Evaluating the Relationship Between Relative Permittivity and Infill Density in 3D Printed Dielectric Slabs

This paper investigates the relationship between relative permittivity and infill density in 3D printed dielectric slabs. As the infill density of a 3D printed substrate is varied, its relative permittivity also varies which affects the performance of radio frequency devices. Hence, it is essential to characterize the relationship between relative permittivity and infill density in 3D printed substrates. To explore this, dielectric slabs with varying sizes and infill densities were additively manufactured using Fused Deposition Modeling and measured for permittivity using reflection/transmission methods in air-filled waveguides. The measured relative permittivity at specific infill density is coined as effective relative permittivity throughout the paper. The relationship between effective relative permittivity and infill density, found to be linear in our preceding simulation study was validated for higher infill densities through empirical measurements. Additionally, the paper presents a novel standardized method using the Weiner bounds to quantify this relationship. The findings indicate that the relationship is linear for the infill layers, however, the inclusion of solid layers impacts the linear relationship. Therefore, an equation is introduced to estimate the permittivity of a 3D printed substrate when solid layers are incorporated. Finally, the practical applicability of this relationship is demonstrated by fabricating a 3D printed patch antenna with a 50% infill density substrate, establishing infill density as a crucial parameter in radio frequency design when using additive manufacturing methods.