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We show that an optical modulator that consists of an integrated dual parallel Mach-Zehnder modulator (dMZM) can be used for obtaining not only optical single-side band modulation but also tunability of optical carrier to sideband ratio (OCSR) simultaneously. Such a modulator will be vital for optimizing the performance of radio over fiber links by improving modulation efficiency and receiver sensitivity and by removing fiber chromatic dispersion induced RF power fading. It is shown that a wide range of OCSR tunability can be obtained by altering bias voltage of dMZM, and optimum OCSR, to maximize the output RF power, depends on RF modulation index and extinction ratio of the integrated dMZM. Good agreement between theory, simulation, and experiment is obtained. For typical extinction ratio and low modulation index, it is found that an OCSR of 0 dB is optimum to maximize RF carrier power. However, for multiband orthogonal frequency-division multiplexing (MB-OFDM) ultra-wideband (UWB) radio, the best error vector magnitude (EVM) of -21.8 dB is obtained experimentally at an OCSR of ~5.4 dB due to avoidance of clipping induced nonlinear distortion.