Closed-Form Formulas for the Stochastic Electromagnetic Field Coupling to a Transmission Line With Arbitrary Loads

Magdowski, Mathias; Vick, Ralf

doi:10.1109/temc.2012.2193130

Cited by 30 publications

(13 citation statements)

References 5 publications

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“…Magdowski derived analytical expressions for the typical case [2], that is: for random illumination. Neither model is transparent, so we will now look for general field-to-trace models (not worst case).…”

Section: State Of the Artmentioning

confidence: 99%

Simple, Taylor-Based Worst-Case Model for Field-to-Line Coupling

Land¹,

Ramdani²,

Perdriau³

et al. 2013

PIER

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Abstract-To obtain Electromagnetic Compatibility (EMC), we would like to study the worst-case electromagnetic field-induced voltages at the ends of Printed Circuit Board (PCB) traces. With increasing frequencies, modelling these traces as electrically short no longer suffices. Accurate long line models exist, but are too complicated to easily induce the worst case. Therefore, we need a simple analytical model. In this article, we predict the terminal voltages of an electrically long, two-wire transmission line with characteristic loads in vacuum, excited by a linearly polarised plane wave. The model consists of a short line model (one Taylor cell) with an intuitive correction factor for long line effects: the modified Taylor cell. We then adapt the model to the case of a PCB trace above a ground plane, illuminated by a grazing, vertically polarised wave. For this case, we prove that end-fire illumination constitutes the worst case. We derive the worst-case envelope and try to falsify it by measurement in a Gigahertz Transverse Electromagnetic (GTEM) cell.

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Section: State Of the Artmentioning

confidence: 99%

Simple, Taylor-Based Worst-Case Model for Field-to-Line Coupling

Land¹,

Ramdani²,

Perdriau³

et al. 2013

PIER

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“…Magdowski et al [6] apply a numerical method to study the stochastic electromagnetic fields coupling to a transmission line in a reverberation chamber and obtain the average responses along the transmission line. They also developed a closed-form formula for the average response at the ends of the transmission line excited by the stochastic electromagnetic fields [7]. However, the results can not be used directly for the PCB trace because there is a substrate in the PCB.…”

Section: Introductionmentioning

confidence: 99%

Numerical and Analytical Analysis of Stochastic Electromagnetic Fields Coupling to a Printed Circuit Board Trace

Xie

Dawson

Yan

et al. 2020

IEEE Trans. Electromagn. Compat.

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Stochastic electromagnetic fields coupling to printed circuit board (PCB) traces are important to the understanding of electromagnetic compatibility at high frequencies when the circuits or systems are electrically large. In this article, it is studied both numerically and analytically, and the factors affecting the absorbed power are investigated. We present new methods to determine the level of coupling on PCB traces or other transmission lines on a dielectric substrate. A Monte Carlo method is applied to generate random uniform fields, and the quasi-TEM transmission line model is employed to compute the response of the trace for each plane wave numerically. In the analytical method, the closed-form expressions of the zero-order and the first-order approximations are established for the PCB trace. Based on the first-order approximation method and the numerical results, a computationally efficient empirical method is developed to estimate the power received. The absorbed power increases with frequency in the electrically short case after which multiple resonances can be seen. The absorbed power in the matched case is neither the largest nor the smallest among all the cases. It increases with the square of the substrate height but decreases with the permittivity of the substrate.Index Terms-Absorption cross section (ACS), printed circuit board (PCB) trace, stochastic electromagnetic fields, transmissionline coupling.

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“…The authors of [4] consider stochastically located small antennas to create stochastic fields in a MSC. Other papers (see, e.g., [5][6][7]) are devoted to the investigation of coupling of a random electromagnetic field to deterministic transmission lines inside stochastic cavities (MSC).…”

Section: Introductionmentioning

confidence: 99%

Propagation of Current Waves along Randomly Located Multiconductor Transmission Lines inside a Rectangular Resonator

Tkachenko

Nitsch

Raya

et al. 2018

Mathematical Problems in Engineering

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Propagation of current waves along randomly located multiconductor transmission lines inside a rectangular resonator is investigated. Two different line configurations are considered: parallel wires and perpendicular lines. The analytical solutions for both types of lines are obtained, using the method of symmetrical lines inside the resonator. Computer realization of this method allows it to obtain a fast solution. Therefore, it becomes possible to investigate statistical properties of induced currents. It could be shown that the mutual coupling of the currents in the wires is strong when the frequency is near resonances in the system "cavity and wires" and relatively small far from these resonances. Stochastization leads to a broadening of the resonance curves.

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Closed-Form Formulas for the Stochastic Electromagnetic Field Coupling to a Transmission Line With Arbitrary Loads

Cited by 30 publications

References 5 publications

Simple, Taylor-Based Worst-Case Model for Field-to-Line Coupling

Simple, Taylor-Based Worst-Case Model for Field-to-Line Coupling

Numerical and Analytical Analysis of Stochastic Electromagnetic Fields Coupling to a Printed Circuit Board Trace

Propagation of Current Waves along Randomly Located Multiconductor Transmission Lines inside a Rectangular Resonator

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