Switching phenomenon of a three-waveguide optical coupler was analyzed by using the coupled mode theory, and the coupling-length of the device was calculated by means of the FDM. CPW traveling-wave electrodes were designed by the CMM and SOR simulation techniques so as to satisfy the conditions of phase-velocity and impedance matching. Traveling-wave modulators were fabricated on a z-cut LiNbO$_3$ substrate. Ti was in-diffused in LiNbO$_3$ to make waveguides and Au electrodes were built on the waveguides by the electroplating technique. Insertion loss and switching voltage of the optical modulator were about 4 ㏈ and 15.6V. Network analyzer was used to obtain S parameters and corresponding RF response. From the measurement, parameters of the traveling-wave electrodes were extracted as such Z$_{c}$=39.2 $Omega$, Neff=2.48, and a0=0.0665/cm((GHz) (1/2)). The measured optical response R(w) was compared with the theoretically estimated and both responses were shown to agree well. The measurement results revealed that the ㏈ bandwidth turned out to be about 13 GHz.z.