Electrical lengths and phase constants of stretchable coplanar transmission lines at GHz frequencies

Elastic, bendable and stretchable electronics establish a new and promising area of multi-physics engineering for a variety of applications, e.g. on wearables or in complex-shaped machine parts. While the area of metamorphic electronics has been investigated comprehensively, the behavior at radio frequencies (RFs), especially in the GHz range, is much less well studied. The mechanical deformation of the soft substrates, for instance, due to stretching, changes the geometrical dimensions and the electrical properties of RF transmission lines. This effect could be desirable in some cases, e.g. for smart devices with shape-dependent transmission or radiation characteristics, or undesirable in other cases, e.g. in feed and distribution networks due to the variable electrical lengths and thus phase variations. This contribution describes the results of a systematic study of the broadband RF properties of coplanar transmission lines on Ecoflex (R) substrates, based on numerical simulations and experimental data. Two types of stretchable transmission line structures were studied: Meander- and circular ring-segmented lines. Modeling and simulation were performed combining a 2D circuit simulation software with electromagnetic full-wave simulations. The experimental part of the work included the fabrication of metamorphic substrates metallized with thin copper layers and systematic measurements of the electrical lengths and phase constants of coplanar waveguides in the frequency range from 1 to 5 GHz based on vector network analysis for different stretching levels. With the given substrate technology, we succeeded in demonstrating stretchability up to a level of 21%, while the theoretical limit is expected at 57%. The meander- and circular-shaped line structures revealed markedly different sensitivities to the stretching level, which was lower for circular structures compared to the meander structures by approximately a factor of three.