Uniform physical theory of diffraction equivalent edge currents fortruncated wedge strips

New uniform closed-form expressions for physical theory of diffraction equivalent edge currents are derived for truncated incremental wedge strips. In contrast to previously reported expressions, the new expressions are well behaved for all directions of incidence and observation and take a finite value for zero strip length. This means that the expressions are well suited for implementation in general computer codes. The new expressions are expressed as the difference between two terms. The first term is obtained by integrating the exact fringe wave current on a wedge along an untruncated incremental strip extending from the leading edge of the structure under consideration. The second term is calculated from an integration of the asymptotic fringe wave (FW) current along another untruncated incremental strip extending from the trailing edge of the structure. The new expressions are tested numerically on a triangular cylinder and the results are compared with those obtained using the method of moments and the previously reported expressions     

MIMO channel statistics in the presence of non-uniform angle spread

We give analytical expressions for correlation, spectrum, level crossing rate, and average fade duration for the multiple-antenna fading channel in the presence of nonuniform power azimuth spectrum (PAS). Classical expressions for uniform PAS are a special case of these expressions. The expressions are valid for any antenna patterns and for any PAS.     

Electromagnetic field of a rectangular patch of uniform and lineardistributions of current

Closed-form expressions for a class of indefinite double integrals are presented. Using these formulas, exact analytical expressions for the magnetic vector potential and the electric and magnetic fields of a rectangular patch of uniform and linear distributions of electric current in an unbounded homogeneous medium are derived. The field expressions obtained are valid everywhere, in particular in the source region. Computed results verifying the correctness and accuracy of these expressions are presented     

On uniform asymptotic Green's functions for the perfectly conducting cylinder tipped wedge

Uniform asymptotic expressions are derived for the Green's functions describing scattering of electric or magnetic type plane waves by a perfectly conducting cylinder tipped wedge (CTW). These expressions are found to agree analytically with heuristic expressions available using the geometrical theory of diffraction (GTD). Numerical comparison of these expressions with results obtained from eigenfunction expansions show good agreement for cylinder diameters >1.5 lambda.     

Closed-form expressions for uniform currents on a wedge illuminatedby TM plane wave

Closed-form expressions for nonuniform currents on a perfectly conducting, infinite wedge illuminated by a transverse magnetic plane wave are presented. The expressions are derived by requiring that they agree with the current predicted by the eigenfunction solution close to the edge and J.B. Keller's geometrical theory of diffraction (1962) far from the edge. The angle of incidence is arbitrary and the expressions remain uniformly valid even for glancing angles of incidence when the geometrical optics boundaries are in the vicinity of the wedge faces. The formulas presented are simple, involving Fresnel functions with complex arguments. These functions can be expressed in terms of complimentary error functions which may be computed using standard subroutine packages. Exact expressions for nonuniform currents are available for the two special cases of half-planes and infinite planes. Closed-form expressions for the axial electric field, and hence all the field components in the vicinity of the wedge axes, are also obtained. Currents computed using expressions obtained are compared with currents computed from the eigenfunction solution of the wedge, with good agreement throughout     

Analytical modeling of MOSFETs channel noise and noise parameters

Simple analytical expressions for MOSFETs noise parameters are developed and experimentally verified. The expressions are based on analytical modeling of MOSFETs channel noise, are explicit functions of MOSFETs geometry and biasing conditions, and hence are useful for circuit design purposes. Good agreement between calculated and measured data is demonstrated. Moreover, it is shown that including induced gate noise in the modeling of MOSFETs noise parameters causes /spl sim/5% improvement in the accuracy of the simple expressions presented here, but at the expense of complicating the expressions.     

Closed-form expressions for the numerical dispersion and reflectionin FEM simulations involving biaxial materials

Closed-form expressions for the numerical errors caused by finite-element discretization of problems involving materials of biaxial permittivity and permeability tensors are developed. In particular, we derive expressions for the numerical dispersion and reflection in both first-order node and edge basis function finite-element formulations in an equilateral triangular mesh. Results using these closed-form expressions are compared to practical numerical simulations. The application of these expressions to the analysis of the performance of the perfectly matched layer boundary is suggested     

On the design of multifilter banks and orthonormal multiwaveletbases

Several forms of parametric expressions for orthogonal multifilter banks are presented. The explicit expressions for a group of orthogonal multifilter banks that generate symmetric/antisymmetric scaling functions and orthonormal multiwavelets are obtained. Based on these parametric expressions for orthogonal multifilter banks, orthonormal multiwavelet pairs with good time-frequency localization are constructed, and examples of optimal multifilter banks are provided     

Depletion region thicknesses in diffused junctions

Closed-form expressions are derived for total thickness of the depletion region and thickness of the depletion region on the n side of the junction. The expressions are applicable to n-p junction devices with either complementary error function or Gaussian impurity distributions. Depletion region thicknesses obtained by evaluation of the closed-form expressions are in excellent agreement with exact numerical calculations.     

Advances in the performance of Reed-Solomon codes

This paper presents generalized expressions for the probabilities of correct decoding and decoder error for Reed-Solomon (RS) codes. In these expressions, the symbol error and erasure probabilities are different in each coordinate in a codeword. The above expressions are used to derive the expressions for reliability and delay for Type-I hybrid ARQ (HARQ-I) systems when each symbol in a packet (multiple codewords per packet) has unique symbol error and erasure probabilities. Applications of the above results are demonstrated by analyzing a bursty-correlative channel in which the symbols and codewords within the packet are correlated     

Closed-form expressions for the even-mode capacitance of thick coupled microstriplines

Closed-form expressions for the even-mode capacitance of the coupled microstriplines with finite strip thickness are derived. The expressions are mainly useful in conductor loss evaluations and are suitable for direct use in computer-aided procedures. The approach used utilises the results that were obtained earlier by conformal mapping techniques. The accuracy of these expressions has been checked against numerical results.     

Effective electromagnetic properties of honeycomb composites, and hollow-pyramidal and alternating-wedge absorbers

Closed-form expressions for the effective electromagnetic material properties of honeycomb composites and electromagnetic absorbers constructed in the shapes of alternating wedges and hollow pyramids are presented. These expressions can be used to efficiently calculate the interaction of electromagnetic fields with periodic structures of said geometries. The effective material properties from these expressions are compared to results obtained from a numerical solution of the actual cross-sectional geometry. Finally, we give guidance on how the expressions presented here and elsewhere can be used for other types of periodic geometries.     

Nonuniform currents on a wedge illuminated by a TE plane wave

Closed-form expressions for nonuniform currents on a perfectly conducting, infinite wedge illuminated by transverse electric (TE) plane wave are presented. These expressions are derived by requiring that they coincide with the current predicted by the asymptotic diffraction method far from the edge and, further, that they agree with the current predicted by the eigenfunction solution at the edge. The angle of incidence is arbitrary and our expressions remain valid even for glancing angles of incidence when either one or both faces of the wedge are in the vicinity of a geometric optic (GO) boundary. Formulas presented here are simple involving the well-known modified Fresnel functions but are not uniform. Exact expressions for nonuniform currents are available for the two special cases of half-plane and infinite plane. For these special cases, our solution reduces to the exact solution. Currents computed using the expressions developed here are compared with currents computed from the eigenfunction solution of the wedge. Good agreement is obtained throughout.     

关于S—盒的布尔函数表达式

提出一种求S—盒的布尔函数表达式的系统方法,并由此法推出了DES中所有S—盒的布尔函数表达式,根据这些布尔函数表达式又导出了DES中S—盒的几点简单性质。     

Availability of a Renewable, Checked System

Recurrent expressions are given for point and interval unavailability of a renewable system subjected to periodic checking/repair. The expressions are generalizations of the basic relations in the theory of discrete renewal processes. The asymptotic limits for long times follow simply from a general theorem of this theory. The connection to previous expressions is established.     

Impedance of an antenna-array element

A number of expressions for calculating the active impedances of the radiating elements of large linear and planar antenna arrays with allowance for the interaction of the entire set of the elements are presented. The expressions are applicable not only to the radiating elements distant from the edge of the array but also to the edge and corner elements. The expressions are based on the formulas for certain sums of elementary and higher transcendental functions that give simple closed-form expressions for the sums of mutual impedances. As an illustration, the resistances of weakly directional radiating elements in dense arrays, where the mutual coupling of the elements is extremely strong and results in important effects, are calculated.     

Analysis of the High Frequency Field Expressions at the Caustic Region of a Spherical Reflector Placed in Chiral Medium

High frequency field expressions are derived around the caustic region of a spherical reflector placed in a homogenous, isotropic and reciprocal chiral medium. Firstly Geometrical Optics (GO) field expressions are derived for the spherical reflector placed in chiral medium. As the GO approximation fails at the vicinity of the caustic therefore, Maslov’s method has been used to find the field expressions which are also valid around the caustic region. Present work is an extension of previous work from two dimensional to three dimensional reflector. Some numerical results including line plots around the focal region of spherical reflector placed in chiral medium are obtained using the derived expressions.     

Harmonic and intermodulation performance of Josephson junctions

In this paper a simple mathematical model is presented for the inherent resistive nonlinearity of a Josephson junction. By incorporating this model in the RSJ model of the Josephson junction, series expressions are obtained for the harmonic and intermodulation performance of Josephson junctions irradiated by multisinusoidal signals. Special cases are considered where the series expressions can be reduced to simple analytical expressions.     

Simple accurate expressions for planar spiral inductances

We present several new simple and accurate expressions for the DC inductance of square, hexagonal, octagonal, and circular spiral inductors. We evaluate the accuracy of our expressions, as well as several previously published inductance expressions, in two ways: by comparison with three-dimensional field solver predictions and by comparison with our own measurements, and also previously published measurements. Our simple expression matches the field solver inductance values typically within around 3%, about an order of magnitude better than the previously published expressions, which have typical errors ground 20% (or more). Comparison with measured values gives similar results: our expressions (and, indeed, the field solver results) match within around 5%, compared to errors of around 20% for the previously published expressions. (We believe most of the additional errors in the comparison to published measured values is due to the variety of experimental conditions under which the inductance was measured.) Our simple expressions are accurate enough for design and optimization of inductors or of circuits incorporating inductors. Indeed, since inductor tolerance is typically on the order of several percent, “more accurate” expressions are not really needed in practice