Lumped circuit elements, statistical analysis, and radio frequency properties of electrical contact

摘要

The lumped circuit elements representing electrical contact of a single and multiple contact points are constructed. The local electrical contact is assumed to be in the form of a cylindrical constriction (connecting bridge) of radius a and axial length 2h, made of the same material as the main conducting current channel of radius b. The resistance, capacitance, and the inductance of the electrical contact are given in terms of a, b, and h, from which the rf properties of electrical contact are obtained. For the case of conducting surfaces with a single connecting bridge with dimension in micron size, the resulting resonant frequency is found to be in the terahertz regime. A statistical analysis on a distribution of these dimensions follows. It is found that for multiple contact points, the quality factor (Q) and the resonance frequency (ω_0) are roughly independent of N, whereas the characteristic impedance (Z_c) is proportional to 1/N, where N represents the number of contact points. The implications of these findings are discussed.