Conductivity Measurement of E-textiles using a Microstrip Ring Resonator

Abstract

A conductivity measurement technique applicable for highly conductive textile materials is presented in this work. We employ a microstrip ring resonator as a test fixture to ease sample preparation and to increase measurement sensitivity. With this, the conductivity of a thin textile can be measured up to 10 6 S/m at 2 GHz. The conductivity value is extracted by comparing the measured and simulated transmission coefficients in an active learning iterative solver based on the surrogate-based optimization. The conductive textiles under test were Zelt and silver-coated e-textile, and the resulted conductivities are 2.29x10 5 and 3.47x10 5 S/m, respectively. These values are close to the DC conductivity given by the manufacturers. Keyword-Conductivity, e-textile, microwave, ring resonator, surrogate-based optimization. I. INTRODUCTION Conductive textiles have been progressively used for designing wearable antennas in Wireless Body Area Network (WBAN) communications and Internet of Things (IoT) applications [1]-[2]. They are highly flexible, durable and restorable, allowing direct integration onto clothing by ordinary sewing or embroidering techniques. They also offer low sheet resistance suitable for efficient current transmission without significant ohmic loss. The usual sheet resistance (R s) of conductive textiles in the market ranges from 0.04~0.4 Ω/sq [3]. In other words, the conductivity (s) is 1.4x10 5-1.3 x 10 6 S/m based on the formula  = 1/(R s t), where t is the thickness of the textile. These values are measured at DC using the well-known four-point-probe or Van der pauw method. For a wearable antenna application, however, it is necessary to acquire  or R s in the microwave regime to promote accurate antenna modeling. In contrast to copious measurement techniques for the permittivity of dielectrics, there is considerably less reported for the conductivity measurement of highly conductive materials ( > 10 5 S/m) at microwave frequencies (> 1 GHz) [3]-[4]. In these methods, resonators are mainly used as a test fixture to capture a slight variation in the quality factor (Q-factor) of low conductive loss materials. Furthermore, the resonators are often in a planar form to ease the measurement of thin foil or textile samples. The material's  is obtained by detecting the perturbation of Q-factor represented in a closed-form equation under the assumption that the radiation loss is trivial. However, in practice, the radiation loss of the half-opened planar resonator may mislead the extracted  and should not be overlooked. As an alternative, full-wave simulation data can be used instead of the approximate closed-form equation to estimate . In a full-wave simulation tool, a resonator identical to the measurement is modeled, and then the simulation data is collected by varying the material property (e.g., ) of a sample under test. Subsequently, the measured and simulation data are compared in an optimization algorithm to find the best fit. Recent reports have verified the effectiveness of this method for the measurement of the dielectric constant ( r) and loss tangent (tan) of an antenna substrate [5]-[6]. In this letter, we propose a conductivity measurement method employing a planar ring resonator. Due to its highly resonating nature at the GHz frequency band, the ring resonator has been previously used for the characterization of low-loss substrates [7]. As in Fig. 1, the planar ring is formed by the conductive textiles of interest. Besides, we use the surrogate-based optimization (SBO) [8] as an adaptive search algorithm to extract s of the ring from the measured and simulation responses. The material samples under test are aluminum foil, conductive Zelt fabric, and silver-coated e-textile.