Dipole Mode Response of a Multiconductor Cable Above a Ground Plane in a Transient Electromagnetic Field

This paper describes an analytical technique that may be used to obtain the worst case dipole mode currents on individual wires of a multiconductor cable as a result of a transient electromagnetic radiation field. The dipole mode response is due to the E field parallel to the length of the cable. To obtain the solution, the conductors and their image in the ground plane are considered as forming a loop, and the resultant loop is solved as a transmission mode loop. The solution is given in matrix form as an upper bound of the true current including both mutual inductive and mutual capacitive coupling. The mathematical results are presented in the time domain and are uniquely applicable to experimental results obtained in EMP simulation with narrow pulse driving fields.     

Modeling of magnetic-field coupling with cable bundle harnesses

A field-to-line coupling model is developed for cable bundle harnesses in terms of the scattering currents and total line voltages. The equivalent distributed sources representing the effects of electromagnetic coupling are expressed as a function of the incident magnetic-field components. Such a formulation is particularly suitable to be used for the analysis of multiconductor transmission lines excited by a transient field, when data for the incident electric field are either inaccurate or not available. This model allows the accurate calculation of the induced voltages and currents on complex cable bundles. The effects on the induced voltages and currents due to ground losses and to the presence of the dielectric sheath in shielded and unshielded cables is discussed, considering bundles excited by either slow or fast transient fields. Numerical applications demonstrate the validity of the proposed procedure.     

Comparison of the transmission line and scattering models forcomputing the HEMP response of overhead cables

The author discusses the use of transmission line and electromagnetic scattering models for computing the induced currents on long above-ground electrical cables, subjected to a transient plane wave excitation. The pertinent equations for determining the excitation electric field along the cable are summarized, along with the expressions which relate the line current to the excitation field. For the transmission line case, the cable current can be expressed in terms of per-unit-length impedance and admittance parameters which are functions of only the line geometry and the frequency. For the scattering case, similar line parameters can be inferred from the form of the solution for the current, but with the line parameters depending on the angles of incidence. Several numerical calculations of the line responses are provided, and these indicate that the transmission line analysis appears to provide response estimates which are smaller than those obtained using the more accurate scattering theory     

A Three-Dimensional Finite-Difference Solution of the External Response of an Aircraft to a Complex Transient EM Environment: Part II-Comparison of Predictions and Measurements

Experimental charge and current measurements have recently been performed on an aircraft when it was exposed to the transient electromagnetic field of an electromagnetic-pulse (EMP) simulator. These new data allow a test of the predictive capabilities of the three-dimensional finite-difference method for realistic aircraft aircraftsimulator-test problems. Comparisons made between measurements and predictions show that the three-dimensional finite-difference technique provides reasonably accurate predictions for the induced currents and charges on a complex object responding to an applied transient electromagnetic field in the presence of a lossy earth.     

Analysis of Crossed Wires in a Plane-Wave Field

The currents and charges induced in a pair of electrically thin crossed wires by a normally incident plane electromagnetic wave are derived by analytical methods. The boundary conditions at the ends and at the junction are explained. The solution of a new integro-differential equation for the currents is obtained in terms of trigonometric and integral-trigonometric functions. Depending on the electrical lengths of the crossed elements and location of their junction a variety of quite different distributions of current and charge obtain. These determine the scattered near and far fields. Graphs of computed currents and charges per unit length on the four arms of several important cases are displayed. The accurate determination of the induced currents and charges on a mathematically tractable structure-the thin-wire cross-is an early step in a study that will proceed to electrically thick cylinders, wide strips, and their junctions in crossed configurations in an effort to gain a meaningful approximate understanding of the currents and charges induced on an aircraft by an electromagnetic pulse.     

Currents induced in a wire cross by a plane wave incident at an angle

The currents induced in a thin-wire cross with equal mutually perpendicular arms by an incident plane electromagnetic wave are determined when the normal to the wave front is perpendicular to the horizontal wire and is at an anglethetawith respect to the vertical wire; the direction of the electric vector in the wave front is arbitrary. The analysis is formulated in general terms but explicit formulas are obtained only for the zero-order currents which are generally adequate to determine the scattered field of very thin wires. The relatively simple formulas consist of even and odd parts for both the vertical and horizontal wires; they include components due to mutual coupling as well as those excited directly by the incident field.     

Current flow in coaxial braided cable shields

In the last few years, much effort has been made to describe the behavior of shielded cables. Many researchers have attempted to understand how an electromagnetic field couples into a braided coaxial cable. There are some important publications on this topic. Nevertheless, up to now, it has not been possible to predict analytically the coupling through a braid shield. An electromagnetic field outside a cable induces a disturbance current in the cable shield. The coupling from the current in the shield into the cable can be described by the transfer impedance. How the current flows in the cable shield is an important quantity in this coupling process. Therefore, to understand the coupling mechanism into a cable, it is necessary to understand the behavior of the current flow in such a braided shield. The paper discusses the current flow in a braided cable shield. The assumption often made in the literature, that a braided shield behaves like a homogeneous tube with apertures, is shown to be inaccurate. It is also shown that the standard braid of the shield used had the same properties as a braid made with insulated wires.     

Transient response of a transmission line excited by anelectromagnetic pulse

The transient response of a lossless transmission line of finite length excited externally by an electromagnetic wave of an arbitrary waveform is studied. By using the Laplace transformation, a solution of the transient current is obtained as a series of analytical functions. Inspection of the solution leads to the conclusion that the response currents at terminals of the line can be equivalently expressed by the components induced at both terminals, and, in addition, the multireflected wave when the line is mismatched. Furthermore, a new equivalent circuit for the coupling phenomenon is discussed     

A Hybrid Electromagnetic-Circuit Method for Electromagnetic Interference Onto Mass Wires

A current decomposition method is proposed for the analysis of field coupling to mass wires near complex structures. The foremost attribute of the method is the decomposition of the current on each wire into push-pull and push-push mode currents. The former refers to the perturbation current accounting for the interactions among the wires within the bundle, whereas the latter represents the interactions between the mass wire bundle and the surrounding structure. Multiconductor transmission line theory is employed to compute the push-pull mode current by using one of the wires in the bundle as the return/reference conductor. Current induced on a test wire located along the reference line is used to compute the push-push mode. For this analysis, we employed the method of moments for the electromagnetic analysis of surrounding structure and simulation program with integrated circuit emphasis (SPICE)-like simulators for the analysis of a circuit model of the transmission lines extracted via the partial element equivalent circuit method. Several validation examples (including transmission lines inside an automobile) are presented. It is also shown that the traditional transmission line theory based on quasi-static analysis fails with increasing complexity of the surrounding structure.     

基于地-线缆耦合的感应电流分析*

高功率、大强度电磁波照射,是飞机在电子对抗中实施电磁干扰的重要手段。在实验室通过电流钳对线缆进行电流注入,从而达到模拟飞机系统间电磁干扰试验的目的。如何从理论上分析照射场在电缆上所感应的电流,是飞机系统间抗扰度实验的重要环节。文章利用有源传输线理论,建立了线缆-大地耦合模型,给出了线缆电流分布与大地电导率、地-线缆高度、线缆长度、线缆两端阻抗以及照射场的频率、幅度等多参数的关系;同时还进行了实测验证。结果表明,理论分析与实测结果基本一致,这为飞机系统间电磁干扰试验的实施提供了必要的理论和数据基础。     

Calculation of radiated electromagnetic fields from cables usingtime-domain simulation

Radiated electromagnetic fields are produced by currents in cables or transmission lines interconnecting various circuits. An elegant method of computing the resultant electromagnetic field, produced by several radiating current elements, is given. The current in each radiating cable is first found from a time-domain simulation algorithm and this may be a steady-state or transient current. The radiated field is then calculated by assuming that a radiating transmission line can be treated as a chain of short radiating dipoles. The problems associated with the calculation of the near-zone term at low frequencies and the overall response near the radiator are clarified. The proposed technique is fully evaluated and compared with other methods     

屏蔽腔内任意高度线缆端接TVS管电路的电磁耦合时域分析

该文基于时域有限差分(FDTD)方法和传输线方程,结合插值技术和牛顿迭代法,提出一种新的时域混合算法,能够快速模拟屏蔽腔内任意高度线缆端接瞬态电压抑制(TVS)管电路的电磁耦合问题,并实现空间电磁场与线缆和电路瞬态响应的同步计算。该算法首先利用FDTD方法结合STL网格剖分技术实现屏蔽腔结构的快速建模以及腔体内空间电磁场分布的准确模拟。然后利用传输线方程结合插值技术建立腔体内线缆的场线耦合模型,结合FDTD方法,迭代求解出线缆上的电压和电流响应。对于线缆端接的TVS管电路,列写电压电流方程,采用牛顿迭代法计算得到电路端口的电压响应。通过与电磁仿真软件的计算结果进行对比,验证了所提时域混合算法的正确性。研究表明,该算法能够很好地应用于屏蔽腔内线缆端接负载的TVS管限幅防护设计。     

Electromagnetic Coupling to an Infinite Cable Placed Behind a Slot-Perforated Screen

We present an analysis of the electromagnetic coupling from an external illuminating field to an infinitely long thin cable placed behind the conducting screen that is perforated by a narrow slot. By using a Fourier transform representation for the unknown electric current on the cable, we obtain an integro-differential equation for the distribution of the electric field in the slot that accounts completely for the coupling. The transfer admittance function so obtained, is in a form very convenient to estimate the electric current on the infinite cable. Results of the slot electric-field distribution and the current induced on the infinite cable are given for a few typical cases. Not surprisingly, the axial distribution of induced voltage on the slot is markedly affected by the presence of the cable.     

Transient response of the infinite cylindrical antenna and scatterer

The transient response of an infinite cylindrical antenna and scatterer is obtained by time gating a time-dependent electric-field integral equation for thin wires of finite-length. The driving point current and broadside radiated field approximate the driving point voltage in the antenna case, while the current excited in the scattering case approximates the time integral of the incident field. This approximate integral relation is used to estimate currents excited on cylindrical structures without employing the complete integral equation solution procedure.     

Theoretical and experimental characterization of theEMP-interaction with composite-metallic enclosures

A numerical procedure is developed for the prediction of the electric and magnetic field distribution inside an enclosure having aluminum and carbon-fiber reinforced composite (CFRC) walls, illuminated by a transient electromagnetic plane wave. The composite panel is simulated by an effective layer model; time-domain surface impedance boundary conditions are enforced on the external faces of the composite slab, to express the relations among the tangential electric and magnetic field components. A coupling model for the calculation of the current induced along thin wires inside the enclosure is presented. The proposed models are implemented in a three-dimensional (3-D) finite-difference time-domain (FDTD) procedure, which is applied to the analysis of the shielding performances of an aluminum box with one CFRC face, illuminated by a transient electromagnetic wave. The computed results are compared with measured data obtained by using a full scale EMP generator     

On Reducing the Lightning Transients in Buried Shielded Cables Using Follow-On Earth Wire

This paper investigates the importance of a follow-on buried bare earth wire for the lightning protection of buried shielded cables. The use of follow-on bare wires for lightning protection of communication towers was suggested as a recommendation in certain standards, without being complemented either by theory or experiments. When lightning transients couple to the cable shields, it induces large currents (depending on the type of coupling) causing transient overvoltages between the inner conductors and the shield. It is shown by simulations based on multiconductor transmission line theory that if the follow-on bare earth conductor is placed in parallel with the shielded cable with the bare earth wire connected to the shield at the current injection end, then the shield current, and thereby, the internal transient voltages of the cable are reduced considerably.     

平面电磁波对双导线传输线终端瞬态响应的求解

随着传输线方法在电磁兼容和电磁干扰分析方面的广泛应用,人们对传输线方程的求解方法也越来越感兴趣.求解传输线方程的方法通常有时域差分方法和频域差分法.而对于平面电磁波对双导线传输线终端的响应,文章给出了其频域解析解,并且运用这个解析解和Fourier变换技术,可以很容易地给出传输线终端的瞬态响应分析.通过数值仿真实验研究三个角度参数φ、α和Ψ在电磁感应中的作用:当φ和α保持不变(或者Ψ和α保持不变),随着Ψ(或者φ)的增大,终端2的感应电流的响应时间缩短,第一阶段的感应时间延长;当φ和Ψ保持不变,随着α的增大,终端2处第一阶段的感应电流也随之减小.     

The shielding of a plane wave by a cylindrical array of infinitely long thin wires

A plane wave is considered to be incident upon a cylindrical array of infinitely long perfectly conducting thin wires. The wave is assumed to have no magnetic field component in the direction of the wire axes. Exact expressions are found for the currents excited on the wires-and for the total electric and magnetic fields. Numerical computations are made to determine the currents on the wires and the fields inside the array. It is discovered that an important parameter is the number of wires in the array divided by the number of wavelengths that can be wrapped around the cylinder. If this parameter is large enough, the current distribution on the wires resembles that of a solid conducting cylinder, and the array of wires tends to behave like an electromagnetic shield. For smaller values of the parameter, the current distribution can be quite different, and the field inside the array may even be enhanced.     

SPICE-like models for the analysis of the conducted and radiated immunity of shielded cables

The aim of this work is the development and validation of compact SPICE models suitable to analyze the conducted and radiated immunity of shielded cables. The reference structures are coaxial cables, and shielded cables with two parallel wires (i.e., twinax cable). The conducted and radiated immunity of the shielded cables are evaluated considering as source a known injected current on the cable shield, and the coupling with an external plane wave electromagnetic field, respectively. The circuit models are validated by comparing the results with those obtained by other approaches. The developed models are then used to quantify the main grounding practices of shielded cables.