Equivalent Dipole Moments Research Articles

A highly accurate and robust source reconstruction method of printed circuit boards based on complex‐valued neural network

SummaryPrinted circuit boards play an increasingly important role in modern electronic systems. Equivalent dipole moments are widely used to reconstruct the radiated fields of printed circuit boards in view of the extremely high complexity. In this paper, an improved source reconstruction method based on complex‐valued neural network is proposed to investigate the radiation properties of printed circuit boards working in microwave frequency band. Firstly, the magnetic field data obtained from the near‐field scanning are utilized to construct a matrix equation based on the source reconstruction theory. Secondly, the kernel of the complex‐valued neural network is constructed through the algorithm of complex numbers, which eventually end up with the novel neural network with the help of the principle of regression optimization. Thirdly, the data obtained from the near‐field scanning are fed into the neural network for effective training to get the equivalent dipole model. Finally, several numerical examples and available measurement results are given to validate the method. Compared with the commonly used Tikhonov regularization method, the proposed method possesses higher accuracy and better robustness in noise suppression.

Dipole-Moment-Based Reciprocity for Practical Desensitization Identification and Mitigation

Radio frequency interference can degrade the receiving sensitivity of antennas. The interference is usually caused by certain coupling structures, such as layouts without adequate grounding for the radio frequency signal return path. Those structures can be modeled as a set of equivalent dipole moments when they are electrically small. Herein, the dipole moment model-based coupling framework is applied to a practical cellphone design case to devise an engineering solution. The coupling framework incorporates dipole moments as radiation sources and a coupling model based on the reciprocity theorem. Unfortunately, near-field scan probes often lack access to all locations, owing to the complex phone platform structure. A combined measurement-simulation method is used to obtain the field quantities lacking direct access to measurements. The dipole-moment-based coupling framework helps estimate the couplings from different noise sources individually. Thus, the priority of solving for better layout designs can be determined according to the coupling estimations. Furthermore, the physics associated with the reconstructed dipole moment can provide insights and suggest possible mitigation methods. Several practical mitigation methods are discussed, including the suppression of the dominant noise source (reducing/cancelling the radiation or suppressing the specific noise spectrum) and the coupling path to the victim antenna.

A Multicomponent Iterative Method for Efficient Source Reconstruction Based on Magnitude-Only and Single-Plane Near-Field Scanning

A multicomponent iterative method is proposed for efficient source reconstruction based on magnitude-only and single-plane near field scanning. Compared with the conventional method filling the multicomponent data into a whole transformation matrix, the multicomponent iterative method can save huge calculation time by evenly reducing the size of the transformation matrix into magnetic group and electric group, without losing solution accuracy of the equivalent dipole moments. The accuracy and efficiency of the proposed source reconstruction is verified on a simulated patch antenna model. The proposed method is also applied to efficiently find the equivalent sources and reconstruct the surface electromagnetic field of a practical serpentine line. For a larger transformation matrix (depending on the factors such as the scanned field components, scanned points, and dipole numbers), the proposed iteration method shows higher efficiency.

Efficient EDM-PO Method for the Scattering From Electrically Large Objects With the High-Order Impedance Boundary Condition

This work proposes an efficient hybrid method consisting of the efficient iterative method of moments–physical optics (EI-MoM-PO) and the equivalent dipole moment (EDM) with the high-order impedance boundary condition (HOIBC) to explore the electromagnetic scattering from the object with an isotropic or anisotropic surface coating. By introducing the HOIBC into the EDM method, the relationship between the equivalent electric and magnetic dipole moments is established. Therefore, the EDM method is extended to general cases. For the composite scattering from electrically large objects including MoM and PO regions, the EDM method is implemented to fill the MoM impedance matrix and to accelerate the evaluation of the coupling between the MoM and PO regions, which considerably improves the computing efficiency. The numerical results indicate that the proposed hybrid method allows for a substantial decrease in computation time. Also, they also agree well with the traditional finite element method, MoM, or MoM-PO method, which proves the validity of the proposed method.

Numerical simulation research of circular dichroism based on a catenary-shaped ultrathin metasurface

The circular dichroism (CD) produced by chiral materials in nature is usually very weak, and is not easy to be detected and analyzed in experiment. In this paper, a catenary-shaped chiral metasurface (CCMS) is proposed to achieve giant CD. The unit of the CCMS is composed of a metal–insulator–metal structure. Its upper and lower layers are composed of catenary-shaped metal elements. Under the excitation of left circularly polarized light and right circularly polarized light, the coupling modes of the equivalent electric dipole moments on the upper and lower metal surfaces are different, which leads to giant CD approaching 0.55. In addition, the CD properties can be tuned by structure parameters, such as the thickness of the intermediate dielectric layer, the length of the catenary-shaped metal elements, the twisted angle of the catenary-shaped metal surfaces of the upper and lower layers, and the period of the structure. By optimizing structure parameters, the maximum CD signal can reach 0.68. The present results would be helpful for designing chiral structures with enhanced CD signal.

Efficient method for the shielding effectiveness of an enclosure with electrically large apertures based on the Cohn model and mirror procedure

An efficient analytical method based on the Cohn model and mirror procedure is proposed for the prediction of the shielding effectiveness (SE) of a rectangular enclosure with electrically large apertures. Firstly, the coupled electromagnetic fields are represented by the equivalent dipole moments located at the centre of the aperture according to the Cohn model, where the dipole moments can be calculated based on the mirror procedure. Then, the vector potentials can be obtained through the relation between the dipole moments and the current distribution. Finally, the total electric fields are obtained by using the vector potentials, thus the SE and most of the resonant modes can be predicted accurately and fast. The SE results which have been verified by the CST over a wide frequency band of 0.01–3.0 GHz show that the proposed method is effective in handling the enclosure with electrically large apertures, including the multiple apertures arranged in different ways and hybrid apertures in different shapes and dimensions.

A New Reconstruction Method for a Source Above an Arbitrarily Shaped Ground Plane

Source reconstruction using equivalent dipole moments to replace the original noise source is widely used in radio frequency interference. The conventional reconstruction methods only work well in the cases of free space or with a large ground plane. In this article a new method is proposed for source reconstruction over an arbitrarily shaped ground plane. It uses the field below the ground plane to eliminate the arbitrary ground effect. Comparing to the method of solving surface integral equation, it is simple and does not need the ground geometric information. The new method is validated in the full-wave simulations.

An efficient method for predicting the shielding effectiveness of an enclosure with multiple apertures

ABSTRACT An efficient analytical method has been proposed for predicting the shielding effectiveness (SE) and resonances of a metallic enclosure with multiple apertures against an external incident plane wave. First, the electromagnetic (EM) field distribution within the enclosure through multiple apertures is represented by the equivalent electric and magnetic dipole moments based on the Bethe’s theory for small aperture coupling. Then, the EM fields in the enclosure can be obtained by using the scalar wave functions, where the unknown coefficients in the functions are related to the equivalent dipole moments. Finally, the analytical method is applied to handle the enclosure with multiple apertures, and corresponding inclusions about the SE and resonances can be obtained. Compared with the full-wave simulation software CST over the frequency range of 0–2.5 GHz, the analytical method is proved to be accurate and effective, which consumes less time than the conventional numerical methods.

Near-Field Scanning-Based Shielding Effectiveness Extraction for Board-Level Shielding Cans

The conventional definition of shielding effectiveness (SE) is well suited for calculations of far-field electromagnetic shielding. However, in the near field, SE calculations are not as straightforward. In radio-frequency interference (RFI) problems, the majority of field coupling occurs in the near field. Thus, a well-defined method for calculating the near-field SE is needed to estimate the suppression of RFI achieved by shielding cans. In this study, a method based on near-field scanning is developed to extract the SE of board-level shielding cans. The SE is defined by modeling the shielded noise source as equivalent dipole moments. The accuracy of the equivalent source is analyzed via the least-square error and correlation coefficient as confidence verification parameters. By applying the reciprocity theorem, the voltage coupled on a planar inverted F antenna from an unshielded and a shielded source is calculated. The coupled voltage from a shielded noise source serves as a reference to validate the effectiveness of the proposed method. Practical shielding cans were used to develop and validate the SE extraction method using full-wave 3D simulations and measurements.

Theoretical Analysis of Parameter Optimization for Lower-Ionosphere Excitation ELF/VLF Waves Based on Chirp-BOK Modulated Heating

To improve the anti-interference for ELF/VLF communication based on modulated heating lower-ionosphere, chirp spread spectrum technology with strong anti-interference is combined with square wave amplitude modulation, a novel method of chirp-BOK modulated heating lower-ionosphere is proposed in this paper. On this basis, to improve the radiation efficiency of ELF/VLF, the effects of heating parameters (effective radiation power, pump frequency, polarization mode, modulation frequency, duty cycle, and bandwidth) on the radiation efficiency of ELF/VLF were analyzed. The results show that the radiation amplitude of ELF/VLF increases with the increase of effective radiation power, while the radiation efficiency increases first and then decreases; the X-mode is better than the O-mode; the radiation intensity of ELF/VLF decreases with the increase of pump wave frequency from 4MHz to 10MHz; the ELF/VLF equivalent dipole moments increase with the rise of modulation frequency from 500Hz to 5kHz; with the change of duty cycle from 10% to 90%, the dipole moments first increase and then decrease, and the optimal range of duty cycle is 40% to 70%; with the increase of bandwidth, the dipole moments are unchanged. Furthermore, the ELF/VLF dipole moments of square wave amplitude modulated heating ionosphere is unchanged before and after the chirp spread spectrum.

Thermal illusion with the concept of equivalent thermal dipole

The research on thermal illusion contributes to both fundamental theories and practical applications. In the existing literatures, the most common mechanism is to design a shell to disguise the inside core. However, the core-shell scheme may be weak to handle many-particle systems because N particles may require N specially-designed shells. This lacks efficiency and restricts practical applications. To solve this problem, we can no longer focus on the local effect of a single particle. In contrast, we should study the macroscopic effect of the N particles by treating each particle as an equivalent thermal dipole. Then, thermal illusion can be achieved when the macroscopic equivalent thermal dipole moments of different systems are equal to each other. This requires only once calculation and contributes to efficiency. Accidentally, the concept of equivalent thermal dipole helps to revisit the well-known Bruggeman theory and provides a clear physical image for it. The proposed scheme is verified by theoretical analyses, finite-element simulations, and laboratory experiments. Our work offers an efficient approach to achieving thermal illusion in many-particle systems, and contributes to potential applications in misleading infrared detection, manipulating heat flux, etc.

Active Control and Biosensing Application of Induced Chirality between Symmetric Metal and Graphene Nanostructures

Induced circular dichroism (ICD) is found between plasmonic nanostructures and chiral molecules, where at least one of them is chiral. However, it is a great challenge to generate ICD only through achiral structures with the simple coupling model. Here, we demonstrate that ICD is approximately contributed by the cross-electromagnetic coupling between equivalent electric dipole moments and magnetic dipole moments for two achiral plasmon nanostructures. To prove electromagnetic couplings between different wavebands, graphene belts are introduced into plasmon nanostructures composing achiral metal-nanorods with graphene-nanobelt arrays (AMGAs). Results showed that ICD signals are achieved in a near-infrared band of metal resonance and a micron band of graphene resonance. Near-field charge distributions of AMGAs reveal the coupling effect between metal-nanorods and graphene-nanobelts. The handedness of AMGAs can be actively controlled by adjusting the Fermi levels of graphene-nanobelts; the strength and reson...

Machine Learning Based Source Reconstruction for RF Desense

In radio frequency interference study, equivalent dipole moments are widely used to reconstruct real radiation noise sources. Previous reconstruction methods, such as least square method (LSQ) and optimization method are affected by parameter selections, such as number and locations of dipole moments and choices of initial values. In this paper, a new machine learning based source reconstruction method is developed to extract the equivalent dipole moments more accurately and reliably. Based on the near-field patterns, the proposed method can determine the minimal number of dipole moments and their corresponding locations. Furthermore, the magnitude and phase for each dipole moment can be extracted. The proposed method can extract the dominant dipole moments for the unknown noise sources one by one. The proposed method is applied to a few theoretical examples first. The measurement validation using a test board and a practical cellphone are also given. Compared to the conventional LSQ method, the proposed machine learning based method is believed to have a better accuracy. Also, it is more reliable in handling noise in practical applications.

Fast solution of near-field time reversal electromagnetic field of sub-wavelength perfect conducting ball arrays

To solve the near-field time reversal electromagnetic fields of sub-wavelength perfect conducting ball arrays rapidly, an analytical formulation is presented based on the equivalent dipole model. As is well known, the efficient use of evanescent information is the key to the realization of sub-wavelength focusing and imaging. However, evanescent components always suffer exponential decays with the increase of propagating distance. Therefore, in order to effectively control the evanescent waves, some measures should be taken in the near field region of the scatters before their amplitudes are reduced to an undetectable level. Since small perfect conducting ball is the basic component of large scatter, the first step should be to study the scattering properties of small perfect conducting ball. The far-field scattering fields of perfect conducting balls have been analyzed for plane waves. However, for spherical waves, the analytical results are not convenient to extend to multi-ball situation since they are all expressed by series. In this paper, the analytical solution to scattering field of the small perfect conducting balls irradiated by spherical radiative waves is analyzed. The result shows that the scattering fields can be approximately equivalent to the superposition of the radiation fields of electrical and magnetic dipoles in some restrictive conditions. The intensity of the equivalent dipole is proportional to the magnitude of the original excitation source dipole. Therefore all the equivalent dipole moments can be calculated easily by setting up the coupling equations between different equivalent dipoles and source dipole. Then, the forward dyadic Green's function can be obtained by combining the vacuum electrical and magnetic Green's function. At the same time, the time reversal dyadic Green's function can be derived through the time reversal cavity theory. Afterwards, the near-field time reversal electromagnetic field of the perfect conductive ball arrays can be calculated directly by the time reversal dyadic Green's function. The results obtained from the proposed method and a numerical software are compared, which shows that a coincidence extent reaches more than 0.95. This confirms the correctness and high efficiency of the proposed method. After that, an imaging experiment is implemented and the result shows that an imaging resolution of 0.3 can be obtained by loading small conducting balls in the near field. All these experiments show that combined with near-field loading of sub-wavelength scatterer arrays, the time reversal technique has the potential to realize super-resolution focusing and imaging.

Induced chirality in micron wave through electromagnetic coupling between chiral molecules and graphene nanostructures

The intricate mechanisms of plasmon-induced circular dichroism (CD) in a visible region are considered based on chemical and physical influences, in which a simple model and formulations are required. Here, we demonstrate theoretically that plasmon-induced CD is approximately contributed by the cross-interaction between equivalent electric and magnetic dipole moments for chiral molecules and plasmon nanostructures. To prove electromagnetic couplings, we introduce graphene into plasmon nanostructures and design asymmetrically inscribed graphene dual-rings arrays (IGDAs) with high-order hybrid modes. Results show that ultrahigh-order plasmon-induced CD signals are achieved in micron wave, which is easily detected by mature microwave technology. The maximum enhancement factor of induced CD could reach up to four orders of magnitude. In addition, an induced CD signal could be tuned only by varying the Fermi energy of IGDAs rather than by varying geometric dimensions. For different molecules, the electromagnetic couplings still hold. The results could be used to dynamically design chiral sensors in biology and chemistry.

A Novel Shielding Effectiveness Matrix of Small Shield Cans Based on Equivalent Dipole Moments for Radio-Frequency Interference Analysis

A definition of a shielding effectiveness (SE) matrix for small shield cans used to suppress intra-system noise coupling in mobile devices is proposed. Assuming shield cans enclosing a noise source can be modeled as equivalent dipole moments along with integrated circuits (ICs), a new SE matrix for radio-frequency interference analysis is defined as a ratio of equivalent dipole moments with and without a shield can. The equivalent dipole moments are experimentally extracted using a GTEM cell and two types of probes (monopole and loop), which mimic well the radiations of ICs. Furthermore, the estimation of suppression of noise coupling to an antenna using the proposed SE matrix is successfully validated through numerical simulations.

Manipulation of electromagnetically induced transparency by planar metamaterial

The transmission characteristics of a planar metamaterial, composed of a metal ring and a regular trigonometry-star-rod (TSR), have been numerically and experimentally investigated in this paper. By rotating the TSR with different angles, this structure will appear to be symmetric or asymmetric toward the incident waves and then finely controls the coupling between the ring and the TSR. Thus, the transmission spectrum of our proposed structure can exhibit an electromagnetically induced transparency (EIT)-like spectral response in microwave region. Owing to the C3 rotational symmetry of the structure, an on-to-off active modulation of the EIT-like transparency window can be realized, and it may serve as the base for a microwave optical switching. Equivalent electric dipole moments couplings are employed to explain the transmission properties. In all, our work provides a way to obtain EIT-like effect, and it may achieve potential applications in filters, sensing and some other microwave devices.

STUDY OF THE SHIELDING EFFECTIVENESS OF DOUBLERECTANGULAR ENCLOSURESWITH APERTURES EXCITED BY AN INTERNAL SOURCE

An analytical formulation has been developed to evaluate the shielding effectiveness (SE) of two coplanar rectangular metallic enclosures with a circular aperture excited by an internal electric dipole source. The formulation consists of three parts: First, the near-field electromagnetic interference (EMI) of the electromagnetic leakage from the aperture is represented by the electric dipole in one enclosure. Then, the aperture equivalent magnetic and electric dipole moments are calculated according to the Bethe's small aperture coupling theory. Finally, the electric field of the other enclosure is derived by using the equivalent magnetic dipole field, equivalent electric dipole field and the corresponding enclosure's Green's functions in the two fields. In this formulation, the electric field of the enclosure can be expressed as a function of the observation point, the aperture's center point, source point, shape of the aperture and enclosure's conductivity. The formulation then is employed to analyze the effect of the above factors on the SE. The analytical results have been successfully compared with the full-wave simulation software Computer Simulation Technology (CST) from 0.3 ∼ 2. 4G Hz.

Rayleigh Model for Electromagnetic Scattering from a Chiral Sphere

Rayleigh model has been proposed to deal with scattering from a small sized chiral sphere. A chiral sphere in Rayleigh size illuminated by electromagnetic waves can be substituted by four Hertzian dipoles. Thus the scattering problem is converted to a radiation problem. The four equivalent dipole moments are solved by applying the boundary conditions of Maxwell equations. Numerical results calculated by the model are compared with analytical solutions and achieve good agreement. Scattering patterns of a small chiral sphere with different chirality parameters are depicted and the effects of the chirality are discussed.

Structure predicts function: Combining non-invasive electrophysiology with in-vivo histology

We present an approach for combining high resolution MRI-based myelin mapping with functional information from electroencephalography (EEG) or magnetoencephalography (MEG). The main contribution to the primary currents detectable with EEG and MEG comes from ionic currents in the apical dendrites of cortical pyramidal cells, aligned perpendicularly to the local cortical surface. We provide evidence from an in-vivo experiment that the variation in MRI-based myeloarchitecture measures across the cortex predicts the variation of the current density over individuals and thus is of functional relevance. Equivalent current dipole locations and moments due to pitch onset evoked response fields (ERFs) were estimated by means of a variational Bayesian algorithm. The myeloarchitecture was estimated indirectly from individual high resolution quantitative multi-parameter maps (MPMs) acquired at 800μm isotropic resolution. Myelin estimates across cortical areas correlated positively with dipole magnitude. This correlation was spatially specific: regions of interest in the auditory cortex provided significantly better models than those covering whole hemispheres. Based on the MPM data we identified the auditory cortical area TE1.2 as the most likely origin of the pitch ERFs measured by MEG. We can now proceed to exploit the higher spatial resolution of quantitative MPMs to identify the cortical origin of M/EEG signals, inform M/EEG source reconstruction and explore structure–function relationships at a fine structural level in the living human brain.