用非均匀网格FDTD法分析介质填充波导和微带线的传输特性
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摘要
本文主要开展非均匀网格FDTD方法在波导和微带线问题中的应用研究,基于非均匀网格法结合Matlab编写了相关计算程序,对多种场域条件下的波导和微带线进行了模拟计算,分析了其相关物理参数或模场特性。
首先,简要综述了各类电磁场问题的常用求解方法,对FDTD方法的发展历程和基本原理进行了综述性分析;结合文献和编程计算经验,阐述了FDTD方法的数值稳定性和数值色散对空间网格和时间步长的要求、介质分界面的处理方法、吸收边界的设置方法以及激励源的选择与设计。基于FDTD方法的数值稳定性和数值色散对空间网格和时间步长的要求,推导出非均匀网格FDTD方法的网格划分公式。
其次,提出用非均匀网格FDTD法计算了部分介质填充矩形波导、部分介质填充双脊波导、部分介质填充三脊波导和部分介质填充非对称脊波导的截止频率,并将计算结果与相关文献的报道结果进行了比较,证明了方法和所编程序的正确性。计算结果表明:非均匀网格FDTD法比均匀网格FDTD法的运行时间节约了10%-20%。
最后,提出用非均匀网格FDTD法分析计算了微带线的特性阻抗及高次模的截止频率。首先用非均匀网格FDTD法计算了矩形-微带内导体同轴传输线、标准微带线、倒置微带线和双带线的特性阻抗,并与相关文献进行了比较,计算结果表明:非均匀网格FDTD法比均匀网格FDTD法的运行时间节约5%-20%。此外还用非均匀网格FDTD法比均匀网格FDTD法计算了屏蔽微带线的各高阶模式的截止特性,并对所作图形进行分析推测。
In this paper, research work on the application of Non-uniform FDTD method in waveguide and microstrip line is carried out. The relative programs are made based on non-uniform grid FDTD method and the Matlab. The electromagnetic fields of the waveguide and microstrip line in different conditions are simulated and calculated. Also some important physics parameters and the mode fields are obtained.
Various methods to analyze electromagnetic field problems are introduced. The development and basic theory of FDTD method are synthetically analyzed. The requirements for the time interval and spatial condition for stability of FDTD method based on different boundary and optimization design excitation sources in making programs are discussed. The formula of non-uniform mesh FDTD method is also derived.
Based on non-uniform FDTD method, the cutoff frequencies of rectangular waveguide partially filled with dielectric are calculated. And the cutoff frequencies of the double- and tri-ridged waveguide, and unsymmetrical ridged waveguide partially filled with dielectric are also calculated. The results agreed well with that of the reported in the literature. It has been shown that non-uniform FDTD method can economize on running time 10%-20%.
Based on the non-uniform FDTD method, the characteristic impedance and high-order mode cutoff frequencies of microstrip line are calculated. First the characteristic impedance of rectangle-microstrip line, the standard microstrip line, inverted microstrip line, and double-microstrip line are calculated by non-uniform FDTD method. The results agree well with that of the reported in the literature. It has been shown that non-uniform FDTD method can economize on running time 5%-20%. The high-order mode cutoff frequencies of microstrip line are calculated, and the change curves are also obtained.
首先,简要综述了各类电磁场问题的常用求解方法,对FDTD方法的发展历程和基本原理进行了综述性分析;结合文献和编程计算经验,阐述了FDTD方法的数值稳定性和数值色散对空间网格和时间步长的要求、介质分界面的处理方法、吸收边界的设置方法以及激励源的选择与设计。基于FDTD方法的数值稳定性和数值色散对空间网格和时间步长的要求,推导出非均匀网格FDTD方法的网格划分公式。
其次,提出用非均匀网格FDTD法计算了部分介质填充矩形波导、部分介质填充双脊波导、部分介质填充三脊波导和部分介质填充非对称脊波导的截止频率,并将计算结果与相关文献的报道结果进行了比较,证明了方法和所编程序的正确性。计算结果表明:非均匀网格FDTD法比均匀网格FDTD法的运行时间节约了10%-20%。
最后,提出用非均匀网格FDTD法分析计算了微带线的特性阻抗及高次模的截止频率。首先用非均匀网格FDTD法计算了矩形-微带内导体同轴传输线、标准微带线、倒置微带线和双带线的特性阻抗,并与相关文献进行了比较,计算结果表明:非均匀网格FDTD法比均匀网格FDTD法的运行时间节约5%-20%。此外还用非均匀网格FDTD法比均匀网格FDTD法计算了屏蔽微带线的各高阶模式的截止特性,并对所作图形进行分析推测。
In this paper, research work on the application of Non-uniform FDTD method in waveguide and microstrip line is carried out. The relative programs are made based on non-uniform grid FDTD method and the Matlab. The electromagnetic fields of the waveguide and microstrip line in different conditions are simulated and calculated. Also some important physics parameters and the mode fields are obtained.
Various methods to analyze electromagnetic field problems are introduced. The development and basic theory of FDTD method are synthetically analyzed. The requirements for the time interval and spatial condition for stability of FDTD method based on different boundary and optimization design excitation sources in making programs are discussed. The formula of non-uniform mesh FDTD method is also derived.
Based on non-uniform FDTD method, the cutoff frequencies of rectangular waveguide partially filled with dielectric are calculated. And the cutoff frequencies of the double- and tri-ridged waveguide, and unsymmetrical ridged waveguide partially filled with dielectric are also calculated. The results agreed well with that of the reported in the literature. It has been shown that non-uniform FDTD method can economize on running time 10%-20%.
Based on the non-uniform FDTD method, the characteristic impedance and high-order mode cutoff frequencies of microstrip line are calculated. First the characteristic impedance of rectangle-microstrip line, the standard microstrip line, inverted microstrip line, and double-microstrip line are calculated by non-uniform FDTD method. The results agree well with that of the reported in the literature. It has been shown that non-uniform FDTD method can economize on running time 5%-20%. The high-order mode cutoff frequencies of microstrip line are calculated, and the change curves are also obtained.
引文
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[9]赵安平,何晓东,余荣金等.一种可用于分析任意介电常数张量的各向异性波导导模的二维时域有限差分模型[J].光子学报,1998,27(10):880-885
[10]朱燕杰,董小鹏,杨晓理等.时域有限差分法在光波导分析中的应用及改进[J].光学学报,2003,23(5):565-571.
[11]刘靖,元秀华,黄德修等.标量FDTD法分析渐变折射率光波导模场分布[J].华中科技大学学报(自然科学版).2002,30(2):63-65.
[12]毛从光,周辉.二维圆柱坐标系中五角形共形网格算法[J].强激光与粒子束,2002,14(6):897-900.
[13]项永华.正方形外导体-微带内导体传输线特性阻抗严格解[J].舰船电子工程,2004,27(3):26-29.
[14]杜正伟,阮成礼.几种新颖传输线的特性阻抗[J].电子科技大学学报(自然科学版),1994,23(4):374-378.
[15]吴正德,张志军等.几种复合传输线特性阻抗的计算[J].电子学报,1995,23(3):82-85.
[16]J P Berenger.A perfectly mathed layer for the absorption of electromagnetic waves[J].J.Comput.Phys,1994,114(2):185-200.
[17]J P Berenger.Perfectly matched layer for the FDTD solution of wave-structure interaction problem[J].IEEE.Trans.Antennas Propagat,1996,AP-44(1):110-117.
[18]J P Berenger.Three-dimensional perfectly matched layer for the absorption of electromagnetic waves[J].J.Comput.Phys.1996,127(2):363-379.
[19]Z S Sacks,Kingsl and D M,Lee D M and Lee J F.A perfectly matched anisotropic absorber for use an absorbing boundary condition[J].IEEE Trans.Antennas Propagat,1995,AP-43(12):1460-1463.
[20]S D Gedney.An anisotropic perfectly matched layer absorbing media for the truncation of FDTD lattices[J].IEEE Trans.Antennas Propagat,1995,AP-44(12):1630-1639.
[21]徐耀忠,杨鸿生,王惠燕.介质加载圆形槽波导的分析[J].微波学报,2004,20(3):26-29.
[22]李春雨,邹振祝.非均匀介质有限元法[J].力学也实践,1999,20:10-12.
[23]Khona Garb,Raphael Kastner.Characteristic Impedance of a Rectangular Double-Ridged TEM Line[J].IEEE Trans.On Microwave Theory and Techniques,1997,45(4):554-557.
[24]王照明,奈守宪等.非线性薄膜波导的有限差分法计算[J].光电子技术与信息,2000,13(2):25-28.
[25]周晓军,喻志远,林为干等.2D-FDTD法计算波导截止频率的激励源设计[J].红外一毫米波学报,1998,17(3):236-240.
[26]崔芙蓉,季飞,胡斌杰等.FDTD法计算波导截止频率时激励源的优化设计[J].华南理工大学学报(自然科学版),2000,28(9):40-44.
[27]李容,张昌林.FDTD法建模中激励源的选择与设置[J].铁道学报,23(4):44-47.
[28]尹家贤,谭怀英,刘克成.FDTD中微带线激励源设置的新方法[J].电波科学学报,2000,15(20):204-207.
[29]张文俊,高磊,谢处方。非均匀网格FDTD法[J].电子学报,1995,23(12):15-17.
[30]张琰,高本庆.FDTD计算中非均匀网格网络的分析及综合[J].电子学报,2001,29(7):965-969.
[31]周国祥,杨明武,侯整风.在直角坐标下一种快速有效产生非均匀FDTD网格的算法[J].微波学报,2002,18(2):67-70.
[32]张玉,梁昌洪.一种新型基站天线的非均匀网格FDTD分析[J].电子与信息学报,2003,25(8):1120-1125.
[33]张玉,李龙,梁昌洪.非均匀网格FDTD分析波导宽边辐射缝隙特性[J].通信学报,2004,25(5):143-147.
[34]H L JIANG.Analysis of computation error in antenna's simulation by using non-uniform mesh FDTD[J].IEICE Trans.1998,E00-A(1):1-9.
[35]E A Navarro,N T Sangary,J Litava.Some considerations on the accuracy of the non-uniform FDTD method and its application to waveguide analysis when combine with the perfectly matched layer technique[J].IEEE Trans,1996,MTT-44(7):1115-1124.
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