Method of Modal Parameters for the Thin-Wire Open-Circuit Wiring Structures and the Singularity Expansion Method

Different numerical methods (MoM, FDTD, etc.) can be used to calculate currents and voltages induced in wiring systems by external EM fields, but they are not very helpful to gain insight into the physics of coupling phenomena, especially in time domain. In contrast, the analytical singularity expansion method (SEM) represents the scattering objects as a set of oscillators, thus giving a physically transparent tool for the description of the coupling phenomena, both in frequency and time domain. The set of SEM poles yields the main contribution for the response function (functional) of the transmission line to the excitation. It also defines the scattering amplitude, response in the time domain, etc. Studies of SEM poles were carried out earlier by analyzing the results of numerical calculations using the Method of Moments (NEC), or using approximate analytical methods for long horizontal wires above ground. Recently, we have proposed to use the previously developed method of modal parameters (MoMP) for the analysis of poles in short-circuited wire structures of arbitrary geometric shape.
In this work, we apply the method of modal parameters for investigation of SEM poles of open-circuit wires. The main accent is done for investigations of pieces of symmetrical wire structures: a straight finite wire in free space, a straight finite wire parallel to a PEC ground, a circle arc and a helix segment. The symmetry of these structures allows a fast calculation of matrix elements in the MoMP, especially for the straight wire where one can obtain explicit analytical result and investigate poles of high layers. The investigation has shown that the real part of the SEM poles for a finite straight wire in free space, a finite straight wire above a ground plane and a circular arc wire increases monotonically with increasing the number of the pole. In contrast, for a large segment of the helix wire, a more complex dependence of the real part of the SEM pole on its number n is observed. This is due to the fact that for some numbers n of the pole there are effective common modes of the current, which corresponds to strong radiation and a large real part of the SEM poles, and for some $n$ there are effective differential modes, which corresponds to weak radiation and a small real part of the SEM poles.