滤波器6-耦合谐振电路20120412

ResearchInstituteofAntenna&RFTechniques第6讲耦合谐振电路《现代射频滤波器理论与设计》陈付昌,涂治红华南理工大学电子与信息学院天线与射频技术研究所TEL:22236201-604Email:[e-mail]enna&RFTechniquesSouthChinaUniversityofTechnology第6讲内容引言耦合谐振电路的耦合矩阵一般耦合理论外部Q值SouthChinaUniversityofTechnologyResearchInstituteofAntenna&RFTechniquesSouthChinaUniversityofTechnology6.1引言耦合谐振电路是在无线通信领域中发挥着重要的作用的窄带带通滤波器设计中的一个重要因素。耦合谐振电路设计滤波器的方法适用于任何类型和任何结构的滤波器。这种设计方法基于谐振器之间的耦合系数和输入输出的外部Q值。ResearchInstituteofAntenna&RFTechniquesSouthChinaUniversityofTechnology6.2耦合谐振器滤波器的耦合距阵电流环路方程电压节点方程磁耦合系数电耦合系数一般耦合系数ResearchInstituteofAntenna&RFTechniquesSouthChinaUniversityofTechnology6.2.1电流环路方程111122112112222112211010NNsNNNNNNNNRjLijLijLiejCjLijLijLijCjLijLiRjLijCResearchInstituteofAntenna&RFTechniquesSouthChinaUniversityofTechnology111211121122221211001NsNNNNNNNRjLjLjLjCiejLijLjLijCijLjLRjLjC[][][]ZieResearchInstituteofAntenna&RFTechniquesSouthChinaUniversityofTechnology对于同步调谐情况0[][]ZLFBWZ0012121,NNLCFBWLLLLCCCC111200022100120001111[]11NNNNNLRLpjjLFBWLFBWLFBWLLjpjLFBWLFBWZLLRjjpLFBWLFBWLFBW001()pjFBWResearchInstituteofAntenna&RFTechniquesSouthChinaUniversityofTechnologyijijijijLMMmLFBW定义：耦合系数和外部Q值011(1,)ieieieRqQFBWiNLQ1211212121[]1NeNNNeNpjmjmqjmpjmZjmjmpqResearchInstituteofAntenna&RFTechniquesSouthChinaUniversityofTechnology对于非同步（异步）调谐情况ijijijLMijLL11121121222121[]1NeNNNNNeNpjmjmjmqjmpjmjmZjmjmpjmqResearchInstituteofAntenna&RFTechniquesSouthChinaUniversityofTechnology111111222220ssNNeeiRabRRabiRResearchInstituteofAntenna&RFTechniquesSouthChinaUniversityofTechnology2212111211111001111110022,1[],[]NNssaassNNRRibbRiSSaeaeeeiZiZLFBWLFBW11211011111102[]21[]NNRRSZLFBWRSZLFBW1211111111112[]21[]NeeNeSZqqSZq根据外部Q值的定义ResearchInstituteofAntenna&RFTechniquesSouthChinaUniversityofTechnology6.2.2电压节点方程11112211211222211221()1()01()0NNsNNNNNNNNGjCvjCvjCvijLjCvjCvjCvjLjCvjCvGjCvjLResearchInstituteofAntenna&RFTechniquesSouthChinaUniversityofTechnology111211121122221211001NsNNNNNNNGjCjCjCjLvijCijCjCvjLvjCjCRjCjL[][][]YviResearchInstituteofAntenna&RFTechniquesSouthChinaUniversityofTechnology对于同步调谐情况0[][]YCFBWY0012121,NNLCFBWLLLLCCCC111200022100120001111[]11NNNNNCGGpjjLFBWLFBWCFBWCCjpjCFBWCFBWZCCGjjpCFBWCFBWCFBW001()pjFBWResearchInstituteofAntenna&RFTechniquesSouthChinaUniversityofTechnologyijijijijCMMmCFBW定义：耦合系数和外部Q值011(1,)ieieieGqQFBWiNCQ1211212121[]1NeNNNeNpjmjmqjmpjmYjmjmpqResearchInstituteofAntenna&RFTechniquesSouthChinaUniversityofTechnology对于非同步（异步）调谐情况ijijijCMijCC11121121222121[]1NeNNNNNeNpjmjmjmqjmpjmjmYjmjmpjmqResearchInstituteofAntenna&RFTechniquesSouthChinaUniversityofTechnology111111222220ssNNivGiabGGabvGResearchInstituteofAntenna&RFTechniquesSouthChinaUniversityofTechnology2212111211111001111110022,1[],[]NNssaassNNGGvbbGvSSaiaiiivYvYLFBWLFBW11211011111102[]2[]1NNGGSYCFBWGSYCFBW1211111111112[]2[]1NeeNNSYqqSYq根据外部Q值的定义ResearchInstituteofAntenna&RFTechniquesSouthChinaUniversityofTechnology6.2.3一般耦合距阵从上面两节的讨论中可以看出，归一化阻抗矩阵和归一化导纳矩阵是一致的。统一的表达式：1211111111112[]2[]1NeeNeSAqqSAq[][][][]AqsIjm其中是[I]一个阶单位矩阵；[q]是一个除外q11=1/qe1和qNN=1/qeN其余元素全为零的N×N阶矩阵；[m]就是通常所说的耦合矩阵，它是一个N×N阶互易矩阵，即mij=mji。对于异步调谐的情况，[m]矩阵的对角线上可以有非零的元素出现。ResearchInstituteofAntenna&RFTechniquesSouthChinaUniversityofTechnology6.3一般耦合理论得到耦合系数后，就需要根据耦合系数确定耦合谐振器之间的物理耦合结构。耦合一般分成电耦合、磁耦合和混合耦合。ResearchInstituteofAntenna&RFTechniquesSouthChinaUniversityofTechnology从参考面和参考面6.3.1对称耦合谐振器分析(I)－电耦合11'TT22'TT112221mmIjCVjCVIjCVjCV11221221mYYjCYYjC对称面是电壁（短路）'TT12emfLCC12mmfLCC2222mmeEmeCffkCff对称面是磁壁（开路）'TTResearchInstituteofAntenna&RFTechniquesSouthChinaUniversityofTechnology6.3.1对称耦合谐振器分析(II)－磁耦合11'TT22'TT从参考面和参考面对称面是电壁（短路）'TT对称面是磁壁（开路）'TT112221mmVjLIjLIVjLIjLI11221221mZZjLZZjL12emfLLC12mmfLLC2222memMemLffkLffResearchInstituteofAntenna&RFTechniquesSouthChinaUniversityofTechnology6.3.1对称耦合谐振器分析(III)－混合耦合11'TT22'TT从参考面和参考面对称面是电壁和磁壁'TT11221221'mYYjCYYjC11221221'mZZjLZZjL12''12''emmmmmfLLCCfLLCC2222''''emmmxemmmffCLLCkffLCLC''''mmxMELCkkkLCResearchInstituteofAntenna&RFTechniquesSouthChinaUniversityofTechnology6.3.2非对称耦合谐振器分析(I)－电耦合谐振条件LRZZ122211221011mmmjLjLjCLCCLCC422121212112210mLLCCLLCLCLC2211221122121,2212121242mmLCLCLCLCLLCLLCCLLC2222220201020121222201022102011212meCkCC0111LC0222LC22212221EK