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.
Highlights
A complete understanding of the propagation of electromagnetic waves inside the dielectric material is of great importance in the modern applications of material design, remote sensing, aerospace, lens manufacturing, electromagnetic absorbers, carbon nanotubes, and polymers, etc. [1]–[3].The associate editor coordinating the review of this manuscript and approving it for publication was Jenny Mahoney.The dielectric properties of the material depend on the internal structure of the particles inside, particles shape, and the fractional volume (f )
The permittivity analysis for both isotropic and anisotropic cases is thoroughly studied including the effects of the direction of excitation: x, y, and z-directions
In this paper, a proposed method based on Maxwell Garnett mixing theory is used to obtain a high-performance RF material, from an existing high thermally stable and compatible material
Summary
A complete understanding of the propagation of electromagnetic waves inside the dielectric material is of great importance in the modern applications of material design, remote sensing, aerospace, lens manufacturing, electromagnetic absorbers, carbon nanotubes, and polymers, etc. [1]–[3]. Jehangir et al.: Application of the Mixing Theory in the Design of a High-Performance Dielectric Substrate the particles as well as their fractional volumes These mixing rules differ based on several factors such as structure or geometry of the particle (sphere, elliptical, disc, cubic, cylindrical, rod, needle-like, or any random shape) and their distribution inside the host material (aligned or randomly distributed). To achieve optimum performance from a PCB at any frequency of operation, several factors are evaluated: dielectric constant (εr ), loss tangent (tanδ), copper roughness, coefficient of thermal expansion (CTE), moisture absorption, and material thickness [10]. The proposed method enables the use of the existing inexpensive materials that provide excellent thermal properties and great compatibility with a multi-layer fabrication process to obtain high RF-performance in terms of desirable εeff and tanδ values for antenna applications. The results are validated in the mm-Wave W-band by loading RO3003 with the complementary cylindrical air particles showing a reduction of 32% and 72% in εeff and tanδ values, respectively
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