Optically coupled linear isolation amplifier requires special care to avoid oscillation in actual applications. In this paper methods to analyze the frequency characteristics of the amplifier are proposed to reveal the cause of oscillation and to provide design guidelines. The loop gain of the amplifier obtained through the equivalent circuit model shows that the phase margin is too small to ensure stable operations. Methods to get non-oscillatory response are proposed and the resulting frequency responses are analyzed. The common method adding a small capacitor to the amplifier is shown to degrade the frequency bandwidth. The frequency response of output voltage explains the need of filter capacitor in output stage. The usefulness of the method is verified through experiments.