A New Model to Determine Effective Permittivity and Resonant Frequency of Patch Antenna Covered With Multiple Dielectric Layers

Abstract

This paper reports a model to determine effective permittivity ( $\varepsilon _{\mathrm {eff}}$ ) and resonant frequency ( $f_{r}$ ) of microstrip patch antenna (MPA) covered with multiple dielectric layers. This model is augmented with a newly developed empirical expression to determine the $\varepsilon _{\mathrm {eff}}$ of multi-layered superstrates over a substrate. The development of empirical formulation makes use of conformal mapping approach (CMA) and series–parallel combination of dielectric boundaries between the ground plane and patch of the MPA. In this work, the MPA is designed on substrate having dielectric constant of $\varepsilon _{1}$ whereas the superstrate layers have dielectric constants of $\varepsilon _{2}$ , $\varepsilon _{3}\ldots \varepsilon _{\mathrm {n}}$ . It is shown that the proposed technique is able to predict the $f_{r}$ of MPA with error of 1.8%, 3.5%, and 1.4% when it is covered with a single dielectric layer with superstrate height of 4.5mm for respective conditions of $\varepsilon _{1}= \varepsilon _{2}$ , $\varepsilon _{1}> \varepsilon _{2}$ and $\varepsilon _{1} ( $\varepsilon _{1}=3.66$ , $\varepsilon _{2}=2.2$ /4.7). Furthermore, the developed technique is analyzed for distinct combination of substrate and two superstrate layers for the cases $\varepsilon _{1}= \varepsilon _{2}> \varepsilon _{3}$ , $\varepsilon _{1}= \varepsilon _{2} , $\varepsilon _{1} \varepsilon _{3}$ , $\varepsilon _{1}> \varepsilon _{2} , and $\varepsilon _{1}> \varepsilon _{2}> \varepsilon _{3}$ . Subsequently, the viability of the proposed technique is demonstrated in practical scenarios for body centric communications by considering single (e.g., jeans cotton, pure cotton, rayon, polyester, felt fabric, terry wool, and leather) and multiple (e.g., wool over jeans cotton and polyester, felt fabric over pure cotton and rayon) layers of textiles over MPA. The measurement results on various dielectric superstrates and textiles show excellent agreement with the corresponding theoretical results and thereby validate the reported theory. Finally, a comparison with the seminal works clearly shows the promise of the reported technique in this paper.