Measurement of conductivity of carbon fibers at microwave frequencies

The paper presents results of measurements conductivity of carbon fibers from DC to 13 GHz. The measurements were performed on the microstrip measurement line, where a section of the line is made from a flat tow of carbon fibers. Physical conductivity of carbon fibers is derived from the measured value of S21 of the section of microstrip line in two steps. First, a tow of fibers is replaced by a homogenous material having an unknown effective conductivity. Then S21 of the section of the microstrip line having metallization made from the effective media is analyzed by 3D fullwave simulation program for a range of effective conductivities. The actual effective conductivity is found iteratively to match the measured and simulated S21 coefficients. Second, S21 of the planar slab having the effective conductivity obtained in the first step is calculated analytically. Then the slab is assumed to have a real microstructure with densely packed carbon fibers. The physical conductivity of the fibers is found iteratively by a local optimization technique, to match the analytical value of S21 and S21 obtained by the fullwave FEM simulation for the slab with carbon fibers.