基于FDTD方法的超宽带电磁场数值模拟
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摘要
超宽带信号是就信号的相对带宽而言,当信号的带宽与中心频率之比大于25%时称为超宽带信号。超宽带电磁波因其频带宽、分辨率高、回波信号能携带被测目标丰富的特征信息等特点,被广泛应用于目标探测和成像领域。本文利用时域有限差分方法对室内环境下电磁波传播特性进行了数值模拟。分别仿真验证了二维,三维情况下FDTD方法的有效性,分析了超宽带脉冲源的性质以及传播特性。
本文所做的工作就是基于电磁波的基本理论:首先介绍了FDTD格式以及各分量节点的取法。然后介绍了FDTD方法的数值稳定性和数值色散问题:包括时间间隔的稳定性要求以及Courant稳定性条件--即空间步长和时间间隔之间所需满足的关系。此外,还介绍了时域有限差分方法的边界条件:先从波动方程角度介绍了FDTD的吸收边界条件,由此引出了Mur的一阶、二阶条件;然后又介绍了一种吸收效果较好的完全匹配层(PML)吸收边界条件。通过分析FDTD的基本算法和将其应用于超宽带电磁脉冲信号的仿真研究需特殊处理的一些方面,建立超宽带电磁脉冲信号传播的FDTD二维及三维算法。分析超宽带电磁脉冲在空气中的能量衰减特性。以FDTD方法理论为基础,制定程序流程,利用MATLAB 7.0软件编程实现。分别以自由空间中高斯脉冲源问题和电偶极子辐射问题为例对程序进行了校验,数值模拟结果与解析结果能很好地符合,证实了所编写程序的有效性和正确性。分析了超宽带电磁脉冲在空气中及在室内环境下与物体作用的传播特性。同时数值模拟分析比较了PML层FDTD仿真中的作用。最后数值模拟分析了超宽带电磁脉冲信号在实际成像中的一个简单应用:模拟简单的室内环境进行FDTD模拟仿真。
A signal is called an Ultra-band signal (UWB) if its ratio of bandwidth to center-frequency exceeds 25%. Since it has many advantages such as high frequency bandwidth, high resolving power, its echo can take abundant characteristic information of the detected target, it has been widely used in target detection and imaging technology. In this paper, the response characteristic of ultra-wideband in indoor environment is simulated numerically based on Finite Difference Time Domain Method. Based on time domain Maxwell Equation, the basic theory of FDTD Method of two-dimensional and three dimensional under Cartesian coordinates are introduced in detail, and the validity of FDTD method is verified by simulation on propagation of UWB pulse in free space.
This paper is based on the basic principle of electromagnetic wave. The FDTD formulation and cell concept are introduced in two-dimensional and three-dimensional Cartesian coordinates. And then, the stability and numerical dispersion of the FDTD method are investigated. The absorbing boundary conditions for FDTD are also discussed in this paper. We first derive the Mur's absorbing boundary conditions, then, an efficient boundary condition is introduced, which is so-called perfectly matched layer(PML).This paper builds the two-dimensional and three-dimensional FDTD algorithm of UWB EM pulse propagation based on the electromagnetic wave principle and FDTD algorithm. We analyze energy attenuation character of UWB in free space and other dielectric objects. Based on theory of FDTD method, we realizing the simulation of FDTD method using MATLAB 7.0 software. The validity and correctness of the simulations are verified by researching on propagation of Gaussian pulse and electric dipole transmitted in free space. And the result turns out the numerical solutions are consistent with analytic solutions. We also analyze the function of the PML layer in FDTD simulation. Finally, we did simulation in an indoor environment using the FDTD method.
本文所做的工作就是基于电磁波的基本理论:首先介绍了FDTD格式以及各分量节点的取法。然后介绍了FDTD方法的数值稳定性和数值色散问题:包括时间间隔的稳定性要求以及Courant稳定性条件--即空间步长和时间间隔之间所需满足的关系。此外,还介绍了时域有限差分方法的边界条件:先从波动方程角度介绍了FDTD的吸收边界条件,由此引出了Mur的一阶、二阶条件;然后又介绍了一种吸收效果较好的完全匹配层(PML)吸收边界条件。通过分析FDTD的基本算法和将其应用于超宽带电磁脉冲信号的仿真研究需特殊处理的一些方面,建立超宽带电磁脉冲信号传播的FDTD二维及三维算法。分析超宽带电磁脉冲在空气中的能量衰减特性。以FDTD方法理论为基础,制定程序流程,利用MATLAB 7.0软件编程实现。分别以自由空间中高斯脉冲源问题和电偶极子辐射问题为例对程序进行了校验,数值模拟结果与解析结果能很好地符合,证实了所编写程序的有效性和正确性。分析了超宽带电磁脉冲在空气中及在室内环境下与物体作用的传播特性。同时数值模拟分析比较了PML层FDTD仿真中的作用。最后数值模拟分析了超宽带电磁脉冲信号在实际成像中的一个简单应用:模拟简单的室内环境进行FDTD模拟仿真。
A signal is called an Ultra-band signal (UWB) if its ratio of bandwidth to center-frequency exceeds 25%. Since it has many advantages such as high frequency bandwidth, high resolving power, its echo can take abundant characteristic information of the detected target, it has been widely used in target detection and imaging technology. In this paper, the response characteristic of ultra-wideband in indoor environment is simulated numerically based on Finite Difference Time Domain Method. Based on time domain Maxwell Equation, the basic theory of FDTD Method of two-dimensional and three dimensional under Cartesian coordinates are introduced in detail, and the validity of FDTD method is verified by simulation on propagation of UWB pulse in free space.
This paper is based on the basic principle of electromagnetic wave. The FDTD formulation and cell concept are introduced in two-dimensional and three-dimensional Cartesian coordinates. And then, the stability and numerical dispersion of the FDTD method are investigated. The absorbing boundary conditions for FDTD are also discussed in this paper. We first derive the Mur's absorbing boundary conditions, then, an efficient boundary condition is introduced, which is so-called perfectly matched layer(PML).This paper builds the two-dimensional and three-dimensional FDTD algorithm of UWB EM pulse propagation based on the electromagnetic wave principle and FDTD algorithm. We analyze energy attenuation character of UWB in free space and other dielectric objects. Based on theory of FDTD method, we realizing the simulation of FDTD method using MATLAB 7.0 software. The validity and correctness of the simulations are verified by researching on propagation of Gaussian pulse and electric dipole transmitted in free space. And the result turns out the numerical solutions are consistent with analytic solutions. We also analyze the function of the PML layer in FDTD simulation. Finally, we did simulation in an indoor environment using the FDTD method.
引文
1朱义君,常力.UWB的主要特点及其在短距离通信中的应用前景[J].电子技术应. 2003(10):6~8
2李唐,刘亚峰.超宽带无线通信技术概述[J].天津通信技术. 2003(4):35~38
3 Terrence W Barrett. History of Ultra Wideband (UWB) Radar Communication:Pioneers And Innovators [J]. Progress in Electromagnetic Research Symposium. Cambridge. 2000
4 R. A. Scholtz, R. Weaver, E. Homier, J. Lee. UWB radio deployment challenges. Proceedings of IEEE International symposium on Personal Indoor Mobile Radio Communications, 2000(1): 620~625
5 A. H. Tewfik , E. Saberinia. High bit rate ultra-wideband OFDM. IEEE Transactions on Communication, 2002, 2260~2264
6 Felsen L B. Transient electromagnetic fields.NewYork: Sprniger-Verlag Berlin Heidelberg, 1976
7彭仲秋.瞬变电磁场.北京:高等教育出版社. 1989
8汪文秉.瞬变电磁场.西安:西安交通大学出版社. 1991
9王秉中.计算电磁学.科学出版社. 2002
10 Harrington R F. Time-Harmonic Electromagnetic Filed. New York: Mc Graw-Hill, 1961
11 Srtatton J A. Electromagnetic Theory. New York: McGraw-Hill,1941
12 Nachman A. Minireview : A brief perspective on computational electromagnetic. Comput.Phys.1996,12,6
13 Yee K S. Numerical Solution of Initial Boundary Value Problems Involving Maxwell’s Equation in Isotropic Media. IEEE Trans on Antennas and propagation,1996,14(8):302~307
14 Berneger J P. A Perfect Matched Layer for the Absorption of Electromagnetic Waves.Computational Physics,1994,114:185~200
15 Beernger J P. Three-Dimensional Perfectly Matched Layer for the Absorption of Electromagnetic waves. Computational Physics,1996,127;363~379
16王长清.电磁场计算中的时域有限差分法.北京:北京大学出版社,1994
17 Raymond Lubbers , Li. Chen. FDTD Calculation of Radiation Patterns ,Impendence and Gain For a Monopole Antenna on a Conducting Box. IEEE Trans. on Antennas and Propagation,1992,AP-40(12):1577-1583
18 Jurgens T G. A Broadband Absorbing Boundary Condition for the FDTD Modeling of Circular Waveguides. IEEE Trans On MIT-S , May.1995:35-38
19 W. P. Delaney. The Changing World, The Changing nature of Conflicts: critical Role for Military Radar .IEEE International Radar Conference 1995, 11~15
20 C. Fowler, J. Entzminger and J. Corum, Assessment of UWB Technology, IEE AES Magazine, November 1990,45~48
21冯奎胜卢万铮朱章虎电磁场数值计算方法分析。山西电子技术2005年第6期
22葛德彪.电磁波时域有限差分方法. 1~2
23 Goldberg M.Stability criteria for criteria for finite difference approximations to parabolic systems[J].Applied Numerical Mathematics,2000,33(15):509~515.
24 Juntunen J S,Tsiboukis T D.Reduction of numerical dispersion in FDTD method through artificial anisotropy[J].IEEE Trans.Microwave Theory Tech.,2000,48(4):582~588.
25 Berenger J P. A Perfectly Matched Layer for the Absorption of Electromagnetic Waves[J]. Journal of Computational Physics, 1994, 114: 185~200.
26 Katzetal D S. Validation and Extension to Three Dimensions of the Berenger PML Absorbing Boundary Condition for FDTD meshes[J]. IEEE Microwave and Guided Wave Letters, 1994, 4(8): 268~270.
27 Berenger J P. Three-Dimensional Perfectly Matched Layer for the Absorption of Electromagnetic Waves[J]. Journal of Computational Physics, 1996, 127: 363~379.
28 Gedney S D. An Anisotropic Perfectly Matched Layer-absorbing Medium for Truncation of FDTD Lattices. IEEE Trans .Antennas and Porpagation. 1996, 44( 12 ) ; 1630~1639
29王长清,祝西里.电磁场计算中的时域有限差分法[M].北京:北京大学出版社,1994.
30 Mur G. Absorbing Boundary Conditions for the Finite-Difference Approximation of The Time Domain Electromagnetic Field Equations [J]. IEEE Trans. Electeomagn. Compat.,1981.23(4):377-382
31杨军,张玉胜,傅君眉。Mur吸收边界条件的校正[J].微波学报,1996,12(10):30~34。
32谭怀英,梁甸农,刘克诚FDTD中一种新截断边界—ST WBC[J].电子学报,2001.29(3):421~422
33邵振海,洪伟。几种新的吸收边界条件在电磁散射中的应用[J].电波科学学报,1994,14(3):287 ~294。
34 Lee Wai, Mittra Ko Rai. A combination of FD-TD and Prony′s methods for analyzing microwave integrated circuits. IEEE MTT,1991,39(12): 2 176~2 181
35 Asi L A, Fai Sha. Dispersion analysis of anisotropic inhomogeneous waveguides using compact 2D-FDTD.Electronic Letters,1992,29(19): 1 451~1 452
36 Toland B, Houshmand B, Itoh T. Modeling of nonlinear active regions with the FDTD method. IEEE Microwave. Guided Wave,Letters,1993, 3(9): 333~335
37高本庆.时域有限差分法[M].北京国防工业出版社.1995
38 Brench C E. Source Selection Criteria for FDTD Models [A]. 1998.191~194.
39王长清,祝西里.电磁场计算中的时域有限差分法[M].北京:北京大学出版社,1994.
40王勇,于大鹏.一种用于UWB通信的正弦调制高斯脉冲[J].无线电通信技术,2005,31(1):9~11.
2李唐,刘亚峰.超宽带无线通信技术概述[J].天津通信技术. 2003(4):35~38
3 Terrence W Barrett. History of Ultra Wideband (UWB) Radar Communication:Pioneers And Innovators [J]. Progress in Electromagnetic Research Symposium. Cambridge. 2000
4 R. A. Scholtz, R. Weaver, E. Homier, J. Lee. UWB radio deployment challenges. Proceedings of IEEE International symposium on Personal Indoor Mobile Radio Communications, 2000(1): 620~625
5 A. H. Tewfik , E. Saberinia. High bit rate ultra-wideband OFDM. IEEE Transactions on Communication, 2002, 2260~2264
6 Felsen L B. Transient electromagnetic fields.NewYork: Sprniger-Verlag Berlin Heidelberg, 1976
7彭仲秋.瞬变电磁场.北京:高等教育出版社. 1989
8汪文秉.瞬变电磁场.西安:西安交通大学出版社. 1991
9王秉中.计算电磁学.科学出版社. 2002
10 Harrington R F. Time-Harmonic Electromagnetic Filed. New York: Mc Graw-Hill, 1961
11 Srtatton J A. Electromagnetic Theory. New York: McGraw-Hill,1941
12 Nachman A. Minireview : A brief perspective on computational electromagnetic. Comput.Phys.1996,12,6
13 Yee K S. Numerical Solution of Initial Boundary Value Problems Involving Maxwell’s Equation in Isotropic Media. IEEE Trans on Antennas and propagation,1996,14(8):302~307
14 Berneger J P. A Perfect Matched Layer for the Absorption of Electromagnetic Waves.Computational Physics,1994,114:185~200
15 Beernger J P. Three-Dimensional Perfectly Matched Layer for the Absorption of Electromagnetic waves. Computational Physics,1996,127;363~379
16王长清.电磁场计算中的时域有限差分法.北京:北京大学出版社,1994
17 Raymond Lubbers , Li. Chen. FDTD Calculation of Radiation Patterns ,Impendence and Gain For a Monopole Antenna on a Conducting Box. IEEE Trans. on Antennas and Propagation,1992,AP-40(12):1577-1583
18 Jurgens T G. A Broadband Absorbing Boundary Condition for the FDTD Modeling of Circular Waveguides. IEEE Trans On MIT-S , May.1995:35-38
19 W. P. Delaney. The Changing World, The Changing nature of Conflicts: critical Role for Military Radar .IEEE International Radar Conference 1995, 11~15
20 C. Fowler, J. Entzminger and J. Corum, Assessment of UWB Technology, IEE AES Magazine, November 1990,45~48
21冯奎胜卢万铮朱章虎电磁场数值计算方法分析。山西电子技术2005年第6期
22葛德彪.电磁波时域有限差分方法. 1~2
23 Goldberg M.Stability criteria for criteria for finite difference approximations to parabolic systems[J].Applied Numerical Mathematics,2000,33(15):509~515.
24 Juntunen J S,Tsiboukis T D.Reduction of numerical dispersion in FDTD method through artificial anisotropy[J].IEEE Trans.Microwave Theory Tech.,2000,48(4):582~588.
25 Berenger J P. A Perfectly Matched Layer for the Absorption of Electromagnetic Waves[J]. Journal of Computational Physics, 1994, 114: 185~200.
26 Katzetal D S. Validation and Extension to Three Dimensions of the Berenger PML Absorbing Boundary Condition for FDTD meshes[J]. IEEE Microwave and Guided Wave Letters, 1994, 4(8): 268~270.
27 Berenger J P. Three-Dimensional Perfectly Matched Layer for the Absorption of Electromagnetic Waves[J]. Journal of Computational Physics, 1996, 127: 363~379.
28 Gedney S D. An Anisotropic Perfectly Matched Layer-absorbing Medium for Truncation of FDTD Lattices. IEEE Trans .Antennas and Porpagation. 1996, 44( 12 ) ; 1630~1639
29王长清,祝西里.电磁场计算中的时域有限差分法[M].北京:北京大学出版社,1994.
30 Mur G. Absorbing Boundary Conditions for the Finite-Difference Approximation of The Time Domain Electromagnetic Field Equations [J]. IEEE Trans. Electeomagn. Compat.,1981.23(4):377-382
31杨军,张玉胜,傅君眉。Mur吸收边界条件的校正[J].微波学报,1996,12(10):30~34。
32谭怀英,梁甸农,刘克诚FDTD中一种新截断边界—ST WBC[J].电子学报,2001.29(3):421~422
33邵振海,洪伟。几种新的吸收边界条件在电磁散射中的应用[J].电波科学学报,1994,14(3):287 ~294。
34 Lee Wai, Mittra Ko Rai. A combination of FD-TD and Prony′s methods for analyzing microwave integrated circuits. IEEE MTT,1991,39(12): 2 176~2 181
35 Asi L A, Fai Sha. Dispersion analysis of anisotropic inhomogeneous waveguides using compact 2D-FDTD.Electronic Letters,1992,29(19): 1 451~1 452
36 Toland B, Houshmand B, Itoh T. Modeling of nonlinear active regions with the FDTD method. IEEE Microwave. Guided Wave,Letters,1993, 3(9): 333~335
37高本庆.时域有限差分法[M].北京国防工业出版社.1995
38 Brench C E. Source Selection Criteria for FDTD Models [A]. 1998.191~194.
39王长清,祝西里.电磁场计算中的时域有限差分法[M].北京:北京大学出版社,1994.
40王勇,于大鹏.一种用于UWB通信的正弦调制高斯脉冲[J].无线电通信技术,2005,31(1):9~11.