Based on the detailed theoretical modelling of Mach-Zehnder Modulator (MZM), considering non-ideal parameters such as extinction ratio and driven-signal unbalanced ratio, a fundamental fibre radio link is presented including optical source, dual-electrode-drive MZM, optical transmission module and photodiode. The all-order analytic responses using dual side band (DSB) and single side band (SSB) modulation schemes are derived. The analysis concentrates on how MZM affects the amplitude and phase (time delay) response performance of a fibre radio link under different modulation modes. According to the theoretical and numerical results, the extinction ratio and driven-signal unbalanced ratio affect only the amplitude response performance of DSB modulation link but affect both the amplitude and the phase response performance of SSB modulation link. The theoretical model and numerical results can provide the basis of qualitative and quantitative analysis of fibre radio application system using MZM such as radio over fibre (RoF) and optical controlled microwave beam forming network.