Random Coupling Model Research Articles

Prediction of Electromagnetic Coupling in Complicated Enclosures With External Excitation Through an Aperture Using Extended Random Coupling Model

Prediction of Electromagnetic Coupling in Complicated Enclosures With External Excitation Through an Aperture Using Extended Random Coupling Model

Random coupling model of turbulence as a classical Sachdev-Ye-Kitaev model.

We point out that a classical analog of the Sachdev-Ye-Kitaev (SYK) model, a solvable model of quantum many-body chaos, was studied long ago in the turbulence literature. Motivated by the Navier-Stokes equationin the turbulent regime and the nonlinear Schrödinger equationdescribing plasma turbulence, in which there is mixing between many different modes, the random coupling model has a Gaussian-random coupling between any four of a large number N of modes. The model was solved in the 1960s, before the introduction of large-N path-integral techniques, using a method referred to as the direct interaction approximation. We use the path integral to derive the effective action for the model. The large-N saddle gives an integral equationfor the two-point function, which is very similar to the corresponding equationin the SYK model. The connection between the SYK model and the random coupling model may, on the one hand, provide new physical contexts in which to realize the SYK model and, on the other hand, suggest new models of turbulence and techniques for studying them.

Time-Domain Generalization of the Random-Coupling Model and Experimental Verification in a Complex Scattering System

Electromagnetic wave scattering in electrically large, irregularly shaped, environments is a common phenomenon. The deterministic, or first-principles, study of this process is usually computationally expensive and the results exhibit extreme sensitivity to scattering details. For this reason, the deterministic approach is often dropped in favor of a statistical one. The random coupling model (RCM) Hemmady et al. [Phys. Rev. Lett. 94, 014102 (2005).] is one such approach that has found great success in providing a statistical characterization for wave chaotic systems in the frequency domain. Here we aim to transform the RCM into the time domain and generalize it to alternative situations. The proposed time-domain RCM (TDRCM) method can treat a wave chaotic system with multiple ports and modes. Two features are now possible with the time-domain approach for chaotic resonators: the incorporation of early time short-orbit transmission path effects between the ports, and the inclusion of arbitrary nonlinear or time-varying port load impedances. We conduct short-pulse time-domain experiments in wave chaotic enclosures, and use the TDRCM to simulate the corresponding experimental setup. We also examine a diode-loaded port and compare experimental results with a numerical TDRCM treatment and find agreement.

Deviations From the Random Plane Wave Field Distribution in Electromagnetic Enclosures

Wave energy distribution within enclosures with irregular boundaries is a common phenomenon in many branches of electromagnetics. If the wavelength of the injected wave is small compared with the structure size, the scattering properties of the enclosure will be extremely sensitive to small changes in geometry or wave frequency. In this case, statistical models are sought. The random coupling model (RCM) is one such model that has been explored through experiments and theory. Previous studies were conducted by injecting waves into high Q cavities in a nearly omnidirectional manner. In this article, a directed beam approach is taken, and relatively low Q cavities are considered. The goal is to determine when the so-called “random plane wave hypothesis,” a fundamental basis of the RCM formulation, breaks down. Results show that injecting such directed beams leads to large deviations in the wave statistics for single realizations of the enclosure geometry. The expected statistics are restored to some degree when multiple realizations are considered.

Time-Varying Radiation Impedance of Microcontroller GPIO Ports and Their Dependence on Software Instructions

The coupling of short wavelength electromagnetic (EM) interference to critical electronic systems in highly reverberant enclosures is a growing concern in the EM interference/compatibility community. In such highly reverberant cavities, prior research has shown that the induced EM fields, voltages, or currents can be modeled using the wave-chaotic random coupling model (RCM). The RCM partitions the interaction within the cavity into a universally fluctuating part, derived from random matrix theory, and a system-specific part, defined by the radiation impedance of the ports of interest, where the voltages or currents are induced. Earlier researchers have treated the radiation impedance as a time-invariant, frequency-dependent complex quantity. This is true for passive structures but is not true for active semiconductor devices, such as microcontrollers, which can exhibit time-varying radiation properties depending on the instruction cycle being executed at a given instant of time. The estimate of such a time-varying radiation impedance and its correlation with instruction cycles in an elemental microcontroller is the focus of this work. Utilizing clustering algorithms, we observe that the measured radiation impedance, as well as radiative emissions, are correlated to the class of instruction cycles being executed. By clustering the radiation impedance and emissions of the general-purpose input/output ports utilizing the class of instructions being executed, predictive models for microcontroller susceptibility can be derived even when detailed knowledge of the specific instruction cycle being executed is unknown a priori. Such a predictive capability can find multiple applications in the EMI/EMC community.

Efficient Statistical Model for Predicting Electromagnetic Wave Distribution in Coupled Enclosures

The Random Coupling Model (RCM) has been successfully applied to predicting the statistics of currents and voltages at ports in complex electromagnetic (EM) enclosures operating in the short wavelength limit. Recent studies have extended the RCM to systems of multi-mode aperture-coupled enclosures. However, as the size (as measured in wavelengths) of a coupling aperture grows, the coupling matrix used in the RCM increases as well, and the computation becomes more complex and time-consuming. A simple Power Balance Model (PWB) can provide fast predictions for the \textit{averaged} power density of waves inside electrically-large systems for a wide range of cavity and coupling scenarios. However, the important interference induced fluctuations of the wavefield retained in the RCM is absent in PWB. Here we aim to combine the best aspects of each model to create a hybrid treatment and study the EM fields in coupled enclosure systems. The proposed hybrid approach provides both mean and fluctuation information of the EM fields without the full computational complexity of coupled-cavity RCM. We compare the hybrid model predictions with experiments on linear cascades of over-moded cavities. We find good agreement over a set of different loss parameters and for different coupling strengths between cavities. The range of validity and applicability of the hybrid method are tested and discussed.

Wave scattering properties of multiple weakly coupled complex systems.

The statistics of the scattering of waves inside single ray-chaotic enclosures have been successfully described by the random coupling model (RCM). We expand the RCM to systems consisting of multiple complex ray-chaotic enclosures with various coupling scenarios. The statistical properties of the model-generated quantities are tested against measured data of electrically large multicavity systems of various designs. The statistics of model-generated transimpedance and induced voltages on a load impedance agree well with the experimental results. The RCM coupled chaotic enclosure model is general and can be applied to other physical systems, including coupled quantum dots, disordered nanowires, and short-wavelength electromagnetic and acoustic propagation through rooms in buildings, aircraft, and ships.

Scattering statistics in nonlinear wave chaotic systems.

The Random Coupling Model (RCM) is a statistical approach for studying the scattering properties of linear wave chaotic systems in the semi-classical regime. Its success has been experimentally verified in various over-moded wave settings, including both microwave and acoustic systems. It is of great interest to extend its use in nonlinear systems. This paper studies the impact of a nonlinear port on the measured statistical electromagnetic properties of a ray-chaotic complex enclosure in the short wavelength limit. A Vector Network Analyzer is upgraded with a high power option, which enables calibrated scattering (S) parameter measurements up to +43dBm. By attaching a diode to the excitation antenna, amplitude-dependent S-parameters and Wigner reaction matrix (impedance) statistics are observed. We have systematically studied how the key components in the RCM are affected by this nonlinear port, including the radiation impedance, short ray orbit corrections, and statistical properties. By applying the newly developed radiation efficiency extension to the RCM, we find that the diode admittance increases with the excitation amplitude. This reduces the amount of power entering the cavity through the port so that the diode effectively acts as a protection element. As a result, we have developed a quantitative understanding of the statistical scattering properties of a semi-classical wave chaotic system with a nonlinear coupling channel.

Extraction of the coupling impedance in overmoded cavities

The radiation impedance is a key parameter in characterizing an antenna, and also particularly important in a statistical model of coupling to an overmoded cavity. Previous methods of measuring the radiation impedance present challenges that can be overcome by applying a time gating method. The time gating method presented here allows one to obtain the radiation impedance from a frequency domain measurement of the reflection coefficient in situ. It has the flexibility of including the effects of internal reflections in the cavity by adjusting the time gating parameters. The method is applied to the random coupling model and is successfully shown to agree with its theoretical predictions.

Revealing underlying universal wave fluctuations in a scaled ray-chaotic cavity with remote injection.

The Random Coupling Model (RCM) predicts the statistical properties of waves inside a ray-chaotic enclosure in the semiclassical regime by using Random Matrix Theory, combined with system-specific information. Experiments on single cavities are in general agreement with the predictions of the RCM. It is now desired to test the RCM on more complex structures, such as a cascade or network of coupled cavities, that represent realistic situations but that are difficult to test due to the large size of the structures of interest. This paper presents an experimental setup that replaces a cubic-meter-scale microwave cavity with a miniaturized cavity, scaled down by a factor of 20 in each dimension, operated at a frequency scaled up by a factor of 20 and having wall conductivity appropriately scaled up by a factor of 20. We demonstrate experimentally that the miniaturized cavity maintains the statistical wave properties of the larger cavity. This scaled setup opens the opportunity to study wave properties in large structures such as the floor of an office building, a ship, or an aircraft, in a controlled laboratory setting.

Nonlinear wave chaos: statistics of second harmonic fields.

Concepts from the field of wave chaos have been shown to successfully predict the statistical properties of linear electromagnetic fields in electrically large enclosures. The Random Coupling Model (RCM) describes these properties by incorporating both universal features described by Random Matrix Theory and the system-specific features of particular system realizations. In an effort to extend this approach to the nonlinear domain, we add an active nonlinear frequency-doubling circuit to an otherwise linear wave chaotic system, and we measure the statistical properties of the resulting second harmonic fields. We develop an RCM-based model of this system as two linear chaotic cavities coupled by means of a nonlinear transfer function. The harmonic field strengths are predicted to be the product of two statistical quantities and the nonlinearity characteristics. Statistical results from measurement-based calculation, RCM-based simulation, and direct experimental measurements are compared and show good agreement over many decades of power.

Analysis of Electromagnetic Pulse Effect Based on Short Orbit Random Coupling Model

In many situations, the random coupling model (RCM) has been successfully demonstrated to predict the electromagnetic pulse effect within a complex enclosure. However, the model sets boundary conditions at infinity when calculating the coupling effect, which causes a problem named the short orbit effect. In this paper, a short orbit random coupling model (SORCM) is proposed by means of defining a short orbit correction coefficient of the radiation impedance in the two-port wave chaotic cavity. The results of the SORCM were compared with the experimental data, which shows that the SORCM is more effective compared with the RCM in predicting the statistical electromagnetic properties. The insights gained from the research can provide guidelines for the design of the electronic equipment.

Prediction of Induced Voltages on Ports in Complex, Three-Dimensional Enclosures With Apertures, Using the Random Coupling Model

A statistical modeling technique known as the random coupling model (RCM) is an effective method for estimating the probabilistic magnitudes of induced voltages on objects within a closed, complex, three-dimensional (3-D) enclosure. The limitations of the RCM to predict electromagnetic wave coupling into an enclosure with apertures are examined. We experimentally demonstrate the applicability of the RCM to estimate the probabilistic magnitudes of voltages induced on ports in a complex 3-D enclosure with an electrically large aperture. This study is a first step toward being able to predict effects on sensitive electronic targets in large, real-world, lossy enclosures such as office buildings, ship compartments, and aircraft compartments.

Random coupling model for the radiation of irregular apertures

AbstractIn this work, we extend results on the coupling of radiation through apertures inside wave chaotic electromagnetic cavities to the short‐wavelength limit. The aperture is assumed to have irregular and smooth boundary geometry. A statistical approach is then used to model both fields in the aperture and in the plane of the aperture. Particular emphasis is devoted to the calculation of the free‐space or radiation aperture admittance matrix, whose ensemble averaged element takes a simple closed‐form expression. The radiation admittance matrix is found to be purely diagonal at relatively short wavelength, and it exhibits unusual frequency behavior. The extreme scenario of an irregular aperture radiating inside an irregular cavity is represented through the random coupling model. This mathematical framework uses a limited number of details of both the aperture and the environment in those problems involving the coupling of an external radiation. The universal fluctuation of the effective area of an electrically large aperture is found for a wave chaotic cavity at variable losses. Results are expected to be useful for the physical understanding of scattering in extremely complicated environments, mode‐stirred reverberation chambers, wireless channels, radar traces, and statistical optics.

Experimental Verification of a Stochastic Topology Approach for High-Power Microwave Effects

The random coupling model (RCM) and Baum-Liu-Tesche EM topology have been well developed to describe the statistical fluctuation of the scattering and impedance matrices of wave-chaotic metallic-enclosed cavity, and the interaction of interconnected networks of complicated enclosures, respectively. In this paper, a stochastic approach that combines these two methods is tested and verified on a network of wave-chaotic metallic cavities, and induced voltage derived by this method is also compared with other methods.

Intensity impulse response of SDM links

We study the response of space-division multiplexed fiber links to an excitation by a short impulse of the optical intensity. We show that, in the presence of full mixing, the intensity impulse response is Gaussian, confirming recently reported experimental observations, and relate its variance to the mean square of the mode dispersion vector of the link τ(->). The good agreement between our theory and the previously published experiments provides solid foundations to the random coupling model of SDM fiber links, and provides a tool for efficient design of MIMO-DSP receivers.

Application of the Random Coupling Model to Electromagnetic Statistics in Complex Enclosures

The effectiveness of the random coupling model (RCM) in predicting electromagnetic wave coupling to targeted electronic components within a complex enclosure is examined. In the short-wavelength limit with respect to the characteristic length of the enclosure, electromagnetic wave propagation within a large enclosure is sensitive to small changes to the interior, or to the boundaries of the enclosure. Such changes can reduce or invalidate the applicability of deterministic predictions of the electromagnetic fields at radiofrequencies (RF) in large enclosures. Under such circumstances, a statistical approach is needed to provide a better understanding of RF coupling to components within large enclosures. In this paper, we experimentally demonstrate the applicability of a statistical technique, the RCM, to estimate the probabilistic magnitudes of RF fields on electrically large components (i.e., long cables, etc.) that are partially shielded within a complex, 3-D enclosure.

Analysis of statistical nature of induced voltages at key points in computer box cavity in different frequency ranges

The statistic characteristic of induced voltages at key points in computer box cavity is researched by means of experiments and the random coupling model （RCM）. It is shown that the experiment results generally agree with the theoretical results in trend. The applicability of RCM in analysis and predication of system-level electromagnetic environment effects is validated. A new method based on statistical electromagnetism should be exploited for the analyses of electromagnetic effects for large scale nonparallel surface electron device-box cavity systems.

Analysis of systemic electromagnetic environment effects based on Random Coupling Model

By experiment and Random Coupling Model（RCM）, the statistic characteristics of induced voltages at key points in computer box cavity are studied. The calculating method and application diagram of RCM is given. Scattering coefficients, the statistic characteristics of normalized scattering coefficient and normalized impedance coefficient are researched by experiment and theory. It is shown that the experiment results generally agree with the theoretical results in trend. Application of RCM is preliminarily discussed. Applicability of analysis and forecast on systemic electromagnetic environment effects based on RCM is validated. Especially, the RCM is applicable to investigation on electromagnetic compatibility, effects and assessment for the large scale nonparallel surface electronic systems.

Predicting the statistics of wave transport through chaotic cavities by the random coupling model: A review and recent progress

In this review, a model (the random coupling model) that gives a statistical description of the coupling of radiation into and out of large enclosures through localized and/or distributed ports is presented. The random coupling model combines both deterministic and statistical phenomena. The model makes use of wave chaos theory to extend the classical modal description of the cavity fields in the presence of boundaries that lead to chaotic ray trajectories. The model is based on a clear separation between the universal statistical behavior of the closed chaotic system, and the deterministic coupling port characteristics. Moreover, the ability of the random coupling model to describe interconnected cavities, aperture coupling, and the effects of short ray trajectories is discussed. A relation between the random coupling model and other formulations adopted in acoustics, optics, and statistical electromagnetics, is examined. In particular, a rigorous analogy of the random coupling model with the Statistical Energy Analysis used in acoustics is presented.