CN-FDTD Method Research Articles

Analysis of Multiconductor Transmission Lines Using the CN-FDTD Method

The Crank–Nicolson (CN) version of the finite-difference time-domain (FDTD) method is applied to the analysis of multiconductor transmission lines (MCTLs). Stability and dispersion issues are investigated for different cases, including single and multiconductor lossless and lossy lines. It is shown that for MCTLs, stability of the CN-FDTD method is conditioned by the structure of coupling matrices. Sufficient conditions for unconditional stability are derived. Four practical problems are analyzed using the CN-FDTD method and the results are compared to measurements and Leap-Frog method. For the first three cases, it is observed that using the CN method, the Courant number can be increased by the factor of 50 with good agreement with measurement results.

A Hybrid CN-FDTD-SPICE Solver for Field-Circuit Analyses in Low-Frequency Wideband Problems

The conventional finite-difference time-domain (FDTD) method is efficient for microwave frequencies, but requires a large number of time steps for low frequencies. In this work, a hybrid Crank–Nicolson (CN) FDTD-SPICE method is applied to field-circuit analyses in low- frequency wideband problems. The unconditionally stable CN-FDTD method is used to give a rapid full wave solution by overcoming the Courant–Friedrichs–Lewy (CFL) condition that constrains the conventional FDTD method at low frequencies. The hybrid CN-FDTD-SPICE method can be used for simulating the interactions between modern electronic circuit systems and a 3-D structure supporting field radiation and interferences. It can greatly improve the computational efficiency over the conventional FDTD method at low frequencies because its time increment can be significantly larger. Three numerical examples are presented to verify the accuracy and efficiency of this hybrid method. Its CPU time is much shorter than that of the conventional FDTD-SPICE method. This CN-FDTD-SPICE method becomes increasingly advantageous when the radiation fields are required as the system integration continues to accelerate.

Computationally Efficient CN-PML for EM Simulations

Since nearly all studies concerning the approximate Crank–Nicolson perfectly matched layer (CN-PML) are limited to 2-D cases, a computationally efficient implementation that can be used to truncate 3-D finite-difference time-domain (FDTD) lattices is presented in this article. More precisely, it is based on the CN direct-splitting (DS) scheme and the bilinear transform (BT) method. This article can fully exploit the unconditional stability of the standard CN-FDTD method and can be free from the Courant–Friedrich–Lewy (CFL) limit; hence, it is especially suitable for situations where space discretization step is much smaller than 1/10th or 1/20th of the smallest wavelength of interest. Aiming at further reducing the requirement of the computer resources, this new implementation can be reformulated in more simple forms if proper auxiliary variables are introduced. It therefore shows a higher iteration speed than other published unconditionally stable PMLs as fewer numbers of arithmetic operations are involved. Finally, three numerical examples, including scatting, transmission, and radiation, are also provided to validate its running time, unconditional stability, and absorption characteristic.

Corrections to “Linear Analysis of High-Frequency Field-Effect Transistors Using the CN-FDTD Method” [Jun 17 1946-1954

In the above-cited paper [1] , the Crank–Nicolson finite-difference time-domain method is used for the analysis of a high-frequency field-effect transistor (FET). However, two references are missed. In addition, there are some errors in (6b), Fig. 2 , and Table I . The reference of Figs. 1 and 2 is [2] . The reference of Table I is [3] . In (6b), $L_{\mathrm {dd}}$ , $L_{\mathrm {gg}}$ , $L_{\mathrm {ss}}$ , $M_{\mathrm {gd}}$ , and $G_{m}$ should be, respectively, $L_{\mathrm {d}}$ , $L_{\mathrm {g}}$ , $L_{\mathrm {s}}$ , $M_{\mathrm {dg}}$ , and $g_{m}$ . The corrected version of Fig. 2 is depicted here, wherein the designations are consistent with the present correction. The corrected table is also reported here, subsequently, wherein the values are valid when the transistor is biased at $V_{\mathrm {ds}} = 3$ V and $I_{\mathrm {ds}} = 10$ mA.

Hybrid Sub-Gridded Time-Domain Method for Ground Penetrating Radar Simulations Including Dispersive Materials

Based on the explicit finite-difference time-domain (FDTD) and implicit Crank–Nicolson (CN) FDTD methods, this paper presents a hybrid sub-gridded scheme whose time step size depends on the coarse grid size for numerically simulating the 3-D ground penetrating radar (GPR) scenarios in lossy, dispersive, and inhomogeneous soils. The time step size of CN-FDTD is independent of the grid size in the dense grid region due to its unconditional stability. Thus, the whole region can be run with a time step size determined by the coarse grid in an absolutely stable fashion. Moreover, a multi-pole Debye dispersion model, solved with auxiliary differential equations (ADEs) for both FDTD and CN-FDTD, is incorporated to simulate realistic GPR scenarios, including the detection of different objects buried in dispersive soils. In order to reduce the matrix size of the 3-D implicit CN-FDTD method, the domain decomposition technique is originally employed to achieve fast calculation. Several numerical examples of the GPR scenarios are provided to demonstrate the accuracy and efficiency of the hybrid sub-gridded ADE-FDTD method.

Notice of Retraction: Analysis of Multiconductor Transmission Lines Using the CN-FDTD Method

The Crank–Nicolson (CN) version of the finite-difference time-domain (FDTD) method is applied to the analysis of multiconductor transmission lines (MCTLs). Stability and dispersion issues are investigated for different cases, including single and multiconductor lossless and lossy lines. It is shown that for MCTLs, stability of the CN-FDTD method is conditioned by the structure of coupling matrices. Sufficient conditions for unconditional stability are derived. Four practical problems are analyzed using the CN-FDTD method and the results are compared to measurements and Leap-Frog method. For the first three cases, it is observed that using the CN method, the Courant number can be increased by the factor of 50 with good agreement with measurement results.

Application of the Crank–Nicolson FDTD method for analysis of a wideband multi-section hybrid coupler

In this paper the Crank---Nicolson (CN) finite-difference time-domain (FDTD) method is applied for the analysis of a planar wideband hybrid coupler. The proposed method is applied for analysis of transmission lines. Stability issue is investigated for different cases, including lossless and lossy transmission lines. Sufficient conditions for unconditional stability are derived. As a practical problem, a wideband compact hybrid coupler working on 1---6 GHz frequency band is analyzed using the CN-FDTD method. Measurement results show that the proposed coupler provides coupling of 3 ± 0.8 dB with 90° ± 0.85° phase shift and demonstrate the return loss and isolation better than 16 dB over 1---6 GHz. To validate the accuracy of the method, the results of this scheme are compared with measurements and the conditional stable leap-frog (LF) FDTD method. It is observed that using the CN-FDTD, the temporal step-size can be increased up to 1500 time compared with the LF-FDTD method with still good agreement with the measured results.

A Study on Plasma Photonic Crystals: Electromagnetic Characteristics Using ICCG-based JEC-CN-FDTD Algorithm

Abstract We extended the current density convolution finite-difference time-domain (JEC-FDTD) method to plasma photonic crystals using the Crank–Nicolson difference scheme and derived the one-dimensional JEC-Crank–Nicolson (CN)-FDTD iterative equation of plasma photonic crystals. The method eliminated the Courant–Friedrich–Levy (CFL) stability constraint and became completely unconditional stable form. The incomplete Cholesky conjugate gradient (ICCG) algorithm is proposed to solve the equation with a large sparse matrix in the CN-FDTD method as the ICCG method improves the speed of convergence, enhances stability, and reduces memory consumption. The JEC-CN-FDTD method is applied to study the characteristics of time domain and frequency domain in the plasma photonic crystal objects. The high accuracy and efficiency of the JEC-CN-FDTD method are confirmed by computing the characteristic parameters of plasma photonic crystals under different conditions such as the electric field distribution of electromagnetic wave, reflection coefficients, and transmission coefficients. Simulation study showed that the algorithm performed stably and could reduce memory consumption and facilitate computer programming.

Effective CNAD- and ADE-Based CFS-PML Formulations for Truncating the Dispersive FDTD Domains

An effective and unsplit-field implementation of the complex frequency-shifted perfectly matched layer (CFS-PML) based on the Crank-Nicolson-approximate-decoupling (CNAD) and the auxiliary differential equation (ADE) method is proposed to truncate the dispersive finite-difference time-domain (FDTD) domains. The proposed formulations take full advantage of the capacity of the CFS-PML for attenuating evanescent waves and reducing late-time reflections. Furthermore, the proposed formulations have an advantage of the unconditional stability of the original CN-FDTD method. Two numerical tests have been carried out to validate the proposed formulations in the two-dimensional FDTD domains composed of the linear Debye and the Lorentz dispersive media, respectively. It is shown in the numerical tests that the proposed formulations can not only increase the time step size over the Courant–Friedrichs–Lewy (CFL) limit as compared with the conventional FDTD, but also hold good absorbing performance.

Error between unconditionally stable FDTD methods and conventional FDTD method

Both the ADI-FDTD method and the CN-FDTD method can be viewed as approximate factorisation of the conventional FDTD scheme, so the error between these methods and the conventional FDTD method is obtained. It is shown that the error is associated with the time step size, the permittivity and the permeability of the medium, and the spatial variation rate of field. The space discretisation has no relation with the error, which is demonstrated by numerical examples.

The unconditionally stable Crank Nicolson FDTD method for three-dimensional Maxwell's equations

In this paper, an accurate and computationally implicit 3D finite-difference time-domain (FDTD) method based on the unconditionally stable Crank–Nicolson scheme (3D CN-FDTD) is presented. The source excitation in 3D CN-FDTD is described and the numerical simulation of the 3D CN-FDTD method is demonstrated through numerical examples. The results of this method, the ADI-FDTD method, and traditional FDTD schemes are compared. A good agreement is obtained for the 3D CN-FDTD method with time steps greatly more than the Courant–Friedrich–Levy (CFL) limit and the traditional Yee FDTD method. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 1619–1622, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21684