A method is proposed to decrease the matching frequency of the recently introduced self-excited electromagnetic bandgap (EBG) resonator antenna (SE-EBG-RA). The method is based on the application of a metal shorting plate at the open end of the antenna which reduces the resonance. EBG unit cells are comprised of thick metal patches on top of a PEC-backed substrate, which are separated by tiny high aspect ratio (HAR) gaps. Two to six cells, each electrically much smaller than wavelength, are deployed in one-dimensional (1-D) as a fragment of EBG microstripline with high radiation properties. Both open-circuit (OC) and short-circuit (SC) versions are presented, the SC version being electrically smaller . The miniaturization effect of dielectric loading of HAR gaps is also examined. The characteristics of proposed structures as improved radiators in terms of bandwidth (BW), size, gain, and efficiency are demonstrated through parametric and comparative analyses and also prototyping. The efficiency, BW, and footprint of the smallest dielectric-loaded version, a two-cell SC SE-EBG-RA, are 96%, 3.5%, and $0.22\lambda \times 0.28\lambda $ , respectively.