The Capacitances and Surface-Charge Distributions of a Shielded Balanced Pair

The capacitance matrix of a straight pair of uniform wires symmetrically placed in a shield is determined theoretically. Exact expressions for the elements of the capacitance matrix are determined as particular elements of the inverse of an infinite matrix which relates the Fourier coefficients of the surface-charge densities on the inner conductors and the shield to the applied voltage excitations on the cable conductors. If the wire diameter is small relative to the wire separation, and if the wire separation is small relative to the shield diameter, then accurate numerical approximations for the elements of the capacitance matrix are obtained to any degree of accuracy by suitably truncating the infinite matrix. Once the elements of the capacitance matrix are determined, then the distributions of the surface-charge densities on the peripheries of the inner conductors, and the shield are determined for any arbitrary excitation of the cable structure. In particular, the various capacitances associated with the cable structure, e.g., the direct, ground, and mutual capacitances, are determined from a comparison of the surface-charge densities resulting from a "balanced" excitation and a "longitudinal" excitation. The Fourier coefficients of the surface-charge densities are required to determine the propagation parameters and the associated propagation modes of the cable structure. The surface-charge distributions are evaluated numerically for a typical standard production cable using 22-gauge wires. The results of this paper will be extended by a perturbational method to include twisted wires in a shield; also, certain types of asymmetries in the cable geometry will be considered. Hence, the propagation constants and the associated propagation modes of unbalanced and/or twisted shielded pair cables can also be determined.     

The Capacitances and Surface Charge Distributions of a Shielded Unbalanced Pair (Short Papers)

The capacitance matrix of an unbalanced shielded pair cable is determined theoretically. The wires of the cable are asymmetrically located about the axis of the shield and have different radii; however, the axes of the wires are restricted to lie on a line passing through the axis of the shield. The elements of the capacitance matrix are determined as particular elements of the inverse of a truncated intinite matrix, which relates the Fourier coefficients of the surface charge densities on the inner conductors and the shield to the applied voltage excitations on the cable conductors. The capacitances and surface charge distributions are evaluated numerically for a shielded pair cable, which, due to inaccuracies in the cable manufacturing processes, has one wire with a smaller or larger radius than the other wire of the pair and/or has one wire closer to or farther from the axis of the shield than the other wire of the pair.     

A new wire node for modeling thin wires in electromagnetic fieldproblems solved by transmission line modeling

A three-dimensional wire node for the numerical solution of electromagnetic field problems by transmission line modeling is discussed. The wire node can represent thin wires in a coarse mesh, thus substantially increasing computational efficiency. The scattering matrix for the node is given, together with a simulation result and comparisons with another method     

Study of electromagnetic wave propagation through dielectric slab doped randomly with thin metallic wires using finite element method

A new numerical simulation method using the finite element methodology (FEM) is presented to study electromagnetic propagation through a dielectric material slab doped randomly with thin and short metallic wires. The FEM approach described in many standard text books and published papers, is appropriately modified to account for the presence of thin and short metallic wires. Using this modified FEM approach, the transmission and reflection characteristics of a material slab (homogeneous dielectric slab doped randomly with thin and short metallic wires) placed in an X-band rectangular waveguide are estimated. The estimated results are compared with the numerical results obtained using the CST microwave studio simulation tool.     

Matrix methods for field problems

A unified treatment of matrix methods useful for field problems is given. The basic mathematical concept is the method of moments, by which the functional equations of field theory are reduced to matrix equations. Several examples of engineering interest are included to illustrate the procedure. The problem of radiation and scattering by wire objects of arbitrary shape is treated in detail, and illustrative computations are given for linear wires. The wire object is represented by an admittance matrix, and excitation of the object by a voltage matrix. The current on the wire object is given by the product of the admittance matrix with the voltage matrix. Computation of a field quantity corresponds to multiplication of the current matrix by a measurement matrix. These concepts can be generalized to apply to objects of arbitrary geometry and arbitrary material.     

Electromagnetic response of two crossing, infinitely long, thinwires

The electromagnetic coupling of two crossed thin wires of infinite length is considered. Two coupled integral equations are obtained, given in terms of generalized impedance functions, for the spectral currents flowing in each wire. The wires may be in a homogeneous medium or over a half-space. The numerical implementation focuses, however, only on the former. The numerical solution may be obtained by either applying moment or multiple scattering methods. The solution obtained from the method of moments is applicable for any wire spacing. Obversely, the multiple scattering method leads to a convenient matrix series solution, which shows that the coupling between wires is proportional to 1/d ² (where d is the wire separation) plus higher order scattering terms     

Analysis of the coupling of an incident wave with a wire inside a cavity using an FEM in frequency and time domains

This paper presents a numerical method based on finite elements in both the frequency and time domains for modeling the coupling of an incident wave with a conducting wire placed inside a metallic cavity having a small aperture. The method uses edge elements on tetrahedra for the electric field representation. The formulation can take into account thin wires as well as lumped elements. In the time-domain approach, the time derivatives are discretized by the Newmark method, which allows obtaining an unconditionally-stable scheme with second-order accuracy. Numerical results are provided to validate the presented method.     

Characteristic Impedance of Integrated Circuit Bond Wires (Short Paper)

In microwave circuit analysis, bond wires are frequently modeled as lumped elements or sections of microstrip. These models are insufficient since part of the wire is suspended above the substrate. This paper shows numerical results that provide the line impedance and effective dielectric constant for a round wire above a grounded dielectric substrate.     

Demonstration of a Time-Domain Integrated Electromagnetic-Field Circuit-Analysis Program

A numerical approach for combining an explicit time-domain electromagnetic computer code with an implicit time-domain circuit code is described. The numerical approach is then demonstrated by predicting plane-wave excitation of a loaded thin wire and the mutual coupling of two thin wires in a box separated by a conductive surface with an aperture. Possible applications to EMC problems are discussed.     

Root-mean-square measure of nonlinear effects to the transient response of thin wires

A root-mean-square (rms) measure of effect of nonlinear loading on the transient response of thin wires is proposed. The transient behavior of nonlinearly loaded wires is analyzed directly in the time domain. The problem is formulated via the space-time Hallen integral equation. The equation is solved by the space-time Galerkin Bubnov boundary element procedure. Numerical results for the transient response of a thin wire computed by a time domain code based on this method are compared with results obtained from a frequency domain code. Some illustrative numerical results for the spatial distribution of the rms values of time varying currents are also presented.     

Theoretical design and predictions of volute antenna performance

To provide generic design guidelines for volute antenna elements over a wide range of parameters, a theoretical formulation and algorithm for computing the antenna radiation field have been developed. The procedure relies on the vector combination of the radiation fields of the helical wires and the end connecting wires with a continuous sinusoidal current distribution along each wire of the volute. The antenna patterns of circularly polarized fields, directivity, 3-dB beamwidth, axial ratio, front-to-back power ratio, etc. can all be calculated from a given set of volute parameters. A practical design example utilizing this procedure is presented     

A Hybrid Electromagnetic-Circuit Method for Electromagnetic Interference Onto Mass Wires

A current decomposition method is proposed for the analysis of field coupling to mass wires near complex structures. The foremost attribute of the method is the decomposition of the current on each wire into push-pull and push-push mode currents. The former refers to the perturbation current accounting for the interactions among the wires within the bundle, whereas the latter represents the interactions between the mass wire bundle and the surrounding structure. Multiconductor transmission line theory is employed to compute the push-pull mode current by using one of the wires in the bundle as the return/reference conductor. Current induced on a test wire located along the reference line is used to compute the push-push mode. For this analysis, we employed the method of moments for the electromagnetic analysis of surrounding structure and simulation program with integrated circuit emphasis (SPICE)-like simulators for the analysis of a circuit model of the transmission lines extracted via the partial element equivalent circuit method. Several validation examples (including transmission lines inside an automobile) are presented. It is also shown that the traditional transmission line theory based on quasi-static analysis fails with increasing complexity of the surrounding structure.     

基于形状的朝向目标布线算法

在传统布线算法的基础上,本文提出了一种无网格布线算法——基于形状的朝向目标线探索法.该布线算法主要针对障碍物外形尺寸多样,已布连线线宽及线间距离可变的布线情况,尤其适用于印刷电路板及集成电路的布线,该算法的基本要素是障碍物的包容矩形和带有预定终点的探索线,且所需存储空间小、布线速度快、布线路径短,具有良好的布线效果.     

Electromagnetic Surface Wave Propagation over a Bonded Wire Mesh

The electromagnetic surface wave that can propagate over a square mesh of intersecting parallel wires is considered. A combined analytical and numerical method developed earlier is employed to deal with the interacting wire currents. For small mesh spacings, the propagation constant is found to be almost independent of the azimuthal direction of propagation. This is in agreement with previous results obtained by Soviet investigators who utilize averaged boundary conditions for analyzing such bonded wire meshes. However, for larger wire spacings, greater than about one tenth of a wavelength, there is a significant dependence on the direction of propagation over the mesh. The validity of describing the wire mesh in terms of an effective transfer inductance and related questions are discussed briefly in the Appendix.     

The Fracture Resistance of Bonded Au Wires for Interconnection

This paper presents the effects of the local strength degradation due to recrystallization and grain growth and the large deformation induced in wire bonding process on the fracture resistance of the bonded Au wires for interconnection. The experimental and numerical results show that, for a wire to deform to the required shape without reduction in the fracture resistance, sufficient ductility is more important than the strength of the wire.      

An accurate thin-wire model for 3-D TLM simulations

Accurate modeling of thin wires in large-scale numerical electromagnetic simulations is very time consuming if fine meshing is adopted. Special treatments of such wires to allow their incorporation into relatively coarse meshes have lead to the development of thin-wire nodes for the transmission-line matrix (TLM) method. Previous models require the use of empirical factors. A novel thin-wire node is presented that is derived from rigorous field theory, requires no empirical factors and is shown to be highly effective. Moreover, virtually no computational overhead is incurred in the use of the new wire node.     

Computation of the Transmission Line Inductance and Capacitance Matrices from the Generalized Capacitance Matrix

In a recent paper [1], a method for computing the per-unitlength generalized capacitance matrix of a system of dielectric-insulated wires was given. In this-paper, a method for computing the per-unitlength inductance and capacitance matrices used in multiconductor transmission-line models in terms of the elements of the generalized capacitance matrix is given. Certain approximate formulas for large wire separations are also given. Rome Air Development Center.     

Analytical approach to temperature evaluation in bonding wires andcalculation of allowable current

Wirebonding is still the most common technique being applied to device assembly. Since the entire electrical power for the chip has to be delivered through the wires, considerable current densities may occur. As a result, bond wires are heated up and in case of too excessive current wires or surrounding materials might suffer and subsequently fail. In order to increase reliability of semiconductor devices it is important to know the resultant temperature due to a given current and deduced from this, the allowable loading so that a maximum temperature will not be exceeded. In this paper universally valid formulas for steady state, single pulse and periodic loading are introduced. They are derived from the heat diffusion equation resulting from a mathematical model which is proposed for simplification. In case of ceramic packages radiation and convection effects are considered whereas conduction through the molding compound is taken into account if the wire is encapsulated in plastic. The formulas also enable comparison between the effects of heat conduction through the wire and through the molding compound. Besides, the system of differential equations considers the temperature dependence of the specific resistance and the thermal conductivity of the wire material. Corrections for very thin plastic packages and multiple bonding are suggested. The formulas have been checked by both experimental data and numerical computation by means of Finite Element Analysis     

Calculation and experimental validation of induced currents on coupled wires in an arbitrary shaped cavity

An efficient numerical technique is presented for the calculation of induced electric currents on coupled wires and multiconductor bundles placed in an arbitrary shaped cavity and excited by an external incident plane wave. The method is based upon the finite-difference time-domain (FD-TD) formulation. The concept of equivalent radius is used to replace wire bundles with single wires in the FD-TD model. Then, the radius of the equivalent wire is accounted by a modified FD-TD time-stepping expression (based on a Faraday's law contour-path formulation) for the looping magnetic fields adjacent to the wire. FD-TD computed fields at a virtual surface fully enclosing the equivalent wire are then obtained, permitting calculation of the currents on the wires of the original bundle using a standard electric field integral equation (EFIE). Substantial analytical and experimental validations are reported for both time-harmonic and broad-band excitations of wires in free space and in a high-Qmetal cavity.     

A method of moments approach for the efficient and accuratemodeling of moderately thick cylindrical wire antennas

This paper introduces a moment-method formulation, which is capable of accurately modeling moderately thick cylindrical wire antennas. New algorithms are presented for the efficient computation of the cylindrical wire kernel and related impedance matrix integrals. These algorithms make use of exact series representations as well as efficient numerical procedures and lead to a significant reduction in overall computation time for thicker wires. Another major advantage of this moment-method technique is that it is no longer restricted by the segment length-to-radius ratio limitations inherent in past formulations, thereby making it possible to achieve solution convergence for a much wider class of wire antenna structures. Several examples illustrating the superior convergence properties of this new moment-method formulation are presented and discussed