Application of the Mixing Theory in the Design of a High-Performance Dielectric Substrate for Microwave and Mm-Wave Systems

Abstract

This paper presents the design and synthesis of a low-loss substrate with low effective permittivity ( $\varepsilon _{eff}$ ) for microwave and mm-Wave applications. The proposed design is based on the two-phase Maxwell Garnet mixing theory, where the $\varepsilon _{eff}$ of the RF substrate can be synthesized depending on the geometry and the permittivity of mixing particles and the permittivity of the host material. A comprehensive review and error analysis of the most common mixing techniques are conducted to guarantee an accurate design for high-performance RF substrates. Several analyses based on the geometries of various particles are carried out to identify the most accurate mixing model used in the design of the proposed substrate. The effects of the direction of excitation as well as the polarization of the incident field on the $\varepsilon _{eff}$ of the anisotropic particle are analyzed and discussed. The proposed method enables the use of existing high-performance materials that do not necessarily provide a low dielectric constant and low loss tangent. For mm-Wave antenna applications, materials with a dielectric constant of 2–4, and loss tangent of less than 0.002 are desirable to maximize gain and radiation efficiency. Commercial RF substrates can satisfy those requirements, however limited thermal expansion coefficient and lamination difficulties increase the cost significantly. The proposed method enables the use of inexpensive materials that provide excellent thermal properties and great compatibility with a multi-layer fabrication process with desirable $\varepsilon _{eff}$ and loss tangent. For validation of the analysis, samples are fabricated and tested in the microwave frequency (S-band) at 3.5 GHz as well as in the mm-Wave frequency (W-band) at 77 GHz. Measured results show a reduction of 45% in the $\varepsilon _{eff}$ and 38% in the loss tangent values in the S-band, and 32% and 72% reduction in $\varepsilon _{eff}$ and tan $\delta $ , respectively, in the mm-Wave frequency band. The measured results are in excellent agreement with the simulation and calculated results.