A cylindrical multiconductor stripline-like microstrip transmissionline

An analytical expression for the Maxwell capacitance matrix of a class of cylindrical inhomogeneous, multiconductor transmission lines is provided. This class includes cylindrical structures symmetrical with respect to the circuit circle and having a symmetry axis. The effective dielectric constant of the line is found to be the arithmetical mean of the dielectric constants of the two media. Hence, this structure enjoys the main advances of the planar stripline-like microstrip systems. It is also pointed out how to obtain elliptical stripline-like microstrip transmission lines     

An intermediate crack model for flaws in piezoelectric solids

Summary The aim of this paper is to study a crack model for piezoelectric bodies. In recent years it became evident that the electrically impermeable or the perfect electric contact boundary conditions on the crack faces are inadequate for many physical situations, over- or underestimating the electric field influence on the propagation process. The crack model here investigated is intermediate between these two limit cases. The generalized plane problem for an infinite piezoelectric body with a central crack is converted into a system of integro-differential equations, then reduced to an integro-differential equation similar to Prandtl's equation of aerodynamics. For poled ceramics with transversely isotropic symmetry, the integral equation is numerically solved using quadrature formulae for both plane and antiplane states of deformation. The energy release rate calculated with the discrete solution is then compared with that given by the exact solution for an elliptic hole embedded in the infinite piezoelectric body. A range of values of the cavity thickness is found, for which the considered crack model is a good approximation of the exact two-body problem, while the impermeable and the perfect contact models are not appropriate.     

An analytical solution for the coupled stripline-like microstripline problem

An analytical method is presented for determining the Maxwell's capacitance matrix of multiconductor shielded microstrips with coupled conductors of arbitrary widths, spacings, and inhomogeneous media, in terms of elliptic integrals. The method is based on conformal mapping and the theory of singular integral equations. Two kinds of problems are presented as examples: the first consists of simple structures with one or two coupled striplines; the other type concerns the general case of multiconductor coupled structures for which simple analytical expressions are not available     

Uniform asymptotic solutions for the two-dimensional potential field problem with joining relations on the surface of a slender body

The 2-dimensional potential field in the whole plane with joining relations on the surface of a slender cylindrical body is studied. The inner solution is obtained by means of a regular perturbation problem and the outer solution is represented as a super position of potentials of point sources and point currents distributed on a segment inside the body. The problem is then reduced to a system of integral equations whose solution is obtained by using the method of Handelsman and Keller. As particular cases the Dirichlet and Neumann boundary-value problems for the domain exterior to a slender body are considered. The paper gives the asymptotic expansion of the logarithmic potential on a segment and some quadrature formulae useful for computing the solution as well.     

An analytical solution to the microstrip line problem

An analytical method for determining the line capacitance of a microstrip line is presented. The solution is exact, but it is expressed by means of the solution of an infinite system of linear equations whose coefficients are the result of certain numerical quadratures. The analysis is carried out for the case of two dielectric substrates. Changes to include additional stratified layers are readily available using the transfer matrix method described by P.M. van Berg et al. (1985). Comparison of the results obtained using the proposed formula with those obtained using exact formulas (available in particular cases) shows that, in cases of practical interest, it is sufficient to consider only the first two equations in the above-mentioned infinite set of linear equations     

Uniform asymptotic solutions for small and large sessile drops

Summary The problem of determining the equilibrium shape of either a small or large sessile drop is studied. By the correspondence principle, the problem of approximating the static meniscus in a vertical right circular cylinder is also solved. A parameter is introduced which is ratio of the physical length scale to the capillary length scale. Perturbation solutions, which are uniformly valid over the entire surface of the drop, are obtained for either small or large values of using the method of successive substitutions. Comparisons of the results with solutions obtained by other approximate methods are presented and discussed. The solutions for small and large values of are then combined using an ad hoc, but straightforward, technique, resulting in an approximate solution which is valid for all positive values of the parameter .     

Asymptotic solutions for two-site non-equilibrium transport

Summary The steepest descent method is used to ascertain the large-time behavior of solute concentrations in homogeneous porous media as determined by advection, diffusion and adsorption-desorption processes; it is found that linear non-equilibrium processes do not, asymptotically, affect the characteristic dispersion length of the transport medium.     

An analytical approach to the analysis of dispersioncharacteristics of microstrip lines

An analytical method for determining the dispersion characteristics of microstrip lines is given. The method uses dual integral equations. The analysis is rigorous, and it expresses the solution of the dispersion equation in terms of the solution of a double infinite system of linear equations. The system coefficients are given by certain quadratures. The numerical examples reveal the high convergence order of the method