Aiming at the problem of high requirement for the signal generator in the Brillouin optical time-domain analysis (BOTDA) system, a quarter of the Brillouin frequency shift (BFS) of modulation is proposed to reduce the required bandwidth of the sensing system. A functional model for solving the intensity of each-order sideband of the output light of electro-optic modulator (EOM) is proposed and applied, so the spectrum with suppressed the carrier and the first-order sidebands while maximizing the second-order sidebands is obtained. Compared with the latest scheme, the intensity of the second-order sidebands is increased by 21.1% based on this functional model. In the experiment, the second-order upper sideband and the second-order lower sideband are used as continuous wave (CW) probe light and pump pulse light, respectively, which ultimately reduces the required bandwidth of radio frequency (RF) signal sources to a quarter of the BFS (reduced from ~11 GHz to ~2.75 GHz), and the frequency sweep range is also reduced to a quarter of the original.