Parameterization of bent coils on curved flexible surface substrates for RFID applications

The read-range of passive inductively-coupled high frequency RFID tags is strongly dependent on the inductance of the antenna-coils. Inductance calculations, whether numerical or analytical, are significantly complicated when the antenna-coil is not planar, but used in a bent state. This latter form of application has been made possible by the development of flexible substrates. A parameterization of the inductance in terms of its geometrical parameters including the bend radius would be advantageous. Therefore, in this work, we demonstrate the possibility of using the Response Surface Method (RSM) based on a suitable Design of Experiment (DOE) to derive a closed-form expression for calculating the inductance of a bent antenna-coil for a given design space. For the regression, we apply a combined approach which could be termed "Physics plus Taylor". In deriving the formula we exploit physical insight to reduce the number of unknown fitting coefficients. For the DOE we implement a so-called space-filling design based on a three-level full factorial design to derive the unknown coefficients. We reach an approximation equation for the inductance with a squared correlation coefficient r(2) of about 99.97% and an accuracy which is consistently better than 3%.