A Geometric Modeling Approach for Flexible, Printed Square Planar Inductors under Stretch

In this work a compact model for square planar inductors printed on flexible substrate is proposed. The approach considers the deformation of the metal traces of square spiral inductors when the substrate is subjected to physical stretch. The model considers a typical pi-network for the device, where each component is calculated for different stretching values adapting widely accepted models on the literature for the total inductance, the AC resistance and the ground coupling and inter-wounding capacitances. Model results are contrasted to 3D full electromagnetic wave simulations under parametric sweeps of the dimensions calculated under stretch. Results show good agreement within a 20 % stretch up to the first resonance frequency of the structure. The model can prove useful for the optimization of component design for printed applications on flexible substrates.