Finite-difference Time-domain Cell Research Articles

Finite-difference time-domain (FDTD) method with non-homogeneous cells filled with voxels

With the objective of reducing the overall number of FDTD cells in applications where the objects of interest are given as sets of voxels, as in bio-electromagnetism, a subcell technique is introduced to allow the FDTD method to account for non-homogeneous cells composed with voxels of different permittivity's. Numerical experiments with dielectric objects are reported to illustrate the effectiveness and the limitations of the method.

Extended FDTD Method for Coanalysis of Superconducting Passive Transmission Lines and Josephson Junction Drivers and Receivers

In rapid single-flux quantum circuits, the signal integrity problem of superconducting passive transmission lines (PTLs) becomes critical. In this article, an extended 3-D finite-difference time-domain (FDTD) method is proposed for coanalysis of superconducting PTLs and Josephson junction (JJ) drivers and receivers. The central difference FDTD scheme is used for PTLs, and the backward difference method is adopted for JJs, which are introduced to FDTD cells as lumped elements. Due to the nonlinearity of JJs, the Newton–Raphson method is introduced to solve the boundary condition of the FDTD method. Compared with the 1-D FDTD method of the transmission line model of PTLs, the proposed method performs full-wave analysis of the physical structure of PTLs. Therefore, the proposed 3-D FDTD method is theoretically more accurate than the conventional method by avoiding parameter extraction and circuit analysis.

FDTD Algorithm for Numerical Anatomical Models With Cells Containing Several Debye Media

In this article, we show that the previously published finite-difference time-domain (FDTD) thin-layer technique in Debye media can also be used to account for FDTD cells filled with several media. This permits either the accuracy to be improved or the computational time to be reduced by increasing the cell size. The numerical experiments were performed with a 2-D slice of an anatomical model.

A modeling method for equivalent source adopting volume structure technique in FDTD

The equivalent source is a widely used approach for simulating hybrid electromagnetic (EM) field-circuit problems. In this approach, three techniques, e.g., the wire, surface, and volume structure, can be employed for embedding lumped circuits into finite difference time-domain cells. However, the volume structure technique introduced in previous studies may result in incorrect answers when addressing problems consisting of electronic devices loaded onto conductor strip gaps. To fix this problem, an extra processing method is proposed. Based on the condition of consistent potential on the same tangent plane in the loading direction, this approach assigns the EM field on the grids occupied by the lumped circuit to obtain the equivalent source information. A numerical example is presented, the structure of which consists of a Schottky diode mounted across a microstrip gap. The results validate the feasibility of the proposed method.

FDTD Modeling for the Accurate Electromagnetic Wave Analysis of Graphene

We develop a finite-difference time-domain (FDTD) method suitable for the electromagnetic (EM) analysis of graphene. In this work, we employ the modified Lorentz model for dispersion modeling, the two-dimensional (2-D) sheet model for geometrical modeling, and the complex-frequency-shifted (CFS)-perfectly matched layer (PML) for the absorbing boundary condition. In specific, the accurate complex-conjugate pole-residue (CCPR) dispersion model is first adapted for the electrical modeling of graphene by using the robust vector fitting. Next, the CCPR parameters are converted to the modified Lorentz parameters and then the modified Lorentz-based dispersive FDTD formulation is used to enhance the computational efficiency. In FDTD cell modeling, the 2-D sheet cells are allocated for graphene rather than the conventional FDTD cell-based modeling. Finally, CFS-PML are employed for terminating the computational domain to avoid the late-time instability. The presented FDTD approach is validated in numerical examples for graphene-based parallel plate waveguides.

A volume structure based ECS-PER algorithm for the hybrid electromagnetic field-circuit simulation

A new algorithm for the hybrid electromagnetic (EM) field-circuit simulation is proposed. It employs the equivalent current source with parallel equivalent resistance (ECS-PER) to simulate the effect of an EM subsystem on a circuit subsystem and adopts the volume structure to map the lumped circuit into the finite-difference time-domain cells. By including an additional current term in Maxwell-Ampere’s Law to represent the current density of the lumped circuit and using the finite difference scheme, the formulas of the proposed volume structure based ECS-PER algorithm is deduced for the first time. Two numerical examples of microwave circuits radiated under external EM incidence are simulated, and the results verify the accuracy and versatility of the proposed algorithm.

Analysis of the Grounding for the Substation Under Very Fast Transient Using Improved Lossy Thin-Wire Model for FDTD

A thin-wire model of conductors with arbitrary cross sections for a finite-difference time-domain (FDTD) method is proposed for the study of lightning transients in electrical systems. The proposed thin-wire model considers both the frequency-dependent characteristics of the wires and the influences of the surrounding media. The model represents a wire using four FDTD cells with an equivalent side length and modified material parameters. A rational equivalent circuit is added at the center edge of the FDTD cells to represent the internal impedance of the wire. An analytical formula for determining the equivalent side length and the modified material parameters of the FDTD cells are also presented. The proposed formula gives a new prospect to build the thin-wire model in FDTD. In this model, the equivalent side length can be set arbitrarily and much larger than the original wire, which can greatly reduce the computation time. Meanwhile, the method can be extended to the thin-wire structure with arbitrary cross sections. The model is verified with various measurements. Finally, a practical grounding grid of a substation with external water supply is analyzed.

Guided resonances on lithium niobate for extremely small electric field detection investigated by accurate sensitivity analysis.

We present a theoretical study of guided resonances (GR) on a thin film lithium niobate rectangular lattice photonic crystal by band diagram calculations and 3D Finite Difference Time Domain (FDTD) transmission investigations which cover a broad range of parameters. A photonic crystal with an active zone as small as 13μm×13μm×0.7μm can be easily designed to obtain a resonance Q value in the order of 1000. These resonances are then employed in electric field (E-field) sensing applications exploiting the electro optic (EO) effect of lithium niobate. A local field factor that is calculated locally for each FDTD cell is proposed to accurately estimate the sensitivity of GR based E-field sensor. The local field factor allows well agreement between simulations and reported experimental data therefore providing a valuable method in optimizing the GR structure to obtain high sensitivities. When these resonances are associated with sub-picometer optical spectrum analyzer and high field enhancement antenna design, an E-field probe with a sensitivity of 50 μV/m could be achieved. The results of our simulations could be also exploited in other EO based applications such as EEG (Electroencephalography) or ECG (Electrocardiography) probe and E-field frequency detector with an 'invisible' probe to the field being detected etc.

A hybrid FDTD-SPICE method for the analysis of microwave circuits

A hybrid full-wave electromagnetic (EM) field-circuit simulation method, which aims at accurately analyzing microwave circuits, is proposed. This method adopts the finite-difference time-domain (FDTD) algorithm for the EM simulation, the sophisticated equivalent models in a general circuit simulato r SPICE for the circuit simulation, and hybridizes the FDTD and SPICE by using the equivalent current source (ECS) approach. Moreover, three techniques, which map a lumped circuit into FDTD cells as a wire, surface or volume structure respectively, are thoroughly studied. The formulae of the ECS with these three techniques are derived and introduced in detail, and their influences on the simulation accuracy are analyzed. The proposed method is applied to two sample circuits, a microstrip line and a frequency selective surface (FSS), both of which are loaded with diode pairs. The simulation results are compared with the measurement ones, and good agreement is observed, indicating the accuracy and versatility of the method.

Incorporating Effective Media in the Finite-Difference Time-Domain Method for Spherical Nanoparticle Modeling

A computational formulation is presented for the low frequency single-cell finite-difference time-domain (FDTD) modeling of nanospheres. The methodology is developed based on the observation that the electrostatic field inside a dielectric sphere is similar in nature to that of an FDTD cell, or equivalently by considering the electromagnetic correspondence between the single electric field component across an FDTD cell edge, and the electric dipole moment induced in an electrically small dielectric sphere when the latter is excited by a plane wave. By rigorously applying effective medium theory the physical existence of a subcell dielectric sphere in the FDTD grid is translated into an equivalent material, characterized by an effective permittivity that obeys the Clausius-Mossotti (CM) mixing rule, appropriately defined across the cell edge parallel to the excitation plane wave. A circuit based methodology is devised that allows to easily incorporate the effective medium representation of a subcell dispersive dielectric sphere into FDTD update equations. The theoretically derived results are supported by numerical experiments.

Optimized Conformal FDTD (2, 4) Method for Calculating Reflected and Diffracted Electromagnetic Fields of Perfectly Conducting Wedges

An optimized conformal finite-difference time-domain (FDTD) (2, 4) method is proposed for calculating reflected, diffracted, and total fields of two- and three-dimensional (2- and 3-D) perfectly conducting (PEC) wedges with an electromagnetic pulse (EMP) incidence, where one low-cost coefficient-modification (CM) technique is implemented for effectively reducing its numerical dispersion error. For the 2-D geometries, both reflected and diffracted fields are extracted from the whole calculation domain of FDTD (2, 4), and excellent agreement is achieved between the calculated diffraction coefficient and the analytical one obtained by high frequency approximation method of UTD. While for the 3-D wedges, even with the coarse FDTD cells adopted, such an optimized method still possesses the capability for getting more accurate diffracted fields in comparison with the conventional FDTD.

Modeling of the perfect electromagnetic conducting boundary in the finite difference time domain method

AbstractThe perfect electromagnetic conducting (PEMC) boundary, a nonreciprocal generalization of both perfect electric conducting (PEC) and perfect magnetic conducting (PMC) boundaries, is modeled in the finite difference time domain (FDTD) method. Since the PEMC boundary condition requires collocation of same components of both electric and magnetic fields at the boundary grids, which is not compatible with the original FDTD algorithm, its implementation in FDTD is challenging and requires modification in the algorithm. To do this task, first, the original FDTD cell is modified by inserting the required field components not present in the original cell. Then, a novel formulation is developed for updating fields' components at the boundary. Modeling of a PEMC planar interface, a corner point, and a wedge point are presented. Finally, numerical examples are presented to show stability, accuracy, and applicability of the proposed approach. Validation is achieved by comparisons with existing analytic methods and/or conventional FDTD for special cases of PEC and PMC boundaries.

A General Method for Modeling Packaged Diode Spanning Multiple Cells in FDTD

In this letter, we propose a general method based on the modified nodal approach (MNA) to incorporate packaged diodes into finite-difference time-domain (FDTD) method with diodes spanning multiple FDTD cells. The approach to fill the extended nodal matrix can be applied to analyze circuits with different topologies. The validity of this method is demonstrated by connecting a packaged diode, MA4E1317, at the end of a microstrip transmission line, which spans three and nine FDTD cells, respectively. Results are in good agreement with those obtained by the commercial circuit simulation package ADS.

An Optimized CFS-PML for Wave–Structure Interaction Problems

The complex frequency-shifted perfectly matched layer (CFS-PML) is optimized for the finite-difference time-domain (FDTD) solution of wave-structure interaction problems. This mainly consists of optimizing the α parameter of the stretching coefficient of the PML in function of the frequency content of the problem to be solved. The resulting CFS-PML is only a few FDTD cells in thickness and can be placed 2 cells from the structure of interest. This renders the computational cost of the simulation of free space small in comparison with the overall cost of the FDTD calculation.

Analysis of Complex Electromagnetic Structures by Hybrid FDTD/WCIP Method

This paper proposes a hybrid full-wave analysis using Finite-Difference Time-Domain (FDTD) and Wave Concept Iterative Process (WCIP) methods, developed to analyze locally arbitrarily shaped microwave structures and Multilayer Planar structure. Using the equivalence principle, the original problem can be decomposed into two sub regions and solve each sub region separately. An interpolation scheme is proposed for communicating between the FDTD fields and WCIP wave, which will not require the effort of fitting the WCIP mesh to the FDTD cells in the interface region. This method is applied to calculate the scattering parameters of arbitrary (3-D) microwave structures. Applying FDTD to 3D discontinuity and WCIP to the remaining region preserves the advantages of both WCIP flexibility and FDTD efficiency. A comparison of the results with the FDTD staircasing data verifies the accuracy of the proposed method.

Full-wave analysis of a microwave rectifying circuit using finite difference time domain algorithm

This article presents a study on calculating the conversion efficiency of a microwave rectifying circuit by using finite difference time domain (FDTD) algorithm. To properly descript the lumped device in FDTD algorithm, the nonlinear lumped network (NL2N)-FDTD method is further extended to model Schottky diode placed across multiple FDTD cells. As a result, a group of formulae are obtained and applied to analyze a typical microwave rectifying circuit, including a nonlinear lumped device of Schottky diode HSMS-282. The good agreement between FDTD analysis results and ADS simulated ones illustrates the validation of the derived formulae and method. This FDTD analytical method can be used to design and optimize rectifying circuits with high radio frequency–direct current conversion efficiency. © 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.26209

Performance of proposed thin‐wire model in finite difference time domain method

AbstractThin‐wire approximation in the finite difference time domain (FDTD) method is important in saving computer resources and truncating central processing unit (CPU) time. Previously, thin wires were mainly realized using the true thin wire (TTW) model, in which electric field components along the wire axis are set at zero, and three methods, in which electric field components along the wire axis are also set at zero and the medium around thin wires is replaced depending on wire radius, are hereafter called the RM model. The former is the most conventional and widely used method; however, its resultant radius is 0.23Δs, supposing that the space under consideration is divided by cubic cells with a Δs of the side length of FDTD cells.The first method of the RM model can realize thin wires having a radius of about 0.15Δs under the conditions we used, in which the time interval is set at a value which is slightly less than Δtc, e.g. 0.9999tc, where Δtc is defined by the Courant condition; in the case of a thin wire having a radius less than 0.15Δs, the FDTD computation suffers from numerical instability. The second method can realize a thin wire having a radius of about 10−4Δs. We need some changes in the numerical electromagnetic analysis program based on the FDTD method to employ these models.The third of the RM model, which has already been proposed by the author and in which the relative permittivity and relative permeability of four FDTD cells closest to a thin wire are replaced according to the radius of the thin wire and Δs, could realize thin wires having a radius of about 10−6Δs without changing the program and numerical instability.In this paper, the third model is extensively investigated and it is demonstrated that we can deal with a thin wire with a radius of about 10−9Δs without numerical instability. The maximum difference in the evaluation of the surge impedance of an open‐ended horizontal wire located 5 m above a perfectly conducting ground is less than 5%. We can easily use the third model even though the program, which is available, has no the specific function of thin‐wire approximation. © 2011 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Locally-Conformal FDTD for Anisotropic Conductive Interfaces

Locally-conformal discretizations have been developed for the finite-difference time-domain (FDTD) method to mitigate staircasing errors that arise in the modeling of arbitrary (e.g., curved, slanted) interfaces by regular orthogonal grids. In particular, locally-conformal algorithms based on the computation of effective material parameters in partially-filled FDTD cells are attractive because they are simple to implement and maintain the basic conditional stability of FDTD, with only minor changes on the Courant limit. In this paper, we propose a new locally-conformal implementation for FDTD tailored for anisotropic conductive interfaces. Instead of employing arithmetic or geometrical averages, we invoke the quasi-static relationship between the current density and the electric field to derive the effective conductivities of partially-filled FDTD cells.

Finite-difference time-domain model for the feeding gap of coaxial probe driven antennas

In the finite-difference time-domain (FDTD) method, a simple and realistic feed model for coaxial probe driven antennas is proposed here. The feed zone of the antenna may be considered as an equivalent source in view of the antenna theory and a load port in view of the transmission line theory. The proposed feed model is constructed by combining the infinitesimal-gap source condition of the antenna and the equivalent load condition of the feed line. It leads to perform no additional FDTD cell modelling of the line. The transient reflected voltage and the input impedance of cylindrical monopole antennas fed by coaxial lines are calculated numerically and then compared with the accurate measurement and a full fine-grid. The FDTD results of the proposed model have a good agreement with the measured data and the fine-grid results.

FDTD Subcell Modeling of the Inner Conductor of the Coaxial Feed: Accuracy and Convergence Analysis

In this paper, we analyze the method of exciting and truncating the coaxial probe used to excite an electromagnetically coupled patch antenna. The goal of the analysis is to avoid the unstable and unreliable behavior of finite-difference time-domain (FDTD) solution. The model considered here is based on the subcell thin wire modeling of inner conductor of a coaxial probe. Two main categories of structures and excitation models are considered. In the first category, the truncated thin wire is separated from the absorbing boundary by two FDTD cells, for several excitation models and their location along the wire. In the second category, the thin wire is extended into the absorbing boundary, and both the hard and the resistive source models are investigated. The comparison of the results for the two aforementioned categories of the FDTD coaxial probe feeds may be of particular interest to computational electromagnetics community, as it may yield insight into the limitations of the most commercial software packages which do not allow for extension of the coaxial probe model into the absorbing boundary