Multiresolution Time-domain Method Research Articles

Transient Analysis of Crosstalk Noise Effects in SWCNT Bundle On-Chip Interconnects Using MRTD Technique

Carbon nanotube bundles are being considered as a potential on-chip interconnect replacement for conventional copper on-chip interconnects in the nanoscale regime of recent IC technology. This paper analyzes the signal integrity analysis of CMOS gate-driven single-walled carbon nanotubes (SWCNTs) bundle on-chip interconnects. The wavelet-based numerical model Multiresolution Time Domain (MRTD) method is used for the transient analysis of SWCNTs bundles on-chip interconnects. The proposed MRTD model is used to perform transient analysis for parameters of signal integrity, peak crosstalk, and propagation delay estimations. The obtained results of the proposed MRTD model are compared with those of the conventional Finite Difference Time Domains (FDTD) model and it is validated with SPICE simulator at 32 nm technology node and also compared with multiwalled CNT (MWCNT) interconnects at 22 nm. The MRTD model results show excellent agreements to SPICE with less than 0.41% error. The elapsed CPU runtimes for the MRTD model are significantly less compared to SPICE. The MRTD model is used to interconnects the model with two and three lines and can be extended to an M-coupled line. The results of the proposed model are closely matched to those of SPICE simulations.

A conformal symplectic multi-resolution time-domain method with ADE-PML

In this paper, the conformal finite-difference time-domain (CFDTD) technique and the concept of effective dielectric constant are applied to symplectic multi-resolution time-domain (SMRTD) algorithm based on Daubechies scaling functions, resulting in a conformal SMRTD (C-SMRTD) method. Moreover, a novel implementation of perfect matched layer with auxiliary differential equation (ADE-PML) is presented for the SMRTD method. Numerical results of the radar cross section (RCS) of a dielectric sphere verify the effectiveness of the C-SMRTD method, which shows good agreement with the results derived by analytical methods. It is also shown that the accuracy of the C-SMRTD method has been significantly improved compared with the MRTD method with step approximation, and the proposed method has an advantage over CFDTD at saving the CPU time and memory. Furthermore, a vault-top tunnel model is established with the proposed method, and the characteristic of the field cross-section distribution of the electromagnetic pulse (EMP) propagation in the tunnel model is also presented and discussed.

Symplectic MRTD for solving three‐dimensional Maxwell equations based on optimised operators

A new set of symplectic operators for the symplectic multi-resolution time-domain (S-MRTD) method is obtained by using the time reversible constraint and the growth factor. Then, the perfectly matched layer absorbing boundary condition based on splitting field technique is introduced into the S-MRTD method and its iterative formula is derived. The stability and numerical dispersion of S-MRTD method with optimised symplectic operators are discussed in detail. Finally, the optimal S-MRTD method is applied to the calculation of electromagnetic radiation and scattering. Numerical calculation and simulation results show that the S-MRTD is more accurate and efficient than the traditional FDTD method.

A Multiresolution Time Domain (MRTD) Method for Crosstalk Noise Modeling of CMOS-Gate-Driven Coupled MWCNT Interconnects

In this paper, the multiresolution time domain (MRTD) method with its unique features is tailored for modeling interconnects. To build further credence to this and its profound existence in the recent state-of-the-art, simulations for inclusive crosstalk noise, on complementary metal-oxide semiconductor gate-driven mutually coupled multi-walled carbon nanotube interconnect lines, using MRTD method and conventional finite-difference time-domain (FDTD) model for 32-nm technology are executed. The results demonstrate the dominance of MRTD model over conventional FDTD in terms of accuracy with respect to recursive simulations of Synopsys HSPICE tool. An average error of less than 0.2% is observed in the estimation of dynamic crosstalk noise analysis. The proposed method is used to model interconnects with two and three mutually coupled lines and can be extended for N-coupled lines. The results of the transient analysis prove the efficiency of MRTD method over HSPICE with respect to computational time. The proposed method can also be used to address the issues of electromagnetic compatibility and electromagnetic interference of on-chip interconnects.

Stability and numerical dispersion analysis of symplectic multi-resolution time-domain method

In this paper, first, the theoretical framework of symplectic multi-resolution time-domain (S-MRTD) method is mentioned, and the order condition of pth-order symplectic integrator is given. Then, the stability and dispersion analysis for symplectic multi-resolution time-domain (S-MRTD) methods are presented. To the best of our knowledge, there is a comperhensive study on the dispersion characteristics for pth-order S-MRTD scheme in the temporal direction, and this study will be useful for the selection and evaluation of various order symplectic integrator propagators. In addition, it is compared with the alternating direction implicit multi-resolution time-domain (ADI-MRTD) and runge-kutta multi-resolution time-domain (RK-MRTD) based on the Daubechies scale functions. Numerical results show high efficiency and accuracy of the S-MRTD method.

ADI-MRTD Algorithm for Periodic Structures Analysis

In this paper, a novel algorithm based on the alternating direction implicit (ADI) multiresolution time-domain (MRTD) method for periodic structure simulation is proposed. By applying the multiresolution analysis in accordance with wavelet theory, the spatial sampling rate of the conventional finite-difference time-domain (FDTD) is significantly reduced by the MRTD method. The ADI method is then used to remove the Courant-Friedrich-Levy (CFL) limit that the MRTD method experiences. The periodic boundary condition (PBC) is directly implemented in the time domain using a constant transverse wave-number (CTW) wave. Numerical results are presented to confirm the efficiency and accuracy of the proposed method.

A novel MRTD model for signal integrity analysis of resistive driven coupled copper interconnects

PurposeThis paper aims to model the coupled on-chip Copper (Cu) interconnects by using the multiresolution time-domain (MRTD) method.Design/methodology/approachThe proposed model is a wavelet-based numerical method for analyzing signal integrity and propagation delay of coupled on-chip interconnects. Moreover, the dependency of crosstalk noise and delay on coupling parasitics (L12, C12) are analyzed.FindingsThe proposed MRTD method captures the behaviour of propagation delay and peak crosstalk noise on victim line against coupling parasitics, which is in close agreement with that of H simulation program with integrated circuit emphasis (HSPICE). The average error for the proposed model is less than 1 per cent with respect to HSPICE for the estimation of peak crosstalk noise voltage.Practical implicationsSimulations are performed using HSPICE and compared with those performed using the proposed MRTD method for global interconnect length with 130-nm technology, where the computations of the proposed model are carried out using Matlab.Originality/valueThe MRTD method with its unique features is tailored for modelling interconnects. To build further credence to this and its profound existence in the latest state-of-art works, simulations of crosstalk noise and propagation delay, for coupled Cu interconnect lines, using MRTD and finite-difference time-domain (FDTD) are executed. The results illustrated the dominance of MRTD method over FDTD in terms of accuracy.

The Alternating Direction Implicit Body of Revolution Multiresolution Time Domain Method with Convolution Perfect Matched Layer

Overmuch memory and time of CPU have been taken by multiresolution time domain (MRTD) method in three-dimension issues. In order to solve this problem, the alternating direction implicit body of revolution multiresolution time domain (ADI-BOR-MRTD) scheme is presented. Firstly, based on body of revolution finite difference time domain (BOR-FDTD) method, equations of body of revolution multiresolution time domain (BOR-MRTD) method are implemented. Then alternating direction implicit (ADI) is introduced into BOR-MRTD method. Lastly, convolution perfect matched layer (CPML) is applied for ADI-BOR-MRTD method. Numerical results demonstrate that ADI-BOR-MRTD method saves more memory and time of CPU than FDTD and MRTD methods.

A research on the electromagnetic properties of Plasma Photonic Crystal based on the Symplectic Finite-Difference Time-Domain method

The Symplectic Finite-Difference Time-Domain (SFDTD) method was applied to simulate the one-dimensional unmagnetized Plasma Photonic Crystal (PPC) with a sandwich structure. Compared with the traditional Finite-difference Time-Domain (FDTD) method, the results from the SFDTD method are reliable and accurate. Also the SFDTD method has better numerical dispersion characteristics than the traditional FDTD method and the Multi-Resolution Time-Domain (MRTD) method too. Electromagnetic propagation process by differential Gaussian pulse is given in the PPC band gap with the SFDTD method used. The influence of the plasma frequency and the thickness ratio of plasma and medium to PPC on the band gap structure is analyzed. The plasma frequency most affects the PPC in low-frequency range. Also the propagation of an electromagnetic wave can be controlled by the thickness ratio of plasma and medium. The results above prove that the SFDTD method can give the right and better results on the research of PPC.

Implementation and application of a convolution PML using the MRTD algorithm

In this paper, a novel implementation of convolution perfectly matched layer (CPML) is proposed for the multiresolution time-domain (MRTD) method. The implementation is completely independent of the host material and easier to obtain than that of the popularly used anisotropic perfectly matched layer, when treating more generalized media. The absorbing effectiveness of the CPML is discussed and validated in a two-dimensional case, and we apply the CPML in three-dimensional cases with different microwave circuit components. Numerical results show that the CPML performs well for absorbing electromagnetic waves in the MRTD scheme.

A Multiresolution Time-Domain Method for LEMP Calculation and Comparison With FDTD

A multiresolution time-domain (MRTD) method is proposed for cloud-to-ground lightning electromagnetic pulse (LEMP) calculation. Scaling function of Daubechies wavelet is chosen for fields expansion, and iterative formulas of MRTD method are derivated in 2-D cylindrical coordinates. First, three double-exponential lightning channel-base current with different rise times have been used for evaluating performance of the finite-difference time-domain (FDTD) method. And then, LEMP of different distances of the lightning channel were calculated with the MRTD method. We examined the MRTD method by comparing the results obtained with the FDTD method. Numerical simulation results show that the MRTD method and FDTD method are consistent with each other for first return stroke, even with a larger grid division. However, for subsequent return stroke, oscillations will be observed in the late response of the waveforms calculated by the FDTD method. Comparing with the FDTD method, the MRTD method suffers less oscillations with the same grid division, and can significantly save both computational memory and CPU time with large gird mesh, as well as good numerical dispersion property.

A Novel Symplectic Multi-Resolution Time-Domain Scheme for Electromagnetic Simulations

A symplectic scheme is applied to the multi-resolution time-domain (MRTD) method, resulting in a highly stable novel symplectic MRTD scheme. First, the time-domain Maxwell's equations are rewritten as a matrix equation. Then, we discretize the Maxwell's equations in the time direction using symplectic propagation integrator (SPI) technique and evaluate the equations in the spatial direction with high order spatial multi-resolution approximation to construct novel symplectic MRTD scheme. The stability and numerical dispersion analysis are also included. Numerical results are given to show the high efficiency and accuracy of the method.

Implementation and analysis of the perfectly matched layer with auxiliary differential equation for the multiresolution time-domain method

A new implementation of perfectly matched layer (PML) with auxiliary differential equation (ADE-PML) is presented for the multiresolution time-domain method. The implementation is easier to obtain and can save more memories than the popularly used PML proposed by Berenger and the anisotropic perfectly matched layer (APML) when a more generalized medium is treated. Numerical results demonstrate that the ADE-PML is more superior to the PML and APML in absorbing propagation modes and low-frequency evanescent modes.

A New Boundary Closure Scheme for the Multiresolution Time-Domain (MRTD) Method

This paper introduces a novel boundary closure treatment for the wavelet based multiresolution time-domain (MRTD) solution of Maxwell's equations. Accommodating non-trivial boundary conditions, such as the Robin condition or time dependent condition, has been a challenging issue in the MRTD analysis of wave scattering, radiation, and propagation. A matched interface and boundary (MIB) method is introduced to overcome this difficulty. Several numerical benchmark tests are carried out to validate the MIB boundary scheme. The proposed boundary treatment can also be applied to other high order finite-difference time-domain (FDTD) approaches, such as the dispersion-relation-preserving (DRP) method. The MIB boundary scheme greatly enhances the feasibility for applying the MRTD methods to more complicated electromagnetic structures.

Analysis of numerical dispersion properties of SFDTD and MRTD schemes

In this paper, the Maxwell's equations are written as Hamilton canonical equations by using Hamilton functional variation method. Maxwell's equations can be discretized with symplectic propagation technique combined with high-order difference schemes approximations to construct symplectic finite difference time domain (SFDTD) method. The high-order dispersion equations of the scheme for space is deduced. The numerical dispersion analysis is included, and it is compared with the multiresolution time-domain (MRTD) method based on the Daubechies scaling functions. Numerical results show high efficiency and accuracy of the SFDTD method.

Research and Application to Electromagnetic Scattering of Conformal MRTD Method Based on Daubechies Scaling Functions

为了降低Yee氏蛙跳式网格划分的台阶误差，该文对3维曲面导体目标进行精确电磁建模，将时域多分辨(MRTD)算法与共形时域有限差分(CFDTD)算法结合，提出一种新的基于Daubechies尺度函数的共形时域多分辨(CMRTD)方法。该文提出将基于Daubechies尺度函数的MRTD迭代公式分解为若干传统FDTD迭代公式的线性组合，然后对最里面回路上的FDTD分解式运用局部共形技术，再将各个分解式进行线性组合，从而得到CMRTD结果。仿真结果表明，CMRTD方法既保持了MRTD方法节省计算资源、计算效率高等优点，同时明显提高了计算的精度。

A LOW-PROFILE UNIDIRECTIONAL CAVITY-BACKED LOG-PERIODIC SLOT ANTENNA

A low-proflle unidirectional cavity-backed coplanar waveguide-fed uniplanar log-periodic slot antenna suitable for the ultra-wideband applications (3{18GHz) is presented. Due to the in- herent balanced structure compared with the unbalanced antennas, such as dipole or loop antenna, the impedance matching and radiation performances of the proposed antenna are quite stable and satisfac- tory. There is a potential advantage for low proflle ultra-wideband unidirectional antennas, and this paper demonstrates a technique for transforming the bidirectional beam into a unidirectional beam by us- ing a special cavity in this ultra-wideband antenna. Meanwhile, the multi-resolution time domain (MRTD) method is applied to analyze this antenna. Experimental results reveal that the cavity has a small afiect on the S-parameter of the origin antenna, and remains the per- fect re∞ection property within the desired operation band.

Novel Auxiliary Differential Equation-Multiresolution Time Domain Scheme for Dispersive Nonlinear Photonic Devices

In this paper, a novel multiresolution time-domain (MRTD) technique is presented for the analysis of second order nonlinearities in dispersive materials. The suggested method implements multiresolution analysis in the context of method-of-moments for the solution of Maxwell's equations. Based on Lorentz model of linear susceptibility, auxiliary differential equations (ADE) are successfully included in order to accurately account for the chromatic dispersion of the dielectric material. Finally, a uniaxial perfectly matched layers (UPML) absorber for MRTD is rigorously incorporated. Various numerical examples demonstrate the stability and numerical precision of the suggested nonlinear MRTD method and its improved numerical efficiency over conventional FDTD.

A Three-Dimensional Locally One-Dimensional Multiresolution Time-Domain Method Using Daubechies Scaling Function

A three-dimensional locally one-dimensional multiresolution time-domain(LOD-MRTD) method is introduced and unconditional stability is proved analytically. The updating formulations have fewer terms on the right-hand side than those of an alternating direction implicit MRTD(ADI-MRTD). The validation of the method is presented using the resonance frequency problem of an empty cavity. The reduction of the numerical dispersion technique is also combined with the proposed method. The numerical examples show that the combined method can improve the accuracy significantly.

Efficient multiresolution time-domain analysis of arbitrarily shaped photonic devices

A multiresolution time-domain (MRTD) technique is proposed and applied to the analysis of arbitrarily shaped photonic devices. The suggested method implements the multiresolution analysis in the context of method-of-moments for the solution of Maxwell's equations. To improve the capabilities of the proposed method, the uniaxial perfectly matched layers absorber for the MRTD is rigorously incorporated and better performance is reported over the conventional finite-difference time-domain. Various numerical examples demonstrate the stability and numerical precision of the suggested MRTD method for both linear and nonlinear applications. Moreover, the application of the suggested MRTD scheme for the design of a photonic crystal-based optical wavelength filter and for the analysis of a frequency converter is presented.