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

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 $(ω0)$ are roughly independent of $N$⁠, whereas the characteristic impedance $(Zc)$ is proportional to $1/N$⁠, where $N$ represents the number of contact points. The implications of these findings are discussed.