Propagation Behavior of Multilayer Microstrips Applied to Interconnects Running Near Embedded Integrated Components

This paper presents a simple and accurate model for the multilayer microstrip, which can be easily implemented using closed-form microstrip design formulas. The model is based on two similar approximations that reduce the multilayer substrate to an equivalent single-layer structure. The shunt impedance parameters per unit length are derived from the complex effective dielectric constant, which is obtained using a variational method. A complex image approach results in the calculation of an effective height that can be used to determine the resistance and inductance per unit length. The goal of the modeling is to predict the behavior of tracks running on top of or underneath components embedded in a printed circuit board. The proposed model is compared to quasi-static electromagnetic simulations. A dedicated test vehicle that allows for the direct extraction of the propagation constant of these multilayer microstrips is manufactured and used to verify the model.