麦克斯韦方程组 微波技术与天线

1.7MaxwellEquations麦克斯韦方程组,GausslawformagnetismAmpereslawGausslawforelectricityFaradayslawofinduction,(2)Hollowwaveguide:Rectangular,Circular,Ridge,Elliptical,Chapter2TransmissionLine,(1)2-wireline：Parallelline，CoaxialLine(Cable),Stripline,Microstripline,双线：平行线，同轴线（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,ParalleltwoLine,平行双线,CoaxialLine,AirDielectricCoaxialCable空气介质同轴电缆,FoamDielectricCoaxialCable泡沫介质同轴电缆,同轴线,Stripline,带状线,MicrostripLine,微带线,Coupled-lineband-passfilter(Equiripple,3rdorder,Fc=1.7GHz,BW=100MHz),http:/paginas.fe.up.pt/hmiranda/etele/microstrip/,http:/paginas.fe.up.pt/hmiranda/etele/microstrip/,Bi-directionalcoupler(Fc=1.83GHz,C=15dB),Stepped-impedancelow-passfilter(Maximallyflat,7thorder,Fc=2.0GHz),http:/paginas.fe.up.pt/hmiranda/etele/microstrip/,Stepped-impedancelow-passfilter(Flattimedelay,5thorder,Fc=700MHz),Commensurated-linelow-passfilter(Equiripple,3rdorder,Fc=1.9GHz),http:/paginas.fe.up.pt/hmiranda/etele/microstrip/,Hairpinband-passfilter(Equiripple,3rdorder,Fc=1.69GHz,BW=100MHz),http:/paginas.fe.up.pt/hmiranda/meteofeup/,SiGeMMICLNAwithintegratedmicrostripBPF,WaveGuide-BendRectangularWG,波导-弯矩形波导,H-TE-T,Magic-T,魔-T,CoaxialToWGAdapter,同轴到波导的适配器,TEM,TEM:TransverseElectromagnetic,横电磁波,TE:TransverseElectric,横电波,TM:TransverseMagnetic,横磁波,TE,TM,TransmissionLineEquations,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+jwLR+jX,G:,G+jwCG+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,Transmissionlineequations（telegrapherequations）传输线方程（电报方程）,Time-harmonicfield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，即电压电流在传输线上的分布情况。,Generalsolution通解,g2=ZY=(R+jwL)(G+jwC),g2=ZY=(R+jwL)(G+jwC),TransmissionLineParameters,Characteristicimpedance特性阻抗,某同轴电缆产品的说明,Propagationconstant传播常数,dB(decibel)andNp(neper)分贝和奈培,a:dB/mNp/m,dB:20log(V1/V2);10log(P1/P2)Np:ln(V1/V2);(1/2)ln(P1/P2),1Np=?dB;1dB=?Np,LosslessTL无耗传输线,R=G=0a=0then,Phasevelocityandwavelengthl相速度和波长l,相位为bz+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？,Phasevelocity相速度,相位为常数,两边对t求导,频率,频率,Wavelength波长,Inputimpedance输入阻抗,z=0时，U(z)=？I(z)=?,2A1=,Terminal（z=0)VoltageandCurrent:Ul=A1+A2Il=(A1-A2)/Z0,终端（z=0）电压和电流,Ul+Z0Il,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.,Opencircuit开路（Zl=）,Shortcircuit短路（Zl=0）,whenz=l/4Zin=?,例题:,LoadImpedance:ZL=100WZ01=50W,z=l/4,findZ02Tomatch（Zin=50W),解:,Reflectioncoefficient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.,ZinandG,Questions,1.GL=0,ZL=?,2.ZL=Z0,Zin(z)=?,3.ZL=Z0,G(z)=?,ZL=Z0