A dual parallel Mach–Zehnder modulator (DPMZM) used for electro-optic conversion of multi-band orthogonal frequency-division multiplexing (OFDM) ultra-wideband (UWB) radio signals in intensity modulated direct detection optical communication systems is optimized theoretically and through numerical simulation. The optimum DPMZM parameters that allow simultaneous mitigation of the second and third order distortion components created by the joint electro-optic converter and photodiode nonlinearities are identified. The corresponding minimum optical signal-to-noise ratio (OSNR) required to achieve a bit error ratio of $10^{-9}$ is also evaluated. An analytical expression showing the relation between the optimum DPMZM parameters under extended voltage levels of the OFDM-UWB signals applied to the DPMZM is proposed and validated. It is shown that the DPMZM performance presents high robustness to deviations from the optimum DPMZM parameters identified. Additionally, it is shown that similar minimum required OSNR levels are obtained with the optimized DPMZM and when the electro-optic conversion is realized by a single MZM.