Simple expressions for constriction resistance of multitude conducting spots were analytically formulated by Greenwood. These expressions, however, include some approximations. Nakamura presented that the constriction resistance of one circular spot computed using the BEM is closed to Maxwell's exact value. This relative error is only e=0. 00162 [%]. In this study, the constriction resistances of two, five and ten conducting spots are computed using the boundary element method (BEM), and compared with those obtained using Greenwood's expressions. As the conducting spots move close to each other, the numerical deviations between constriction resistances computed using Greenwood's expressions and the BEM increase. As a result, mutual resistance computed by the BEM is larger than that obtained from Greenwood's expressions. The numerical deviations between the total resistances computed by Greenwood's expressions and that by the BEM are small. Hence, Greenwood's expressions are valid for the total constriction resistance calculation and can be applied to problems where only the total resistance of two contact surfaces, such as a relay and a switch, is required. However, the numerical deviations between the partial resistances computed by Greenwood's expression and that by the BEM are very large. The partial resistance calculations of multitude conducting spots are beyond the applicable range of Greenwood's expression, since Greenwood's expression for constriction resistance of two conducting spots is obtained by assuming that the conducting spots are equal size. In particular, the deviation between resistances of conducting spots, which are close to each other, is very large. In the case of partial resistances which are significant in semiconductor devices, Greenwood's expressions cannot be used with high precision.

In this paper, we present an analysis of the microstrip lines whose strip conductors are of various cross-sections, such as rectangular cross-section, triangle cross-section, and half-cycle cross-section. The method employed is the boundary integral equation method (BIEM). Numerical results for these microstrip lines demonstrate various shape effects of the strip conductor on the characteristics of lines. The processing technique on the convergence of the Green's function is also described.

In this paper, we present an analysis of microstrip line with a trapezoidal dielectric ridge in multilayered media. The method employed in this characterization is called partial-boundary element method (p-BEM) which provides an efficient technique to the analysis of the structures with multilayered media. To improve the convergence of the Green's function used in the analysis with the P-BEM, we employ a technique based on a combination of the Fourier series expansion and the method of images. Treatment on convergence for the boundary integrals is also described. After this treatment, it requires typically one tenth or one hundredth of Fourier terms to obtain the same accuracy compared with the original Green's function. Numerical results are presented for two microstrip lines that have a trapezoidal dielectric ridge placed on a one-layered substrate and a two-layered substrate. These numerical results demonstrate the effects on the characteristics of the microstrip line due to the existence of the dielectric ridge as well as the second layer between the ridge and the fundamental substrate.

For the expansion of using the integral equation methods on wave-field analysis, a new method called "Source and Radiation Field Solution" is suggested. This solution uses a couple of integral equations. One of them is the traditional integral expression giving the scattered field from the wave source, another is newly proposed one which expresses the wave source from both of the source and the scattered field, by using the conjugate Green function expression. Therefore this method can derive both of the source and the scattered field at the same time by coupled two equations. For showing the effect of this method, we analyze scattering problems for dielectrics in this paper.

In this paper, we present for the first time two three-dimensional analytical electrostatic Green's functions for shielded and open arbitrarily multilayered medium structures. The analytical formulas for the Green's functions are simply expressed in the form of Fourier series and integrals, and are applicable to the arbitrary number of dielectric layers. In combination with the complex image charge method, we demonstrate an efficient application to analyze microstrip discontinuities in a three-layered dielectric structure. Numerical results for the capacitance associated with on open-end discontinuity show good agreement with those from a previous paper and the effectiveness of using the analytical Green's functions to analyze three-dimensional electrostatic problems.

In this paper, we presented an analysis of single and coupled microstrip lines covered with protective dielectric film which is usually used in the microwave integrated circuits. The method employed in the characterization is called partial-boundary element method (p-BEM). The p-BEM provides an efficient means to the analysis of the structures with multilayered media or covered with protective dielectric film. The numerical results show that by changing the thickness of the protective dielectric films such as SiO2, Si and Polyimide covered on these lines on a GaAs substrate, the coupled microstrip lines vary within 10% on the characteristic impedance and within 25% on the effective dielectric constant for the odd mode of coupled microstrip line, respectively, in comparison with the structures without the protective dielectric film. In contrast, the single microstrip lines vary within 4% on the characteristic impedance and within 8% on the effective dielectric constant, respectively. The protective dielectric film affects the odd mode of the coupled lines more strongly than the even mode and the characteristics of the single microstrip lines.