Propagation Constants of a Waveguide Containing Parallel Sheets of Finite Conductivity

The propagation constants of a rectangular waveguide containing periodic, parallel sheets having finite conductivity were determined using an iterative computer program. The dispersion equation was found in a matrix formulation which was conducive to computer solution. This equation was solved for various values of conductivity and sheet spacing. Comparisons were made with the propagation constants found assuming an infinite array of thin parallel resistive sheets in free space for the case where the direction of propagation and the electric field vector were both parallel to the sheets. The propagation constants for the infinite array case have been determined by both conformal mapping techniques for certain limiting conditions and by a computer solution of the dispersion equation for sheet spacings and conductivities of interest. The results should prove useful for the design of absorbing elements and terminations for waveguides.     

Compact Subthreshold Current Modeling of Short-Channel Nanoscale Double-Gate MOSFET

A physics-based compact subthreshold current model for short-channel nanoscale double-gate MOSFETs is presented. The potential is modeled using conformal mapping techniques in combination with parabolic approximations. For subthreshold conditions, we have assumed that the electrostatics is dominated by capacitive coupling between the body electrodes. Hence, the potential is obtained as an analytical solution of the 2-D Laplace equation. The current modeling is based on drift-diffusion theory. The modeling results are in good agreement with those of numerical simulations without the use of adjustable parameters.     

Numerical Stability and Numerical Dispersion of Compact Conformal Mapping 2D-FDTD Method Used for the Dispersion Analysis of Waveguides

In dispersion analysis of waveguides with particular cross-section by compact 2D-FDTD method, using conformal-boundary coordinates can obtain high computational accuracy. The transformation from conformal-boundary coordinates to rectangular coordinates can be done by conformal mapping technique in order to match Yee algorithm. In this paper, numerical stability and numerical dispersion equation of compact conformal mapping 2D-FDTD (CCM-2D-FDTD) method are derived. It is shown that the upper limit of Courant number for CCM-2D-FDTD is always smaller than 1/√2. As an example, the dispersion equation is used to examine the impact of number of cell for circular waveguide.     

A Method of Calculating the Characteristic Impedance of a Strip Transmission Line to a Given Degree of Accuracy

The calculation of the characteristic impedance of the strip transmission line TEM-mode can be reduced to the solution of a two-dimensional potential equation with the strip cross section determining the boundary conditions. Usually this potential equation is solved by conformal mapping, but only the most simple shapes permit exact mapping. Approximations may require considerable work and their accuracy is uncertain. This paper describes an alternative numerical method which is particularly suitable for boundaries consisting of any number of straight lines and right angles. It is based on relaxation methods, but by using also variational principles it derives an approximate value for the impedance, and an upper and lower bound with a difference as small as desirable.     

The Discrete Variational Conformal Technique for the Calculation of Strip Transtission-Line Parameters

This paper describes a new method of obtaining the transmission line properties of strip transmission lines whose geometrical configurations would make them difficult to analyze with other available techniques. The Discrete Variational Conformal (DVC) technique relies on conformal transformations to obtain the simplest possible representation of the Green function for the configuration of interest. This Green function is then used with an assumed charge distribution in the plane of the original configuration, and in a novel variational expression for the modal capacitance. The resulting equation is particularly well suited for numerical evaluation. Sample configurations are used to compare DVC to other techniques: Exact conformal mapping, Method of Moments, Full Wave solutions, and a Transverse Transmission Line Method. Two examples of application of DVC to asymmetric configurations are given.     

Companding and random quantization in several dimensions

The problem of implementing multidimensional quantizers is discussed. A general equation is derived that can be used to evaluate the performance of multidimensional compandors. It is demonstrated that the optimal compandor must be conformal almost everywhere. An example is given to show that asymptotically optimal performance could be obtained through nonconformal companding schemes. Random quantizers are discussed and two techniques are evaluated for reducing memory and computation time in the implementation of such devices.     

计算复杂形状波导截止频率的高效方法

提出一种使用保角变换结合矩量法,计算复杂形状波导截止频率的新方法,该方法采用解析法或数值法,把复杂截面的波导变换为圆形区域,再采用矩量法求解波导的截止频率。实验结果验证了该方法的有效性。     

Transmission-Line Properties of Parallel Strips Separated by a Dielectric Sheet

A transmission line is made of a symmetrical pair of strip conductors, or a single strip and a ground plane, on opposite faces of a sheet of dielectric material. There is computed, to a close approximation, the relations among the dielectric constant of the sheet, the effective dielectric constant of the sheet and the empty space, the shape ratio, and the wave resistance, for the entire range of possible values. These relations are summarized in a graphical chart covering the range of practical interest. The computation is based on conformal mapping of the dielectric boundary on coordinates such that its effect can be most closely evaluated by simple principles. All relations are approximated in terms of ordinary functions (exponential and hyperbolic). Of particular interest is the effective filling fraction of the dielectric material, which depends mainly on the shape ratio and only slightly on the dielectric constant. Explicit formulas are given for analysis or synthesis.     

Three-Dimensional Closed-Form Model for Potential Barrier in Undoped FinFETs Resulting in Analytical Equations for $V_{T}$ and Subthreshold Slope

An analytical approach for modeling the electrostatic potential in nanoscale undoped FinFETs is derived. This method uses a 2-D solution for this potential within a double-gate FET and takes into account the top gate electrode as the third dimension by applying the conformal mapping technique. Herewith, an analytical closed-form model for the height of the potential barrier below threshold is defined which includes 3-D effects. From that, models for subthreshold slope and threshold voltage of nanoscale triple-gate FETs are derived. The results are in good agreement with numerical device simulation results and measurements for channel lengths down to 20 nm.      

A new analytical method of solving 2D Poisson''s equation in MOS devices applied to threshold voltage and subthreshold modeling

In this paper we present a new theoretical approach in MOS modeling to derive analytical, physics-based model equations for the geometry and voltage dependence of threshold voltage and for the subthreshold behavior of short-channel MOSFETs. Our approach uses conformal mapping techniques to analytically solve the two-dimensional Poisson equation, whereby inhomogeneous substrate doping is taken into account. The presented model consists of analytical equations in closed form and uses only physically meaningful parameters. Therefore, the results are not only useful in circuit simulators but also in calculations of scaling behavior, where planned processes can be investigated. Comparison with numerical device simulation results and measurements confirm the high accuracy of the presented model.     

Analysis of Hall-plate shaped Van der Pauw structures

This paper considers circular and rectangular Van der Pauw structures with finite edge contacts, having two orthogonal axes of symmetry. Using conformal transformations, analytical solutions of the potential problems have been found. Approximate formulae are also given (a) for the circular sample if the contacts are small, and (b) for the rectangular sample if one pair of contacts is small and the other pair coincides with the short sides. It is shown that rectangular Hall plates can be used for measurements of sheet resistance at zero magnetic field. For the latter case numerical results are tabulated.     

An exact derivation of contact resistance to planar devices

An imperfect, rectangular contact to a semiconducting sheet is formulated as a mixed boundary-value problem. This problem is solved by conformal mapping to yield the complex potential function as an eigenfunction expansion. The result can be used to calculate exact contact resistance if specific contact resistivity is known. With voltage probing data, it can also be used to confirm estimates of specific contact resistivity. The expression for contact resistance resembles that for a perfect (lossless) contact^1–2 but includes an extra term involving the lowest-order coefficient a₀ from the expansion. Contact resistances are calculated and compared with the values obtained from three approximate models; the lossless contact, transmission line,^3–4 and extended transmission line models.^5–6 Up to a common normalization constant, the contact resistances predicted by all models are completely determined by two dimensionless parameters. These define the validity ranges for the approximate models. Compared to the present model, the extended transmission line model appears to be a very satisfactory approximation if the ratio of electrode length to sheet thickness is not less than 0.5.     

Millimetric V-groove guide and components

A characteristic equation of single V-groove guide has been derived using the transverse resonance technique. This equation is much less complex and tedious to solve when compared with that obtained by the conformal mapping technique. The computed results are within 1% of the published experimental values for the cut-off wavelengths at X-band and 100 GHz. The present analytical approach is to approximate the central groove region by a large number of rectangular steps and the previously derived analytical solution for the rectangular-groove guide are applied to predict the propagation characteristics of single V-groove guide. A number of components in V-groove guide which have very similar characteristics to those of the rectangular-groove counter-part have been reviewed. It is noted that both the E-plane and H-plane cylindrical bends in both rectangular-groove and V-groove guides had unacceptably high-loss and a satisfactory solution have yet to be reached.     

平面镜像法与有源保角变换

本文把镜像法与复保角变换有机地结合起来。指出对于实际中的一大类问题,只须采用平面镜像做基本模型,而对复杂形状作有源保角变换,就可以归结为平面镜像。特别有兴趣的是变换后的求解区域可以允许存在原问题∞处的镜像电荷,从而突破了一般镜像法的一个准则。     

Comments On "Conformal Transformations Combined With Numerical Techniques, With Applications To Coupled-Bar Problems"

The writer lists additional references on recent developments on the conformal mapping method which may be of interest to microwave specialists.     

Quasi-static solutions of multilayer elliptical, cylindrical coplanar striplines and multilayer coplanar striplines with finite dielectric dimensions - asymmetrical case

In this paper, fast, accurate, and simple analytic closed-form expressions are presented in order to calculate the quasi-TEM parameters of multilayer elliptical coplanar stripline (CPS), multilayer cylindrical CPS, and multilayer CPS, with finite dielectric dimensions by using conformal mapping techniques. The obtained computer-aided-design-oriented expressions are quite accurate and easy to apply in designing microwave integrated circuits and antenna applications. The results have also been compared with the ones of another conformal mapping method available in the literature and also confirmed analytically.     

Characteristic impedance of coaxial lines bounded by N-regular polygons

A very simple equation based on conformal mapping and domain variational theory is given for the characteristic impedance of a coaxial system consisting of an N-regular polygon and a circle.     

A general approach to analysis of distributed resistive structures

A new general method for calculation of thin-film-distributed resistive structures is presented. This method is based on the conformal mapping of the analyzed domain on the complex upper half-plane and the determination of the complex potential function as the solution of a boundary-values Volterra problem. Although the method inherently applies only to single-connected domains with known conformal representations on the upper half-plane, it may be extended also to other symmetrical multiple-connected configurations and in all cases when the positions of the conducting terminals in the upper half-plane are known. Two examples of application are given.     

Finite boundary corrections to coplanar stripline analysis

Analytic closed-form expressions for impedance and effective dielectric constant for coplanar striplines (c.p.s.) with finite substrate thickness are obtained using conformal mapping techniques. The limit, beyond which the results of an infinite dielectric approximation are no longer valid, is presented.     

Theoretical and experimental characteristics of single V-grooveguide for X-band and 100 GHz operation

A conformal mapping technique for single-groove guide is discussed and applied to grooves of V-shaped cross section. The approach is to transform the V-groove guide into the parallel-wall guide filled with a nonisotropic and nonuniform medium. Experimental measurements at X-band and 100 GHz confirm the theoretical predictions. The characteristic equation and scale factor of the fundamental mode are developed, and its propagation characteristics are given graphically for several normalized groove dimensions