大学物理大学-射频电路第05讲圆波导与同轴线

ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology圆波导同轴线第5讲内容ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology5.1圆波导圆波导指横截面为圆形的空心金属管。场方程（纵向场表示法）只要求出纵向场，其它场分量可由上式求出。ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology和满足波动方程在圆柱坐标中表示为：边界条件为0zraE0zraHr理想导体表面切向电场为零222200tzcztzczEkEHkH22222211trrrrzHzEResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnologyTM波应用分离变量法，令代入方程，得0zH()()jzzERre2222222201()0cdmddRdRmkRdrrdrr上式等号左边只含与r有关的项，右边只含与φ有关的项。欲使此式对一切的r、φ值均成立，等式两边应分别等于同一常数m2，即22222221crdRrdRkrRdrRdrResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology上面第一式的通解为根据圆周自然边界条件，得m为整数.第二式为贝塞尔方程，其通解为12coscossin0,1,2,sinmAmAmAmmL0123456789101112-0.4-0.200.20.40.60.81kcrJ0J1J2J30123456789101112131415-1-0.8-0.6-0.4-0.200.20.40.60.81kcrN1N2N312()()()mcmcRrBJkrBNkr()mcJkr()mcNkrResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology根据自然边界条件：得根据理想导体表面边界条件,得截止波数为m阶Bessel函数的第n个零点。截止波长20B()0mcJka1,2,mncpknaL2cmnap(0)zErmnpResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology于是，TMmn模的电场纵向分量为显然，TMm0模不存在。相位常数与波阻抗分别为0cos0,1,2,(),sin1,2,3,jzmnzmmmpEEJremnaLL2222mncrTMrpkkaEEZHHkResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnologyTE波同理,可得圆柱形波导中TE波的为为m阶Bessel函数导数的第n个零点。TE波的相位常数与波阻抗分别为zH0zE0cos0,1,2,()sin1,2,3,jzzmcmmHHJkremnLLmncpka()0mmnJp2cmnapmnp2222mncrTErpkkaEEkZHHResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology()mcJkrResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology圆波导模式分布ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology圆波导的模式简并现象模式简并是指两种模式的m,n值不同，场结构不同，但截止波长相同，传输特性相同圆波导有两种简并现象，一种是TE0n和TM1n的简并。因为，故另一种是极化简并，模式的m，n相同，场分量相同，只是极化面旋转了90度当m不为零时，圆波导因为存在极化简并，使得信号传输中可能产生极化面偏转，故很少用于长距离传输01nnccTETM'01nnPPResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology极化简并ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology圆波导常用的三个模式圆波导常应用TE11、TE01和TM01模TE11模主模与矩形波导TE10模相近，可用作矩形—圆波导转换存在极化简并可用作极化衰减器、波形转换器或铁氧体环形器等ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology11c3.41TEaEHResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology圆波导TE11模的电场动态图ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology圆波导TE11模的电场动态图ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology圆波导TE11模的电场动态图ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology圆波导TE11模的磁场动态图ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology圆波导TE11模的磁场动态图ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology圆波导TE11模的磁场动态图ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology矩形波导TE10模与圆波导TE11模转换器ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnologyTE01模—圆波导中损耗最低的模式高次模场强轴对称，无极化简并电流无纵向分量损耗最低，频率升高，损耗下降可用于长距离传输线作高Q谐振腔ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnologyTE01模场与壁面电流分布01c1.64TEaEHResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology圆波导TE01模的电场动态图ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology圆波导TE01模的磁场动态图ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology圆波导TE01模的磁力线动态图ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology圆波导TE01模的电流动态图ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnologyTE01模高Q谐振腔ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnologyTM01模高次模场强轴对称，无简并轴线上纵向电场最强壁面上只有纵向电流可作雷达旋转关节ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology01c2.62TMaEHTM01模场与壁面电流分布图中虚线为电力线ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology圆波导TM01模的电场动态图ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology圆波导TM01模的电场动态图ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology圆波导TM01模的电场动态图ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology圆波导TM01模的磁场动态图ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology圆波导TM01模的磁场动态图ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology圆波导TM01模的磁场动态图ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology圆波导TM01模的电流动态图ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology5.2同轴线同轴线是由两根共轴的圆柱导体所组成，内外导体间均匀填充时，主模为TEM波，也可传输TE、TM波（高次模）。ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnologyTEM波根据Maxwell方程组，同轴线TEM波满足于是0zzEH10rrjEjHEr()10rjHjErHrr000jzrrzrzEEerEHEEHHResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnologyTEM模场分布EHResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTechnology同轴线横截面TEM模电场动态图ResearchInstituteofAntennas&RFTechniquesSouthChinaUniversityofTe