Improved variational method for spreading resistance calculations

An improved version of the variational method has been developed for spreading resistance calculations, based on a different source function from one used previously. This new version is capable of great accuracy, yielding results which for most practical purposes can be regarded as indistinguishable from those obtained from the exact method using the mixed boundary value approach. At the same time, it retains the main advantage, namely, speed of computation, of the variational method. Thus, in its present form, the variational method can be used in place of the exact method for accurate determination of both the correction factors and the source current density, especially where speed of computation is an important consideration.     

Spreading resistance calculations by the use of Gauss-Laguerre quadrature

The Gauss-Laguerre quadrature is proposed as a numerical method for calculating the correction factor integrals that occur in spreading resistance calculations. The method is very efficient in terms of computation time and memory storage, requiring only 33 integrand values for each integral evaluation. The accuracy of the method has been investigated for a variety of graded structures, and found to be better than 5%. As a test of its practical utility, the method has been used in the correction of the spreading resistance profile of a practical buried layer structure, and it has been found that the CPU time taken to correct the entire profile of 57 data points is 1.0 min on an IBM 1130 System with a 16K word (16 bit) memory or 0.4 sec on a UNIVAC 1100/10 Multiprocessor System with a 393K word (36 bit) memory. These times are a factor of 6 to 8 less than those required by using the previously proposed adaptive Simpson's rule to compute the correction factor integrals.     

An efficient numerical scheme for spreading resistance calculations based on the variational method

This paper presents a simple and efficient numerical scheme for evaluating the correction factor integrals that arise in the variational method. The scheme is a modification of one recently proposed by Berkowitz and Lux for the uniform flux method. The abscissae and the weights required for the integration are given in a form which allows the numerical scheme to be readily implemented. Using this scheme, it takes, on an average, 0.8 sec to compute one value of correction factor on an Apple II Microcomputer. For a slab of varying thickness, backed by either a perfectly conducting or a high resistivity substrate, the correction factors obtained agree with those derived from the exact constant-potential method to within 1%.     

Spreading resistance calculations for graded structures based on the uniform flux source boundary condition

In the approximate calculations of spreading resistance correction factors, two different types of boundary conditions over the source region have hitherto been assumed, viz., a uniform flux distribution, and the specific flux distribution that obtains in the classical solution for the infinitely thick slab. This paper presents results of a theory which has been derived for multilayer structures by using the uniform source flux distribution. The results given include those obtained for a series of exponentially-graded structures of varying steepness in the resistivity profile, whose thickness h₁ ranges from 0.1 to 10 times the circular source contact radius, a. The results show that, as a rule, for an insulating substrate and (h′₁/a) < 0.5, the uniform flux assumption leads to correction factors which differ at most by about 3% from those derived from the infinitely-thick slab flux assumption, while for a conducting substrate and (h′₁/a) = 0.1 to 10, there is a difference of about 8%. Whatever the nature of the resistivity profile studied, it has been found that the difference is never greater than about 8%.     

Adaptive thresholding by variational method

When using thresholding method to segment an image, a fixed threshold is not suitable if the background is uneven. Here, we propose a new adaptive thresholding method using variational theory. The method requires only one parameter to be selected and the adaptive threshold surface can be found automatically from the original image.     

Spreading resistance in submicron MOSFET's

The spreading resistance due to current crowding at the end-points of an FET channel is investigated. An analytic expression is derived giving this resistance as function of a few parameters. Two-dimensional numerical simulations, using finite-element techniques, confirm the accuracy of the simple analytical approach. For short channel devices the current crowding effect is found to give a nonnegligible contribution to the total source resistance. In order to optimize the FET performance, the geometry and conductivity of the source/drain regions must be carefully designed, trading off short channel effect and transconductance degradation.     

Spreading resistance of multiple-layer cylindrical structures

The potential distributions and spreading resistances of multiple-layer cylindrical structures are analysed. Computed results are compared with the measured thermal impedance of a practical heatsink.     

Spreading resistance correction formula more suited for the Gauss-Laguerre quadrature

A modified formula is derived for the calculation of the correction factor in spreading resistance measurements. Due to its better convergence this formulation yields more accurate results when the Gauss-Laguerre quadrature formulae are used for the integration. In this way the obtained accuracy is found to be always better than 0.15% compared to 1.3% when the classic formulation is used. A very high accuracy for the correction factor is shown to be very important since an error of 2% in the correction factors may result in a 16% error in the derived resistivities.The CPU time when using the new formula is always smaller than or equal to the time used for the classic formulation and is typically about 15 seconds on a IBM 3033 computer for the calculation of 300 points.     

A variational method for multiple-image blending

The main aim of this paper is to develop an algorithm for blending of multiple images in the image-stitching process. Our idea is to propose a variational method containing an energy functional to determine both a stitched image and weighting mask functions of multiple input images for image blending. The existence of the solution of the proposed energy functional is shown. We also present an alternative minimizing algorithm to solve the proposed model numerically and show the convergence of this algorithm. Experimental results show that the proposed model works effectively and efficiently and that the proposed method is competitive with the tested existing methods under noisy conditions.     

Modal analysis of strip-loaded diffused optical waveguides by a variational method

The propagating modes supported by strip-loaded three-dimensional diffused optical waveguides are analyzed in detail theoretically by using a variational method. Some typical numerical examples of the propagation constants and the field distributions are illustrated. The dependence of propagation characteristics on the geometrical parameters of the loading dielectric strip is discussed.     

On the variational aspects of the moment method [electromagnetics]

The variational properties of the moment method as applied via the electric field integral equation (EFIE) to perfectly conducting radiators and scatterers with time-harmonic excitation are discussed. It is shown that the admittance, impedance, gain and radar cross-section can be expressed in terms of the self-reaction or the mutual reaction of the electric current distribution induced on the body. Subject to the above restrictions and assuming the usual reciprocity theorems are applicable, it is shown that the reaction is stationary with Galerkin's method, but it is not when the non-Galerkin moment method is applied in the customary manner. Numerical results are included to compare the performance of the variational and nonvariational moment method     

A multilayer exponential model for spreading resistance calculations

A new multilayer approach to spreading-resistance correction-factor calculations is proposed, based on the approximation of the graded resistivity profile by a series of exponential functions. The existence of a recurrence formula for the integration factor in the correction factor integral makes the proposed model a practical alternative to Schumann and Gardner's staircase model. Although a factor of 3 slower in terms of computation time, the exponential model yields results much closer to the true profile than the staircase model, particularly in cases where the profile has very steep gradient but where the available measurement data points are sparse.     

A variational method for designing adaptive bandlimited wavelets

This paper proposes a new method of estimating an orthogonal bounded spectrum wavelet from a given signal. The method is based on minimizing the distance of the wavelet and the given signal in the sense of the metric of the L ² space. In this method, the amplitude and phase of the mother wavelet are optimized simultaneously. The Lagrange multipliers technique is applied to consider the constraints due to the bounded spectrum wavelet and orthogonality conditions. The variational method reduced the optimal matching problem to the solution of a set of functional equations for the amplitude and phase of the optimal-matched bandlimited wavelet spectrum. Continuous functional equations are written with respect to Fourier coefficients of phase of transfer function of the quadrate low-pass filter at the sampled frequencies, and asset of discrete algebraic equations allows us to design the wavelet directly from the signal of interest. To demonstrate the performance of the presented method in this paper, it is employed to determine the matched wavelets of some specified signals.     

An algebraic method for reliability calculations

This paper evaluates the reliability behaviour of a complex system consisting of three sub-systems G₁, G₂ and G₃ connected in parallel redundancy (1-out-of-3: G). These sub-systems are nothing but three power generators in a power house which are connected with switching devices. By the application of Boolean function technique and the theorem of summation of probabilities of compatible events, a symbolic expression for reliability of such a complex system has been evaluated by considering that failure times for various components of the complex system follow arbitrary distributions. In particular, reliability has been evaluated for exponential and Weibull distributions. Moreover, an important parameter, viz. MTTF, has also been computed for exponential failure rates of the units comprising the system. A numerical example, along with graphs, is discussed at the end to highlight the important results.     

Postprocessing of FDTD solutions for precise calculations of eigenfrequencies of photonic periodic structures utilizing the variational expression

This paper presents a method that improves by orders of magnitude the accuracy of the finite-difference time-domain (FDTD)-calculated eigenfrequencies of photonic crystals. The method utilizes a variational expression for the eigenfrequencies of periodic structures. Applications to perfect crystals, waveguides, and resonant cavities are demonstrated. The paper confirms that the method can reduce the computational time by more than 90% while obtaining accuracy in frequency comparable to that obtained solely by the conventional FDTD method.     

Microwave measurement of surface resistance by the parallel-platedielectric resonator method

Analysis and experimental results are presented for a parallel-plate dielectric resonator method to measure the surface resistance of conducting or superconducting plates. In the present paper, three main questions are considered in detail: the influence of the relative sizes of the conducting or superconducting plates on the measured value of the surface resistance R_s; the influence of the shape of the plates on the R_s measurement; and how to interpret obtained results. Measurements were made at resonant frequencies of 14.1-14.5 GHz in a temperature range between 77 and 300 K     

Bistatic RCS calculations with the vector parabolic equation method

The vector parabolic equation (PE) method provides accurate solutions for electromagnetic scattering from three-dimensional (3-D) objects ranging from a size comparable to the wavelength of the incident wave to several tens of wavelengths. A paraxial version of Maxwell's equations is solved with a marching solution that only requires limited computing resources, even for large scatterers. By decoupling the PE paraxial direction from the direction of incidence, the bistatic radar cross section (RCS) can be computed at all scattering angles. A sparse-matrix formulation is used to implement electromagnetic boundary conditions, ensuring that polarization effects are treated fully. Computing costs are kept to a minimum through the use of a double-pass method so that calculations can be carried out on a desktop computer for realistic targets and radar frequencies. The method has been validated on simple canonical shapes and tested on complex targets     

Numerical instabilities of the moment method in waveguide calculations

Unstable results were obtained when utilising the moment method in parallel-plate-waveguide problems. The cause of the instability is determined. The introduction of a missing boundary condition leads to very satisfactory numerical results.     

Capacitance calculations for cable harnesses using the method ofmoments

A method of moments procedure to obtain the capacitance matrix for a cable harness is presented. The geometry consists of multiple, parallel, insulated wires, possibly above a ground plane. The method uses Fourier harmonic expansion functions for the total charge and Galerkin testing functions. The capacitance matrix is obtained by the relationship of free charge to potential. Computed and experimental results are presented and compared to exact analytical solutions when possible