Two types of absolute displacement sensors have been developed for vibration control. One is first-order differential type for the field of precise structure, and the other is second-order differential type for the field of large-scale structure. In particular, authors have proposed the former one to reduce amplifications of high frequency noises induced by twice differentiations. However, it is revealed that bandwidth of the proposed sensor is narrow to control leading-edge anti-vibration apparatuses. Therefore, this paper considers bandwidth expansion of the first-order differential type absolute displacement sensor in low frequency region. At first, dynamics of the displacement sensors are investigated based on root locus analysis. This is because the bandwidth expansion has a limitation due to high frequency resonance. Next, since there is trade-off between detection sensitivity and the bandwidth, the sensitivity is improved by detecting back electromotive forces from not only a calibration coil but also a forcer coil. Finally, the bandwidth of the proposed sensor is expanded in low frequency region, and results are shown in experiments.