We investigated electro-optic modulator structures to target low drive voltage, high-speed modulation, and small device size with c-axis grown BaTiO3/MgO ferro-electric thin films. In this study, the calculations are focused on the ideal thin film with a quadratic relation between the half-wave drive voltage Vπ and the interaction length L in the electro-optic modulation case we obtained in previous work. With the quadratic electro-optic modulating relation and the optimal rib waveguide structure of BaTiO3/MgO thin films, the frequency-voltage-size performances for 2.5GHz, 10GHz, 40GHz, and 100GHz modulation bandwidths have been obtained under half-wave drive voltages of 0.8V, 1.6V, 3.0V and 4.8V, respectively, for the ideal film with r51=730 pm/V at 1550nm wavelength, where both the phase velocity matching condition and the conductor induced microwave attenuation are considered. The required device lengths to achieve these four typical values of modulation bandwidth are 3.3 mm, 0.8 mm, 0.4 mm and 0.2 mm, respectively. With the c-axis grown BaTiO3/MgO crystal thin films and the quadratic electro-optic modulating relation, an electro-optic coefficient of reff=180 pm/V for the c-axis grown BaTiO3/MgO ferro-electric thin films was measured, which is relatively far from the ideal value of r51=560 pm/V. copyright The Electrochemical Society.