arXiv subjects

Utkarsh R. Patel

Publications and source records attributed to Utkarsh R. Patel.

15 recordsLinked to original sources

arXiv2022

Wigner-Smith Time Delay Matrix for Electromagnetics: Guiding and Periodic Systems with Evanescent Modes

The Wigner-Smith (WS) time delay matrix relates an electromagnetic system's scattering matrix and its frequency derivative. Previous work showed that the entries of WS time delay matrices of systems excited by propagating waves consist of volume integrals of energy-like field quantities. This paper introduces a generalized WS relationship that applies to systems excited by mixtures of propagating and evanescent fields. Just like its predecessor, the generalized WS relationship allows for the identification of so-called WS modes that interact with the system with well-defined time delays. Furthermore, a technique is developed to compute the WS time delay matrix of a composite system from the WS time delay matrices of its subsystems. Numerical examples demonstrate the usefulness of the generalized WS method when characterizing time delays experienced by fields interacting with guiding and periodic structures that have ports supporting evanescent modes.

eess.SY↗

arXiv2022

Wigner-Smith Time Delay Matrix for Electromagnetics: Systems with Material Dispersion and Losses

The Wigner-Smith (WS) time delay matrix relates a system's scattering matrix to its frequency derivative and gives rise to so-called WS modes that experience well-defined group delays when interacting with the system. For systems composed of nondispersive and lossless materials, the WS time delay matrix previously was shown to consist of volume integrals of energy-like densities plus correction terms that account for the guiding, scattering, or radiating characteristics of the system. This study extends the use of the WS time delay matrix to systems composed of dispersive and lossy materials. Specifically, it shows that such systems' WS time delay matrix can be expressed by augmenting the previously derived expressions with terms that account for the dispersive and lossy nature of the system, followed by a transformation that disentangles effects of losses from time delays. Analytical and numerical examples demonstrate the new formulation once again allows for the construction of frequency stable WS modes that experience well-defined group delays upon interacting with a system.

physics.comp-ph↗

arXiv2022

Wigner-Smith Time Delay Matrix for Acoustic Scattering: Computational Aspects

The Wigner-Smith (WS) time delay matrix relates an acoustic system's scattering matrix to its wavenumber derivative. The entries of the WS time delay matrix can be expressed in terms of energy density-like volume integrals, which cannot be efficiently evaluated in a boundary element method framework. This paper presents two schemes for efficiently populating the WS time delay matrix. The direct formulation casts the energy density-like volume integrals into integrals of the incident field and the field and/or its normal derivative over the scatterer surface. The indirect formulation computes the system's scattering matrix and its wavenumber derivative, again via surface integration, and then invokes the WS relationship to compute the WS time delay matrix. Both the direct and the indirect formulations yield equivalent results and can be easily integrated into standard boundary element codes.

cs.CE↗

arXiv2022

Wigner-Smith Time Delay Matrix for Acoustic Scattering: Theory and Phenomenology

The Wigner-Smith (WS) time delay matrix relates a lossless system's scattering matrix to its frequency derivative. First proposed in the realm of quantum mechanics to characterize time delays experienced by particles during a collision, this article extends the use of WS time delay techniques to acoustic scattering problems governed by the Helmholtz equation. Expression for the entries of the WS time delay matrix involving renormalized volume integrals of energy densities are derived, and shown to hold true independent of the scatterer's geometry, boundary condition (sound-soft or sound-hard), and excitation. Numerical examples show that the eigenmodes of the WS time delay matrix describe distinct scattering phenomena characterized by well-defined time delays.

cs.CE↗

arXiv2021

Wigner-Smith Time Delay Matrix for Electromagnetics: Theory and Phenomenology

Wigner-Smith (WS) time delay concepts have been used extensively in quantum mechanics to characterize delays experienced by particles interacting with a potential well. This paper formally extends WS time delay theory to Maxwell's equations and explores its potential applications in electromagnetics. The WS time delay matrix relates a lossless and reciprocal system's scattering matrix to its frequency derivative and allows for the construction of modes that experience well-defined group delays when interacting with the system. The matrix' entries for guiding, scattering, and radiating systems are energy-like overlap integrals of the electric and/or magnetic fields that arise upon excitation of the system via its ports. The WS time delay matrix has numerous applications in electromagnetics, including the characterization of group delays in multiport systems, the description of electromagnetic fields in terms of elementary scattering processes, and the characterization of frequency sensitivities of fields and multiport antenna impedance matrices.

physics.comp-ph↗

arXiv2020

Wigner-Smith Time Delay Matrix for Electromagnetics: Computational Aspects for Radiation and Scattering Analysis

The WS time delay matrix relates a lossless and reciprocal system's scattering matrix to its frequency derivative, and enables the synthesis of modes that experience well-defined group delays when interacting with the system. The elements of the WS time delay matrix for surface scatterers and antennas comprise renormalized energy-like volume integrals involving electric and magnetic fields that arise when exciting the system via its ports. Here, direct and indirect methods for computing the WS time delay matrix are presented. The direct method evaluates the energy-like volume integrals using surface integral operators that act on the incident electric fields and current densities for all excitations characterizing the scattering matrix. The indirect method accomplishes the same task by computing scattering parameters and their frequency derivatives. Both methods are computationally efficient and readily integrated into existing surface integral equation codes. The proposed techniques facilitate the evaluation of frequency derivatives of antenna impedances, antenna patterns, and scatterer radar cross sections in terms of renormalized field energies derived from a single frequency characterization of the system.

physics.comp-ph↗

arXiv2019

A Fast Macromodeling Approach to Efficiently Simulate Inhomogeneous Electromagnetic Surfaces

The full-wave simulation of complex electromagnetic surfaces such as reflectarrays and metasurfaces is a challenging problem. In this paper, we present a macromodeling approach to efficiently simulate complex electromagnetic surfaces composed of PEC traces, possibly with fine features, on a finite-sized multilayer dielectric substrate. In our approach, we enclose each element of the structure with a fictitious surface. By applying the equivalence principle on each surface, we derive a macromodel for each element of the array. This macromodel consists of a linear operator that relates the equivalent electric and magnetic current densities introduced on the fictitious surface. Mutual coupling between the elements of the structure is captured by the equivalent current densities in a fully accurate way. The crux of the proposed technique is to solve for equivalent current densities on the fictitious surface instead of directly solving for the actual current densities on the original scatterer. When simulating complex surfaces, this approach leads to fewer unknowns and better conditioning. We also propose a rigorous acceleration algorithm based on the fast Fourier transform to simulate electrically large surfaces. Numerical results demonstrate that the proposed approach is significantly faster and requires less memory than commercial solvers based on the surface integral equation method, while giving accurate results.

cs.CE↗

arXiv2019

A Complete Surface Integral Method for Broadband Modeling of 3D Interconnects in Stratified Media

A surface integral equation solver is proposed for fast and accurate simulation of interconnects embedded in stratified media. A novel technique for efficient computation of the multilayer Green's function is proposed. Using the Taylor expansion of Bessel functions, the computation of Sommerfeld integrals during the method of moments procedure is reduced to simple algebraic operations. To model skin effect in conductors, the single-source differential surface admittance operator is extended to conductors in stratified media. To handle large realistic structures, the adaptive integral method is developed for a multilayer environment in a generalized manner that poses no restrictions on layout of conductors, and requires no special grid refinement, unlike previous works. The proposed method is made robust over a wide frequency range with the augmented electric field integral equation. Realistic structures of different shapes and electrical sizes are successfully analyzed over a wide frequency range, and results are validated against a commercial finite element tool.

physics.comp-ph↗

arXiv2017

A Macromodeling Approach to Efficiently Compute Scattering from Large Arrays of Complex Scatterers

Full-wave electromagnetic simulations of electrically large arrays of complex antennas and scatterers are challenging, as they consume large amount of memory and require long CPU times. This paper presents a new reduced-order modeling technique to compute scattering and radiation from large arrays of complex scatterers and antennas. In the proposed technique, each element of the array is replaced by an equivalent electric current distribution on a fictitious closed surface enclosing the element. This equivalent electric current density is derived using the equivalence theorem and it is related to the surface currents on the scatterer by the Stratton-Chu formulation. With the proposed approach, instead of directly solving for the unknown surface current density on the scatterers, we only need to solve for the unknowns on the equivalent surface. This approach leads to a reduction in the number of unknowns and better conditioning when it is applied to problems involving complex scatterers with multiscale features. Furthermore, the proposed approach is accelerated with the adaptive integral equation method to solve large problems. As illustrated in several practical examples, the proposed method yields speed up of up to 20 times and consumes up to 12 times less memory than the standard method of moments accelerated with the adaptive integral method.

cs.CE↗

arXiv2016

A Novel Single-Source Surface Integral Method to Compute Scattering from Dielectric Objects

Using the traditional surface integral methods, the computation of scattering from a dielectric object requires two equivalent current densities on the boundary of the dielectric. In this paper, we present an approach that requires only a single current density. Our method is based on a surface admittance operator and is applicable to dielectric bodies of arbitrary shape. The formulation results in four times lower memory consumption and up to eight times lower time to solve the linear system than the traditional PMCHWT formulation. Numerical results demonstrate that the proposed technique is as accurate as the PMCHWT formulation.

cs.CE↗

arXiv2015

Skin Effect Modeling in Conductors of Arbitrary Shape Through a Surface Admittance Operator and the Contour Integral Method

An accurate modeling of skin effect inside conductors is of capital importance to solve transmission line and scattering problems. This paper presents a surface-based formulation to model skin effect in conductors of arbitrary cross section, and compute the per-unit-length impedance of a multiconductor transmission line. The proposed formulation is based on the Dirichlet-Neumann operator that relates the longitudinal electric field to the tangential magnetic field on the boundary of a conductor. We demonstrate how the surface operator can be obtained through the contour integral method for conductors of arbitrary shape. The proposed algorithm is simple to implement, efficient, and can handle arbitrary cross-sections, which is a main advantage over the existing approach based on eigenfunctions, which is available only for canonical conductor's shapes. The versatility of the method is illustrated through a diverse set of examples, which includes transmission lines with trapezoidal, curved, and V-shaped conductors. Numerical results demonstrate the accuracy, versatility, and efficiency of the proposed technique.

cs.CE↗

arXiv2015

MoM-SO: a Complete Method for Computing the Impedance of Cable Systems Including Skin, Proximity, and Ground Return Effects

The availability of accurate and broadband models for underground and submarine cable systems is of paramount importance for the correct prediction of electromagnetic transients in power grids. Recently, we proposed the MoM-SO method for extracting the series impedance of power cables while accounting for skin and proximity effect in the conductors. In this paper, we extend the method to include ground return effects and to handle cables placed inside a tunnel. Numerical tests show that the proposed method is more accurate than widely-used analytic formulas, and is much faster than existing proximity-aware approaches like finite elements. For a three-phase cable system in a tunnel, the proposed method requires only 0.3 seconds of CPU time per frequency point, against the 8.3 minutes taken by finite elements, for a speed up beyond 1000 X.

cs.CE↗

arXiv2015

Accurate Impedance Calculation for Underground and Submarine Power Cables using MoM-SO and a Multilayer Ground Model

An accurate knowledge of the per-unit length impedance of power cables is necessary to correctly predict electromagnetic transients in power systems. In particular, skin, proximity, and ground return effects must be properly estimated. In many applications, the medium that surrounds the cable is not uniform and can consist of multiple layers of different conductivity, such as dry and wet soil, water, or air. We introduce a multilayer ground model for the recently-proposed MoM-SO method, suitable to accurately predict ground return effects in such scenarios. The proposed technique precisely accounts for skin, proximity, ground and tunnel effects, and is applicable to a variety of cable configurations, including underground and submarine cables. Numerical results show that the proposed method is more accurate than analytic formulas typically employed for transient analyses, and delivers an accuracy comparable to the finite element method (FEM). With respect to FEM, however, MoM-SO is over 1000 times faster, and can calculate the impedance of a submarine cable inside a three-layer medium in 0.10~s per frequency point.

cs.CE↗

arXiv2014

Proximity-Aware Calculation of Cable Series Impedance for Systems of Solid and Hollow Conductors

Wide-band cable models for the prediction of electromagnetic transients in power systems require the accurate calculation of the cable series impedance as function of frequency. A surface current approach was recently proposed for systems of round solid conductors, with inclusion of skin and proximity effects. In this paper we extend the approach to include tubular conductors, allowing to model realistic cables with tubular sheaths, armors and pipes. We also include the effect of a lossy ground. A noteworthy feature of the proposed technique is the accurate prediction of proximity effects, which can be of major importance in three-phase, pipe type, and closely-packed single-core cables. The new approach is highly efficient compared to finite elements. In the case of a cross-bonded cable system featuring three phase conductors and three screens, the proposed technique computes the required 120 frequency samples in only six seconds of CPU time.

cs.CE↗

arXiv2014

Fast Computation of the Series Impedance of Power Cables with Inclusion of Skin and Proximity Effects

We present an efficient numerical technique for calculating the series impedance matrix of systems with round conductors. The method is based on a surface admittance operator in combination with the method of moments and it accurately predicts both skin and proximity effects. Application to a three-phase armored cable with wire screens demonstrates a speed-up by a factor of about 100 compared to a finite elements computation. The inclusion of proximity effect in combination with the high efficiency makes the new method very attractive for cable modeling within EMTP-type simulation tools. Currently, these tools can only take skin effect into account.

cs.CE↗