A Model for Equivalent Loss Tangent of Multilayered Media for Automotive Radar Applications

In this paper, a mathematical equation to obtain the effective loss tangent of a multilayered medium is derived. This equation is applied to obtain the effective loss tangent of a car bumper with multiple paint layers on it. The equation is derived using two models - a parallel plate capacitor model and a transmission/reflection coefficient model. The accuracy of the equation is verified and compared using EM simulations. For the EM simulation we use two structures one where both bumper and paint materials are replaced by a single effective medium and the other where only the paint layers are replaced by a single effective medium, while the bumper is kept as it is. The EM simulations have been performed at the 77 GHz frequency band (Automotive collision avoidance radar). The simulation time for antenna gain is reduced by 88 % and 57 % for an antenna in the presence of the first and second EM structures respectively. The antenna gain obtained using the second EM structure shows a near 100 % match with that of the actual multilayered bumper and paint structure.