Effective Relative Permittivity Determination of 3D Printed Artificial Dielectric Substrates Based on a Cross Unit Cell

This paper proposes closed-form analytical models for the determination of the effective relative permittivity of 3D printed artificial dielectric substrates based on a cross unit cell. The parallel plate capacitor approach is used to describe the real physical shape of the unit cell allowing to include anisotropic properties as well. A detailed comparison of the analytical models and effective medium approximations is carried out for air host material and inclusion materials with relative permittivities in the range from 2.5 to 1000 and the inclusion volume fraction from 0.1 to 1. It is observed that the proposed models predict the effective relative permittivity with much better accuracy than frequently used effective medium theory-based formulas and due to their closed-form expressions provide faster calculations than numerical methods. The proposed models were verified experimentally, achieving a very good agreement with simulations