The design of disturbance observer (DOB) requires a low pass filter (LPF) to satisfy the causality and prevent the inner-loop from algebraic loop. The bandwidth of the LPF is desired to be as high as possible to estimate the disturbances in a wide frequency range. However, it is very-well known that the bandwidth of DOB is limited by noise and robustness. This paper shows that the bandwidth limitation of DOB becomes more severe if the plant includes time delay. Furthermore, a new design constraint on the parameters of the LPF of DOB is proposed to obtain predefined performance and robustness criteria. A second order plant model that includes time delay is analyzed and simulation results are given to show the validity of the proposed method.