matching 阻抗匹配 §2.3 Microwave Network Analysis 微波网络分析 2
●●● Microstrip line ●●●● ●●●●● ●●●0 ●●●●0 Substrate ●●●● ●●●● ●● Ground Ground Ground o1/2o 3
3 Ground Ground Substrate Ground Microstrip line
●●● ●●●● S 2.1 Transmission line ●●●● ●●●0 ●●●●0 ●●●0 ●●● ● physical dimension 物理尺寸 Normalized 18 waveguide wavelength length 波导波长 归一化长度 Circuit analysis ī17> 4
§2.1 Transmission line physical dimension 物理尺寸 waveguide wavelength 波导波长 Transmission line: l 1 l 1 Normalized length 归一化长度 Circuit analysis l 1 4 l g
●●● ●●●● ●●●● ●●●● ●●●● 1.Lumped element model for a transmission line ●●●● 传输线的集总参数模型 2.Wave Propagation on a Transmission Line 波在传输线上的传播 3.Lossless of Transmission Lines无损耗的传输线 4.Terminated Transmission Lines终止传输线 5.Special Case of Terminated Transmission Lines 终止传输线的特例 6.Generator and Load Mismatches 源和负载的匹配 5
1. Lumped element model for a transmission line 传输线的集总参数模型 2. Wave Propagation on a Transmission Line 波在传输线上的传播 3. Lossless of Transmission Lines无损耗的传输线 4. Terminated Transmission Lines终止传输线 5. Special Case of Terminated Transmission Lines 终止传输线的特例 6. Generator and Load Mismatches 源和负载的匹配 5
●●● 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