Analysis of planar circuits using an unconditionally stable 3D ADI-FDTD method

The alternating direction implicit finite-difference time-domain (ADI-FDTD) method is an unconditionally stable numerical scheme, being proposed to remove stability limitations in conventional FDTD methods. Though the computation efficiency has been improved by ADI-FDTD, significant errors have been observed at large time steps. By compensating truncation errors, a low error ADI-FDTD method in Debye media is proposed based the ER(error reduced)-ADI-FDTD, complete three dimensional equations are derived. Simulation results are anlalyzed and compared with existing methods.

In this paper, based on quadratic interpolation in time domain, an improved first-order absorbing boundary condition (ABC) for the alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method is developed. The ABC is derived in two half-time steps iteration form which is very suitable for the ADI-FDTD method. The reflection of the ABC caused by both the truncated error and the phase velocity error is analyzed in detail. The phase velocity estimation and nonuniform cell are adopted to improve the performance of the ABC. Numerical results show that efficient improvement on the absorbing performance is achieved based on these methods.

In this letter, an efficient high-order absorbing boundary condition for the alternating-direction-implicit-finite-difference time-domain (ADI-FDTD) method is developed. The proposed high-order absorbing boundary condition (ABC) has very high numerical efficiency because it can keep the tri-diagonal matrix form during the ADI iteration. The absorbing performance of the proposed ABC is analyzed theoretically. To verify the performance of the proposed high-order ABC, a rectangular waveguide problem which has very strong dispersion characteristic is analyzed with the ADI-FDTD method. Numerical results show that the proposed high-order ABC has excellent absorbing performance.

In contrast to the preceding chapter, we here discuss the analysis of triplate-type planar circuits having arbitrary shapes. All the methods described in the present chapter are naturally computer-oriented.

This paper describes the relaxation technique for the alternating direction implicit finite-difference time-domain (ADI-FDTD) method. The ADI-FDTD method is computationally more complicate than the conventional FDTD and this method requires solving the tridiagonal matrix equation. Thus, this method may require more computational cost than the conventional method due to the large scale tri-diagonal matrix solution corresponding to a large number of meshes. In this paper, relaxation-based solution technique is discussed for the matrix solution and a simple numerical example is shown. As a result, it is confirmed that ADI-FDTD method with the relaxation technique is useful for the electromagnetic field simulation

This paper presents the implementation of the Mur absorbing boundary condition (ABC) for the two-dimensional (2-D) transverse electric (TE) leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method. The electric and magnetic field components for the leapfrog ADI-FDTD method are updated implicitly and thus, additional considerations need to be ensured for implementation of the boundary conditions. The first-order Mur updating equation is implemented for both the electric and magnetic field updates. Numerical results for the reflection errors and late time stability are presented.

This paper introduces an unconditionally stable alternating-direction implicit finite-difference time-domain (ADI-FDTD) method enhanced with thin-wire and thin-slot models for efficient simulation of shielded enclosures containing multiscale structures, such as thin wires and thin slots. Conventional FDTD methods face two major challenges in this context: first, the spatial scales of thin wires and slots necessitate excessively fine meshing, and second, the explicit method is bound by the Courant-Friedrichs-Lewy (CFL) stability condition. These limitations collectively result in prohibitive computational costs. Our proposed approach overcomes these hurdles by integrating the unconditionally stable ADI-FDTD scheme with dedicated thin-wire and thin-slot representation models. Detailed iterative formulations are derived, and the unconditional stability of the proposed method is rigorously demonstrated. Numerical examples confirm that our method achieves comparable accuracy at a substantially reduced computational burden over the traditional FDTD approach. Finally, we demonstrate that this hybrid algorithm enables high-precision analysis of the shielding effectiveness (SE) of metallic enclosures under arbitrary wave incidence with markedly improved efficiency.

A three-dimensional (3-D) finite difference time domain (FDTD) algorithm with perfectly matched layer (PML) absorbing boundary condition (ABC) is presented for general inhomogeneous, dispersive, conductive media. The modified time-domain Maxwell's equations for dispersive media are expressed in terms of coordinate-stretching variables. We extend the recursive convolution (RC) and piecewise linear recursive convolution (PLRC) approaches to arbitrary dispersive media in a more general form. The algorithm is tested for homogeneous and inhomogeneous media with three typical kinds of dispersive media, i.e., Lorentz medium, unmagnetized plasma, and Debye medium. Excellent agreement between the FDTD results and analytical solutions is obtained for all testing cases with both RC and PLRC approaches. We demonstrate the applications of the algorithm with several examples in subsurface radar detection of mine-like objects, cylinders, and spheres buried in a dispersive half-space and the mapping of a curved interface. Because of their generality, the algorithm and computer program can be used to model biological materials, artificial dielectrics, optical materials, and other dispersive media.

With the rapid development of Bluetooth wireless communication, it's highlighted now to applying micro-electro-mechanical systems (MEMS) technique in the radio frequency (RF) field to manufacture broadband Bluetooth antennas. The 10 dB bandwidth and efficiency of the micromachined Bluetooth antenna designed in this paper are more than 11% and 68% respectively; the length is less than 1/10 wavelength. The alternating direction implicit finite-difference time-domain (ADI-KDTD) method for a full three-dimensional (3-D) wave presented is used for modeling and analyzing the micromachine antenna for the first time. Numerical simulation results are compared to those using the conventional 3D finite-difference time-domain (FDTD) method. It is more efficient than the conventional 3-D FDTD method in terms of the central processing unit time if the size of the local minimum cell in the computational domain is much smaller than the other cells and the wavelength.

The traditional approach of implementing FDTD techniques is to develop different sets of update relations that accommodate for different computational regions, for example, normal FDTD and absorbing boundary condition (ABC) regions. In particular, when a perfectly matched layer (PML) is used for termination of computational grids, we have to deal with a number of field regions in terms of PML faces, edges, and corners which adds a tremendous work load and complexity to the programming environment. This paper aims to develop an efficient approach to analyze and design cylindrical MMICs. In it, we present a unified non-uniform cylindrical finite difference time domain (NU-CFDTD) algorithm in conjunction with an anisotropic perfectly matched layer (APML) ABC in a stretched-coordinate mapping system. The algorithm uses only one set of update equations to handle all computational regions, no matter if they are normal FDTD or PML regions. We determine a non-uniform grid pattern depending on the circuit density for a specific structure to save computational resources, while remaining satisfactory accuracy. In particular, the present algorithm can characterize different material regions by simply assigning different material parameters.

In the preceding chapters, only the analysis of planar circuits has been considered. As pointed out in Sect. 1.2.3, however, an important significance of the planar circuit concept lies in that, if the design technique for an arbitrarily shaped planar circuit is established in the future, it will offer an exact and efficient design tool for the microwave integrated circuit (IMC).

We extend Berenger's perfectly matched layers (PML) to conductive media. A finite-difference-time-domain (FDTD) algorithm with PML as an absorbing boundary condition is developed for solutions of Maxwell's equations in inhomogeneous, conductive media. For a perfectly matched layer in a conductive medium, an additional term involving the time-integrated electric field has to be introduced to account for the coupling between the loss from the PML and the normal conduction loss. This absorbing boundary condition is proven to be highly effective for the absorption of outgoing waves at the computational edge even when a dipping interface intersects the outer boundary. The algorithm is validated by analytical solutions, and is also compared with Liao's absorbing boundary condition. Numerical results for subsurface radar measurements are shown to demonstrate the applications of this method. © 1997 John Wiley & Sons, Inc. Microwave Opt Technol Lett14, 134–137, 1997

A simple, efficient, and unified source excitation scheme for the finite-difference time domain (FDTD) analysis of both waveguides and microstrip circuits is developed and validated. In this scheme, by moving the source plane several cells inside the terminal plane and adding the excitation wave as an extra term in the FDTD equation, the interaction between the excitation and reflected waves are totally separated in time domain. Hence, for both waveguide and microstrip discontinuities, absorbing boundary conditions can be applied on the terminal plane directly. In particular, for microstrip circuits, our scheme does not induce any source distortions when a simplified field distribution is used as the excitation. Consequently, the terminal plane can be moved very close to the discontinuity and thus significant computational savings are achieved. In addition, for microstrip systems, the validity and efficiency of the Mei's simplified field distribution are evaluated and confirmed for the first time.

It is shown that the description of absorbing boundary condition algorithms (ABCs) in terms of single incident plane waves does not provide sufficient information for choosing the best ABC for planar waveguide termination. A technique for optimizing the ABCs that results in a return loss from a wideband pulse less than -50 dB is demonstrated. This technique reduces the risk of loss of accuracy due to mode conversion at the boundary. The use of these optimized ABCs considerably improves analysis results for an important category of microstrip components. For boundaries transverse to the direction of propagation, it is shown that inaccuracy and late time instability can result if the boundary is placed in regions of high field strength.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In this work, a method is presented to extend the convolutional perfectly matched layer (C-PML) to simulate acoustic wave propagation in elastic media with a second-order equation formulation. This non-physical layer is used at the computational edge of a finite element method algorithm in frequency domain, and a pseudo-spectral algorithm in time domain, as an absorbing boundary condition (ABC) to truncate unbounded media. Numerical results show that the C-PML ABC attenuates the outgoing surface waves more effectively than classical PML ABC as proposed by Berenger [J. Comput. Phys. 114, 195-200 (1994)] for electromagnetic waves in the case of oblique incidence, where the PML method suffers from large spurious reflections. Moreover, a modification of the proposed C-PML formulation is also discussed in order to stabilize the absorbing layer in anisotropic solids where numerical instabilities can appear.