Empirical Formula of Cavity Dominant Mode Frequency for 60-GHz Cavity-Backed Wide Slot Antenna

An empirical formula of the dominant mode resonant frequency of the cavity which is used to back a wide slot antenna is presented. The antenna is formed by etching a wide slot onto the broad wall of a substrate integrated waveguide (SIW) cavity fed by an SIW through an inductive coupling window. The widely slotted cavity resonates at the dominant mode when the wide slot radiates. Based on the analysis of the field distribution in the slotted-cavity, an empirical formula is derived to determine the dominant mode resonant frequency of the cavity with respect to the width to length ratio (WLR) of the etched slot. The empirical formula is numerically verified at a 60-GHz band.