Fredholm resolvents, Wiener-Hopf equations, and Riccati differential equations

We shall show that the solution of Fredholm equations with symmetric kernels of a certain type can be reduced to the solution of a related Wiener-Hopf integral equation. A least-squares filtering problem is associated with this equation. When the kernel has a separable form, this related problem suggests that the solution can be obtained via a matrix Riccati differential equation, which may be a more convenient form for digital computer evaluation. The Fredholm determinant is also expressed in terms of the solution to the Riccati equation; this formula can also be used for the numerical determination of eigenvalues. The relations to similar work by Anderson and Moore and by Schumitzky are also discussed.     

Integral-equation approach to the abrupt-depletion approximation in semiconductor components

By using the abrupt-depletion approximation, one obtains a linear equation for the minority-carrier concentration in a semiconductor. This equation describes the diffusion and the recombination statistics of the carriers under steady-state conditions. In a 2-dimensional geometry, this equation can be replaced by an equivalent integral equation, so that the given problem can be easily solved numerically.     

Modelling DC characteristics of static induction transistors

To analyse and design non-linear circuits using static induction transistors (SITs), a new empirical equation is presented to relate drain current to drain-source and gate-source voltages. The parameters of this equation can easily be obtained from the drain characteristics of the SIT. Using this equation, a closed-form expression can be obtained for the amplification factor of the SIT. Good agreement is obtained between the predicted and experimental results.     

Solutions for Some Waveguide Discontinuities by the Method of Moments (Short Papers)

The electromagnetic boundary value problem of two waveguides coupled by an aperture or an aperture in a waveguide radiating into free space may be described by an integral equation. An analytical solution to this integral equation cannot be readily found due to the complexity of the kernel. However, extremely useful results may be obtained if the method of moments is employed to reduce the integral equation to a matrix equation which can be solved by known methods. In this short paper, series and shunt slots in a rectangular waveguide are analyzed using this technique.     

ALPS-A new fast frequency-sweep procedure for microwave devices

The discretization of Maxwell equations results in a polynomial matrix equation in frequency. In this paper, we present a robust and efficient algorithm for solving the polynomial matrix equation. To solve this equation for a broad bandwidth, one previously performs a discrete frequency sweep where the resulting matrix needs to be inverted at numerous frequencies, while current procedure requires only one matrix inversion. Speed improvements compared to the discrete sweep range from 10 to 100 times, depending on number of resonance peaks encountered     

A note on the method of analytical regularization

Many problems of electromagnetics are governed by singular integral equations of the first kind. As discussed by Nosich (1999), it is often possible to obtain a different equation describing the problem by applying the method of analytical regularization, and analytically inverting part of the original equation. The transformed equation is of the second kind. Therefore, as a rule, it is usually preferable to apply a numerical method to the transformed equation than to the original one. What appears to be an exception to that rule is discussed in the present paper: under proper conditions, and for a particular numerical method, results obtained by application to the transformed equation are shown to be identical to those obtained by application to the original equation. Some consequences of this equivalence are discussed     

同心导体圆盘-圆环结构散射场的一种分析方法

本文从电场积分方程出发,经傅氏变换,并分离出电荷对散射场的贡献,导出了平面波投射于同心圆盘-圆环结构时,分析散射场的一个形式简单且便于求解的积分方程。当平面波正投射时解法尤为简单。据此求解圆盘和/或圆环结构上感应电流分布和相应的散射场。为验证本方法的准确性,对圆盘雷达散射截面(RCS)的计算结果与精确解进行了比较,结果吻合很好。文中还给出了当平面波正投射时,同心圆盘-圆环结构上感应电流各分量的幅度分布和散射场分布。     

A multigrid method for solution of the diffusion equation in VLSI process modeling

If an implicit time discretization method is used for the diffusion equation, a large equation system has to be solved. In this work, a ν-cycle multigrid method was employed for this purpose. It can be easily applied to any 9-point approximation for nonlinear second-order differential operators, requires no iteration parameters, and can compete with other fast solvers [7]. The storage needed is 6 times the number of grid points.     

Transient analysis of two semiconductor devices under circuit-loaded operation conditions

A new method of numerical analysis for semiconductor devices is described. The analysis is carried out by solving a set of fundamental equations which govern the device characteristics and the circuit equation which indicates the circuit condition, simultaneously. Here, instead of Poisson's equation used as one of the fundamental equations in most reported analyses, a "current equation" is used, which represents the device current consisting of conduction current and displacement current. Current equation can be directly substituted into the circuit equation, so the solution obtained from this analysis has self-consistency between device characteristics and circuit condition, Furthermore, the time variations for I-V characteristics, carrier concentration distribution, and electric field distribution for an individual device can be obtained. As a calculation example, the transient characteristics of two diodes with reverse biased condition are calculated. Avalanche oscillation is found for both diodes with opposite phase after avalanche breakdown.     

Theoretic curves of drift transistor current gain

Intrinsic common-base, short-circuit current gain analysis of drift transistors may be aided by means of a simplified approximation equation. The accuracy of the equation may be controlled by the investigator. A graphic solution for determining this parameter of moderate drift field transistors may be obtained by using the arcs of circles. The interrelation between the graphic analysis and the theoretic approximation provides a flexible yet accurate method of analyzing this parameter.     

波导系统中电子注辐射过程的能量守恒关系

本文应用电磁场的算子理论求出了在任意截面的波导系统内,由电子注电流所激励的电磁场的公式。在这一公式中由单位功率流下的场代替了一般并矢格林函数中的归一化本征常数;这样,不但可以证明激励过程中的能量守恒关系,还可以比较方便地应用到各种实际的电子器件的互作用理论中去。     

Analysis of elliptical waveguides by differential quadrature method

A new approach for elliptical waveguide analysis is presented in this paper. This approach applies the global method of a differential quadrature (DQ) to discretize the Helmholtz equation and then reduces it into an eigenvalue equation system. All the cutoff wavelengths from low-to high-order modes can be simultaneously obtained from the eigenvalues of the equation system. The present solver is general, which can be applied to elliptical waveguides with arbitrary ellipticity. It is demonstrated in this paper that the DQ results are in excellent agreement with theoretical values using just a few grid points and, thus, requiring very small computational effort     

The electron beam in a cathode-ray tube

The beam in a cathode-ray tube is described by a "paraxial" Liouville equation. This equation takes into account the thermal spread of the electrons as well as the influence of the space charge of the beam. The solution of this equation is given. An ordinary differential equation is derived for the beam radius. The equation has been solved in the field-free region outside the gun. The result is presented in graphs which can be applied to the determination of the spot size on the screen of a cathode-ray tube.     

Current induced on a conducting strip which resides on the planar interface between two semi-infinite half-spaces

An analysis is described for determining the current induced by a known excitation on a conducting strip which resides on the planar interface between two semi-infinite homogeneous half-spaces of different electromagnetic properties. The perfectly conducting flat strip is of infinite extent and the excitation is transverse magnetic to the strip axis. An integral equation for the induced current is formulated and it is shown that its kernel which is in general a Sommerfeld-type integral can be expressed in closed form when the permeabilities of the two media are the same. Under this practical condition the integral equation is solved numerically and data are presented for cases of interest. For the electrically narrow strip, the integral equation is approximated and this approximate equation is solved analytically.     

Optimal nonlinear filtering for independent increment processes--Part II

The main result obtained in Part I [1]--which is contained in Theorem1of Part I--is generalized and extended in several ways. First, a new basic stochastic integro-partial differential equation for the conditional probability density function for the state of a nonlinear dynamic system with disturbance noise given noisy nonlinear measurements of the state is derived under the less restrictive assumption that the disturbance noise is an arbitrary independent increment process with an infinitely divisible distribution, and the measurement noise is a Gaussian independent increment process with an infinitely divisible distribution. It is then shown that, under proper restrictions, this basic equation reduces to either the Fokker-Planck equation for diffusion processes or the Kolmogorov-Feller equation for jump processes. Also, it is shown that this basic equation contains the earlier results of Kushner [2] and Wonhamt [3] as special cases. Next, it is shown how the result represented by this basic equation can be easily extended to include the case where the disturbance noise is a Markov process of the type initially assumed for the state of the dynamic system. Finally, it is shown that, in contrast to results obtained by Bryson and Johansen [4] and Cox [5] for the linear, Gaussian case, it is not generally possible to extend the result represented by this basic equation to include either the case where the measurement noise is a Markov process of the type initially assumed for the state of the dynamic system, or the case where the covariance matrix of the Gaussian measurement noise is singular. However, some incomplete results indicating when such extensions might be possible are given.     

Vector Variational Formulation of Electromagnetic Fields in Anisotropic Media

Maxwell's equations can be cast into a basic differential operator equation, the curlcurl equation, which lends itself easily to variational treatment. Various forms of this equation are associated with problems of practical importance. The formulation includes the treatment of loss-free anisotropic media. The boundary conditions associated with electromagnetic-field problems are treated in detail and the uniqueness of the solution is discussed. A functional is derived for the curlcurl equation in Cartesian and cylindrical coordinates.     

A Theoretical Study of the High-Frequency Performance of a Schottky-Barrier Field-Effect Transistor Fabricated on a High-Resistivity Substrate

The short-circuit admittance parameters for a silicon Schottky-barrier field-effect transistor (SBFET) fabricated on a high-resistivity substrate are calculated from first principles ignoring the effects of minority carriers. The calculations show the maximum frequency of oscillation for a device with a 1-/spl mu/m gate to be 17.9 GHz, neglecting the parasitic associated with the contact metallizations, and 14.7 GHz when the parasitic are included. In order to describe the dynamic behavior of the device, the static properties must first be obtained. The simultaneous solution of Poisson's equation and the continuity equation, both in two dimensions, gives the static charge and potential distribution in the device. The effects of a field-dependent mobility are included in the continuity equation. Using the results of static two-dimensional solutions, a one-dimensional device model is developed that permits the dynamic device behavior to be described by a one-dimensional linear ordinary differential equation. By solving this equation under appropriate boundary conditions, the device y parameters are found as functions of frequency. Calculated results are shown to be in good agreement with published experimental data.     

Dispersion Characteristics of a Cylindrical Electromagnetic Band Gap Structure

In this letter, a new analytical expression for the dispersion equation of radially periodic structures is derived. The periodic structure is considered as a set of parallel cylindrical frequency selective surfaces, and the dispersion equation is calculated by using a transmission line model. Using this result, the dispersion proprieties of cylindrical electromagnetic bandgap structures composed of continuous or discontinuous metallic wires are presented. It is shown that the band structures of these materials can be determined by using the proposed dispersion equation. Cylindrical periodic materials have potential applications for designing directive antennas, circular high impedance surfaces, or agile antennas     

Green's Function Treatment of Edge Singularities in the Quasi-TEM Analysis of Microstrip

A new Green's function approach to the quasi-TEM analysis of microstrip is presented. By expressing the charge density on the strip conductor as the sum of a singular term, derived from the consideration of a Motz expansion, and a continuous term, the integral equation defining this charge density is transformed into an integral equation for the continuous term. An accurate numerical solution to this new integral equation can be obtained by approximating the continuous term by a low-order unit-pulse expansion. It is seen that the numerical scheme developed in this work is both easy to implement and rapidly convergent, thus making it an excellent choice for use in microwave CAD packages.     

一种改进的各向异性扩散模型

各项异性扩散方程是一种经典的图像去噪方法,但该方法在去除噪声的过程中会造成一定程度的模糊边缘。对此文中提出了一种基于改进的各向异性扩散方程的图像去噪方法,通过在其能量泛函的目标函数中添加残差项,使能量泛函的极小解更加接近原始的函数,可取得比其更好的去噪效果。文中方法可看作是各项异性扩散方程和全变差模型的结合。实验表明,新提出的方程相对经典的方程有较好的边界处理效果和更高的信噪比。