Regularized solution to the problem of calculation of shaping electrodes for three-dimensional paraxial electron beams

Two forms of the regularized solution for the potential outside a paraxial beam with an arbitrary spatial curve as the axis and arbitrary cross section are obtained using the zero-order approximation of the multiscale method. A beam with invariable arbitrary cross section, which is localized near a screw line with a regular sequence of virtual emitters and is described by the exact solution of the equations of paraxial theory, is considered as an example.     

Electromagnetic scattering and radiation by surfaces of arbitraryshape in layered media. I. Theory

An accurate and general procedure for the analysis of electromagnetic radiation and scattering by perfectly conducting objects of arbitrary shape embedded in a medium consisting of an arbitrary number of planar dielectric layers is developed. The key step in this procedure is a formulation of the so-called mixed-potential electric field integral equation (MPIE) that is amenable to an existing advanced solution technique developed for objects in free space and that employs the method of moments in conjunction with a triangular-patch model of the arbitrary surface. Hence, the goal is to immediately increase analysis capabilities in electromagnetics, yet remain compatible with the large existing base of knowledge concerning the solution of surface integral equations. Three alternative forms of the MPIE in plane-stratified media are developed, and their properties are discussed. One of the developed MPIEs is used to analyze scatterers and antennas of arbitrary shape that penetrate the interface between contiguous dielectric half-spaces     

The echo area of a perfectly conducting prolate spheroid

An approximate general solution for the electromagnetic backscattering by a perfectly conducting prolate spheroid is derived. The solution is obtained from an estimate of the solution to a transient scattering problem which is deduced, in part, from the known time-dependent backscattered waveform for a perfectly conducting sphere. From the analysis the echo signal as a function of the source frequency for arbitrary orientation of the spheroid and arbitrary linear polarization of the incident plane electromagnetic wave can be predicted in the resonance region. Calculated results for a 2:1 axial ratio spheroid are compared with experimental data for two principal polarizations and major axes ranging from 0.32 to 1.59 wavelengths.     

Electromagnetic Waves in Toroidal Vessels of Arbitrary Cross Section Filled with Radially Inhomogeneous Dielectric Medium

In this paper, analytical solutions of Maxwell's equations in cylindrical coordinates are presented for toroidal resonators filled with homogeneous or inhomogeneous unmagnetized plasma or another dielectric medium. It is shown that the electromagnetic boundary conditions valid on a conducting toroidal surface of arbitrary meridional cross section can be satisfied by the general solution since the general solution contains an infinite set of arbitrary constants. A method is given to show how these constants and the eigenfrequency of the resonator can be calculated for a given cross section of the toroidal vessel.     

Analysis of oscillator synchronization conditions

The problem of determining the synchronization conditions of an arbitrary oscillator by a small periodic arbitrary waveform signal is considered. It is shown that the problem solution can be found from the existence conditions of small-signal linear system solution. An explicit equation for the oscillator locking range is derived, which can be easily included into a circuit simulation program. A comparison with well-known equations is carried out for a number of special cases. The validity of the suggested approach is verified by the numerical simulation results.     

Reflection of electromagnetic waves from oscillating surfaces

The problem of reflection of electromagnetic waves from oscillating surfaces is discussed. Using the induction theorem, the interface is replaced by equivalent current sources that radiate into an unbounded medium. Spatial movement is ascribed to these sources to account for oscillations of the surface. The general solution for the far-field due to any arbitrary surface motion is developed. A few deterministic and random functions for surface motion are considered. Most of the initial discussion pertains to normal reflection from planar surfaces, but the solution is also obtained for arbitrary incidence and for an oscillating cylinder.     

Coupling by slots in rectangular waveguides with arbitrary wall thickness

A method for evaluating the coupling between two rectangular waveguides, coupled by a slot of arbitrary dimensions in a wall of arbitrary thickness is described. The method is based on the solution, by numerical techniques, of a pair of coupled integral equations. Results for typical shunt and series slots are presented.     

Application of adaptive basis functions for a diagonal moment matrix solution of arbitrarily shaped three-dimensional conducting body problems

We present the application of specially constructed adaptive basis functions that generate a diagonal matrix in the method of moments solution procedure for the calculation of scattered electromagnetic fields from arbitrarily shaped conducting bodies excited by a plane electromagnetic wave. The arbitrary body is modeled using planar triangular patches. The crucial step in the solution procedure is the construction of the adaptive basis functions to generate the diagonal matrix. This task is accomplished with the help of well-known RWG basis functions. The solution thus obtained is very efficient, accurate, and applicable to truly arbitrary bodies. Several numerical examples are presented to validate the new method.     

Bounds and approximations for optimum combining of signals in the presence of multiple cochannel interferers and thermal noise

We derive an upper bound and investigate some approximations on the symbol error probability (SEP) for coherent detection of M-ary phase-shift keying, using an array of antennas with optimum combining in wireless systems in the presence of multiple uncorrelated equal-power cochannel interferers and thermal noise in a Rayleigh fading environment. Our results are general and valid for an arbitrary number of antenna elements as well as an arbitrary number of interferers. In particular, the exact SEP is derived for an arbitrary number of antennas and interferers; the computational complexity of the exact solution depends on the minimum number of antennas and interferers. Moreover, closed-form approximations are provided for the cases of dual optimum combining with an arbitrary number of interferers, and of two interferers with an arbitrary number of antenna elements. We show that our bounds and approximations are close to Monte Carlo simulation results for all cases considered in this paper.     

Electromigration behavior under a unidirectional time-dependentstress

The problem of current induced electromigration in VLSI interconnects, under an arbitrary time-dependent stress, is considered within the drift/diffusion model. It is shown that, by transforming into the convected frame and solving the resulting moving boundary problem, the vacancy build-up may be followed by solving two coupled integral equations. The important large-time behavior is obtained using standard asymptotic techniques. A series solution and an approximate small-time solution are also derived. It is found that, for a unidirectional periodic stress, the equivalent dc current, appropriate to EM reliability tests is the periodic average value. In addition a design rule for arbitrary time-dependent stress is suggested     

Characteristic Impedance of Transmission Lines with Arbitrary Dielectrics Under the TEM Approximation (Short Paper)

This paper gives a procedure for computing the characteristic impedances of TEM or quasi-TEM transmission lines with arbitrary cross sections and arbitrary dielectrics. Special consideration is given to conductors of finite cross-sectional extent. The solution is obtained by the method of moments using pulse functions for the expansion of charge density and point matching for testing. Numerical examples are given and compared with solutions obtained by other methods.     

Scattering from cylinders with arbitrary surface impedance

This paper presents an integral equation method for the solution of the field scattered by a set of cylinders with arbitrary cross-sectional shape, and arbitrarily varying anisotropic surface impedance. The integral equations are given for an arbitrary source with arbitrary harmonic variation along the cylinder axis. The scattering problem can be solved for arbitrary three-dimensional sources by expansion of the source in a Fourier integral over the axial propagation constant. The integral equations have been programmed for a CDC 1604A computer. The program developed has been used to solve a great variety of scattering, antenna, and propagation problems, and, depending upon accuracy desired, will handle cylinders up to about 150-wavelengths total perimeter. Numerical results on scattering from cylinders with specific cross sections are presented to illustrate the utility of the program developed.     

Weighted least-squares design and characterization of complex FIRfilters

The paper presents two novel weighted least-squares methods for the design of complex coefficient finite impulse response (FIR) filters to attain specified arbitrary multiband magnitude and linear or arbitrary phase responses. These methods are computationally efficient, requiring only the solution of a Toeplitz system of N linear equations for an N-length filter that can be obtained in o(N²) operations. Illustrative filter design examples are presented     

Electromagnetic plane wave scattering by a system of two uniformlylossy dielectric prolate spheroids in arbitrary orientation

By means of modal series expansions of electromagnetic fields in terms of prolate spheroidal vector wave functions, an exact solution is obtained for the scattering by two uniformly lossy dielectric prolate spheroids in arbitrary orientation embedded in free space, the excitation being a monochromatic plane electromagnetic wave of arbitrary polarization and angle of incidence. Rotational-translational addition theorems for spheroidal vector wave functions are employed to transform the outgoing wave from one spheroid into the incoming wave at the other spheroid. The field solution gives the column vector of the unknown coefficients of the series expansions of the scattered and transmitted fields expressed in terms of the column vector of the known coefficients of the series expansions of the incident field and the system matrix which is independent of the direction and polarization of the incident wave. Numerical results in the form of curves for normalized bistatic and monostatic radar cross sections are given for a variety of two-body system of uniformly lossy dielectric prolate spheroids in arbitrary orientation having resonant or near resonant lengths and different distances of separation     

Practical technique for the successive overrelaxation method

An empirical method is proposed in order to estimate the successive overrelaxation parameter for the solution of Laplace's equation over an arbitrary region.     

Generalized quasi-harmonic method for analyzing phase-locked systems

The quasi-harmonic linearization method is generalized to the case where the anticipated solution to the nonlinear differential equation of a phase-locked system involves an arbitrary number of harmonics. Governing relationships, which make it possible to find l-multiple φ cycles and investigate their stability, have been derived for the system of an arbitrary order. The examples illustrating the analysis of the third-order system are presented.     

Scattering of forward bulk magnetostatic waves by a defect of the surface of a ferromagnetic film magnetized at an arbitrary angle

The solution for the diffraction problem of scattering of magnetostatic waves by an arbitrary shallow defect situated under the surface of a ferromagnetic film magnetized at an arbitrary angle is obtained in the quasi-static approximation. Expressions for the energy flux density of scattered magnetostatic waves in the far-field zone are found. The results of computations of the time-averaged flux density of bulk magnetostatic waves reflected from rectangular and circular shallow irregularities are presented.     

Numerical and experimental studies of current distributions on thinmetallic posts inside rectangular waveguides

A fast converging and stable moment method solution for the current distribution on arbitrary size rectangular obstacles mounted transversely inside the rectangular waveguide has been developed. A special arrangement of piecewise sinusoidal and pulse basis functions has been utilized to determine the transverse current distributions on the obstacles and their scatterings in the waveguide. The method has been compared well with the Marcuvitz's results for the inductive and capacitive posts and the experimental data of an arbitrary size rectangular obstacle     

A transform solution for the fields from a current element

A new but general method of solution applicable to any radiation problem which can be reduced to an inhomogeneous wave equation for an arbitrary source in a given medium is used to solve for the vector potential of an infinitesimal dipole radiating in free space. The solution of this simple problem yields insight into the use of this method for the solution of more complicated problems.     

微粒粒度两种表述对其形体影响因子的影响

对任意形体微粒粒度提出了基于椭圆模型的等效面积粒度表述法和内切圆粒度表述法,基于这两种表述方法,分别对微粒形体影响因子的表述及其解进行了讨论,通过对解的动态特征比较,确立了内切圆粒度表述法是一种任意形体微粒粒度表述的好方法,并对其数值解进行拟合,为任意形体微粒特征概率分布函数反演方程提供了较好的反演理论依据.