时域有限差分法在汽车电磁兼容性分析中的应用与研究
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摘要
时域有限差分法(FDTD)作为一种典型的全波时域分析方法备受关注,并迅速的发展。它直接将有限差分式代替Maxwell时域场旋度方程中的微分式,能直接反应电磁波的时域特性,并充分而形象的描绘电磁波的传播和与目标的相互作用过程,得到复杂物理过程的清晰物理图像。随着汽车上的电子产品越来越多,使其电磁兼容问题变得极为复杂,对汽车电磁兼容性的研究也变得尤为重要。为了在汽车设计及其生产初期能够发现自身或与环境的不兼容性,避免进行二次修改造成的损失与降低成本,提高解决问题的效率,把数学建模和数字仿真技术应用到汽车EMC研究上具有很高的价值,并为汽车电磁兼容性检验和防护设计提供理论依据。
本文在前人研究的基础上,分析了空间和时间离散间隔对数值色散及数值稳定性的要求,通过对空间PML构造及PML中分裂场的特性分析,提出一种简化形式的PML参数设置方法去简化计算机编程,提高计算效率。通过对实测点火系特征频率的提取构造得到更符合实际点火系辐射特性的双重调制激励源,并模拟了在此激励源激励下的点火系、暖风电机产生的辐射场的传播。最后对辐射场对受扰设备的耦合干扰进行了分析,并对缝隙处的场值进行了计算,配合实验进行了一些比较和研究,得到了比较满意的检测结果。
A lot of respects of modern technology are relevant to electric magnetic field, especially in the high-frequency electric magnetic field. As the electrical products on the automobile is getting more and more, its electromagnetic compatibility (EMC) problems become more complex. Many automobile manufacturers have attached great importance to the automotive EMC Research. Automotive Electromagnetic Compatibility Study is to ensure that when the car is in the process of running, the electrical and electronic equipment on the car does not influence each other, and can work compatibly. The entire automobile can resist external interference, and don't release the interference which exceeds the allowed scope to other equipment outside or in the environment. The purpose of EMC test is to analyze and estimate the incompatible phenomenon that may exist in advance, Pre-test, Preventive designation and solve the present problem before designing finished. On the basis research of FDTD in this paper, for the Prediction of EMC in Automotive electrical equipment,we compare the outcome results of forecasts with actual test results or actual project experiences. To check their consistency and use it provide a certain extent theoretical guidance for the designation and production. This article reads as follows:
1、Electromagnetic problems in the finite difference time domain method.
The FDTD method is first proposed by K.S.Yee in 1966.Since it is established directly on all electromagnetic field problems which is to meet on the basis of Maxwell's equations. Therefore its solving train of thought is clear, easily realized and developed continually. The FDTD method is a time-domain approach, and any one distribution of the field which been interested in can be got. The computer animation simulation of Electromagnetic wave propagation can be achieved. Through the use of pulse excitation with Fourier transformation, we can get the contained response of effective spectrum of pulse through calculating, compared with the frequency domain methods which will save a substantial amount of computing time. The way to solve these problems is universal, and the only difference with other numerical methods lies in its geometry and electromagnetic parameters. The electromagnetic compatibility issues are major concerned in all the spectrum of radiation equipments. It is precisely because of broadband characteristics of equipment radiation that led to the interference to other equipments. In order to access the spectrum of researched problem promptly, The FDTD method is a good algorithm. It can get all value of electromagnetic fields at any time. With Fourier transformation, their spectral response can be got. FDTD method regards Yee grids as discrete modules for the space field and turns Maxwell's curl equation into the difference equation to solve in the time frame step by step. It is concise to understand, and can combine with the computer to deal with very complicated electromagnetic problems. In the second chapter the basic principles of FDTD method is introduced, Derivate the FDTD differential formulas of the one-dimensional and three-dimensional circumstances in Cartesian coordinate system. And present how to deal with the equivalent parameters in cube cellular simplely.
2、The numerical dispersion and stability conditions.
Using FDTD method makes Maxwell's curl equation approximate and receive a group of coupling differential equations, only when the solution of differential equations is convergence or stability, the results of FDTD method can be meaningful. Convergence means that when the dispersed interval tends to zero, the solving of differential equations tends to the solving of original equation at the space point of all times consistent and arbitrary. Stability is such a basic condition, in such conditions the numerical solution of differential equations with time step will not unlimited increase. So as to ensure that the error between the numerical solution of differential equations and the original equation is strict bounded. In the third chapter we mainly discuss the constraints for time and discrete intervals of space as the stability and convergence of discrete Maxwell's equations, and the numerical dispersion analysis of space intervals.
3、The Simplified absorbing boundary conditions of PML.
From the beginning of simple interpolation border to later widely used Mur absorbing boundary, and the development of PML absorbing boundary in recent years. Its absorption is getting better and better. Because of the constraints of computer's capacity, the calculation of FDTD is only in a limited region. It is impossible to calculate the infinite structure directly. Therefore, we must set appropriate absorpting boundary conditions at the truncation department. To use the limited space grids to simulate open unlimited space or long unlimited transmission structure. Then to simulate a open domain of electromagnetic scattering process. Chapter IV presents the MUR absorbing boundary conditions and PML absorbing boundary conditions. On the basis of understanding of the parameter settings in the two-dimensional of PML. It is easy to extent to set parameters of 3D case. The simplification of PML application and programming realization are presented based on the PML structure and computing characteristics of the split fields in FDTD calculation. So that make the parameter settings of absorption boundary conditions in the program of MATLAB of FDTD method become clear and simple. Through calculating the split fields in FDTD, we get radiation field of 3D line source in the simplification of the PML, and contrast the PML and Mur method which used on the modulation excitation source to calculat the input impedance of shielding. At last the feasibility of simplified setting is drawn.
4、Excitation source technology and the construction of excitation source in automotive.
Practical electromagnetic issues always contain excitation source. So select a reasonable excitation source can avoid the harmful effects of the cut-off frequency component and can be effective in raising the calculation efficiency of FDTD method. Significant savings of time and computer memory space. In order to introduce the appropriate excitation source into numerical calculation of FDTD method. So simulate the problem of EMC correctly is very important. In the fifth chapter is a variety of excitation source technology. Through collecting the acquisition and experimental testing of the characteristic spectrum of vehicle ignition system, we get the actual amplitude and frequency points of interference which exceed the safety threshold. On the basis of proposing switch function, we applicate them into the amplitude and frequency of switch function to get correct modulation excitation source's simulation of interference which caused by the actual ignition system.
5、The FDTD analysis of Electromagnetic radiation inside the automotive.
The existence of major electromagnetic environment of vehicles is analyzed. According to Chapter IV from the radiation of electromagnetic interference of the actual data collection, we get the double modulation Time-harmonic field excitation source. We calculate the the radiation field of ignition System using FDTD method, and Simulate the spreading of radiation through different aperture size in different frequency radiation field. And extract the data of designated point in modulation field in order to compare with the experimental results. At the same time, we analysed the interference source of inductive load through modeling. And get the output map of inductive load in different response. Using the modulated excitation source to simulate the radiation of heater machine through the heater-hole of automotive in the method of FDTD analysis. Finally, calculated the value of radiation field in the gap through FDTD method, and analysed the interference of sensitive equipments' radiation field by means of the coupling. To provide a theoretical calculation basis of taking measures for minimizing the interference by the disturbance.
本文在前人研究的基础上,分析了空间和时间离散间隔对数值色散及数值稳定性的要求,通过对空间PML构造及PML中分裂场的特性分析,提出一种简化形式的PML参数设置方法去简化计算机编程,提高计算效率。通过对实测点火系特征频率的提取构造得到更符合实际点火系辐射特性的双重调制激励源,并模拟了在此激励源激励下的点火系、暖风电机产生的辐射场的传播。最后对辐射场对受扰设备的耦合干扰进行了分析,并对缝隙处的场值进行了计算,配合实验进行了一些比较和研究,得到了比较满意的检测结果。
A lot of respects of modern technology are relevant to electric magnetic field, especially in the high-frequency electric magnetic field. As the electrical products on the automobile is getting more and more, its electromagnetic compatibility (EMC) problems become more complex. Many automobile manufacturers have attached great importance to the automotive EMC Research. Automotive Electromagnetic Compatibility Study is to ensure that when the car is in the process of running, the electrical and electronic equipment on the car does not influence each other, and can work compatibly. The entire automobile can resist external interference, and don't release the interference which exceeds the allowed scope to other equipment outside or in the environment. The purpose of EMC test is to analyze and estimate the incompatible phenomenon that may exist in advance, Pre-test, Preventive designation and solve the present problem before designing finished. On the basis research of FDTD in this paper, for the Prediction of EMC in Automotive electrical equipment,we compare the outcome results of forecasts with actual test results or actual project experiences. To check their consistency and use it provide a certain extent theoretical guidance for the designation and production. This article reads as follows:
1、Electromagnetic problems in the finite difference time domain method.
The FDTD method is first proposed by K.S.Yee in 1966.Since it is established directly on all electromagnetic field problems which is to meet on the basis of Maxwell's equations. Therefore its solving train of thought is clear, easily realized and developed continually. The FDTD method is a time-domain approach, and any one distribution of the field which been interested in can be got. The computer animation simulation of Electromagnetic wave propagation can be achieved. Through the use of pulse excitation with Fourier transformation, we can get the contained response of effective spectrum of pulse through calculating, compared with the frequency domain methods which will save a substantial amount of computing time. The way to solve these problems is universal, and the only difference with other numerical methods lies in its geometry and electromagnetic parameters. The electromagnetic compatibility issues are major concerned in all the spectrum of radiation equipments. It is precisely because of broadband characteristics of equipment radiation that led to the interference to other equipments. In order to access the spectrum of researched problem promptly, The FDTD method is a good algorithm. It can get all value of electromagnetic fields at any time. With Fourier transformation, their spectral response can be got. FDTD method regards Yee grids as discrete modules for the space field and turns Maxwell's curl equation into the difference equation to solve in the time frame step by step. It is concise to understand, and can combine with the computer to deal with very complicated electromagnetic problems. In the second chapter the basic principles of FDTD method is introduced, Derivate the FDTD differential formulas of the one-dimensional and three-dimensional circumstances in Cartesian coordinate system. And present how to deal with the equivalent parameters in cube cellular simplely.
2、The numerical dispersion and stability conditions.
Using FDTD method makes Maxwell's curl equation approximate and receive a group of coupling differential equations, only when the solution of differential equations is convergence or stability, the results of FDTD method can be meaningful. Convergence means that when the dispersed interval tends to zero, the solving of differential equations tends to the solving of original equation at the space point of all times consistent and arbitrary. Stability is such a basic condition, in such conditions the numerical solution of differential equations with time step will not unlimited increase. So as to ensure that the error between the numerical solution of differential equations and the original equation is strict bounded. In the third chapter we mainly discuss the constraints for time and discrete intervals of space as the stability and convergence of discrete Maxwell's equations, and the numerical dispersion analysis of space intervals.
3、The Simplified absorbing boundary conditions of PML.
From the beginning of simple interpolation border to later widely used Mur absorbing boundary, and the development of PML absorbing boundary in recent years. Its absorption is getting better and better. Because of the constraints of computer's capacity, the calculation of FDTD is only in a limited region. It is impossible to calculate the infinite structure directly. Therefore, we must set appropriate absorpting boundary conditions at the truncation department. To use the limited space grids to simulate open unlimited space or long unlimited transmission structure. Then to simulate a open domain of electromagnetic scattering process. Chapter IV presents the MUR absorbing boundary conditions and PML absorbing boundary conditions. On the basis of understanding of the parameter settings in the two-dimensional of PML. It is easy to extent to set parameters of 3D case. The simplification of PML application and programming realization are presented based on the PML structure and computing characteristics of the split fields in FDTD calculation. So that make the parameter settings of absorption boundary conditions in the program of MATLAB of FDTD method become clear and simple. Through calculating the split fields in FDTD, we get radiation field of 3D line source in the simplification of the PML, and contrast the PML and Mur method which used on the modulation excitation source to calculat the input impedance of shielding. At last the feasibility of simplified setting is drawn.
4、Excitation source technology and the construction of excitation source in automotive.
Practical electromagnetic issues always contain excitation source. So select a reasonable excitation source can avoid the harmful effects of the cut-off frequency component and can be effective in raising the calculation efficiency of FDTD method. Significant savings of time and computer memory space. In order to introduce the appropriate excitation source into numerical calculation of FDTD method. So simulate the problem of EMC correctly is very important. In the fifth chapter is a variety of excitation source technology. Through collecting the acquisition and experimental testing of the characteristic spectrum of vehicle ignition system, we get the actual amplitude and frequency points of interference which exceed the safety threshold. On the basis of proposing switch function, we applicate them into the amplitude and frequency of switch function to get correct modulation excitation source's simulation of interference which caused by the actual ignition system.
5、The FDTD analysis of Electromagnetic radiation inside the automotive.
The existence of major electromagnetic environment of vehicles is analyzed. According to Chapter IV from the radiation of electromagnetic interference of the actual data collection, we get the double modulation Time-harmonic field excitation source. We calculate the the radiation field of ignition System using FDTD method, and Simulate the spreading of radiation through different aperture size in different frequency radiation field. And extract the data of designated point in modulation field in order to compare with the experimental results. At the same time, we analysed the interference source of inductive load through modeling. And get the output map of inductive load in different response. Using the modulated excitation source to simulate the radiation of heater machine through the heater-hole of automotive in the method of FDTD analysis. Finally, calculated the value of radiation field in the gap through FDTD method, and analysed the interference of sensitive equipments' radiation field by means of the coupling. To provide a theoretical calculation basis of taking measures for minimizing the interference by the disturbance.
引文
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