For mobile communication systems, small size and low profile antennas are necessary. Planar printed antennas such as slot antenna and microstrip antenna are attractive for their use in mobile and wireless communication systems due to their low profile compact size , . However, because of the electro-magnetic interference, radiation of omni directional antenna such as the slot antenna is remarkably deteriorated if the metal block of RFIC (radio frequency integrated circuit) or body of a car approaches to the back of the antenna. Patch antenna is one of the solutions to overcome these problems . However, radiation efficiency and bandwidth of a patch antenna decreases rapidly as the thickness of the substrate decreases, and also one-sided directional patch antenna has large ground plane. Therefore, miniaturized antennas on thinner substrate are necessary for future 3-dimension packaging techniques in integrating with RF-chips. In our previous works, we presented the design theory of the one-sided directional electrically small antenna (ESA) composed of an impedance matching circuit, a half wavelength (λ/2) top metal and a bottom floating metal layer for IMS (@2.4GHz) application .