Relative permittivity estimation of patch antennas on FR4 substrates for S and C frequency bands

This article proposes an empirical methodology for accurately estimating the relative permittivity ${\epsilon }_r$ of FR4 boards, which is essential for designing microstrip antennas at S and C frequency bands. As the relative permittivity of dielectric materials changes with frequency, the proposed method involves selecting a known starting value of ${\epsilon }_r$ for an FR4 board and then simulating the reflection coefficient S₁₁ parameters of an antenna design. These simulated parameters are then compared to the measured S₁₁ parameters of a fabricated antenna. A value of ${\epsilon }_r$ = 4.55 is accurately determined when the two S₁₁ parameters converge close to the desired design frequency. With the FR4 ${\epsilon }_r$ value obtained from this methodology, a slot patch antenna is designed for a frequency of 4 GHz, obtaining a reflection coefficient of |Γ| = 0.035, a bandwidth BW = 117 MHz, and a standing wave ratio (SWR) of 1.0746. The proposed methodology can be used as a tool to estimate the ${\epsilon }_r$ of various substrates that are not characterized at high frequencies.