1、1.7 Maxwell Equations 麦克斯韦方程组,Gauss law for magnetism Amperes law Gauss law for electricity Faradays law of induction,(2) Hollow waveguide: Rectangular, Circular, Ridge, Elliptical,Chapter 2 Transmission Line,(1) 2-wire line： Parallel line，Coaxial Line(Cable), Stripline, Microstrip line,双线： 平行线， 同轴线
2、（电缆）， 带状线，微带线,空心波导（按截面分）：矩形，圆形 ，脊形，椭圆形,传输线,Parallel two Line,平行双线,Coaxial Line,Air Dielectric Coaxial Cable 空气介质同轴电缆,Foam Dielectric Coaxial Cable 泡沫介质同轴电缆,同轴线,Stripline,带状线,Microstrip Line,微带线,Coupled-line band-pass filter (Equiripple, 3rd order, Fc = 1.7 GHz, BW = 100 MHz),http:/paginas.fe.up.pt/h
3、miranda/etele/microstrip/,http:/paginas.fe.up.pt/hmiranda/etele/microstrip/,Bi-directional coupler (Fc=1.83 GHz, C = 15 dB),Stepped-impedance low-pass filter (Maximally flat, 7th order, Fc = 2.0 GHz),http:/paginas.fe.up.pt/hmiranda/etele/microstrip/,Stepped-impedance low-pass filter (Flat time delay
4、, 5th order, Fc = 700 MHz),Commensurated-line low-pass filter (Equiripple, 3rd order, Fc = 1.9 GHz),http:/paginas.fe.up.pt/hmiranda/etele/microstrip/,Hairpin band-pass filter (Equiripple, 3rd order, Fc = 1.69 GHz, BW = 100 MHz),http:/paginas.fe.up.pt/hmiranda/meteofeup/,SiGe MMIC LNA with integrated
5、 microstrip BPF,Wave Guide -Bend Rectangular WG,波导 -弯矩形波导,H-T E-T,Magic-T,魔-T,Coaxial To WG Adapter,同轴到波导的适配器,TEM,TEM : Transverse Electromagnetic,横电磁波,TE : Transverse Electric,横电波,TM : Transverse Magnetic,横磁波,TE,TM,Transmission Line Equations,传输线等效电路模型 （建立一维坐标，正方向向左，用 z 来表示）,传输线方程,z,0,R:,R+jwL R+jX
6、,G:,G+jwC G+jB,单位长度电阻,单位长度电感,L:,阻抗,单位长度电导,C:,单位长度电容,导纳,量纲：欧姆/米,量纲：亨利/米,量纲：,量纲：,量纲：,量纲：,KVL:基尔霍夫电压定律,？,KCL:基尔霍夫电流定律,Transmission line equations （ telegrapher equations ） 传输线方程（电报方程）,Time-harmonic field 时谐场,一阶常微分方程,二阶常微分方程,g2=ZY=(R+jwL)(G+jwC),g2=ZY=(R+jwL)(G+jwC),求该二阶常系数常微分方程组的解，得到电压，电流与z的关系，即电压电流在传输
7、线上的分布情况。,General solution 通解,g2=ZY=(R+jwL)(G+jwC),g2=ZY=(R+jwL)(G+jwC),Transmission Line Parameters,Characteristic impedance 特性阻抗,某同轴电缆产品的说明,http:/ constant传播常数,dB (decibel) and Np (neper)分贝和奈培,a : dB/m Np/m,dB : 20log(V1/V2) ; 10log(P1/P2)Np : ln(V1/V2) ; (1/2) ln(P1/P2),1Np=?dB ; 1dB=?Np,Lossless
8、TL 无耗传输线,R=G=0 a=0 then,Phase velocity and wavelength l 相速度和波长l,相位为 b z+wt, b 和w 都看成是常数，则z 和 t 的变化都可以改变相位,注意：下面电压的方程，与前面的有什么不同？,Phase velocity 相速度,相位为常数,两边对 t 求导,频率,频率,Wavelength 波长,Input impedance 输入阻抗,z=0时，U(z)=？I(z)=?,2A1=,Terminal（z=0) Voltage and Current:Ul=A1+A2 Il=(A1-A2)/Z0,终端（z=0）电压和电流,Ul+Z
9、0Il,Ul-Z0Il,2A2=,2A1=,Ul+Z0Il,Ul-Z0Il,2A2=,例题：传输线的特性阻抗Z0=50欧姆，在下列情况下距负载l/8处的 输入阻抗为多少？1.负载为75欧姆。2.负载为50欧姆。3.负载为0欧姆。4.负载为5000M欧姆。,解：1.,2.,3.,4.,Open circuit 开路（Zl= ）,Short circuit 短路（Zl=0 ）,when z=l/4 Zin=?,例题:,Load Impedance : ZL=100W Z01=50 W,z=l/4,find Z02To match （Zin=50W),解:,Reflection coefficien
10、t 反射系数,例题：负载的反射系数为0.5+0.866j，1.距负载l/3处的反射系数为多少？2.距负载7l/12处的反射系数为多少？,解:,1.,2.,Zin and G,Questions,1. GL=0, ZL=?,2. ZL=Z0, Zin(z)=?,3. ZL=Z0, G(z)=?,ZL=Z0,Zin(z)= Z0,G(z)=0,Voltage Standing Wave Ratio (VSWR) 电压驻波比,Example:,A lossless 50W transmission line is terminated in a load of 35+j55W Find VSWR,Solution：,
