FDTD在工程瞬态电磁学中的应用
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摘要
瞬态电磁学的在各种实际工程中得到广泛应用。本论文用时域有限差分（FDTD）
方法分析目标瞬态电磁散射特性。应用FDTD方法，本文分析了自由空间实用复杂
目标宽频带散射特性以及有耗地面附近或者有耗地下目标的瞬态散射特性。文中还
提出了计算变化非常缓慢脉冲的一种瞬态计算方法。
对自由空间目标，文中首先提出了一种适应于FDTD方法的具有复杂几何外形
目标电磁建模方法。对于任何复杂目标，按照本文给出的方法步骤，就可以给出其
正确的离散模型。在此基础上，本文分析了某些型号飞机在自由空间的散射问题。
这类实用目标在其谐振波段电磁散射特性的研究在短波（HF）超视距雷达对目标的探
测方面具有实际应用价值。短波超视距雷达一般工作频段为3～15MHz，对于所测定
的目标而言，属于谐振区或瑞利区目标。此外，随着隐身技术的发展，在目标上全
部或部分涂覆或者采用吸波材料以降低雷达散射截面（RCS）在军事上日益受到重视并
获得应用。同样，我们利用FDTD方法来分析具有涂覆雷达吸波材料的机翼、腔壁
内部填充有耗介质的飞机进气道唇口的散射问题。由于所关心的是目标在一个频段
范围内的RCS，因此采用瞬态FDTD方法首先得到目标的时域响应，然后通过Fourier
变换得到频域响应。
对界面附近目标，本文在FDTD方法中引进时域表面阻抗边界条件（SIBC）来模
拟有耗地面对电磁波的反射。从Fresnel反射系数出发以及应用拉普拉斯变换，我们
推导了适于FDTD的时域SIBC。时域SIBC的引入避免了传统FDTD方法在处理两
截面附近目标时所遇到的困难，这些困难包括要考虑地下吸收边界；重新设置激励；
为照顾地下有耗介质网格尺寸要受到很大限制，从而使得计算量变得非常大等。应
用表面阻抗边界条件，本文分析了电磁脉冲对有耗地面附近传输线电缆的干扰问题。
由于这种方法的FDTD计算区域不需要延伸到地下中，从而简化了计算处理。
对地下目标，我们分析了在地面放置阶跃函数源或冲击函数源时地下目标的电
磁散射问题。在地面上加以适当激励脉冲，通过地表面处测得的感应电动势可以探
测和了解地下目标的一些特性以及地下地层结构状况。这一问题涉及电磁波在半空
间有耗介质中的传播和散射过程。在阶跃函数源激励下，电磁场在有耗地下的传播
过程具有较为复杂特性，一般而言具有波动特性。然而，在其后期由于变化较缓慢
位移电流可以忽略，传播的扩散特性占据绝对优势，我们可以应用扩散方程来处理。
此外，在扩散方程FD数值求解的DuFort-Frankel方法中注意到扩散方程的DuFort-
Frankel离散式等同于一定等效介电系数下有耗介质波方程的离散式，因此通过在扩
——
散方程中引进虚拟位移电流将扩敌方程近似为用尼波动方程，这样就可以借助FDTD
方法分析地下扩滋问题．
另外，我们将酞射传递函数杨念引进FDTD方法中分析极度缀馒变化脉冲散射。
FDTD方法对离散时间间隔有一定的要求。核电磁脉冲或者雷电电磁脉冲在一个急
速上升（前沿）过程后耍经历一个非常平缀的下降过程，因此完成这种脉冲人射下目
标的散射计算需要大量时间步。为了解诀这个矛盾，本文将散射传递函数（幼咖虹闻
Transfer FunchO4 S用概念引进到FDTD计算中。采用一个宽度较小的高斯脉冲进
行FDTD计算，然后迟过变换得到目标对双抬数脉冲的散射，节约了计算时间和内
存。
Transient electromagnetic analysis is widely applied in many electronic engineering
areas. In this dissertation, Transient electromagnetic scattering from objects are studied by
using the Fiite-Diffa~ence Time-Domain (FDTD) method. The following problems are
considered: the wide-band scattering from complicated objects in free space, the time-
domain surface current of a cable above a lossy ground, and transient scattering from
barred targets in lossy ground. And also, we present a hybrid STF-FDTD approach to
compute the EM scattering with an extremely slow-decaying pulse incidence.
Firstly, we study the wide-band EM scattering from a target of complicated geometrical
shape or material composition in free space. A scheme for modeling a complicated object
for FDTD computation is presented. Making up the descriptive file for the objects, we can
obtain the discretized EM model using this algorithm. The EM scattering from an airplane
is then analyzed within frequency range 3-15MHz based on the above object modeling.
These studies found their practical values in the beyond-horizon radar detection areas.
Next, we analyze the transient EM scattering of an airfoil and a lip of an inlet and their
RCS reductions by partially RAM coating or filling. In all the above analysis, pulse
incidences are used in the FDTD calculations and the transient scattering fields are
computed. We can transfer these time-domain results into frequency-domain with the help
of Fast Fourier Transform (FFT).
Secondly, the transient EM scattering analysis of targets above a lossy ground is
proceeded. Surface impedance is introduced into the FDTD method. Based on the Fresnel
reflective coefficient and Laplace Transform, we derive the time-domain Surface
Impedance Bouixlary Condition (SIBC) available for the FDTD method. The lossy ground
is then replaced by this time-domain SIBC, reducing the solution space and producing
significant computational savings. By using this approach, we study the problem of. EM
pulse coupling into a cable above a lossy ground.
Next, we enhance the FDTD method for simulating transient EM surveys for
underground objects, in which a step or impulse excitation is laid on the ground surface
and the electromotive force (EMF) is measured along the ground surface. Normally the
transmission of the electromagnetic fields in lossy medium is characterized with wavelike
and diffusive features. In the condition that conductivity a is much large and permittivity
s much small, the wavelike feature vanishes very quickly (and it is difficult to simulate in
桰l?
the numerical methods), leaving only difftmive behavior. Thus the fields under ground
satisfy the diffusion equation. By comparison of the Green抯 function of damped wave
equation and diffusion equation, we introduce an artificial displacement current term in the
diffusion equation, which leads to the DuFort-Frankel method and FDTD method in the
transient scattering analysis for underground targets.
Finally, we present a hybrid approach of scattering t.raisfer function (5Th) and finite
difference time domain (FDTD) for the calculation of electromagnetic transient responses
when the incident wave is an extremely slow-de醓ying pulse, e.g., double-exponential
pulse. First, we introduce the scattering transfer function (STF) concept into the scattering
system based on the principle of the linear system theory, by using a fast-decaying pulse as
an incident wave with the bandwidth of interest. Next, we derive the scattering respon
方法分析目标瞬态电磁散射特性。应用FDTD方法，本文分析了自由空间实用复杂
目标宽频带散射特性以及有耗地面附近或者有耗地下目标的瞬态散射特性。文中还
提出了计算变化非常缓慢脉冲的一种瞬态计算方法。
对自由空间目标，文中首先提出了一种适应于FDTD方法的具有复杂几何外形
目标电磁建模方法。对于任何复杂目标，按照本文给出的方法步骤，就可以给出其
正确的离散模型。在此基础上，本文分析了某些型号飞机在自由空间的散射问题。
这类实用目标在其谐振波段电磁散射特性的研究在短波（HF）超视距雷达对目标的探
测方面具有实际应用价值。短波超视距雷达一般工作频段为3～15MHz，对于所测定
的目标而言，属于谐振区或瑞利区目标。此外，随着隐身技术的发展，在目标上全
部或部分涂覆或者采用吸波材料以降低雷达散射截面（RCS）在军事上日益受到重视并
获得应用。同样，我们利用FDTD方法来分析具有涂覆雷达吸波材料的机翼、腔壁
内部填充有耗介质的飞机进气道唇口的散射问题。由于所关心的是目标在一个频段
范围内的RCS，因此采用瞬态FDTD方法首先得到目标的时域响应，然后通过Fourier
变换得到频域响应。
对界面附近目标，本文在FDTD方法中引进时域表面阻抗边界条件（SIBC）来模
拟有耗地面对电磁波的反射。从Fresnel反射系数出发以及应用拉普拉斯变换，我们
推导了适于FDTD的时域SIBC。时域SIBC的引入避免了传统FDTD方法在处理两
截面附近目标时所遇到的困难，这些困难包括要考虑地下吸收边界；重新设置激励；
为照顾地下有耗介质网格尺寸要受到很大限制，从而使得计算量变得非常大等。应
用表面阻抗边界条件，本文分析了电磁脉冲对有耗地面附近传输线电缆的干扰问题。
由于这种方法的FDTD计算区域不需要延伸到地下中，从而简化了计算处理。
对地下目标，我们分析了在地面放置阶跃函数源或冲击函数源时地下目标的电
磁散射问题。在地面上加以适当激励脉冲，通过地表面处测得的感应电动势可以探
测和了解地下目标的一些特性以及地下地层结构状况。这一问题涉及电磁波在半空
间有耗介质中的传播和散射过程。在阶跃函数源激励下，电磁场在有耗地下的传播
过程具有较为复杂特性，一般而言具有波动特性。然而，在其后期由于变化较缓慢
位移电流可以忽略，传播的扩散特性占据绝对优势，我们可以应用扩散方程来处理。
此外，在扩散方程FD数值求解的DuFort-Frankel方法中注意到扩散方程的DuFort-
Frankel离散式等同于一定等效介电系数下有耗介质波方程的离散式，因此通过在扩
——
散方程中引进虚拟位移电流将扩敌方程近似为用尼波动方程，这样就可以借助FDTD
方法分析地下扩滋问题．
另外，我们将酞射传递函数杨念引进FDTD方法中分析极度缀馒变化脉冲散射。
FDTD方法对离散时间间隔有一定的要求。核电磁脉冲或者雷电电磁脉冲在一个急
速上升（前沿）过程后耍经历一个非常平缀的下降过程，因此完成这种脉冲人射下目
标的散射计算需要大量时间步。为了解诀这个矛盾，本文将散射传递函数（幼咖虹闻
Transfer FunchO4 S用概念引进到FDTD计算中。采用一个宽度较小的高斯脉冲进
行FDTD计算，然后迟过变换得到目标对双抬数脉冲的散射，节约了计算时间和内
存。
Transient electromagnetic analysis is widely applied in many electronic engineering
areas. In this dissertation, Transient electromagnetic scattering from objects are studied by
using the Fiite-Diffa~ence Time-Domain (FDTD) method. The following problems are
considered: the wide-band scattering from complicated objects in free space, the time-
domain surface current of a cable above a lossy ground, and transient scattering from
barred targets in lossy ground. And also, we present a hybrid STF-FDTD approach to
compute the EM scattering with an extremely slow-decaying pulse incidence.
Firstly, we study the wide-band EM scattering from a target of complicated geometrical
shape or material composition in free space. A scheme for modeling a complicated object
for FDTD computation is presented. Making up the descriptive file for the objects, we can
obtain the discretized EM model using this algorithm. The EM scattering from an airplane
is then analyzed within frequency range 3-15MHz based on the above object modeling.
These studies found their practical values in the beyond-horizon radar detection areas.
Next, we analyze the transient EM scattering of an airfoil and a lip of an inlet and their
RCS reductions by partially RAM coating or filling. In all the above analysis, pulse
incidences are used in the FDTD calculations and the transient scattering fields are
computed. We can transfer these time-domain results into frequency-domain with the help
of Fast Fourier Transform (FFT).
Secondly, the transient EM scattering analysis of targets above a lossy ground is
proceeded. Surface impedance is introduced into the FDTD method. Based on the Fresnel
reflective coefficient and Laplace Transform, we derive the time-domain Surface
Impedance Bouixlary Condition (SIBC) available for the FDTD method. The lossy ground
is then replaced by this time-domain SIBC, reducing the solution space and producing
significant computational savings. By using this approach, we study the problem of. EM
pulse coupling into a cable above a lossy ground.
Next, we enhance the FDTD method for simulating transient EM surveys for
underground objects, in which a step or impulse excitation is laid on the ground surface
and the electromotive force (EMF) is measured along the ground surface. Normally the
transmission of the electromagnetic fields in lossy medium is characterized with wavelike
and diffusive features. In the condition that conductivity a is much large and permittivity
s much small, the wavelike feature vanishes very quickly (and it is difficult to simulate in
桰l?
the numerical methods), leaving only difftmive behavior. Thus the fields under ground
satisfy the diffusion equation. By comparison of the Green抯 function of damped wave
equation and diffusion equation, we introduce an artificial displacement current term in the
diffusion equation, which leads to the DuFort-Frankel method and FDTD method in the
transient scattering analysis for underground targets.
Finally, we present a hybrid approach of scattering t.raisfer function (5Th) and finite
difference time domain (FDTD) for the calculation of electromagnetic transient responses
when the incident wave is an extremely slow-de醓ying pulse, e.g., double-exponential
pulse. First, we introduce the scattering transfer function (STF) concept into the scattering
system based on the principle of the linear system theory, by using a fast-decaying pulse as
an incident wave with the bandwidth of interest. Next, we derive the scattering respon
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