# Passive Intermodulation at Contacts of Rough Conductors
###### Abstract  
Passive intermodulation (PIM) is a niggling phenomenon that debilitates the performance of modern communications and navigation systems. PIM products interfere with information signals and cause their nonlinear distortion. The sources and basic mechanisms of PIM have been studied in the literature but PIM remains a serious problem of signal integrity. In this paper, the main sources and mechanisms of PIM generation by joints of good conductors are discussed. It is shown that the passive electrical, thermal and mechanical nonlinearities are intrinsically linked despite their distinctively different time scales. The roughness of the contact surfaces plays an important role in PIM generation by conductor joints. A review of the PIM phenomenology at the contacts of the good conductors suggests that novel  
processes [37, 40, 46, 47], surface roughness [32, 48, 49] and contact mechanical deformations [49, 50, 51, 52, 53]. The advent of micro-electro-mechanical systems (MEMS) has sparked extensive investigations of the electrical contacts with rough surfaces and their RF performance. Whilst the mechanical properties of MEMS have been explored in great detail (see [50, 51, 52, 53] and references therein) the existing models were developed for the linear devices operated with weak RF signals. The effect of high RF power on the contacts and junctions of conductors with rough surfaces were studied only in coaxial connectors [38, 39, 40] and waveguide flanges [54]. The practical means of mitigating nonlinear distortions and PIM in passive RF circuits remain predominantly semi-empirical [10, 55]. The analysis and prediction of PIM effects with the aid of multiphysics models proved to be a challenging task. The published PIM studies are normally limited to a single dominant mechanism of nonlinearity. However, the stochastic nature of multifarious sources of weak nonlinearities and their intrinsic links dictates the need for multiphysics models and novel simulation tools. The diverse physical nature of PIM sources also requires that several concurrent mechanisms of nonlinearity are considered together. It is necessary to note that the linearisation techniques used for power amplifiers are not suitable for mitigating PIM in the passive components of RF front-end and antennas due to absence of the real-time feedback required for signal predistortions.) PIM products generated by junctions of conductors with rough surfaces are usually characterised with the aid of the equivalent electrical circuit models. The lumped element model, proposed in [54], has been applied to the analysis of PIM in waveguide flanges where the physical dimensions of surface asperities are much smaller than the wavelengths of high-power RF signals. The parameters of this equivalent circuit depend not only on the electrical properties of the contact materials but also on their thermal and mechanical properties and the surface finish. Therefore, the concurrency of multiphysics effects is an essential feature of PIM in passive RF circuits and devices. The PIM in coaxial connectors has recently been examined in [56, 57, 58] with the help of an equivalent circuit model from [54]. The relationship between an applied force and a contact linear resistance is evaluated in [59] using [PERSON]'s _empirical_ law. It suggests that the contact resistance decreases as the square root of applied force when nonlinearity is approximated by a Taylor series. The simulation and measurement results presented in [59] are in fair agreement owing to the empirical description of the linear elements and data fitting for the nonlinear sources. The main types of contact nonlinearities in the conductor joints and connectors can be cast in the three broad groups: (i) electrical, (ii) thermal and (iii) mechanical.