Y.W. Liu

Computation of capacitance matrix for integrated circuit interconnects using on-surface MEI method

In this letter the capacitance matrix of integrated circuit interconnects has been successfully calculated by using the on-surface MEI (OSMEI) method. The OSMEI method uses the same mesh as the method of moments (MoM), but generates highly sparse matrixes. Thus, computation memory can be greatly reduced. The reason the sparse matrixes can be generated is that the local relationship between the potentials and charge densities on the mesh nodes can be numerically found by the MEI method. This approach is verified by two-dimensional (2-D) and three-dimensional (3-D) examples of the integrated circuit interconnects with errors within 2%-4%.

Differential formulation of on-surface measured equation of invariance for 2-D conducting scatterings

In the area of electromagnetic scattering computation, a number of fast computation methods have been proposed. The method of the measured equation of invariance (MEI), originally designed to terminate finite difference/element meshes close to the scatterer surface, is now walking into the area of integral equations to generate the sparse matrix by using the reciprocity theorem. We propose a simple approach, the on-surface measured equation of invariance (OSMEI) method, to generate a circle band matrix for solving electromagnetic scattering problems. The OSMEI is used to discretize field components directly on the surface of the scatterer rather than using any integral or differential equation. This can be done because the invariant principle of fields local relation in the MEI method is ingeniously used. A great advantage of the OSMEI over the conventional boundary integration (BI) and differential equation (DF) methods is that the OSMEI generates both the least number of the unknowns and a circle band sparse matrix. So, the computation memory can be greatly reduced, and the computation speed can be dramatically accelerated. Several examples demonstrate that the results of the OSMEI are in excellent agreement with those of analytical solutions and the moment method for scattering of conducting circular and rectangular cylinders.

Radiation extraction for transmission-line interconnects

An extraction technique of radiation sources for non-uniform, transmission-lines has been introduced for the first time. The technique is to substitute solutions of the method of moments (MoM) for the lossless finite-length non-uniform transmission-line into modified transmission-line equations with dependent radiation sources to extract transmission-line parameters and the radiation source parameters.

A new approach to decompose MoM matrix to sparse matrices by using the concept of MEI method

Previously, fast computational methods based on directly thinning the matrix of method of moments (MoM), such as impedance matrix localization (IML), wavelet expansions, and reduced expansion and field testing (REFT), have been introduced. In this paper, we propose a simpler approach to thin the MoM matrix by using the concept of measured equation of invariance (MEI). This approach is referred to as matrix decomposition by MEI (MDMEI). A little effort is required to add the resulting method to any of a variety of MoM programs for solving problems of wire antennas, and conducting object scattering.

A Simple Mom Loading Technique Used in Microstrip Circuits

This paper presents a simple method of moment (MoM) technique to deal with an arbitrary load of a microstrip line. The loading condition of the microstrip line is equivalent to adding a loading voltage element to the excitation voltage vector in the MoM. Since the loading voltage satisfies Ohms law, the voltage can be represented by product of unknown currents and given loads. Alter half-basis functions are introduced at the input port and loading end, for all the impedance elements of the MoM matrix, only the elements involved by the half-basis functions need to be changed. The results of current and voltage on the microstrip line terminated with arbitrarily impedance calculated by the MoM agree well with the ones by transmission line analysis.

Capacitance extraction of integrated-circuit interconnects by matrix decomposition based on MEI concept

Abstract Recently, fast computational methods based on directly thinning the matrix of Method of Moment (MoM), have been introduced. In this paper, we propose a simply technique, based on the concept of Measured Equation of Invariance (MEI), to thin the MoM matrix numerically. This technique is referred to as Matrix Decomposition by MEI (MDMEI). A little effort is required to add the MDMEI to any of the variety of MoM programs for electromagnetic problems, such as the electrostatic problems, wire antennas, and two-dimensional (2-D) conducting object scattering. However, in this paper we only demonstrate how MDMEI is used in the capacitance extraction in integrated-circuit interconnects. The approach is verified by 2-D and 3-D examples with computing errors within 2–4%. For the present achievement, the sparsity rates of the resultant matrices in MDMEI depend on the problem to be solved. Further research is required to keep the bandwidths unchanged with object size increasing so that the sparsity rates of the MDMEI matrices are expected to improve.

Acceleration of on-surface MEI method by new metrons and FMM for 2-D conducting scattering

A new kind of metron is proposed and rapid integration provided by fast multipole methods (FMM) is implemented to dramatically reduce the CPU time of finding the MEI coefficients in the on-surface measured equation of invariance (OSMEI) method. The numerical example of the scattering of a large conducting elliptical cylinder shows that the computation speed is at least one order of magnitude faster than that of the original OSMEI, where sinusoidal metrons are used, and about 25% faster than that of the FMM, where the iteration method is used.

A matrix decomposition technique based on the concept of measure and its application to planar phased dipole arrays

Full impedance matrices of the method of moments (MoM) type have been decomposed into sparse matrices in the application of on-surface measured equation of invariance (OSMEI) (Rius et al. (1996, 1997)). The objectives in Rius are to find continuous current distributions on scatterers. Thus, the concept of metron and measure is justified under the postulate that the local relation between fields and current densities is an invariant of the excitation. In this paper, we have extended the concept to dipole arrays, where the objective is to find the discrete driving point currents. Numerical results show that using the windowed metrons presented in this paper, the sparsity rate of the sparse matrices can be kept within 1%, while the E- and H-plane patterns are still in good agreement with the MoM results except for the farthest side lobes of the H-plane patterns.

Computation of capacitance matrix of integrated-circuit interconnects using on-surface MEI method

The on-surface MEI (OSMEI) method is successfully developed to compute the capacitance matrix of integrated-circuit interconnects. The OSMEI method uses the same mesh as MoM, but generates highly sparse matrices. The approach is verified by 2-D and 3-D examples with computing errors within 2/spl sim/4 percent.

Absorbing boundary conditions for measured equation of invariance in time domain

The measured equation on invariance is applied in time domain (TDMEI) to find the absorbing boundary conditions. The TM radiation of a line source at 1/4 computational domain in a 2-D free space is used as a test example to examine how good the TDMEI is in comparison with conventional absorbing boundary conditions (ABC), such at Murs (1981) 2nd order ABC and perfectly matched layer (PML), etc. It is found that the TDMEI is more accurate than both ABC and PML for the radiation problem.